06 Velocity Modeling

GOCAD® 2009.
1 User Guide
Part VI Velocity Modeling

© 1997–2009 Paradigm B.V. and/or its affiliates and subsidiaries. All rights reserved.
The information in this document is subject to change without notice and should not be construed as a commitment by Paradigm B.V. and/
or its affiliates or subsidiaries (collectively, "Paradigm"). Paradigm assumes no responsibility for any errors that may appear in this
document.
The Copyright Act of the United States, Title 17 of the United States Code, Section 501 prohibits the reproduction or transmission of
Paradigm’s copyrighted material in any form or by any means, electronic or mechanical, including photocopying and recording, or by any
information storage and retrieval system without permission in writing from Paradigm. Violators of this statute will be subject to civil and
possible criminal liability. The infringing activity will be enjoined and the infringing articles will be impounded. Violators will be personally
liable for Paradigm’s actual damages and any additional profits of the infringer, or statutory damages in the amount of up to $150,000 per
infringement. Paradigm will also seek all costs and attorney fees. In addition, any person who infringes this copyright willfully and for the
purpose of commercial advantage or private financial gain, or by the reproduction or distribution of one or more copies of a copyrighted
work with a total retail value of over $1,000 shall be punished under the criminal laws of the United States of America, including fines and
possible imprisonment.
The following are trademarks or registered trademarks of Paradigm B.V. and/or its affiliates or subsidiaries (collectively, "Paradigm") in
the United States or in other countries: Paradigm, Paradigm logo, Alea, Coherence Cube, Director, DirectorGeo, EarthStudy 360, Echos,
Epos, FastVel, FracMV, GeoDepth, Geolog, GeoScene, GeoSec, GeoSteer, GOCAD, Interpret, Jacta, Kine3D, OpenGeo, OpsLink,
Probe, Pump-It, Rock & Fluid Canvas, SeisEarth, SeisFacies, SeisX, SKUA, SolidGeo, StratEarth, Stratimagic, Sysdrill, UVT Transform,
Vanguard, VoxelGeo, and/or other Paradigm products referenced herein. All other company or product names are the trademarks or
registered trademarks of their respective holders.
Alea and Jacta software under license from TOTAL. All rights reserved.
Some components or processes may be licensed under one or more of U.S. Patent Numbers 5,570,106; 5,615,171; 6,765,570; and
6,690,820.
Some components or processes are patented by Paradigm and/or one or more of its affiliates under U.S. Patent Numbers 5,563,949;
5,629,904; 5,838,564; 6,092,026; 6,430,508; 6,819,628; 6,859,734; 6,873,913; 7,095,677; 7,123,258; 7,295,929; and 7,295,930. In
addition, there may be patent protection in other foreign jurisdictions for these and other Paradigm products.
All rights not expressly granted are reserved.
Published June 22, 2009

Contents
Part VI Velocity Modeling

Chapter 1 Constructing 3D Models ........................................................................... 1-1
1.1 Constructing a Model3d ............................................................................... 1-2
1.1.1 Common Attributes of Models ......................................................... 1-2
Regions ............................................................................................1-2
Layers ...............................................................................................1-3
1.1.2 Procedure to Construct a Model3d ................................................... 1-3
1.1.3 Creating a New Model3d From Surfaces............................................ 1-4
1.1.4 Adding Surfaces to a Model3d.......................................................... 1-5
1.1.5 Deleting or Detaching Surfaces from a Model3d ................................ 1-6
1.1.6 Building a Model3d .......................................................................... 1-6
1.1.7 Rebuilding a Model3d ...................................................................... 1-7
1.1.8 Editing a Model3d............................................................................ 1-7
Making Surfaces and Regions Geologically Consistent ........................1-7
Removing Free Horizon Extremities in a Given Region .........................1-9
Removing All Free Extremities from a Horizon ...................................1-10
1.1.9 Creating and Working with Layers in a Velocity Model ......................1-10
Creating Default Layers in a Velocity Model ......................................1-11
Creating a Layer from a Region in a Velocity Model ..........................1-11
Deleting a Layer in a Velocity Model.................................................1-12
Renaming a Layer in a Model3d .......................................................1-12
1.1.10 Working with Regions in a Model3d ................................................1-13
Adding a Region to a Velocity Model Layer.......................................1-13
Moving a Region to a Different Velocity Model Layer ........................1-13
Deleting a Region from a Velocity Model Layer .................................1-14
Finding a Region Name in a Velocity Model ......................................1-14
Contents iii
Paradigm™
Renaming a Region in a Velocity Model ........................................... 1-15

1.2 Constructing a Voxet Model ........................................................................ 1-16
1.2.1 Procedure to Construct a Voxet Model ............................................ 1-16
1.2.2 Adding Surfaces to a Voxet Model Build List .................................... 1-17
1.2.3 Removing Surfaces from a Voxet Model Build List ............................ 1-18
1.2.4 Building a Voxet Model................................................................... 1-19
1.2.5 Creating and Working with Layers in a Voxet Model ........................ 1-19
1.2.6 Working with Regions in a Voxet Model .......................................... 1-20
Finding a Region Name ................................................................... 1-20
Collapsing Small Regions in a Voxet Model ...................................... 1-20
1.2.7 Creating and Editing Voxet Model Properties ................................... 1-20
Chapter 2 Defining Property Values for Velocity Models ......................................... 2-1

2.1 Procedure to Define Velocity Model Property Values ....................................... 2-2
2.2 Understanding the Property Model Editor ...................................................... 2-3
2.2.1 About the Property Model Editor Interface......................................... 2-3
2.2.2 Working with the Variable Type Menu ............................................... 2-4
2.2.3 Common Variable Definition Parameters............................................ 2-6
Variable Name.................................................................................. 2-6
Shoot Direction ................................................................................ 2-7
Shoot Position .................................................................................. 2-8
Impact Point .................................................................................... 2-8
2.3 Defining Layer Property Values Directly ........................................................ 2-10
2.3.1 Assigning Constant Values to Properties or Variables ........................ 2-10
2.3.2 Defining Properties or Variables by Using Linear Functions................ 2-10
2.3.3 Defining Properties or Variables by Using Interpolation ..................... 2-11
2.3.4 Defining Properties or Variables from Grid Properties ....................... 2-13
2.3.5 Defining Values from Surface or Layer Boundary Properties .............. 2-14
Defining Values from Surface Boundaries......................................... 2-14
Defining Values from Layer Boundaries ............................................ 2-15
Notes on Defining Values from Surfaces and Layers.......................... 2-18
2.4 Defining Properties or Variables by Using Property Functions ......................... 2-20
2.4.1 Defining Properties or Variables by Using Linear Functions................ 2-20
2.4.2 Defining Properties or Variables by Using Exponential Functions ....... 2-22
2.4.3 Defining Property Functions by Using Scripts.................................... 2-23
About Script Property Functions ...................................................... 2-23
Creating Script Property Functions................................................... 2-24
2.5 Reviewing the Effect of a Property Function ................................................. 2-25
2.5.1 Painting a Voxet with a Velocity Model Property .............................. 2-25
2.6 Adding Properties to Velocity Models ........................................................... 2-27
2.7 Deleting Properties from Velocity Models ..................................................... 2-28
iv Contents GOCAD® 2009.1 User Guide

Part
VI
Modeling
Velocity
Chapter 3 Creating Grid Properties with Geostatistical Functions ........................... 3-1
3.1 Geostatistics System File Formats................................................................... 3-2
3.1.1 GS File ............................................................................................. 3-2
Variogram and Associated Parameters File Format ..............................3-2
GS File Examples ...............................................................................3-3
3.1.2 Column_Average_Map File ............................................................... 3-4
3.1.3 Scattergram File ............................................................................... 3-4
3.1.4 External_Histogram File .................................................................... 3-5
3.1.5 Facies_Map File ................................................................................ 3-5
3.1.6 Annealing_Schedule File ................................................................... 3-5
3.2 Estimating Grid Properties with Kriging Algorithms ........................................ 3-6
3.2.1 Estimating Properties with Kriging .................................................... 3-6
3.2.2 Estimating Properties with Kriging with Trend .................................... 3-7
3.2.3 Estimating Properties with Kriging with External Drift ........................ 3-9
3.2.4 Estimating Properties with Bayesian Kriging......................................3-10
3.2.5 Estimating Properties with Collocated Cokriging ...............................3-12
3.2.6 Estimating Properties with Indicator Kriging .....................................3-13
3.3 Running Geostatistical Simulations ...............................................................3-16
3.3.1 Running Sequential Gaussian Simulations (SGS) ................................3-16
3.3.2 Running Non-Conditional Sequential Gaussian Simulations ...............3-18
3.3.3 Running Collocated Cokriging Simulations .......................................3-20
3.3.4 Running Sequential Indicator Simulations (SIS)..................................3-22
3.3.5 Running Annealing Simulations .......................................................3-24
3.3.6 Running Cloud Transform Simulations with P-Fields ..........................3-27
3.3.7 Performing Categorical Histogram Corrections .................................3-29
3.3.8 Performing Continuous Histogram Corrections .................................3-30
3.3.9 Filling Grids with Facies Map Data....................................................3-31
Chapter 4 Performing Velocity Conversions ............................................................. 4-1

4.1 Converting the Velocity Type in One Domain .................................................. 4-2
4.2 Converting the Velocity Type in Different Domains ......................................... 4-3
Chapter 5 Performing Time and Depth Domain Conversions ................................... 5-1

5.1 Converting Objects Using a Velocity Cube...................................................... 5-2
5.2 Converting a Seismic Cube ........................................................................... 5-4
5.3 Reassigning an Object to the Correct Domain ................................................ 5-6
Index ..................................................................................................Index-1
Rock & Fluid Canvas™ 2009 | Epos™ 4.0 Contents v

Paradigm™
vi Contents GOCAD® 2009.1 User Guide

1
Constructing 3D Models
In this chapter • "Constructing a Model3d," page 1-2 • "Constructing a Voxet Model,"

page 1-16
Overview There are two types of model objects in Paradigm™ GOCAD ® 2009: the Model3d, which
is the main focus of this chapter, and the Voxet model.
1-1
Paradigm™
1.1 Constructing a Model3d

• "Common Attributes of Models," page 1-2
• "Procedure to Construct a Model3d," page 1-3
• "Creating a New Model3d From Surfaces," page 1-4
• "Adding Surfaces to a Model3d," page 1-5
• "Deleting or Detaching Surfaces from a Model3d," page 1-6
• "Building a Model3d," page 1-6
• "Editing a Model3d," page 1-7
• "Creating and Working with Layers in a Velocity Model," page 1-10
• "Working with Regions in a Model3d," page 1-13
1.1.1 Common Attributes of Models

There are three sets of common Attributes common to models in the Attribute Manager:
• Regions
• Layers
• Fault blocks
Regions
In a model object, a region is a closed space bounded by Surfaces and/or the edges
(boundaries) of the model.
Figure 1–1 Model region

area
Individual
regions
If there are any regions in the model, their names appear in the Regions area. You can
adjust the attributes associated with each region.
• Visible. Turns the display of all selected regions on and off.
• Region check boxes. When the Visible check box is selected, turns the display of
individual regions on and off.
• Region color. Changes the display color of an individual region.
Voxet models are visualized through their parent Voxets. (Select the Voxet model in the
Attribute Manager, but display the Voxet itself in the 3D Viewer.)
1-2 Constructing 3D Models GOCAD® 2009.1 User Guide

Part
VI
Modeling
Velocity
Layers
A layer is composed of one or more geologically related regions (for example, a layer of
sand faulted into two separate bodies). For information on creating and working with
layers, see "Creating and Working with Layers in a Velocity Model" on page 1-10.
By default, a layer is named after its top bounding surface.This is to follow the geologic
convention of naming a surface Top of Something. For example, the name "Top of
Miocene" implies that the layer below the Top of Miocene surface is the Miocene layer.
Figure 1–2 Model layer

area
Tip If you think that there If there are any layers in the model, their names appear in the lower half of the Layers
are layers in your model but area. You can adjust the attributes associated with each layer.
they do not appear in the
Layers area, there may be • Visible. Turns the display of all selected layers on and off.
leaks in your model (a layer
needs to be completely • Layer check boxes. When the Visible check box is selected, turns the display of
bounded by Surfaces and/or individual layers on and off.
model boundaries).
• Layer color. Changes the display color of an individual layer.
Voxet Models are visualized through their parent Voxets. (Select the Voxet Model in the
Attribute Manager, but display the Voxet itself in the 3D Viewer.)
1.1.2 Procedure to Construct a Model3d

Table 1–1 outlines the basic functions to facilitate constructing 3D models and modifying
them after construction.
Table 1–1 Basic functions

for creating and To do this See this procedure
modifying 3D models Create a Model3d from one or more "Creating a New Model3d From
Surfaces Surfaces" on page 1-4
Add Surfaces to the Model3d you "Adding Surfaces to a Model3d" on
created 1 page 1-5
Delete or detach Surfaces from the "Deleting or Detaching Surfaces from
Model3d you created 1 a Model3d" on page 1-6
Force an update of the Model3d "Building a Model3d" on page 1-6
based on any surface additions,
deletions, or detachments 2
Recreate the Model3d from its input "Rebuilding a Model3d" on page 1-7
Surfaces 3
1. You can choose whether to incorporate the Build function into your changes,
prompting the program to recompute and update the model immediately. If
you forego an automatic build to save computation time, changes will not
take effect until you run the Build function as a separate step.
2. The Build function does not take into account any changes to the input
Surfaces themselves.
3. The Rebuild function is most useful when there have been changes to the
input Surfaces, and you want to re-cut them.
Rock & Fluid Canvas™ 2009 | Epos™ 4.0 1.1 Constructing a Model3d 1-3
Paradigm™
1.1.3 Creating a New Model3d From Surfaces

When you create a new Model from a set of Surfaces, each surface intersects each face of
the model, and surfaces may also intersect each other, or "self-intersect" (so that the
program can detect regions enclosed by surfaces). This operation can take some time to
carry out.
Figure 1–3 Model3d

examples
Regular model Model with intersecting surfaces
To create a new 1 Select the Surface commands, click the Model3d menu, and then click From
Model3d from a set Surfaces to open the dialog box.
of Surfaces
2 In the Name box, type the name of the new model.

3 In the Surface surfaces box, enter one or more surfaces to use in building the
model.
4 If you want to create copies of the input surfaces before modifying their topology
(cutting them) to construct the model, select the Copy check box.
Note Each copied surface is named according to the convention model name_surface name.
For example, if you add a surface H1 to a model m1, the new surface will be called m1_H1.
5 If you want to indicate that the surfaces are self-intersecting, select the Self
intersection check box. If you clear this check box, the program will compute only
the area between each surface and the voxet itself.
Note 99% of the time, surfaces are not self-intersecting.
6 If you want the program to define the Model3d borders consistently, select the
Define borders check box.

Part
VI
Modeling
Velocity
7 If you want the program to update the model immediately when you click OK or
Apply, select the Build check box.
Note If you select this check box, the cut operations will be run on all surfaces.
8 Click OK to carry out the command and close the dialog box, or click Apply to carry
out the command and leave the dialog box open.
1.1.4 Adding Surfaces to a Model3d

Use this function to add new surfaces to a model after it is created.
To add surfaces to a 1 Select the Surface commands, click the Model3d menu, and then click Add Surface
Model3d to open the dialog box.
2 In the Model3d box, enter one or more existing models to which the surfaces will be
added.
3 In the Surface surfaces box, enter one or more surfaces to be added to the model.
4 If you want to create copies of the added surfaces before modifying their topology
(cutting them) to construct the model, select the To copy check box.
Note Each copied surface is named according to the convention model name_surface name .
For example, if you add a surface H1 to a model m1, the new surface will be called m1_H1.
Paradigm™
1.1.5 Deleting or Detaching Surfaces from a

Model3d
Use this function to delete surfaces from a model after it is created.
To delete surfaces 1 Select the Surface commands, click the Model3d menu, and then click Kill Surface
from a Model3d to open the dialog box.
2 In the Model3d box, enter one or more existing models from which the surfaces will
be deleted.
3 In the Surface surfaces box, enter one or more surfaces to be deleted from the
model.
1.1.6 Building a Model3d

When you run a "build," the program analyzes the types of changes that occurred to the
model, such as adding or deleting surfaces, and performs the operations necessary to
recompute the model regions. (If only surfaces were deleted, no intersection phase is
necessary, and the build should be relatively fast.)
To build a Model3d 1 Select the Surface commands, click the Model3d menu, and then click Build to
open the dialog box.
2 In the Model3d box, enter one or more models to build.

Part
VI
Modeling
Velocity
3 If the surfaces in the model are already pre-cut and you want the program to
construct the model without finding the intersection between all the surfaces, clear
the With cut check box.
1.1.7 Rebuilding a Model3d

Using this command, you can recreate a model (see "Creating a New Model3d From
Surfaces" on page 1-4), including re-cutting all the input surfaces. The "rebuild" function
actually modifies the input data on which the model is built. In contrast, the regular
"build" function updates the model only, based on added or deleted input data,
To rebuild a Model3d 1 Select the Surface commands, click the Model3d menu, and then click Rebuild to
2 In the Model3d box, enter one or more models to rebuild.

1.1.8 Editing a Model3d

For information, see:
• "Making Surfaces and Regions Geologically Consistent," page 1-7
• "Removing Free Horizon Extremities in a Given Region," page 1-9
• "Removing All Free Extremities from a Horizon," page 1-10
Making Surfaces and Regions Geologically Consistent

You can use a model to detect geologic inconsistency between geologic surfaces. This
function does the following:
• Removes pieces of surfaces which are not geologically correct
• Removes parts of top surfaces that are inside intrusive regions
Paradigm™
• Removes parts of top surfaces that are above their erosion surfaces (the erosion
surface is younger than the horizon, but part of the horizon is above the erosion
surface)
• Automatically rebuilds the model regions
As shown in the left image of Figure 1–4, two horizons of older age than the salt body
penetrate the salt volume, splitting the salt region into 3 regions. The right image displays
the results of the "Make surfaces and regions geologically consistent" function. The non-
geologic parts have been removed, creating a hole inside the two horizons and a unique
region.
Important In order for the algorithm to work properly, you must first set geologic
information on all of the different surfaces (see Part IV: Foundation Modeling, "Defining
and Working with Geologic Features" on page 8-1). In Figure 1–4, the salt surface was
declared an intrusive surface with an age younger than the two top surfaces.
Figure 1–4 Making

figures geologically
consistent
Before After
To make a Model3d 1 Select the Surface commands, click the Model3d menu, point to More, and then
geologically click Make Geological Consistency to open the dialog box.
consistent
2 In the Model3d box, enter one or more models to make geologically consistent.
Note You must still run the "build" function separately to rebuild the model itself. (See
"Building a Model3d" on page 1-6.)

Part
VI
Modeling
Velocity
Removing Free Horizon Extremities in a Given Region
Use this function to automatically remove free radial edges from all horizon surfaces
within one given region of a model. This function can be especially useful for removing
free extremities extending outside of the model in the Universe region (see Figure 1–5
for an example).
Figure 1–5 Removing free

horizon extremities in a
region
Before removing free extremities After removing free extremities
To remove free 1 Select the Surface commands, click the Model3d menu, point to More, and then
horizon extremities in click Remove Free Extremities to open the dialog box.
a given region
2 In the Model3d box, enter one or more models.

3 In the Region box, enter the name of the region in which horizon extremities will be
removed.
Paradigm™
Removing All Free Extremities from a Horizon

Use this function to automatically remove free radial edges, or extremities, from one
horizon surface throughout all regions of a model. This function can be especially useful
when the model has been constructed from surfaces in which borders have been
extended to ensure intersections between faults and horizons.
Figure 1–6 Removing free

extremities from a
horizon
Before removing free extremities After removing free extremities
To remove all free 1 Select the Surface commands, click the Model3d menu, point to More, and then
extremities from a click Remove Horizon Free Extremities to open the dialog box.
horizon
2 In the Model3d box, enter one or more models.

3 In the AtomsSet horizon box, enter the name of the horizon surface from which
extremities will be removed.
1.1.9 Creating and Working with Layers in a

Velocity Model
The first three functions described in this section are valid for both Model3ds and Voxet
Models.
• "Creating Default Layers in a Velocity Model," page 1-11
• "Creating a Layer from a Region in a Velocity Model," page 1-11
• "Deleting a Layer in a Velocity Model," page 1-12
• "Renaming a Layer in a Model3d," page 1-12

Part
VI
Modeling
Velocity
Creating Default Layers in a Velocity Model
You can automatically compute a default set of layers for a velocity model. This function
groups regions into layers by using geologic information attached to the surfaces
bounding the regions. To ensure that this function works properly, be sure to set geologic
information for fault and boundary surfaces (see Part IV: Foundation Modeling, "Defining
and Working with Geologic Features" on page 8-1). If no geologic information is set, all
surfaces are assumed to be top surfaces, and the stratigraphic time is computed from the
lowest z value of the surface; this can lead to errors in layer computation.
To create a default 1 Select the Surface commands, click the Model3d menu, and then click Create
layer set Defaults to open the dialog box.
– or –
Select the Voxet or SGrid commands, click the Model menu, and then click Create
Defaults to open the dialog box.
2 In the Model box, enter one or more models in which the layer set will be created.
Important The model must contain regions.
Creating a Layer from a Region in a Velocity Model

Use this function to create a layer from a specific region in a velocity model.
To create a layer from 1 Select the Surface commands, click the Model3d menu, and then click Create One
a region to open the dialog box.
– or –
Select the Voxet or SGrid commands, click the Model menu, and then click Create
One to open the dialog box.
2 In the Model box, enter one or more models to which the layer will be added.
3 In the Layer name box, type the name of the new layer.
4 In the Region box, enter the name of the region from which the layer will be created.
Paradigm™
Deleting a Layer in a Velocity Model

Use this function to delete a layer from a velocity model.
To delete a layer from 1 Select the Surface commands, click the Model3d menu, and then click Remove
a velocity model Layer to open the dialog box.
– or –
Select the Voxet or SGrid commands, click the Model menu, and then click Remove
Layer to open the dialog box.
2 In the Model box, enter one or more models from which the layer will be deleted.
3 In the Layer box, enter the layer to be deleted.
Renaming a Layer in a Model3d

Use this function to rename a layer in a Model3d.
To change a layer 1 Select the Surface commands, click the Model3d menu, and then click Rename to
name in a velocity open the dialog box.
model
2 In the Model box, enter one or more models containing the layer to be renamed.
3 In the Layer box, enter the layer to be renamed.
4 In the New name box, type the new name of the layer.

Part
VI
Modeling
Velocity
1.1.10 Working with Regions in a Model3d
Most of the functions described in this section are valid for both Model3ds and Voxet
Models. The model is rebuilt automatically after each of these functions.
• "Adding a Region to a Velocity Model Layer," page 1-13
• "Moving a Region to a Different Velocity Model Layer," page 1-13
• "Deleting a Region from a Velocity Model Layer," page 1-14
• "Finding a Region Name in a Velocity Model," page 1-14
• "Renaming a Region in a Velocity Model," page 1-15
Adding a Region to a Velocity Model Layer

Use this function to add a region to a layer within a velocity model.
To add a region to a 1 Select the Surface commands, click the Model3d menu, point to Region, and then
velocity model layer click Add to Layer to open the dialog box.
– or –
Select the Voxet or SGrid commands, click the Model menu, and then click Add to
Layer to open the dialog box.
2 In the Model box, enter one or more models.

3 In the Region box, enter the region to be added to the layer.
4 In the Layer box, enter the destination layer.
Moving a Region to a Different Velocity Model Layer

Use this function to move a region to a different layer within a velocity model.
To move a region to a 1 Display the model regions and layers in the 3D Viewer.
different layer
2 Select the Surface commands, click the Model3d menu, point to Region, and then
click Move to Layer.
– or –
Select the Voxet or SGrid commands, click the Model menu, and then click Move
to Layer.
3 In the 3D Viewer, click the region to be moved, then click the destination layer.
Paradigm™
Deleting a Region from a Velocity Model Layer

Use this function to delete a region from a layer within a velocity model.
To delete a region 1 Select the Surface commands, click the Model3d menu, point to Region, and then
from a layer click Remove from Layer to open the dialog box.
– or –
Select the Voxet or SGrid commands, click the Model menu, and then click Remove
from Layer to open the dialog box.

3 In the Region box, enter the region to be deleted from the layer.
4 In the Layer box, enter the target layer.
Finding a Region Name in a Velocity Model

Use this function to find the name of a specific region within a velocity model.
To find the region Do one of the following:

name of a displayed
region ♦ Select the Voxet or SGrid commands, click the Model menu, point to Region, click
Find Name, and then click the region in the 3D Viewer.
– or –
Click Get XYZ Coordinate on the Camera Tools toolbar, and then click the
region in the 3D Viewer.
The region name is displayed in the status bar.
Region name

Part
VI
Modeling
Velocity
Renaming a Region in a Velocity Model
Use this function to rename a region within a velocity model.
To rename a region 1 Select the Surface commands, click the Model3d menu, point to Region, and then
click Rename to open the dialog box.
– or –
Select the Voxet or SGrid commands, click the Model menu, and then click Rename
to open the dialog box.

3 In the Region box, enter the region to be renamed.
4 In the New name box, type the new name of the region.
Paradigm™
1.2 Constructing a Voxet Model

For information and instructions, see:
• "Procedure to Construct a Voxet Model," page 1-16
• "Adding Surfaces to a Voxet Model Build List," page 1-17
• "Removing Surfaces from a Voxet Model Build List," page 1-18
• "Building a Voxet Model," page 1-19
• "Creating and Working with Layers in a Voxet Model," page 1-19
• "Working with Regions in a Voxet Model," page 1-20
• "Creating and Editing Voxet Model Properties," page 1-20
1.2.1 Procedure to Construct a Voxet Model

Table 1–2 outlines the basic functions to facilitate constructing Voxet Models and
modifying them after construction.
Table 1–2 Basic functions

for creating and To do this See this procedure
modifying Voxet Models Specify the surfaces to be included in "Adding Surfaces to a Voxet Model
the Voxet Model 1 Build List" on page 1-17
Exclude surfaces from a Voxet Model 1 "Removing Surfaces from a Voxet

Model Build List" on page 1-18
Perform the initial build of the Voxet "Building a Voxet Model" on
Model or force an update based on page 1-19
any surface additions or deletions 2
1. You can choose whether to incorporate the Build function into your changes,
prompting the program to recompute and update the model immediately. If
you forego an automatic build to save computation time, changes will not
take effect until you run the Build function as a separate step.
2. The Build function does not take into account any changes to the input
surfaces themselves.
About Voxet Models When you create a Voxet, an empty Voxet Model is created automatically as well. A Voxet
Model is the gridded volume confined within the cage of the Voxet. You can cut the Voxet
Model volume with Surfaces to create gridded sub-volumes. A layer is a contiguous sub-
volume. A Voxet Model, therefore, is a bounded volume that consists of gridded sub-
volumes called layers.
Theoretically, a Voxet Model has at least one layer (the entire Voxet volume), but for
practical purposes, a Voxet Model is considered empty until you create at least one sub-
volume within the model (see "Building a Voxet Model" on page 1-19).
Since building a Voxet Model is simpler than building a Model3d, it can be helpful to build
a Voxet Model to check the validity of layers before building a Model3d. In an effective
Voxet Model, the Voxet should be smaller than all the Surfaces that will to cut the Voxet
walls, creating layers.

Part
VI
Modeling
Velocity
Building effective In the left Voxet in Figure 1–7, all the sub-horizontal Surfaces cut all four walls of the
Voxet Models Voxet, and there is room above the top and below the bottom Surface. A Voxet Model
built from those Surfaces and the Voxet will have six layers (and six regions in the Voxet).
In the right Voxet in Figure 1–7, the Voxet is so big that it does not intersect any of the
Surfaces. A Voxet Model built from those Surfaces and the Voxet will have only two
layers: the layer inside the middle closed Surface and the layer outside it.
Figure 1–7 Voxet

examples
Effective Voxet Ineffective Voxet
A Voxet created from an object box (see Part IV: Foundation Modeling, "Creating a Voxet
from an Objects Box" on page 5-9) is meant to include all objects selected; therefore, we
do not recommend building a Voxet Model from that set of objects. To guarantee proper
intersections (cutting), create the Voxet from end points (see Part IV: Foundation
Modeling, "Creating a Voxet from Corner Points" on page 5-7), in which you can specify
the XYZ locations of the Voxet corner points.
Visualizing Voxet Voxet Models are visualized through their parent Voxets. (Select the Voxet Model in the
Models Attribute Manager, but display the Voxet itself in the 3D Viewer.) When you successfully
create a layer in a Voxet Model, a region is automatically created in the corresponding
Voxet. You can also view the regions in the Voxet to visualize the Voxet Model.
Voxet Model • When you build a Voxet Model, part of the process is cutting the Voxet with the
warnings Surfaces, which cuts the connectivity in the Voxet. (See Part IV: Foundation Modeling,
"Cutting a Voxet with Surfaces" on page 5-11.)
• Once you have built a Voxet Model, do not add or delete a Surface and rebuild (see
"Voxet Model warnings" on page 1-17).
1.2.2 Adding Surfaces to a Voxet Model Build List

Use this function to specify the Surfaces to be included in a Voxet Model. After specifying
the surfaces, you can proceed to build the Voxet Model (see "Building a Voxet Model" on
page 1-19), or you can continue to modify the build list by adding or deleting other
surfaces.
Important Once you have built the Voxet Model, do not add or delete Surfaces and
rebuild.
Rock & Fluid Canvas™ 2009 | Epos™ 4.0 1.2 Constructing a Voxet Model 1-17
Paradigm™
To add surfaces to the 1 Display the Voxet and the Surfaces in the 3D Viewer. In order to create valid regions
build list of a Voxet in the model, the Surfaces must cut one another and/or the Voxet walls (see
Model Figure 1–7 on page 1-17).
2 Select the Voxet commands, click the Model menu, and then click Add Surfaces to
3 In the Voxet box, enter one or more voxets.

Note A Voxet Model is always attached to a Voxet.
4 The names of the displayed Surfaces will be listed automatically in the Surface
surfaces box.
Note The Voxet Model will not actually be built until you execute the Build function (see
"Building a Voxet Model" on page 1-19).
1.2.3 Removing Surfaces from a Voxet Model Build

List
Use this function to specify Surfaces to be excluded from a Voxet Model. After specifying
the surfaces, you can proceed to build the Voxet Model (see "Building a Voxet Model" on
page 1-19), or you can continue to modify the build list by adding or deleting other
surfaces.
Important Once you have built the Voxet Model, do not add or delete Surfaces and
rebuild.
To remove Surfaces 1 Select the Voxet commands, click the Model menu, and then click Remove
from the build list of Surfaces to open the dialog box.
a Voxet Model

3 The names of the displayed Surfaces will be listed automatically in the Surface
surfaces box.

Part
VI
Modeling
Velocity
Note The Voxet Model will not actually be built until you execute the Build function (see
"Building a Voxet Model" on page 1-19).
1.2.4 Building a Voxet Model

Use this function to build a Voxet Model.
To build a Voxet Model, you must first add Surfaces to its build list (see "Adding Surfaces
to a Voxet Model Build List" on page 1-17). The Surfaces must intersect one another or
the Voxet walls in order to create layers (see Figure 1–7 on page 1-17). Avoid modifying a
Voxet Model once you have built it (see "Voxet Model warnings" on page 1-17).
Note that Voxet Models are visualized through their parent Voxets. (Select the Voxet
Model in the Attribute Manager, but display the Voxet itself in the 3D Viewer.) When you
successfully create a layer in a Voxet Model, a region is automatically created in the
corresponding Voxet. As an option, you can also view the regions in the Voxet to visualize
the Voxet Model.
To build a Voxet 1 Select the Voxet commands, click the Model menu, and then click Build to open the
Model dialog box.

Tip Grouping regions into 3 If you want to construct the layers only, select the Layers check box. Alternatively,
layers automatically can you can construct layers manually (see "Creating Default Layers in a Velocity Model"
reduce the number of
on page 1-11).
regions dramatically in cases
where two surfaces are very Important Layer construction relies on the presence of geologic Information for
close to each other. each horizon and fault (see Part IV: Foundation Modeling, "Defining and Working
with Geologic Features" on page 8-1).
1.2.5 Creating and Working with Layers in a Voxet

Model
For information, see "Creating and Working with Layers in a Velocity Model" on
page 1-10.
Rock & Fluid Canvas™ 2009 | Epos™ 4.0 1.2 Constructing a Voxet Model 1-19
Paradigm™
1.2.6 Working with Regions in a Voxet Model

• "Finding a Region Name in a Velocity Model," page 1-14
• "Collapsing Small Regions in a Voxet Model," page 1-20
Finding a Region Name

See "Finding a Region Name in a Velocity Model" on page 1-14
Collapsing Small Regions in a Voxet Model

Use this command to modify the topology of a Voxet. This command creates a hole inside
the boundary of a small region, which is then absorbed into a larger region and
disappears. If the small region was bounded by more than one region, there is no way to
control the region into which the small region will be absorbed.
To collapse small 1 Select the Voxet commands, click the Model menu, and then click Remove Small
regions Regions to open the dialog box.

3 In the nb cells box, enter the region threshold size. Every region smaller than the size
you specify will be collapsed into neighboring regions.
1.2.7 Creating and Editing Voxet Model Properties

For information about other editing commands for Voxet Models and instructions, see
"Editing a Model3d" on page 1-7. In addition, you can use the Property Model Editor
tools with Voxet Models and Model3ds, as described in Chapter 2, "Defining Property
Values for Velocity Models."

2
Defining Property Values for
Velocity Models
In this chapter • "Procedure to Define Velocity Model • "Defining Properties or Variables by

Property Values," page 2-2 Using Property Functions," page 2-20
• "Understanding the Property Model • "Reviewing the Effect of a Property
Editor," page 2-3 Function," page 2-25
• "Working with the Variable Type • "Adding Properties to Velocity
Menu," page 2-4 Models," page 2-27
• "Defining Layer Property Values • "Deleting Properties from Velocity
Directly," page 2-10 Models," page 2-28
Overview In a velocity model such as a Model3d or a Voxet model, properties cannot be attached to
data points (as in geometric objects) because there is no connection between the
Surfaces. Instead, you can use the Property Model Editor in Paradigm™ GOCAD® 2009 to
define property values (such as velocity) for each model layer through mathematical
methods including constants, variables, and functions. Functions, which vary in
complexity, can in turn include elements such as defined variable, the properties and xyz-
positions of nearby Voxets and Surfaces, mathematical equations, and so on.
2-1
Paradigm™
2.1 Procedure to Define Velocity Model

Property Values
Table 2–1 Workflow for
defining property values For this step See
1 Create a velocity model "Constructing a Model3d" on page 1-2
with regions – or –
"Constructing a Voxet Model" on page 1-16
2 Create layers in the velocity "Creating and Working with Layers in a Velocity Model" on page 1-10
model
3 Create global properties "Adding Properties to Velocity Models" on page 2-27
(property names) for the
velocity model
4 Define property values for "Defining Layer Property Values Directly" on page 2-10
the layers using the – or –
Property Model Editor "Defining Properties or Variables by Using Property Functions" on
page 2-20
2-2 Defining Property Values for Velocity Models GOCAD® 2009.1 User Guide
Part
VI
Modeling
Velocity
2.2 Understanding the Property Model
Editor
• "About the Property Model Editor Interface," page 2-3
• "Working with the Variable Type Menu," page 2-4
• "Common Variable Definition Parameters," page 2-6
2.2.1 About the Property Model Editor Interface

The Property Model Editor is a tool for creating property values (such as velocity) for the
various layers of a model. The Property Model Editor (see Figure 2–1) is composed of three
main areas: the model selector, the property tree, and the value definition area. You can
also use the Property Model Editor to review any existing properties or variables for the
layers within the model.
Figure 2–1 Property Model Editor
Model
selector
Commands
Property list
Variable type
Value
definition
Rock & Fluid Canvas™ 2009 | Epos™ 4.0 2.2 Understanding the Property Model Editor 2-3
Paradigm™
To open the Property 1 Select the Voxet or SGrid commands, click the Model menu, and then click Editor
Model Editor to open the dialog box.
– or –
Select the Surface commands, click the Model3d menu, and then click Editor to
– or –
In the Object Tree, right-click any velocity model property (a shortcut menu opens),
and then click Editor.
2 In the Model box, enter the velocity model for which you want to define properties.
Important Ensure that the velocity model contains, at a minimum, regions and layers.
For more information, see Table 2–1 on page 2-2.
2.2.2 Working with the Variable Type Menu

You can define property values for the layers in your model by using constants, variables,
and functions. Functions, which vary in complexity, can in turn include elements such as
defined variables ("intermediate variables"), the properties and xyz-positions of nearby
Voxets and Surfaces, mathematical equations, and so on.
Figure 2–2 Property tree
Global property
Layer
Variable
Layer-specific properties
Tip A special layer called When you create a new property, it is global, or applicable to the whole model
Everywhere facilitates (see Figure 2–2). Every layer in the model will contain the property, but the layer-specific
creating variables that will
values are initially undefined. You must define properties for each layer individually, as the
be available in all layers, and
a special Property Model
different layers in a model do not share property functions or variables. Since variables or
called All Properties functions that you define in one layer do not apply to other layers, you can duplicate the
enables the creation of same variable and function names in different layers.
variables that will be
available in all Property
Use the Add Variable, Remove Variable, and Add Property commands to:
Models.
• Create properties for the model, if you have not already done so (for instructions, see
"Adding Properties to Velocity Models" on page 2-27)
• Create or delete variables or functions that define property values
Note You can define a variable either as a separate step or "on demand," while filling out the
value definition area (shown in Figure 2–1 on page 2-3).
The value definition area displays the details of the property or variable definition selected
in the Variable type box.
Part
VI
Modeling
Velocity
This menu of value definition types contains:
• Five options to define layer property values directly (see "Defining Layer Property
Values Directly" on page 2-10)
• Three options to define layer property values using property functions (see "Defining
Properties or Variables by Using Property Functions" on page 2-20)
Table 2–2 Variable

definitions Variable definition For information, see
Undefined
Build In
Constant "Assigning Constant Values to Properties or Variables," page 2-10
Linear Function "Defining Properties or Variables by Using Linear Functions," page 2-20
Exponential Function
Script "Defining Property Functions by Using Scripts," page 2-23
Linear Function of Property "Defining Properties or Variables by Using Linear Functions," page 2-10
Interpolated Property "Defining Properties or Variables by Using Interpolation," page 2-11
From Grid Property "Defining Properties or Variables from Grid Properties," page 2-13
From Surface or Layer "Defining Values from Surface or Layer Boundary Properties," page 2-14
Boundary Property
To define a property 1 If you need to create a new variable, do the following:

or variable (overview)
Note You can define a variable either as a separate step or "on demand," while filling out the
value definition area.
a In the property tree (see Figure 2–2), click the layer to which the variable will
belong.
b Click Add Variable. The Variable Name dialog box appears.
c In the Name box, type the name of the new variable.

d Click OK. The new variable appears in the property tree.
2 In the property tree, click the property or variable that you want to define or edit.
Paradigm™
3 If you are defining the property or variable for the first time, select an option in the
Variable type box. (The default variable type is as Undefined.)
Note Each option in the Variable type box brings up a different panel, as indicated in
Figure 2–2.
4 Define the parameters of the selected option in the value definition area. (See
"Defining Layer Property Values Directly" on page 2-10 or "Defining Properties or
Variables by Using Property Functions" on page 2-20.)
5 Click Update Variable Definition to apply your changes.
2.2.3 Common Variable Definition Parameters

Many property/variable definition options share the following common parameters or
concepts:
• "Variable Name," page 2-6
• "Shoot Direction," page 2-7
• "Shoot Position," page 2-8
• "Impact Point," page 2-8
Variable Name
Direct property If you are defining a layer property directly using one of the options in the Variable type
definitions menu, ensure that the Variable name displayed matches the name of the layer property
you are defining; otherwise, the program assumes that you are defining an intermediate
variable to be used in a property function (see "Defining Properties or Variables by Using
Property Functions" on page 2-20).
Intermediate If you are defining an intermediate variable to be used in a property function, ensure that
variables the Variable name displayed is different than the name of the layer property; otherwise,
the program assumes that you are defining the layer property itself.
Part
VI
Modeling
Velocity
Variables in different When you create (define) a variable, it is associated with a specific layer and property,
layers outside of which it has no meaning. If you want to use the variable in any other layers,
you must recreate the variable in the other layers. Since the various layers do not share
data, you can duplicate the same variable and function names in different layers.
Shoot Direction
Shoot direction, which is also known as the search direction or dir_Z, specifies the
direction along which to search for impact points (see "Impact Point" on page 2-8). There
are four shooting directions, but not all of them are available in every menu. In the
Property Model Editor, only the first three are available; in the Constraints menu (in the
Surface commands), only the fourth is available.
dir_Z = +1 GOCAD searches in the positive Z (up) direction from the shoot position (see "Shoot
Position" on page 2-8), as shown in panel b in Figure 2–3.
dir_Z = -1 GOCAD searches in the negative Z (down) direction from the shoot position, as shown in
panel b in Figure 2–3.
two_way GOCAD searches in both the positive and negative Z directions from the shoot position,
as shown in panel a in Figure 2–3.
This option overwrites the dir_Z = +1 or dir_Z = -1 options. When shooting two ways,
you can only shoot from inside (see "from_inside" on page 2-8).
dir_XYZ GOCAD will shoot along the direction specified by the vector dir_XYZ. (Actually, GOCAD
will shoot along both the positive and negative directions specified by this shoot position.)
Figure 2–3 Shooting direction/shooting point combinations
z a
zb
zc
two_way dir_z = -1 dir_z = +1

from_inside from_inside from_inside
zc
zd
dir_Z = +1 dir_Z = -1
from_outside from_outside
Paradigm™
Shoot Position
Shoot position is also known as the shooting point. This parameter, which is used with the
Add Variable command only, defines the starting point of the shoot (search).
There are two shoot position options: from_inside and from_outside (in dialog boxes,
you select from_outside by clearing the from_inside check box or option). See
Figure 2–3 on page 2-7.
from_inside GOCAD searches from the given point in the layer for which you are defining a property
variable, along the specified shoot direction to search for the specified source object(s).
See panels a, b, and c in Figure 2–3 on page 2-7.
When shooting two ways (see "two_way" on page 2-7), you can only search from inside.
from_outside GOCAD first gets outside of the layer from the given point (along the direction opposite
the specified shoot direction). Once outside the layer, GOCAD keeps moving (along the
direction opposite to the specified shoot direction) until it reaches a point below (or
above, if the shoot direction is Z-) all points in the given layer. See panels c and d in
Figure 2–3 on page 2-7. GOCAD then shoots from that outside point, along the specified
shoot direction, to look for an impact point on the specified source object(s).
Impact Point
The impact point is the first point GOCAD encounters on the specified source object(s)
along the specified shoot direction.
In some geological formations (such as folded or thrusted Surfaces), there can be more
than one intersection between the shooting path and the specified source object(s) (see
the left panel of Figure 2–4). Only the first of such intersections is the impact point.
Actually, GOCAD stops searching in that particular direction once it finds an intersection.
Multiple impact If the shoot direction is two-way, but only one impact point is needed, GOCAD will search
points in both directions to find impact points. It will keep the closest one if it finds two (one in
each direction).
Figure 2–4 Impact points

and the geometry of the X X
source Surface
X X
X
X X
dir_Z = -1 dir_Z = 1
points in the layer
dir_shoot
source surface (the surface with the property you want)
X impact points on the source surface
Part
VI
Modeling
Velocity
No impact point If GOCAD cannot find an impact point along the specified shoot direction(s) for a given
point in the model layer, the value of that particular variable at that point will be null. See
the right panel of Figure 2–4.
The following are graphic examples of how GOCAD finds the impact points under
different circumstances:
• Figure 2–5 on page 2-12
Paradigm™
2.3 Defining Layer Property Values Directly

For information and instructions, see:
• "Assigning Constant Values to Properties or Variables," page 2-10
• "Defining Properties or Variables by Using Linear Functions," page 2-10
• "Defining Properties or Variables by Using Interpolation," page 2-11
• "Defining Properties or Variables from Grid Properties," page 2-13
• "Defining Values from Surface or Layer Boundary Properties," page 2-14
2.3.1 Assigning Constant Values to Properties or

Variables
To assign a constant 1 In the property tree, click the property or variable that you want to define or edit.
value to a property or
2 In the Variable type box, select Constant.
variable
3 In the Constant value box, type a numerical constant value to assign to the variable.
2.3.2 Defining Properties or Variables by Using

Linear Functions
This definition option is similar to defining property variables by using interpolation (see
"Defining Properties or Variables by Using Interpolation," page 2-11), except that the top
and bottom Surfaces are replaced by the upper and lower bounding Surfaces of a model
layer.
This definition option can be useful when there is more than one top and/or more than
one bottom bounding Surface for the layer of interest. This definition option ensures that
at any given point in the selected layer, the variable will find two impact points to get an
interpolated (extrapolated) Value, since a layer, by definition, is completely bounded.
(There is one exception: when part of the bounding surface of the given layer is the
bounding box of the model, GOCAD may not be able to locate an impact point.)
Part
VI
Modeling
Velocity
To define a property 1 In the property tree, click the property or variable that you want to define or edit.
or variable by using a
2 In the Variable type box, select Linear Function of Property.
linear function
3 In the Referenced layer box, select the name of the referenced layer whose
bounding Surfaces will be the source Surfaces.
Important Ensure that the property you want is defined on all of those Surfaces.
4 In the Referenced property box, enter the name of the property on the bounding
Surfaces of the selected referenced layer. (This does not have to be the same name as
the name of the variable or the name of the layer property.)
5 If you want to add a constant value to the referenced property, type a number in the
Value to add to referenced property box.
6 If you want to multiply the referenced property by a constant scaling factor, type a
number in the Scaling factor (multiple) to apply to referenced property box.

Interpolation
This definition option finds the property values at two impact points (see "Impact Point"
on page 2-8), one from each of the two specified source boundaries, and performs a
linear interpolation (or extrapolation) to find a value for the variable at (X, Y, Z).
GOCAD finds the top and bottom impact points by shooting two ways (see "two_way"
on page 2-7) to the top source boundary and the bottom boundary surface from the
given point (see "from_inside" on page 2-8).
Figure 2–5 presents graphic examples of where impact points may be located. The terms
"top source Surface" and "bottom source Surface" do not imply relative positions to each
other or to the selected model layer. The terms are only used to remind you that you need
two source Surfaces.
Rock & Fluid Canvas™ 2009 | Epos™ 4.0 2.3 Defining Layer Property Values Directly 2-11
Paradigm™
Figure 2–5 Finding the Top source surface Top source surface
two impact points on the
two source Surfaces for a
given point in a model X XX X X X
layer Model layer Model layer
X X
X X X
Bottom source surface Bottom source surface
Each boundary property is defined as a function: P ( x, y, z ) = P o + ( Z – Z o )

Where P(x,y,z) is the linear property function, Z is the coordinate at a given set of (x,y,z)
points, and Po is a variable. Therefore, this definition option performs an interpolation
between two linear functions of two boundaries.
or variable by using
2 In the Variable type box, select Interpolate Property.
interpolation
3 To define Ptop, the variable representing the top boundary, do one of the following:
• To assign a constant, click Constant, and then type a numerical constant in the
box.
• To set Ptop to equal another variable in the model, click Variable, and then
select the variable in the box.
4 To define Ztop, the Z value of the top boundary, do one of the following:
box.
• To set Ztop to equal the Z of another surface/layer, click Variable, and then
Part
VI
Modeling
Velocity
5 To define Pbot, the variable at the origin of the bottom boundary, do one of the
following:
box.
• To set Pbot to equal another variable in the model, click Variable, and then
6 To define Zbot, the Z value of the bottom boundary, do one of the following:
box.
• To set Zbot to equal the Z of another surface/layer, click Variable, and then
2.3.4 Defining Properties or Variables from Grid

Properties
This definition option creates a variable whose value at a given point in the selected layer
is defined by the value of a Voxet property at the same (X,Y,Z) position. The name of the
Voxet property need not be the same as the name of the variable or the layer property
that you are defining.
To use this definition option, you must have a Voxet with the desired property. Ideally,
choose a Voxet that has the same or greater spatial extent as your model in order to avoid
a possible core dump.
or variable from a
2 In the Variable type box, select From Grid Property.
grid property
3 In the Voxet box, enter the name of the Voxet that includes the property you want.
4 In the Property box, enter the name of the property.
5 If you want to extrapolate the property outside the Voxet, select the Extrapolate
check box.
Paradigm™
6 If you want to set the point where the values are not defined as the specified default
value, select the Use the default value check box, and then type a number in the
box.
2.3.5 Defining Values from Surface or Layer

Boundary Properties
• "Defining Values from Surface Boundaries," page 2-14
• "Defining Values from Layer Boundaries," page 2-15
• "Notes on Defining Values from Surfaces and Layers," page 2-18
This definition option creates a variable whose value at a point (X, Y, Z) is determined by a
property value on the selected boundary at the same (X,Y) position. The boundary can be
either a Surface or a layer. In other words, GOCAD does the following:
• Shoots from a point (X, Y, Z) inside the layer of the model directly upward or
downward until it hits the selected source boundary
• Sets the property value at that impact point as the value of the variable at the (X, Y, Z)
shooting point
Defining Values from Surface Boundaries

Figure 2–3 on page 2-7 illustrates the parameters used in this definition option, and
Figure 2–6 on page 2-15 presents graphic examples of where impact points may be
located. These figures may help you better understand the roles of theses parameters.
To use this definition option, your model must include a Surface with the desired property.
The name of the Surface property need not be the same as the variable or the layer
property.
Ideally, choose a Surface that has the same or greater spatial extent in the X and Y
directions as the layer. If some points in the layer have no impact point (as shown in the
right panel of Figure 2–4 on page 2-8), the following may happen:
• If the variable is an intermediate variable (to be used in a property function), you may
run into problems.
• If the variable is being defined as the property, there will be a no-data value at those
points without an impact point, which is acceptable.
Vertical location is important as well. If the shoot direction is purely upward, for example,
the Surface should exist above all points of the layer in order for GOCAD to find an
impact point for every point in the selected layer.
Part
VI
Modeling
Velocity
Figure 2–6 Finding a property value on the source Surface for a given point in the model layer
Not the source Surface Not the source Surface
Layer Layer
Source surface Source surface
two_way=on, from_inside=on Z=-1, two_way=off, from_inside=off
Not the source Surface Not the source Surface
Layer Layer
Source surface Source surface
Z=-1, two_way=off, from_inside=on Z=+1, two_way=off, from_inside=on
Defining Values from Layer Boundaries

A source Surface is any Surface that:
• Serves as a bounding Surface of the specified layer
• Lies in the path of a shooting ray
Figure 2–7 presents graphic examples of where impact points may be located.
Paradigm™
Figure 2–7 Finding a property value on the bounding Surfaces of the source layer for a given point in the model layer
A source Surface A source Surface
X X X X
Source layer & Source layer &
Model layer Model layer
X
X
two_way=on, from_inside=on Z=-1, two_way=off, from_inside=off
X
Source layer & Source layer &
Model layer Model layer
X
X
X
X X
Z=-1, two_way=off, from_inside=on Z=+1, two_way=off, from_inside=on
This definition option can be useful when there is more than one top and/or more than
one bottom bounding Surface for the layer of interest. This definition option ensures that
at any given point in the selected layer, the variable will find a Value (an impact point),
since a layer, by definition, is completely bounded. (There is one exception: when part of
the bounding surface of the given layer is the bounding box of the model, GOCAD may
not be able to locate an impact point.)
Part
VI
Modeling
Velocity
or variable from a
2 In the Variable type box, select From Surface or Layer Boundary Property.
surface or layer
boundary
3 Do one of the following:

• To calculate a variable from a layer boundary, skip to step 6.
• To calculate a variable from a surface boundary, click Surface.
4 In the Surface box, enter the name of the Surface that includes the property you
want.
5 In the Surface property box, enter the name of the property on the selected
Surface. (This does not have to be the same name as the name of the variable or the
name of the layer property.)
Skip to step 9.
6 Click Layer.
7 In the Layer box, enter the name of the Source (target) layer whose bounding
Surfaces will be the source Surfaces.
Important Ensure that the property you want is defined on all of those Surfaces.
8 In the Property box, enter the name of the property on the bounding Surfaces of the
selected source layer (This does not have to be the same name as the name of the
variable or the name of the layer property.)
Paradigm™
9 If you want GOCAD to search for impact points in only one shoot direction, do one of
the following:
• To search upward, select 1 in the Z coordinate of projection vector box. (See
"dir_Z = +1" on page 2-7.)
• To search downward, select -1 in the Z coordinate of projection vector box.
(See "dir_Z = -1" on page 2-7.)
10 If you want GOCAD to ignore the dir_z parameter and to search for impact points in
both shoot directions, select the Two-way projection check box. (See "two_way"
on page 2-7 and Figure 2–3 on page 2-7.)
Important When searching two ways, you can only shoot from inside Be sure to also
select the Offset from boundary check box in step 11.
11 If you want GOCAD to shoot from inside, select the Offset from boundary check
box. To shoot from outside, clear the check box. (See "Shoot Position" on page 2-8
and Figure 2–3 on page 2-7.)
12 If you want to set the point where the values are not defined as the specified default
value, select the Use the default value check box, and then type a number in the
box.
Notes on Defining Values from Surfaces and Layers

• In a Model3d, GOCAD recognizes not only which objects form the bounding Surface
of a layer, but also which portion of the objects really form the boundaries. In a Voxet
Model, however, GOCAD only recognizes whole Surfaces, not the separate portions.
You must ensure that your specifications will direct GOCAD to find the proper impact
points. This important concept is illustrated in Figure 2–8.
Part
VI
Modeling
Velocity
Figure 2–8 Model types
and impact points S1 S1
X
X
pA pA
dir_Z = -1 dir_Z = -1 L1
L1
from_inside = off from_inside = off
Model3d Voxet Model b
S2 a S2
pB
X
X
pB
pA pA
L2 L2
dir_Z = -1 dir_Z = -1
from_inside = off from_inside = off d
Model3d c Voxet Model
• Given the same shoot specifications (Z+ from outside, target layer Surface L1) and
geology, the two types of models may produce different impact points for a given
point in a layer. This is because a Model3d recognizes different portions of an object,
while a Voxet Model does not.
• In panel a of Figure 2–8, Only the lower portion of the closed Surface S1 is
recognized as part of the bounding Surface of the layer L1; therefore, GOCAD
ignores the first intersection with S1 and chooses the second one as the impact point.
• In panel b of Figure 2–8, GOCAD recognizes S1 as a whole as part of the bounding
Surface of the layer L1, and therefore chooses the first intersection with S1 as the
impact point.
• In panels c and d of Figure 2–8, the two models produce the same impact point for
point A (pA), because the from_outside shooting point is lower. (The shooting point
only needs to be higher than any point in the layer L1.) At point B (pB), however, the
two models will again produce different impact points.
Paradigm™
2.4 Defining Properties or Variables by Using

Property Functions
You can use these definition options to create property functions of varying complexity.
Add Functions:
• Undefined
• Build In
• Constant
• Linear Function (For information, see "Defining Properties or Variables by Using Linear
Functions" on page 2-20.)
• Exponential Function
• Script (For information, see "Defining Property Functions by Using Scripts" on
page 2-23.)
• Linear Function of Property
• Interpolated Property
• From Grid Property
• From Surface or Layer Boundary Property
Linear functions: Linear functions have the following form:
P ( p ) = P o ( p ) + K ( p ) × ( Z ( p ) – Zo ( p ) )
If you use user-defined variables in a linear function, define the variables (see "Working
with the Variable Type Menu" on page 2-4) after you define the function itself.
Exponential functions: Exponential functions have the following form:
[ K × ( Z( p) – Zo( p )) ]
P ( p ) = Po ( p )
Scripts: Script syntax is similar to the awk or C programming language.
If you use user-defined variables in a script function, you can define the variables (see
"Working with the Variable Type Menu" on page 2-4) either before or after you define
the function itself.
• "Defining Properties or Variables by Using Linear Functions," page 2-20
• "Defining Properties or Variables by Using Exponential Functions," page 2-22
• "Defining Property Functions by Using Scripts," page 2-23
•

Linear Functions
Use this definition option to define the layer property as either
• A simple linear function of Z (the Z coordinate of the given (x, y, z) point)
P ( x, y, z ) = Po + K × ( Z – Z o )
Part
VI
Modeling
Velocity
Where P(x, y, z) is the linear property function, Z is the Z coordinate of the given (x, y,
z) point, and P o, K, and Z o are constants.
• A complex linear function:
P ( x, y, z ) = Po ( x, y, z ) + K ( x, y, z ) × ( Z – Z o ( x, y, z ) )
where P(x, y, z) is the linear property function, Z is the Z coordinate of a given point,
and Po, K and Z o are variables that you can define using one of the definition options
found in "Working with the Variable Type Menu" on page 2-4.
To define a value by 1 In the property tree, click the property or variable that you want to define or edit.
using a linear
2 In the Variable type box, select Linear Function.
function
3 To define P0 (as in P(X, Y, Z) = P0+ K * (Z -Z0)), do one of the following:

box.
• To set P0 to equal another variable in the model, click Variable, and then select
the variable in the box.
4 To define K (as in P(X, Y, Z) = P0+ K * (Z -Z0)), do one of the following:
box.
• To set K to equal another variable in the model, click Variable, and then select
5 To define Z0 (as in P(X, Y, Z) = P0+ K * (Z -Z0)), do one of the following:
box.
• To set Z0 to equal another variable in the model, click Variable, and then select
6 To make Z positive upward, select the Z is positive upward check box.
To make Z positive downward, clear the check box.
Rock & Fluid Canvas™ 2009 | Epos™ 4.0 2.4 Defining Properties or Variables by Using Property Functions 2-21
Paradigm™

Exponential Functions
Use this definition option to define the layer property as either
• A simple linear function of Z (the Z coordinate of the given (X, Y, Z) point)
P(X, Y, Z) = P0 * exp [K * (Z -Z0)]
where P(X, Y, Z) is the linear property function, Z is the Z coordinate of the given (X, Y,
Z) point, and P0, K and Z0 are constants.
• A complex linear function
P (X, Y, Z) = P0 (X, Y, Z) + K (X, Y, Z) * (Z - Z0 (X, Y, Z))
where P(X, Y, Z) is the linear property function, Z is the Z coordinate of a given point,
and P0, K and Z0 are variables that you can define using one of the definition options
found in "Working with the Variable Type Menu" on page 2-4.
To define a value by 1 In the property tree, click the property or variable that you want to define or edit.
using an exponential
2 In the Variable type box, select Exponential Function.
function
3 To define P0 (as in P(X, Y, Z) = P0+ K * (Z -Z0)), do one of the following:

box.
• To set P0 to equal another variable in the model, click Variable, and then select
4 To define K (as in P(X, Y, Z) = P0+ K * (Z -Z0)), do one of the following:
box.
• To set K to equal another variable in the model, click Variable, and then select
5 To define Z0 (as in P(X, Y, Z) = P0+ K * (Z -Z0)), do one of the following:
box.
• To set Z0 to equal another variable in the model, click Variable, and then select
Part
VI
Modeling
Velocity
6 To make Z positive upward, select the Z is positive upward check box.
To make Z positive downward, clear the check box.
2.4.3 Defining Property Functions by Using Scripts

• "About Script Property Functions," page 2-23
• "Creating Script Property Functions," page 2-24
About Script Property Functions

Use this definition option to create sophisticated property functions. You need at least
minimal knowledge of the awk or C programming languages to take full advantage of
this powerful tool.
All variables used in a property script (except the three built-in variables, X, Y, and Z) must
be defined as variables for the layer property by using the definition options found in
"Working with the Variable Type Menu" on page 2-4.
The name of another property (or the name of a variable in another property) in the
selected layer (or any other layer) is not recognized as a pre-defined variable for a
property script. If you want to use another property (or a variable in another property) as
a variable in the current property script, you must define a new variable for the current
property, giving the new variable the same definition as the other property (or the variable
in the other property).
Script syntax The syntax used to define a script property function is similar to the C programming
language. All script functions must be enclosed in { }. All operations must end with ";"
and be enclosed in { }. You can include the following components in your script:
• numbers
• the variables X, Y, and Z
• Variables that you have defined for a specific layer property
• logical expressions such as
&&, ||, ==, !, <, <=, >, >=, if, else,
• the following 11 pre-defined functions:
• sqrt (x) = the square root of x

• exp(x) = e x
• log(x) = ln(x)
• log10(x) = log10 (x)
• cell (x) = the closest integer that is greater than or equal to x
• floor (x) = the closest integer that is less than or equal to x
• fabs (x) = the absolute value of (x)
• pow (x, y) = xy
• cos (x) = Cosine (x)
• sin (x) = Sine (x)
• tan (x) = Tangent (x)
Rock & Fluid Canvas™ 2009 | Epos™ 4.0 2.4 Defining Properties or Variables by Using Property Functions 2-23
Paradigm™
Examples of script • { if (PERM>0.3) {OIL=PORO*(1-WATER);} else {OIL = 0;} }

functions • { if (PORO<=0.01 || PERM<=0.1) {OIL=0;} else
{OIL=PORO*OILSAT;} }
• { PVEL=sqrt ( (LAM + 2*MEU) / RHO );}
Creating Script Property Functions

If there are any variables in the script you are going to write, define them using the
definition options found in "Working with the Variable Type Menu" on page 2-4.
To create a script 1 In the property tree, click the property or variable for which you want to create a
property function function.
2 In the Variable type box, select Script.
3 Create the script by doing one of the following:

• Type the name and the text of the script function in the Script box.
Note The name of the function must be identical to the name of the property you are
defining. Also, you must declare all variables (including X, Y, Z, if there are any) used in the
function. Separate the names of the variables by a space. If you fail to declare a variable
that you have used in the function, GOCAD will not be able to recognize it as a variable or
to fetch its definition.
• To load a previously saved function, click Load. The Load File dialog box appears
and prompts you to select the text file that contains the function you want.
Note Ensure that all the variables are defined, which you can do after the function is
created.
4 If you want to save your script function, click Save As. The Save File dialog box
appears and prompts you to save the function as a text file under a file name that you
specify.
Note Only the definition of the function itself is saved, not the definition of the variables used
in the function.

Important Once created, script functions are not easily deleted.
Part
VI
Modeling
Velocity
2.5 Reviewing the Effect of a Property
Function
• "Painting a Voxet with a Velocity Model Property," page 2-25
2.5.1 Painting a Voxet with a Velocity Model

Property
Since there is no actual substance in a model layer, there is no media to support the
visualization of a property function in a layer. To view a property function, you must paint
the function onto a Surface or a Voxet, then display the Surface (or Voxet Sections) with
the painted property.
To use this function, you must have a Voxet. Ideally, choose a Voxet that has the same or
greater spatial extent as your model.
To paint a Voxet with 1 To create a property in a Voxet, see Part IV: Foundation Modeling, "Copying,
a property Deleting, and Renaming an Object Property" on page 11-5.
2 Select the Voxet commands, click the Property menu, and then click With Property
Model to open the dialog box.
– or –
Select the Voxet or SGrid commands, click the Model menu, and then click Paint
Voxet to open the dialog box.
– or –
Select the Surface commands, click the Model3d menu, and then click Paint Voxet
to open the dialog box.
3 In the Model box, enter the model that contains the property function.
4 In the Property box, enter the property that you want to review.
5 In the Layer name box, select the layer to which the property function is attached.
6 In the Voxet voxet box, select the Voxet onto which you want to paint the selected
model property.
7 In the Voxet Property box, select the name of the property that you want to paint
over.
Note The selected property will be painted over by values derived from the property function in
the model.
Rock & Fluid Canvas™ 2009 | Epos™ 4.0 2.5 Reviewing the Effect of a Property Function 2-25
Paradigm™
Part
VI
Modeling
Velocity
2.6 Adding Properties to Velocity Models
Use this function to create global properties for velocity models. You can also designate a
property class for each property. Property classes are used to set up a set of universal
statistical parameters so that all the properties that you define as being in the same
property class will be in the same statistical pool.
For example, you may have three different type of permeability measurements: one from
core samples, one from skin damage estimation and one from theoretical calculation. You
could name them permc, perms and permt, respectively.
If you assign all three to the same property class, say Perm, then data points from all three
properties will be included when you calculate the mean (or any other statistical measure)
of the property class perm.
To add a property to a 1 Select the Voxet or SGrid commands, click the Model menu, and then click Add
velocity model Property to open the dialog box.
– or –
Select the Surface commands, click the Model3d menu, and then click Add
Property to open the dialog box.
– or –
From the Property Model Editor, click Add Property.
2 In the Model box, select the model for which you want to create a new property.
3 In the Property box, type in the name of the new property you want to create.
4 Press TAB or click in the Property class box; the name you entered in the property
box in step 3 will reappear here.
If you want to create a new property class name, type the new name in the Property
class box.
Rock & Fluid Canvas™ 2009 | Epos™ 4.0 2.6 Adding Properties to Velocity Models 2-27
Paradigm™
2.7 Deleting Properties from Velocity

Models
For information, see Part IV: Foundation Modeling, "Copying, Deleting, and Renaming an
Object Property" on page 11-5.
3
Creating Grid Properties with
Geostatistical Functions
In this chapter • "Geostatistics System File Formats," • "Running Geostatistical Simulations,"

page 3-2 page 3-16
• "Estimating Grid Properties with
Kriging Algorithms," page 3-6
Overview This chapter describes the geostatistical functions that can be applied on grids (SGrids
and Voxets). This chapter assumes that you are familiar with geostatistical concepts and
terminology and have the necessary background to run geostatistical applications. If you
need more information on any of the terms or methods used in this chapter, please see
Statistics for Engineers and Geoscientists, J.L. Jensen et al., Prentice Hall, 1996. The
geostatistical applications in this part of Paradigm™ GOCAD ® 2009 use the standard
GSLIB from Stanford University (GSLIB: Geostatistical Software Library and User's Guide,
C.V. Deutsch & A.G. Journel Oxford Press, 1992).
3-1
Paradigm™
3.1 Geostatistics System File Formats

The following sections describe additional files and formats needed for running some of
the geostatistical commands in GOCAD.
• "GS File," page 3-2
• "Column_Average_Map File," page 3-4
• "Scattergram File," page 3-4
• "External_Histogram File," page 3-5
• "Facies_Map File," page 3-5
• "Annealing_Schedule File," page 3-5
3.1.1 GS File
• "Variogram and Associated Parameters File Format," page 3-2
• "GS File Examples," page 3-3
Variogram and Associated Parameters File Format

A GS file has the following parameters stored in the specified sequence:
1 COORDINATE_SYSTEM XYW
2 KRIGING_TYPE 1
3 MAX_CLOSE m
4 KRINGING_OPTION 1
5 SEARCH_ELLIPSOID α β θ S F T
6 COVARIANCE MODEL TNVar n
7 type1 α1 β1 θ1 S1 F1 T1 NVar1
. .
. .
. typen αn βn θn Sn Fn Tn NVarn
. END
n+5
n+6
These are user-specified parameters, which must be entered as shown.
Explanation of 1 The coordinate system can be either XYZ, XYW, or UVW.

individual lines in a
2 This line is ignored, but it must be present as shown.
GS file
3 This line gives the maximum number of data points, m, that will be used to krige the
property value at any given node. Only the closest m points are used.
4 This line specifies simple kriging (0) or ordinary kriging (1).
5 This line describes the search ellipsoid in the uvw or XYZ coordinate system.
• α is the angle with the first axis (U or X).
• β is the angle with the second axis (V or Y).
• θ is the angle with the third axis (W or Z).
• S is the length of the search radius ellipsoid along the first axis.
• F is the length of the search radius ellipsoid along the second axis.
• T is the length of the search radius ellipsoid along the third axis.
3-2 Creating Grid Properties with Geostatistical Functions GOCAD® 2009.1 User Guide
Part
VI
Modeling
Velocity
6 This line describes the variogram model.
• TNVar is the sill (total variance) of the variogram model.
• n is the number of nested components of the variogram model.
7 This line describes the first component of the nested variogram model.
• type1 is the type of theoretical variogram used in the component. It must be one
of the following (in upper case): SPHERICAL, GAUSSIAN, EXPONENTIAL, or
POWER.
• αn βn θn Sn Fn Tn are the parameters of the variogram ellipsoid, similar to those
at line 5.
• NVar1 is the variance contribution of the first component.
• The rest of the files describe the rest of the components in the variogram model.
• The last line must be as shown.
GS File Examples
Below are examples (with comments) of two types of variogram files:
• "Indicator simulation example" on page 3-3
• "Gaussian simulation example" on page 3-4
Indicator simulation # Comment lines start with this symbol

example # coordinate system can either be XYZ, XYW, or UVW
# in this example, XYW is chosen; therefore, the areal correlation
# ranges are in real-world coordinates and the vertical correlation
# range is in normalized (0 to 1) coordinate
COORDINATE_SYSTEM XYW
# not used
KRIGING_TYPE 0
# maximum number of nearby data for kriging
MAX_CLOSE 16
# 0 = simple kriging; 1 = ordinary kriging
KRIGING_OPTION 0
# 3 cutoffs
NB_CUT_OFFS 3
# first cutoff is 0.268 with cumulative probability of 25%
# second cutoff is 0.300 with cumulative probability of 50%
# third cutoff is 0.332 with cumulative probability of 75%
CUT_OFFS 0.268 0.25 0.300 0.50 0.332 0.75
# search ellipsoids corresponding to each cutoff
# format: angle1 angle2 angle3 range1 range2 range3
SEARCH_ELLIPSOID 45. 0. 0. 5000. 2500. 0.2
# covariance model for each cutoff
# format COVARIANCE_MODEL sill number_of_nested_structures
# model_type angle1 angle2 angle3 range1 range2 range3
contribution
# model type can either be SPHERICAL EXPONENTIAL GAUSSIAN or POWER
# in this example, there is only 1 nested structure, so only one model
line
# is needed
# covariance for first cutoff
COVARIANCE_MODEL 1. 1
SPHERICAL 45. 0. 0. 3000. 500. 0.1 1.
# covariance for second cutoff
SPHERICAL 0. 0. 0. 2500. 2500. 0.1 1.
# covariance for third cutoff
Rock & Fluid Canvas™ 2009 | Epos™ 4.0 3.1 Geostatistics System File Formats 3-3
Paradigm™
SPHERICAL 135. 0. 0. 3000. 250. 0.1 1.
END
Gaussian simulation # coordinate system can either be XYZ, XYW, or UVW

example # in this example, XYW is chosen; therefore, the areal correlation
# ranges are in real-world coordinates and the vertical correlation
# range is in normalized (0 to 1) coordinate
COORDINATE_SYSTEM XYW
# not used
KRIGING_TYPE 0
# maximum number of nearby data for kriging
MAX_CLOSE 16
# 0 = simple kriging; 1 = ordinary kriging
KRIGING_OPTION 0
# search ellipsoid
# generally, one should make the ranges of the search ellipsoid
# larger than the correlation ranges
# format: angle1 angle2 angle3 range1 range2 range3
# covariance model
# format COVARIANCE_MODEL sill number_of_nested_structures
# model_type angle1 angle2 angle3 range1 range2 range3
contribution
# model type can either be SPHERICAL EXPONENTIAL GAUSSIAN or POWER
# in this example, there is only one nested structure, so only one model
line
# is needed
SPHERICAL 0. 0. 0. 2000 2000 0.2 1.
END
3.1.2 Column_Average_Map File

This file is needed for block kriging and simulated annealing (see "Running Annealing
Simulations" on page 3-24). This example uses an SGrid with the dimensions
138x33x100. The first two lines must start with NX and NY, which specify the number of
cells in the u and v directions, followed by NX*NY lines of data (one data per line) that
represent the column averages.
NX 138
NY 33
0.23
...
0.30
3.1.3 Scattergram File

This file is needed for cloud transformations with P-fields (see "Running Cloud Transform
Simulations with P-Fields" on page 3-27). This file has no header lines, just two columns
of data.
Independent_VariableDependent_Variable
0.1 1.5
0.1 1.3
0.1 1.6
...
1.2 3.9
Part
VI
Modeling
Velocity
3.1.4 External_Histogram File
This file is needed for simulated annealing (see "Running Annealing Simulations" on
page 3-24) and continuous histogram correction (see "Performing Continuous Histogram
Corrections" on page 3-30). This file has no header lines, just a column of data.
Data_Value
GOCAD then constructs the histogram using the data read in from the file.
1.0
0.9
...
1.2
3.1.5 Facies_Map File

This file is needed for Fill From Facies Map (see "Filling Grids with Facies Map Data" on
page 3-31). This file has a header line for user identification (not used in the algorithm),
followed by a series of data lines in the following format:
X_coord Y_coord Facies_value
1230303.0 39393939.0 1
...
3030303.0 10393030.0 3
3.1.6 Annealing_Schedule File

This file is needed in Simulated Annealing (see "Running Annealing Simulations" on
page 3-24).
# Comment lines start with this symbol
#but there are no real comments because if the variables
#are not obvious, it will take too long to define them
# comments
INITIAL_TEMPERATURE 0.001
REDUCTION_FACTOR 0.1
# controls how temperature is lowered, 0<λ<1
MAX_PERTURB 1000.
MAX_PERTURB_PER_TEMP 10.
# maximum number of perturbation at any one temperature.
#Temperature is multiplied by a reduction factor when that number is
reached
MAX_SUCC_PERTURB_PER_TEMP 3.
#maximum number of successful perturbation for any one temperature.
#Temperature is multiplied by a reduction factor when that number is
reached
MIN_OBJECTIVE 0.001
REPORT_INTERVAL 0.2
#controls screen dump of objective function values
STOPPING_NUMBER 5
#represents the number of times MAX_PERTURB_TEMP is reached before the
algorithm stops
Rock & Fluid Canvas™ 2009 | Epos™ 4.0 3.1 Geostatistics System File Formats 3-5
Paradigm™
3.2 Estimating Grid Properties with Kriging

Algorithms
There are several types of kriging offered in the Geostatistics menu:
• "Estimating Properties with Kriging," page 3-6
• "Estimating Properties with Kriging with Trend," page 3-7
• "Estimating Properties with Kriging with External Drift," page 3-9
• "Estimating Properties with Bayesian Kriging," page 3-10
• "Estimating Properties with Collocated Cokriging," page 3-12
• "Estimating Properties with Indicator Kriging," page 3-13
Kriging processes are more sophisticated than traditional interpolation processes in that
they enable you to specify statistical anisotropy in terms of variogram parameters. If you
also want to model heterogeneity in the property, GOCAD offers various types of
stochastic simulation processes (see "Running Geostatistical Simulations" on page 3-16).
3.2.1 Estimating Properties with Kriging

The kriging algorithm provides a minimum error-variance estimate at any unsampled
location.
You must have an ASCII file containing the variogram data and an object that can serve as
the property source ("hard data" should lie at least partially inside the SGrid or Voxet).
To run kriging to 1 Display the SGrid or Voxet and the property object in the 3D Viewer.
create SGrid or Voxet
2 On the Voxet, SGrid, or General menu bar, click the Geostatistics menu, and then
properties click Kriging to open the dialog box.
3 In the Grid Object box, enter one or more Voxets or SGrids.

4 In the Region name box, enter the grid object region in which the kriging will be
performed.
Note By default, kriging will be performed for all points (everywhere) on the grid.
5 In the Discrete property server by box, enter the object that carries the existing
property values.
6 In the By region box, enter the input data region.
7 In the Property box, select the object property to be used in the operation.
Part
VI
Modeling
Velocity
8 In the New property prefix box, type the prefix for the created properties. (For
example, if you type Kriging_, the two new created properties will be named
Kriging_estimate and Kriging_variance.)
9 To specify the ASCII file that contains the variogram data (see "GS File" on page 3-2),
enter the path to the file in the GS file box.
– or –
Click to open the Select Text File dialog box, find and select the file you want,
and then click OK.
10 If you want to set options for the variogram and associated parameters, click
Advanced to expand the dialog box.
a In the Kriging Type box, select one the following kriging options:
• Simple. Residuals are computed from the mean of the data and kriged.
• Ordinary. Input data values are used directly for the kriging.
• Use_variogram_file_setting. Use the type set in the variogram file.
b To allow for the possibility that the result at a cell containing data points is not
kriged, but rather directly assigned from input data in that cell, select one of the
following data value assignment options:
• No data assignment. All cells are kriged.
• Assign data to nearest cells. In any particular cell, the data point closest to
the cell center is assigned as the estimation at the cell.
• Assign mean at cell center. The mean of all the data points in a particular
cell is assigned as the cell value.
If you choose this option, also select a method of computing the mean in the
Mean computation type box, and type the value for the exponent (in the
standard mean power equation) in the Power mean power box.
3.2.2 Estimating Properties with Kriging with Trend

In kriging with trend (also known as universal kriging), the modeled property is assumed
to follow a trend that is only a function of the location coordinates.
the property source (it should lie at least partially inside the SGrid or Voxet).
Rock & Fluid Canvas™ 2009 | Epos™ 4.0 3.2 Estimating Grid Properties with Kriging Algorithms 3-7
Paradigm™
To run kriging with 1 Display the SGrid or Voxet and the property object in the 3D Viewer.
trend to create SGrid
or Voxet Properties click Kriging with Trend to open the dialog box.

performed.
property values.
– or –
and then click OK.
10 In the Kriging Type box, select one the following kriging options:
11 To allow for the possibility that the result at a cell containing data points is not kriged,
but rather directly assigned from input data in that cell, do one of the following to
assign data values to cells:
Part
VI
Modeling
Velocity
• Select the Assign data to nearest cells check box. In any particular cell, the
data point closest to the cell center is assigned as the estimation at the cell.
• Clear the Assign data to nearest cells check box. All cells are kriged.
12 In the Trend Model area, select the check boxes representing the trend components
you want.
• a, u, a5v2, or a9vw. The trend is a function of a, u+a5v2+a9vw.
• a, a5, or a9. These are unknown weights that will be estimated during the
kriging process.
3.2.3 Estimating Properties with Kriging with

External Drift
In kriging with external drift, the trend is a linear function of a secondary property (drift)
that does not have to be in the same units as the data.
To run kriging with 1 Display the SGrid or Voxet and the property object in the 3D Viewer.
external drift to
create SGrid or Voxet click Kriging with External Drift to open the dialog box.
properties

performed.
property values.
Paradigm™
8 In the Drift Property box, enter the secondary property that exists everywhere on the
Grid.
– or –
and then click OK.
3.2.4 Estimating Properties with Bayesian Kriging

Bayesian kriging is similar to "Estimating Properties with Kriging with External Drift" on
page 3-9, except that the drift property must be in the units of the data being estimated.
Part
VI
Modeling
Velocity
To run Bayesian 1 Display the SGrid or Voxet and the property object in the 3D Viewer.
kriging to create
SGrid or Voxet click Bayesian Kriging to open the dialog box.
properties

performed.
property values.
8 In the Guess Property box, enter the secondary property that exists everywhere on
the Grid and has the same units as the property being estimated (selected in step 7).
– or –
and then click OK.
Paradigm™
but rather directly assigned from input data in that cell, select one of the following
data value assignment options:
• Assign data to nearest cells. In any particular cell, the data point closest to the
cell center is assigned as the estimation at the cell.
• Assign mean at cell center. The mean of all the data points in a particular cell is
assigned as the cell value.
3.2.5 Estimating Properties with Collocated

Cokriging
Use collocated cokriging to fill the selected SGrid or Voxet with property values (to assign
property values to all the nodes in the SGrid or Voxet).
the property source (it must lie at least partially inside the SGrid or Voxet).
The SGrid or Voxet must have a property that will be used as the soft data (see step 9).
To run collocated 1 Display the SGrid or Voxet and the property source object in the 3D Viewer.
cokriging to create
SGrid or Voxet click Collocated Cokriging to open the dialog box.
properties
Part
VI
Modeling
Velocity
performed.
property values.
7 In the Property box, select the object property to be used as the source for kriging.
This property is considered the hard data.
9 In the Soft data box, enter the name of the SGrid or Voxet property that will be used
as the soft data in the cokriging.
10 In the Correlation coefficient box, type a positive number between 0 and 1,
specifying the scale factor of the variogram data for the soft data.
– or –
and then click OK.
Note The variogram is used by the hard data, then scaled by the factor specified in step 10 on
page 3-13 and used by the soft data. If the file is not in the default directory, you must include
the proper path in the file name.
but rather directly assigned from input data in that cell, select one of the following
data value assignment options:
• Assign data to nearest cells. In any particular cell, the data point closest to the
cell center is assigned as the estimation at the cell.
• Assign mean at cell center. The mean of all the data points in a particular cell is
assigned as the cell value.
3.2.6 Estimating Properties with Indicator Kriging

Use indicator kriging to fill the selected SGrid or Voxet with property values (to assign
property values to all the Nodes in the SGrid or Voxet).
Paradigm™
To run indicator 1 Display the SGrid or Voxet and the property source object in the 3D Viewer. Display
kriging to create a SGrid or Voxet Section with the property on which you want to run kriging.
SGrid or Voxet 2 On the Voxet, SGrid, or General menu bar, click the Geostatistics menu, and then
properties click Indicator Kriging to open the dialog box.

performed.
5 In the Discrete property server by box, enter the object whose property will be the
source for kriging.
7 In the Property box, select the object property to be used as the source for kriging.
example, if you type CutOff_, the two new created properties will be named
CutOff_1, CuttOff_2, and so on.) The number of properties is equal to the number
of cutoffs specified in the variogram file.
– or –
and then click OK.
Note If the file is not in the default directory, you must include the proper path in the file
name.
Part
VI
Modeling
Velocity
11 In the Distribution Type box, select the type of distribution function to be used.
Your selection determines how the cutoff value given in the variogram files are used
to define the indicator kriging (IK) stages and how the input property values are
interpreted in each stage.
• PDF (Probability Density Function). In each threshold value kriging, a data
point equal to that value is considered 1 and a data point not equal to that value
is considered 0. For discrete properties only.
• CDF (Cumulative Distribution function). In each interval kriging, a data point
within that interval is considered 1 and a data point outside of that range is
considered 0. For continuous and discrete properties.
Paradigm™
3.3 Running Geostatistical Simulations

There are several types of geostatistical simulations offered in this menu:
• "Running Sequential Gaussian Simulations (SGS)," page 3-16
• "Running Non-Conditional Sequential Gaussian Simulations," page 3-18
• "Running Collocated Cokriging Simulations," page 3-20
• "Running Sequential Indicator Simulations (SIS)," page 3-22
• "Running Annealing Simulations," page 3-24
• "Running Cloud Transform Simulations with P-Fields," page 3-27
• "Performing Categorical Histogram Corrections," page 3-29
• "Performing Continuous Histogram Corrections," page 3-30
• "Filling Grids with Facies Map Data," page 3-31
A simulation method is more sophisticated than a kriging process in that it enables you
not only to specify statistical anisotropy in terms of variogram parameters (as kriging
does), but also to model heterogeneity by adding a random factor.
3.3.1 Running Sequential Gaussian Simulations

(SGS)
You can perform sequential Gaussian simulations, based on the selected property source
and user-provided variogram data, to fill the selected Voxet with property values (to
assign property values to all the Nodes in the SGrid or Voxet).
This function generates default property names to store the result of each realization. If
the default name already exists, the result of the current realization will replace the
existing values.The default names of the created properties are SGS_simulation_1,
SGS_simulation_2,..., SGS_simulation_n; where n is the specified number of
simulations run.
Part
VI
Modeling
Velocity
To run an SGS to 1 On the Voxet, SGrid, or General menu bar, click the Geostatistics menu, and then
create SGrid or Voxet click Sequential Gaussian Simulation (SGS) to open the dialog box.
properties

3 In the Region name box, enter the region in which the simulation will be performed.
Property values outside the selected region will not be altered.
Note By default, the simulation will be performed for the entire grid object (everywhere).
source for the simulation.
6 In the Property box, select the object property to be used as the source for the
simulation.
7 If you want to use a user-specified histogram, do the following:
a Select the Use external histogram check box.
b In the External histogram box, enter the distribution that you want to use.
c To view the distribution or to create a new one, click . The Distribution

Manager appears.
Note By default, the input data histogram is used to transform the input and realizations into
and out to a normal score space.
8 In the New property prefix box, type the prefix for the created properties.
9 In the Min box, type the low-cut value of the simulation value range (enter a
reasonable number).
10 In the Max box, type the high-cut value of the simulation value range (enter a
reasonable number).
Tip Be conservative; each 11 In the Number of realizations box, type a positive integer specifying the number of
simulation can take a while, simulations to be performed.
and each simulation creates
a new property.
Rock & Fluid Canvas™ 2009 | Epos™ 4.0 3.3 Running Geostatistical Simulations 3-17
Paradigm™
12 In the Seed box, type any number. (It will be used to start the random number
generation process.)
– or –
and then click OK.
name.
15 To perform the simulation recursively, select the Multi-grid simulation check box.
(For large grids, this speeds up the operation and produces realizations that are truer
to the variogram.)
3.3.2 Running Non-Conditional Sequential Gaussian

Simulations
You can perform non-conditional sequential Gaussian simulations, based on user-provided
histogram parameters and variogram data, to fill the selected SGrid or Voxet with
property values (to assign property values to all the Nodes in the SGrid or Voxet).
You must have an ASCII file containing the variogram data.
Part
VI
Modeling
Velocity
To run a non- 1 On the Voxet, SGrid, or General menu bar, click the Geostatistics menu, and then
conditional SGS to click Unconditional SGS to open the dialog box.
create SGrid or Voxet
properties

4 In the Property class box, type the name of a new property class. (Property classes
are used to set up a set of universal statistical parameters so that all the properties
that you define as being in the same property class will be in the same statistical pool.
For example, you can share color maps and their minimum and maximum settings.)
a Select the Use distribution object check box.
b In the Distribution object box, enter the distribution that you want to use.

Manager appears.
d Skip to step 10.
7 In the Distribution Type box, select the type of distribution function to use:
• Normal. The mean is 0, and the sigma is 1/3 of the constant.
• Log-normal. The logarithm of the Normal distribution.
• Uniform. The min is -constant, and the max is +constant.
Paradigm™
8 If you selected Normal or Log-normal in step 7, do the following:

a type the Mean of the distribution function in the Mean box (enter a reasonable
number).
b In the Sigma box, type the standard deviation of the distribution function (enter
a reasonable number).
9 If you selected Uniform in step 7, do the following:
a In the Min box, type the low-cut value of the simulation value range (enter a
reasonable number).
b In the Max box, type the high-cut value of the simulation value range (enter a
reasonable number).
a new property. 11 In the Seed box, type any number. (It will be used to start the random number
– or –
and then click OK.
name.
to the variogram.)
3.3.3 Running Collocated Cokriging Simulations

You can perform collocated cokriging simulations, based on the selected property source
and user-provided variogram data, to fill the selected SGrid or Voxet with property values
(to assign property values to all the Nodes in the SGrid or Voxet).
the property source (it must lie at least partially inside the SGrid or Voxet). The SGrid or
Voxet must have a property that will be used as the soft data (see step 12).
Part
VI
Modeling
Velocity
To run collocated 1 Display the SGrid or Voxet and the property source object in the 3D Viewer.
cokriging simulations
to create SGrid or click Collocated Cokriging SGS to open the dialog box.
Voxet properties

simulation.
a Select the Use external histogram check box.
b In the External histogram box, enter the distribution that you want to use.

Manager appears.
reasonable number).
Paradigm™
reasonable number).
12 To specify soft data information, do the following:
• In the Soft data box, enter the name of the SGrid or Voxet property that will be
used as the soft data in the cokriging.
• Select the option indicating whether you want GOCAD to use soft data from the
entire grid or from the region only.
13 In the Correlation coefficient box, type a positive number between 0 and 1,
specifying the scale factor of the variogram data for the soft data.
a new property. Tip Be conservative; each simulation can take a while, and each simulation creates a new
property.
– or –
and then click OK.
Note The variogram is used by the hard data, then scaled by the factor specified in step 13 and
used by the soft data. If the file is not in the default directory, you must include the proper path
in the file name.
to the variogram.)
3.3.4 Running Sequential Indicator Simulations

(SIS)
You can perform sequential indicator simulations, based on the selected property source
and user-provided variogram data, to fill the selected SGrid or Voxet with property values
(to assign property values to all the Nodes in the SGrid or Voxet).
Part
VI
Modeling
Velocity
To run an SIS to create 1 On the Voxet, SGrid, or General menu bar, click the Geostatistics menu, and then
SGrid or Voxet click Sequential Indicator Simulation (SIS) to open the dialog box.
properties

simulation.
8 In the Distribution Type box, select the type of distribution function to be used.
Your selection determines how the cutoff value given in the variogram files are used
to define the indicator kriging (IK) stages and how the input property values are
interpreted in each stage.
• PDF (Probability Density Function). In each threshold value kriging, a data
point equal to that value is considered 1 and a data point not equal to that value
is considered 0. For discrete properties only.
• CDF (Cumulative Distribution function). In each interval kriging, a data point
within that interval is considered 1 and a data point outside of that range is
considered 0. For continuous and discrete properties.
reasonable number).
reasonable number).
Paradigm™
– or –
and then click OK.
name.
to the variogram.)
but rather directly assigned from input data in that cell, select one of the following to
• Assign most dominant value to cell. GOCAD computes the most dominant
value in the cell, using all the volumes falling in that cell, and assigns that data
value.
• Assign nearest data to cell. GOCAD finds the closest value to the center of the
cell and assigns that data value.
3.3.5 Running Annealing Simulations

You can perform annealing simulations to populate the grid with property values. Original
property data are carried by another object.
You need the following to perform this function:
• An SGrid or Voxet
• An object that carries a discrete property (it should at least partially overlap the SGrid
or Voxet spatially)
• An ASCII file containing the variogram data
• An annealing schedule file
Part
VI
Modeling
Velocity
To run an annealing 1 On the Voxet, SGrid, or General menu bar, click the Geostatistics menu, and then
simulation click Simulated Annealing to open the dialog box.

simulation.
reasonable number).
reasonable number).
– or –
Paradigm™
and then click OK.
name.
11 To specify the ASCII file that contains the annealing schedule (see
"Annealing_Schedule File" on page 3-5), enter the path to the file in the Schedule
box.
– or –
and then click OK.
12 In the Nlags box, type a positive integer specifying the number of variogram lags to
be honored in the Annealing. (The default is 250.)
13 If you want to specify soft data information, do the following:
a Select the Honor correlation coefficient check box
b In the Soft data box, enter the name of the SGrid or Voxet property that will be
used as the soft data.
c In the Correlation coefficient box, type the correlation coefficient between the
property and the soft data.
14 If you want to specify the map containing column averages, do the following:
a Select the Honor column average map check box.
b Enter the path to the map file (see "Column_Average_Map File" on page 3-4) in
the Map file box.
– or –
Click to open the Select Text File dialog box, find and select the file you
want, and then click OK.
15 If you want to use an external histogram stored in an ASCII file, do the following:
a Select the Honor external histogram check box.
b Enter the path to the file (see "External_Histogram File" on page 3-5) in the Hist
file box.
– or –
Part
VI
Modeling
Velocity
3.3.6 Running Cloud Transform Simulations with P-
Fields
Performs cloud transform simulations in the selected region of an SGrid. You must have a
text file containing variogram information and a text file that contains the calibration
(scattergram) information.
To run a cloud 1 On the Voxet, SGrid, or General menu bar, click the Geostatistics menu, and then
transform simulation click Cloud Transform (with P-Field) to open the dialog box.

4 In the Grid input property box, select the property to be used as the input data.
5 If you set an input property as a constraint on the cloud transform, select the
Conditional pfield check box, and then do the following:
• In the Discrete property server by box, enter the object that carries the
conditioning data.
• In the By region box, enter the input data region.
• In the Property box, select the object property to be used as the conditioning
data.
6 In the Property class box, type the name of a new property class. (Property classes
are used to set up a set of universal statistical parameters so that all the properties
that you define as being in the same property class will be in the same statistical pool.
For example, you can share color maps and their minimum and maximum settings.)
Paradigm™
– or –
and then click OK.
name.
9 Select one of the following kriging options:

10 To specify the ASCII file that contains the calibration data (see "Scattergram File" on
page 3-4), enter the path to the file in the Cloud file box.
– or –
and then click OK.
11 In the Null data value in cloud file box, type the value used to represent null value
in the scattergram.
12 In the Cloud transform binning box, select the type of binning to use in the cloud
transform.
• Number of bins. If you select this option, also type a positive integer specifying
the fixed number of bins in the Num bins box.
• Data points per bin. If you select this option, also type a positive integer
specifying the fixed number of data points per bin in the Data per bin box.
• Discrete Indep. Var. Indicators will be treated as discrete values.
simulation can take a while, simulations to be performed. (The default is 1.)
a new property. Tip Be conservative; each simulation can take a while, and each simulation creates a new
property.
generation process. The default is 101.)
to the variogram.)
Part
VI
Modeling
Velocity
3.3.7 Performing Categorical Histogram
Corrections
You can transform an existing SIS PDF (categorical) realization to honor a user-specified
PDF exactly. You must have a text file containing variogram information and a property
that contains the kriging variance information
To perform a 1 On the Voxet, SGrid, or General menu bar, click the Geostatistics menu, and then
categorical histogram click Categorical Histogram Correction to open the dialog box.
correction

5 In the Realization to be corrected box, select the property (realization) to be
corrected.
6 If you want to specify how much the realization point can be modified, select the Use
kriging Variance check box, and then select the variance in the Kriging variance
box.
– or –
and then click OK.
Note The PDF specified in this file is used to correct the input realization.
Paradigm™
3.3.8 Performing Continuous Histogram

Corrections
You can condition the result of a simulation to fit an external histogram. The histogram
can be an existing distribution, a single-column ASCII data file, or a property on an user-
specified GOCAD object. To perform this function, you must have a text file containing
variogram information and a property that contains the kriging variance information.
To perform a 1 On the Voxet, SGrid, or General menu bar, click the Geostatistics menu, and then
continuous histogram click Continuous Histogram Correction to open the dialog box.
correction

4 In the Realization to be corrected box, select the property (realization) to be

corrected.
5 In the New property name box, type the name of the new grid object property that
will store the result of the realization. (By creating a new property, you avoid
modifying the input property.)
6 If you want to specify how much the realization point can be modified, select the Use
kriging Variance check box, and then select the variance in the Kriging variance
box.
7 If you want to use a histogram created from a property on a GOCAD object, do the
following:
• In the Discrete property server by box, enter the object that will be used to
construct the histogram.
• In the By region box, enter the object region that will be used to build the
histogram.
Part
VI
Modeling
Velocity
• In the Property box, select the object property that will be used to build the
histogram.
8 If you want to use an external histogram, do the following:
• Click Histogram from parametric distribution.
• In the External histogram box, enter the distribution that you want to use.

Manager appears.
9 If you want to use a histogram stored in an ASCII file, do the following:
• Click Histogram from ASCII file.
• Enter the path to the file (see "External_Histogram File" on page 3-5) in the Hist
file box.
– or –
10 fudging factor: A positive number (keyboard-entry), specifying how much the input
realization can be changed. The larger the number, the more the input realization is
allowed to change. Default=0.5.
11 x window size: The u-dimension of the search window used to find neighboring
cells for calculating the average at any given cell.
12 y window size: The v-dimension of the search window used to find neighboring
13 z window size: The w-dimension of the search window used to find neighboring
3.3.9 Filling Grids with Facies Map Data

You can partially fill a grid with data from a facies map, then fill in the rest with property
values generated by SIS.
You must have a text file containing variogram information and a text file that contains
the facies map information.
Paradigm™
To fill a grid with 1 On the Voxet, SGrid, or General menu bar, click the Geostatistics menu, and then
facies map data click Fill from Facies Maps to open the dialog box.

property values.
7 In the Property box, select the object property to be used as the input data.
8 Enter the path to the ASCII facies map file (see "Facies_Map File" on page 3-5) in the
Map file box.
– or –
and then click OK.
Note The facies map contains X, Y and facies values in each line.
9 In the Map sampling rate box, type a positive number between 0 and 100,
indicating the percentage of the SGrid region space that should be filled with a
vertical projection of the facies map data. (The rest of the space will be filled with
simulated values.)
– or –
Part
VI
Modeling
Velocity
and then click OK.
11 In the Map weight box, type a positive number between 0 and 100, specifying the
weight percentage assigned to the map data. (The weight percentage of the property
specified in step 7 will be 100 - the map weight.)
12 In the Well weight box, type a positive number between 0 and 100, specifying the
weight percentage assigned to the well facies proportions.
13 In the Variogram file weight box, type a positive number between 0 and 100,
specifying the weight percentage assigned to the variogram file facies proportions.
generation process. The default is 101.)
Paradigm™
4
Performing Velocity
Conversions
In this chapter • "Converting the Velocity Type in One • "Converting the Velocity Type in
Domain," page 4-2 Different Domains," page 4-3
Overview The Velocity commands consist of a series of functions that perform velocity conversions
and time-to-depth conversions (or depth-to-time conversions).
Velocity can originate from different sources. The Velocity cube can be directly imported,
computed from regional data within Paradigm™ GOCAD ® 2009 using mathematical
functions, or computed from field data (such as well logs, checkshots, stacking velocity, or
VRMS) using geostatistical operations and/or interpolation methods.
GOCAD can convert velocity from the following source types:
• Average, interval, RMS, or depth velocity (time domain)
• Average, interval, RMS, or time velocity (depth domain)
4-1
Paradigm™
4.1 Converting the Velocity Type in One

Domain
Use this function to convert velocity within the same domain. (For example, if the velocity
is in time, the converted Velocity must also be in time.)
To convert velocity in 1 On the Velocity menu bar, click Velocity Conversion, and then click Voxet: In One
one domain Domain to open the dialog box.
2 In the Voxet Velocity Cube box, enter the name of the Voxet object that carries the
velocity to be converted.
3 In the Input Velocity Property box, enter the velocity property to be converted.
4 In the Velocity Type box, select the type of the velocity to be converted.
Note The Voxet can be in either the time domain (pick a type from the first four choices) or the
depth domain (pick from the last four choices). RMS types are for stacking velocity.
5 In the Output Velocity Property box, enter the name of the velocity property
obtained by conversion of the input velocity.
6 In the Velocity Type box, select the type of the velocity obtained by the conversion.
Important If you selected a two-way time velocity in step 4, you must select another
two-way time velocity type here. If the conversion to be performed is from the time/
depth domain to the depth/time domain, use the function described in "Converting
the Velocity Type in Different Domains" on page 4-3.
4-2 Performing Velocity Conversions GOCAD® 2009.1 User Guide

Part
VI
Modeling
Velocity
4.2 Converting the Velocity Type in Different
Domains
Use this function to convert velocity from one domain (time/depth) to another domain
(depth/time). GOCAD creates a new cube carrying the converted velocity during the
conversion. This cube is in the final domain space (if the initial velocity is in time, the
created Voxet will be in the depth domain).
To convert velocity in 1 On the Velocity menu bar, click Velocity Conversion, and then click Voxet: In
different domains Different Domains to open the dialog box.
2 In the Voxet velocity cube box, select the name of the Voxet object that carries the
velocity to be converted.
3 In the Input velocity property box, enter the velocity property to be converted.
4 In the Velocity type box, select the type of the velocity to be converted.
Note The Voxet can be in either the time domain (pick a type from the first four choices) or the
depth domain (pick from the last four choices).
5 In the Velocity unit box, select the units in which the velocity is measured:
• m/s (two-way time). The time it takes, measured in meters per second, to go
from the datum to a given point and back.
• ft/s (two-way time). The time it takes, measured in feet per second, to go from
the datum to a given point and back.
• m/s (one-way time). The time it takes, measured in meters per second, to go
from the datum to a given point.
• ft/s (one-way time). The time it takes, measured in feet per second, to go from
the datum to a given point.
Rock & Fluid Canvas™ 2009 | Epos™ 4.0 4.2 Converting the Velocity Type in Different Domains 4-3
Paradigm™
Tip In the example in 6 In the Output voxet name box, type the name of the Voxet to be created. Since the
step 6, the depth cube will domain is changing, the converted velocity must be in a different Voxet.
be between 0 and 7500 m,
but you may not want the Example In the case of conversion from time to depth, if the time cube is between 0 and 6 s
full cube for the current and the maximum average velocity is 2500m/s, the depth cube will be between 0 and 7500m
stage of the modeling. You (with a conversion factor of 2). Therefore, if the same input Voxet had been used, most of the
might only want the sub- converted velocity would have fallen outside the input cube.
volume included between 0
and 5000. 7 In the Starting Z box, type the starting Z value of the Voxet in the final domain.
Tip In the example in step 6 8 In the Ending Z box, type the final Z value of the Voxet in the final domain.
(sub-volume from 0 to
5000m), the value entered is 9 In the Number of W steps box, type the number of samples along the depth/time
5000. axis.
10 In the Output velocity property box, enter the name of the velocity obtained by
conversion.
11 In the Velocity type box, select the type of the velocity obtained by the conversion.
Note You must select a different domain than the one selected in step 4. If you selected a two-
way time average velocity in step 4, you must select a depth type velocity here. If the
conversion to be performed is from the time/depth domain to the depth/time domain, use the
function described in "Converting the Velocity Type in Different Domains" on page 4-3.
12 Select the option that indicates whether the new converted velocity will be stored in
memory or on disk:
• Store in memory.
• Store on disk.
4-4 Performing Velocity Conversions GOCAD® 2009.1 User Guide

5
Performing Time and Depth
Domain Conversions
In this chapter • "Converting Objects Using a Velocity • "Reassigning an Object to the Correct
Cube," page 5-2 Domain," page 5-6
• "Converting a Seismic Cube,"
page 5-4
Overview The Velocity commands consist of a series of functions that perform velocity conversions
and time-to-depth conversions (or depth-to-time conversions).
The time-to depth conversion functions convert Paradigm™ GOCAD ® 2009 Objects from
one domain (time/depth) to the other domain (depth/time).
Velocity can originate from different sources. The Velocity cube can be directly imported,
computed from regional data within GOCAD using mathematical functions, or computed
from field data (such as well logs, checkshots, stacking velocity, or VRMS) using
geostatistical operations and/or interpolation methods.
5-1
Paradigm™
5.1 Converting Objects Using a Velocity

Cube
Use this function to convert GOCAD Objects, except cross-sections and 2D-Grids, from
one domain (time/depth) to the other domain (depth/time) using an average velocity
cube.
Use the function described in "Converting the Velocity Type in One Domain" on page 4-2
to convert any type of velocity to the required average velocity.
The object conversion is a simple vertical stretch using the Z = time * velocity equation
type.
When the seismic amplitude is converted, the vertical wavelet is resampled between the
time and depth domains.
To convert from one 1 On the Velocity menu bar, click Time-Depth Conversion, and then click Convert
domain to another Object Using Velocity to open the dialog box.
domain using velocity
cube
2 In the Object list box, enter one or more GOCAD Objects to be converted (excluding
seismic cubes; see "Converting a Seismic Cube" on page 5-4).
3 If you want to create copies of the Objects before converting them, select the Copy
the Objects before conversion check box.
Note GOCAD prefixes the names of the copied Objects with time_ or depth_.
4 In the Voxet velocity cube box, enter the name of the Voxet carrying the average
velocity.
Note The velocity cube must be in same domain as the Objects to be converted.
5 In the Average velocity box, enter the name of the average velocity.
5-2 Performing Time and Depth Domain Conversions GOCAD® 2009.1 User Guide
Part
VI
Modeling
Velocity
7 Select the option indicating the type of conversion to be performed:
• Time to depth conversion.
• Depth to time conversion.
8 Select the option indicating the type of seismic reference datum:
• Constant. Equal to a constant.
• Varying. Defined by a Surface or 2D-Grid.
Rock & Fluid Canvas™ 2009 | Epos™ 4.0 5.1 Converting Objects Using a Velocity Cube 5-3
Paradigm™
5.2 Converting a Seismic Cube

Use this function to convert any attribute of a seismic cube from one domain (time/depth)
to another domain (depth/time) using an average velocity. Usually, the amplitude is the
attribute to be converted.
Use the function described in "Converting the Velocity Type in One Domain" on page 4-2
to convert any type of velocity to the required average velocity.
To convert Seismic 1 On the Velocity menu bar, click Time-Depth Conversion, and then click Seismic
cube to time or to Cube Conversion to open the dialog box.
depth using average
velocity
2 In the Voxet seismic box, enter the name of the Voxet that contains the seismic
attribute to be converted.
3 In the Seismic properties box, enter one or more seismic properties to be converted.
(Amplitude is the default, but you can choose any other attribute(s).)
4 Select the option indicating the type of conversion to be performed:
• Time to depth conversion.
• Depth to time conversion.
5 In the Voxet velocity cube box, enter the name of the Voxet that contains the
average velocity. The velocity cube can be in the same domain as the seismic cube, or
it can be in another domain.
6 In the Average velocity box, enter the name of the average velocity used during the
seismic attribute conversion.
Part
VI
Modeling
Velocity
Tip In the example in 8 In the Output Voxet Name box, type the name of the Voxet to be created. The new
step 8, the depth cube will Voxet will define how deformed/stretched the resampled wavelet will be.
be between 0 and 7500 m,
but you may not want the Example In the case of conversion from time to depth, if the time cube is between 0 and 6 s
full cube for the current and the maximum average velocity is 2500m/s, the depth cube will be between 0 and 7500m
stage of the modeling. You (with a conversion factor of 2). Therefore, if the same input Voxet had been used, most of the
might only want the sub- converted velocity would have fallen outside the input cube.
volume included between 0
and 5000. 9 In the Starting Z box, type the starting Z value of the Voxet in the final domain.
Tip In the example in step 8 10 In the Ending Z box, type the final Z value of the Voxet in the final domain.
(sub-volume from 0 to
5000m), the value entered is 11 In the Number of depth/time steps box, type the number of samples along the
5000. depth/time axis.
12 Select the option that indicates the property size of the Voxet:
• Create as 32 bits.
Note If the property is created as 8 bits, GOCAD reduces the memory used for the display
without sacrificing visual accuracy.
13 If you chose Create as 8 bits in step 12 and you want to define the data spread of
the converted property as -127 to 127, select the Is signed check box. Otherwise,
the data spread is assumed to be 0 to 255.
14 Select the option that indicates whether the new converted velocity will be stored in
memory or on disk:
• Store in memory.
• Store on disk.
15 Select the option that indicates the interpolation method to be used in the
conversion:
• Wavelet. A sync interpolation used for amplitude-like properties.
• Linear. Used for velocity-type properties.
• Closest value. Used for facies-like properties.
Rock & Fluid Canvas™ 2009 | Epos™ 4.0 5.2 Converting a Seismic Cube 5-5
Paradigm™
5.3 Reassigning an Object to the Correct

Domain
Tip When you originally If data objects are loaded, imported, or created in the wrong domain, you can reassign
import data, you can select the data to the correct domain. Objects in the time domain can be reassigned to the
the proper domain in the
depth domain, and vice versa.
Advanced area of most
import dialog boxes. For No unit conversion is applied when objects are reassigned. For example, if the original
more information, see Z value of an object in the time domain is 1000–1200 ms, then after reassigning it to the
Part II: Data Import and
depth domain, its Z value will be 1000–1200 m.
Export, "Basic Concept for
Importing Data" on For more information, see the following topics:
page 1-6.
• "To check the domain of a single object" on page 5-6
• "To reassign an Object to the correct domain" on page 5-6
To check the domain ♦ Right-click the object in the Object Tree, click Attributes in the shortcut menu, and
of a single object then click the Info tab.
– or –
♦ Display the object in the 3D Viewer, click Get XYZ Coordinate on the Camera
Tools toolbar, and then click the object. Look at the units in the Information pane.
To reassign an Object 1 On the Velocity menu bar, click Time-Depth Conversion, and then click Reassign
to the correct domain Correct Domain to open the dialog box.
2 In the Object list box, enter one or more Objects to be reassigned to the other
domain.
Index
A constant property G
variable 2-10
Add Function geostatistics
menu 2-20 continuous histogram
estimation method
correction 3-30
add Surface (to Bayesian
Model) 1-5 create
kriging 3-10
add surfaces (to property
collocated
VoxetModel) 1-17 function 2-20
cokriging 3-12
attributes of create default LayerSet
indicator
Model Model3d 1-11 kriging 3-13
common 1-2 kriging 3-6
D kriging with external
drift 3-9
B define
kriging with
Bayesian kriging 3-10 property
trend 3-7
function 2-20
build (Model3d) 1-6 simulation methods
dir_Z 2-7
build (Voxet collocated
Model) 1-19 direction
cokriging 3-20
shoot 2-7
nonconditional
SGS 3-18
C
categorical histogram F SCloud
transform 3-27
correction 3-29 fill grid from facies
map 3-31 sequential gaussian
cloud transform (w/ P-
simulation 3-16
field) 3-27 from_inside 2-8, 2-18
sequential indicator
collocated cokriging from_outside 2-8
simulation 3-22
estimation 3-12 function
simulated
simulation 3-20 property annealing 3-24
constant 2-10 function 2-20
Index-1
Paradigm™
tools M remove surfaces (from

categorical VoxetModel) 1-18
Menu
histogram
Add Function, see Add
correction 3-29
Function menu S
continuous
histogram script
correction 3-30 N of property
fill grid from facies functions 2-23
name of
map 3-31 sequential gaussian
a variable in Property
simulation 3-16
Function 2-6
nonconditional 3-18
I New menu
sequential indicator
impact point 2-8 Model 1-2
simulation 3-22
on bounding nonconditional SGS
shoot
surfaces 2-18 Voxet simulation 3-18
direction 2-7
on bounding surfaces,
direction (Fig) 2-7
Fig. 2-19
P impact point 2-8
on Surfaces for
interpolation, parameters position 2-7
Fig. 2-12 shoot parameters 2-6 position(Fig) 2-7
indicator kriging 3-13 property shoot parameters 2-6
in Voxet 3-13 function 2-20 shooting point 2-7
linear function 2-20 simulated
script function 2-23 annealing 3-24
K Simulation menu
script function
kriging 3-6 components 2-23 in Voxet 3-16
Kriging menu script function Surface
in SGrid 3-6 examples 2-24 property
kriging with external syntax 2-23 variable in
drift 3-9 Property Model Model 2-14
kriging with trend 3-7 Editor 2-10
property variable
V
L constant 2-10
variable name 2-6
from a Surface 2-14
layer 1-16 variogram
from a Voxet 2-13
display 1-3 ASCII file
linear examples 3-3
property R Voxet
function 2-20 remove Surface (from property
Model) 1-6 variable in
Model 2-13
Index-2 GOCAD® 2009.1 User Guide

06 Velocity Modeling

Uploaded by

Copyright:

Available Formats

06 Velocity Modeling

Uploaded by

Document Information

Copyright

Available Formats

Share this document

Share or Embed Document

Sharing Options

Did you find this document useful?

Is this content inappropriate?

Copyright:

Available Formats

06 Velocity Modeling

Uploaded by

Copyright:

Available Formats

GOCAD® 2009.

Part VI Velocity Modeling

Published June 22, 2009

Part VI Velocity Modeling

Renaming a Region in a Velocity Model ........................................... 1-15

Chapter 2 Defining Property Values for Velocity Models ......................................... 2-1

iv Contents GOCAD® 2009.1 User Guide

Chapter 4 Performing Velocity Conversions ............................................................. 4-1

Chapter 5 Performing Time and Depth Domain Conversions ................................... 5-1

Rock & Fluid Canvas™ 2009 | Epos™ 4.0 Contents v

vi Contents GOCAD® 2009.1 User Guide

In this chapter • "Constructing a Model3d," page 1-2 • "Constructing a Voxet Model,"

1.1 Constructing a Model3d

1.1.1 Common Attributes of Models

Figure 1–1 Model region

1-2 Constructing 3D Models GOCAD® 2009.1 User Guide

Figure 1–2 Model layer

1.1.2 Procedure to Construct a Model3d

Table 1–1 Basic functions

1.1.3 Creating a New Model3d From Surfaces

Figure 1–3 Model3d

Regular model Model with intersecting surfaces

2 In the Name box, type the name of the new model.

1-4 Constructing 3D Models GOCAD® 2009.1 User Guide

1.1.4 Adding Surfaces to a Model3d

1.1.5 Deleting or Detaching Surfaces from a

1.1.6 Building a Model3d

2 In the Model3d box, enter one or more models to build.

1-6 Constructing 3D Models GOCAD® 2009.1 User Guide

1.1.7 Rebuilding a Model3d

2 In the Model3d box, enter one or more models to rebuild.

1.1.8 Editing a Model3d

Making Surfaces and Regions Geologically Consistent

• Removes parts of top surfaces that are inside intrusive regions

Figure 1–4 Making

1-8 Constructing 3D Models GOCAD® 2009.1 User Guide

Figure 1–5 Removing free

Before removing free extremities After removing free extremities

2 In the Model3d box, enter one or more models.

Removing All Free Extremities from a Horizon

Figure 1–6 Removing free

Before removing free extremities After removing free extremities

2 In the Model3d box, enter one or more models.

1.1.9 Creating and Working with Layers in a

1-10 Constructing 3D Models GOCAD® 2009.1 User Guide

Creating a Layer from a Region in a Velocity Model

Deleting a Layer in a Velocity Model

Renaming a Layer in a Model3d

1-12 Constructing 3D Models GOCAD® 2009.1 User Guide

Adding a Region to a Velocity Model Layer

2 In the Model box, enter one or more models.

Moving a Region to a Different Velocity Model Layer

Deleting a Region from a Velocity Model Layer

2 In the Model box, enter one or more models.

Finding a Region Name in a Velocity Model

To find the region Do one of the following:

1-14 Constructing 3D Models GOCAD® 2009.1 User Guide

2 In the Model box, enter one or more models.

1.2 Constructing a Voxet Model

1.2.1 Procedure to Construct a Voxet Model