GEOPHYSICS, VOL. 49. NO. 8 (AUGUST 1984); P. 1188-1195.

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Rock lithology and porosity determination

from shear and compressional wave velocity

S. N. Domenico*

After a hiatus of several years following the initial development

ABSTRACT and testing of a hydraulic vibrator S-wave source (Cherry and
Waters, 1968; Erickson et al., 1968), the Continental Oil Com-
Data examined in this study are previously published
pany developed an improved vibrator that was tested jointly by
laboratory shear (S) and compressional (P) wave veloci-
13 petroleum companies in 18 areas of the coterminous United
ty measurements on water-saturated sandstone, cal-
States from February, 1977 to March, 1978. Since then, several
careous sandstone, dolomite, and limestone cores, as
United States and European geophysical service companies
well as laboratory porosity measurements on the sand-
have begun offering S-wave surveys. A second S-wave source
stone and limestone cores. Sandstone and limestone po-
developed concurrently with the latest vibrator source, and also
rosities range from ,092 to ,299 and from X106to .229,
proven effective, consists of three parallel Primacord (deton-
respectively. Differential pressure was varied from 500
ating cord) strings buried in shallow trenches a few inches
to 6000 psi, corresponding to approximate burial depths
apart. A recent development in well surveying that appears
from 290 to 3460 m, respectively.
promising is simultaneous S- and P-wave velocity well logging.
Sandstone, limestone, and dolomite are effectively
A well sonde developed by OYO Instruments, Inc., of Japan,
separated by Poisson’s ratio cr or, equivalently, by the
has been tested successfully to a depth of 480 m (Ogura et al.,
ratio of P- to S-wave velocity. Separation of sandstone
1980).
and limestone appears to result from the difference in cr
The development of methods for generation and recording of
of the matrix material, namely, quartz (.056) and calcite
S-waves requires companion efforts to extract useful infor-
(.316), respectively.
mation from these emerging ,exploration techniques. Perhaps
An empirical function, l/V = A + B+, was fit by re-
foremost objectives are identification of rock lithology and
gression analysis to sandstone and limestone velocity (V,
porosity. In the following the feasibility of identifying sandstone
and V,) versus porosity (+) values at each differential
and limestone, and of determining the porosity of each from S-
pressure. In this equation A and B are constants at each
and P-wave velocities are examined. This study, of course, is
pressure, A being approximately equal to the reciprocal
only a small beginning in the examination of many potential
matrix velocity. Decreasing standard deviation indicates
uses.Among these are identification of other lithologies, poros-
that the equation becomes an appreciably more accu-
ity type (e.g., fractures), permeability, and pore fluid. In addition
rate representation of the measured data as pressure
to velocities, relative S- and P-wave attenuation must be exam-
increases. Average values of A are near reciprocal veloc-
ined to assessits potential in identifying rock properties.
ities of quartz (sandstone averages) and calcite (lime-
stone averages). The constant B, rate of change of re-
ciprocal velocity with porosity, is a critical measure of BASIC DATA
the sensitivity of velocity to porosity, hence the useful-
ness of velocity in estimation of porosity. Sandstone Data for this study were taken from Pickett (1963). These are
S-wave B values are from 2 to 5 times greater than all (1) laboratory S- and P-wave velocity measurements on water-
other values, indicating that sandstone S-wave velocity saturated sandstone, calcareous sandstone, dolomite, and lime-
is by far the most sensitive to porosity variation. Least stone cores, and (2) laboratory porosity measurements on the
sensitive is limestone P-wave velocity. sandstone and limestone cores. Differential pressure was varied
from 500 to 6000 psi. Sandstone porosities range from ,092 to
.299 and limestone porosities range from .006 to .229. Precise
INTRODUCTION measurements on the sandstone and limestone cores were sup-
plied by Pickett (personal communication).
Application of elastic shear (S) waves in seismic petroleum Histograms of the porosity measurements on 21 sandstone
exploration has developed considerably in the past few years. and 25 limestone cores are shown in Figure 1. Plotted are the

Presentedat the 53rd Annual International SEG Meeting September 13, 1983, in Las Vegas. Manuscript received by the Editor October 18, 1983;
revised manuscript received January 9, 1984.
*NORSHIR Consultants,Inc., 4685 S. Maplewood Avenue, Tulsa, OK 74135.
0 1984 Society of Exploration Geophysicists. All rights reserved.
1188
 Rock Lithology and Porosity from V, and V, 1189
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10c
9
Limestone
Total no.
P - samples - 25 0 1 2 3
z Depth in km
z
5
B 5-
2 - FIG. 2. Differential pressure versus depth assuming hydrostatic
5 - 3 3 conditions and a brine pore fluid containing 300 000 ppm of
z dissolved solids.
2 2

0
0.1 0.2 0.3
Porosity (0)
ters on the numerous graphs which follow. It has been demon-
strated (Hicks and Berry, 1956) and now is universally accepted
FIG. 1. Histograms of measured porosities in 21 sandstone cores
that velocity is dependent principally upon differential pressure
(top) and 25 limestone cores (bottom).
rather than upon geostatic or pore fluid pressure separately.

IDENTIFICATION OF LITHOLOGY

number of cores (samples) in each .025 porosity interval. Unfor- S-wave velocities (V,) and P-wave velocities (V’) given by
tunately, the porosities are not evenly distributed, especially the Pickett (1963)were used to determine Poisson’s ratio (o),
sandstone porosities, nearly half of which are in the .175-.200
0.5( I,/v,)2 - 1
interval. Approximately one-third of the limestone porosities 0= (1)
are in the .025-.050 range. Needless to say, it is extremely (VP/v,)’ - 1 ’
difficult to acquire rock samples of like lithology, consolidation, for each rock sample (core) at each differential pressure. Pois-
etc., with a substantial range of porosities. Thus, although the son’s ratio is the ratio of strain normal to strain parallel to a
porosity distribution is considerably less than ideal, the suite of uniaxial stress applied to a unit cube of the rock; thus, it is
sandstone and of limestone cores acquired by Pickett is unique related to compressibility. Limiting values are 0 (parallel strain
in the wide range of porosities present in samples which other- is accounted for solely by change in volume, i.e., no normal
wise appear to be quite similar.
strain) and 0.5 (no volumetric change). Thus, compressibility
Before proceeding with discussions of data analyses, it is
decreasesas Poisson’s ratio increases. A histogram of Poisson’s
advisable to define differential pressure, mentioned above, more ratio for each of the four rock types is shown in Figure 3. The
precisely and describe its relationship to depth of burial. Differ- number of samples in successive0.1 intervals is shown. Sand-
ential pressure is the difference between geostatic (overburden) stone, dolomite, and limestone samples appear nearly separated
pressure and pore fluid pressure. Given a rate of increase of
on the Poisson’s ratio scale. Ninety percentile points are as
each pressure with depth, we may relate differential pressure to follows :
burial depth. A generally accepted nominal rate for geostatic
pressure is 1 psi/ft (3.28 psi/m) of depth. Normal pore fluid Poisson’s ratio
pressure is equivalent to that exerted by a column of the pore Rock type 90-percentile points
fluid extending to the surface (i.e., hydrostatic pressure). For
present purposes it is assumed that the pore fluid pressure is Sandstone 0.17-0.26
normal and that the fluid is a brine containing approximately Dolomite 0.27-0.29
300 000 ppm of dissolved solids. The density of this brine then Limestone 0.2990.33
results in an increase of .47 psi/ft (1.54psi/m) of depth. Thus, the
differential pressure increases at a rate of .53 psi/ft (1.74 psi/m) Sandstone has the largest range of values; however, the number
of depth. The differential pressure in psi is plotted versus depth of sandstone samples is nearly three times the number of dolo-
in kilometers in Figure 2. This graph may be used to convert mite and limestone samples. The calcareous sandstone range,
the differential pressure scale to approximate depth in kilome- 0.22 to 0.27, corresponds to upper sandstone values, likely a
 1190 Domenico

.4 I I I I I I

Total no. calcite

P
E _ samples - 117
1 - -_)
10
B _ 7_
22 -
0 -
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Sandstone

L
Total no.
M samples = 41

10

0
1.4 1.5 1.6 1.7 l-8 1.9 2.0
0
Dolomite Velocity ratio IVplV,)

mlb
Total no.
samples-44
FIG. 4. Poisson’s ratio versus velocity ratio graph on which
10 quartz and calcite values are indicated (Table l), as well as the
range of sandstone and limestone values (Figure 3).

:F rtn 0 bt;;;ye

Calcareous sandstone
(2)

where

+ = porosity,
FIG. 3. Poisson’s ratio histograms derived from laboratory S-
and P-wave velocity measurements on sandstone, dolomite, V, = velocity of the matrix (solid) material,
limestone, and calcareous sandstone cores (samples).
and

VW= water velocity.

This function is often called the “time-average” equation.

result of the calcareous content. The low number of calcareous
Equation (2) has been used routinely to determine porosity
sandstone samples, however, reduces the significance of these
from water-saturated sand and sandstone velocities observed
values.
on continuous velocity logs. Often V’, is varied (unrealistically)
For at least two of the rock types, sandstone and limestone,
to account for velocity variations due to depth, consolidation,
the separation appears to result from the overriding effect of the
shale contamination, etc.
difference in Poisson’s ratio of matrix material, quartz, and
Pickett (1963) proposed the velocity-porosity function
calcite, respectively. Velocities, velocity ratio, Poisson’s ratio,
and density of these two minerals are listed in Table 1. Also
given is the ratio of corresponding values. Poisson’s ratio of
quartz is less than two-tenths that of calcite. This difference is
related to the difference in S-wave velocities, that of quartz where V is either S-wave or P-wave velocity, and A and B are
being substantially greater. P-wave velocities and densities are constants for a given rock type. This may be related to the
nearly equal. The difference in quartz and limestone Poisson’s
ratio is further illustrated in the graph of this ratio versus the
ratio VP/V, in Figure 4. The range of sandstone and limestone
values, as indicated in Figure 3, is also shown. The separation
of sandstone and limestone values appears to result from the Table I. Comparison of mineral properties (from Anderson and Lieber-
large difference in quartz and calcite Poisson’s ratios. man, 1966).

Velocities
VELOCITY-POROSITY EMPIRICAL FUNCTIONS (km/s)
Poisson’s Density
A simple empirical function relating P-wave velocity to po- Mineral V, v, t;iv, Ratio (o) (g/cm?
rosity was proposed by Wyllie et al. (1956, 1958). These workers
Quartz 4.153 6.057 1.458 0.056 2.65
demonstrated that P-wave velocity in “clean” water-saturated
Calcite -3.243 -6.259 1.930 _
0.316 2.71
sands and sandstones at appreciable depths is related to poros-
ity by Ratio 1.281 0.968 0.177 0.98
 Rock Lithology and Porosity from VP and V, 1191

Depth in km Depth in km

0 1 2 3
1
O-W
I \
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t .
.. P -wave illVpi
---%_ ---.- __&___+JIJQd 4.O
l.
‘.--_
---__ 0.133

I
.. G --_.__. -_._--- ml .A_
-.- --e---- --e------_-.-___. 0.119
---.___ O.WP - 5.0
----__._d-_--.

7 j _t___~---7-_-~--_~_0.Wbf
‘
I
I 0 1 2 3 4 5 6
0 1 2 3
Differential pressure in kpsi
Differential pressure in kpsi

FIG. 5. Measured reciprocal velocity versus differential pressure FIG. 6. Measured reciprocal velocity versus differential pressure
in three sandstone cores of low, intermediate, and high poros- in three limestone cores of low, intermediate, and high porosity.
ity.

Table 2. Constants, standard deviation (SD.), and correlation coefficient (C.C.) derived from regression
analysis fit of l/V = A + B$ to sandstoneand limestone velocity-porosity laboratory measurements.

Sandstone Limestone

Differential S-Wave
pressure -
(psi) A B S.D. C.C. A B SD. C.C.

500 234.9 1337.8 36.9 .91 333.4 649.0 27.0 .85

1000 239.8 1156.7 24.9 .94 323.3 451.8 15.6 .89
2000 237.2 992.4 17.2 .95 318.5 374.8 13.0 .89
3000 230.1 930.3 17.3 .95 314.1 335.5 Il.9 .89
4000 226.6 915.3 13.7 .96 311.5 304.7 11.1 .88
5000 224.7 893.9 12.3 .97 309.1 286.9 10.7 .88
6000 223.4
-- 889.0 12.3 .97 307.3 273.3 10.5 .87
Avg. A 231.0 316.7
(240.X)* (308.4)**

Differential P-Wave
pressure
(psi) A B S.D. C.C. A B S.D. CC.

500 163.1 573.8 7.2 .97 171.3 370.8 Il.2 .91

1000 164.7 499.8 5.8 .98 168.7 283.1 9.1 .90
2000 165.2 427.1 4.2 .98 167.3 241.3 8.5 .89
3000 164.9 390.4 4.1 .98 166.1 215.4 8.2 .87
4000 163.7 376.9 3.6 .98 165.1 197.9 7.9 .86
5000 162.8 370.5 3.5 .99 164.2 186.9 7.8 .85
6000 162.7 364.2 3.3 .99 163.5 178.8 7.8 .84
Avg. A 163.9 166.6
(165.1)* (159.8)**

Note: Dimensionsof A and S.D. are ps/m. Dimensionsof B are ps,/m/unitporosity,that is, for 4 expressed
in fractional porosity.
*Quartz reciprocal velocity
**Calcite reciprocal velocity
 1192 Domenico

P,+ (psi)

l 500
Legend:
= ml0
06ooO

600
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. Time-average
/’
. \
/:

FIG. 7. Plot of measured reciprocal velocity versus porosity in FIG. 8. Plot of measured reciprocal velocity versus porosity in
sandstone cores at differential pressures of 500,2000, and 6000 limestone cores at differential pressures of 500, 2000, and 6000
psi. Solid curves are regression analysis fits of equation (3) with psi. Solid curves are regression analysis fits of equation (3) with
the standard deviation (S.D.) indicated on each. The dashed the standard deviation (S.D.) indicated on each. The dashed
line for P-wave reciprocal velocity is from equation (2) (time- line of P-wave reciprocal velocity is from equation (2) (time-
averaging equation) using appropriate matrix and water veloci- average equation) using appropriate matrix and matrix veloci-
ties. ties.

time-average equation by rewriting equation (2) limestone cores, were supplied by Pickett. Velocities were mea-
sured at seven differential pressures: 500, 1000, 2000, 3000,
1
_=_ 1
+ +-++. (4) 4000, 5000, and 6000 psi. These simulated depths ranged from
v, Kl ( w m> 290 m (945 ft) to 3450 m (11 320 ft).
Thus, the two equations are identical when In Figures 5 and 6, S- and P-wave reciprocal velocities
measured on three sandstone and three limestone cores, respec-
*=-$ tively, are plotted versus differential pressure. Measured poros-
In ities are low, intermediate, and high for each rock type. Re-
ciprocal velocity decreases with increasing differential pressure,
and
the rate of decrease decreasing with increase in porosity (i.e., the
B=$-4. curves flatten as porosity decreases). It is likely that the initial
“w “m rapid reciprocal velocity decrease with increasing pressure is
In practice, A does appear to be determined principally by due to the closing of elongated pores (e.g., cracks), all of which
matrix velocity; however, B is determined by other rock are essentially closed at a differential pressure of about 2000 psi
properties such as consolidation, pore geometry, and differ- (e.g., Toksoz et al., 1976).
ential pressure. Whereas application of the time average equa- Equation (3), l/V = A + B$, was fit by regression analyses
tion is restricted to sands and sandstones at sufficient depths, to sandstone and limestone reciprocal velocities measured at
Pickett’s equation appears to be applicable to other rock types each differential pressure versus corresponding measured po-
over a greater range of depths providing that the constant B is rosities. The constants A and B, standard deviation (S.D.), and
adjusted, usually empirically, for each rock type. correlation coefficient (CC.) derived from the analyses are
listed in Table 2. As examples of these analyses, reciprocal
velocities at differential pressures of 500,2000, and 6000 psi are
DATA ANALYSIS plotted in Figure 7 for sandstone cores and in Figure 8 for
limestone cores. In each case the tit of equation (3) is shown.
Laboratory-measured S- and P-wave velocities, and poros- As differential pressure is increased, scatter of points (Figures
ities of 21 water-saturated sandstone and 2.5 water-saturated 7 and 8) is reduced, especially S-wave points for which the
 Rock Lithology and Porosity from VP and V,

Depth in km

A
- S-wave
--- P-wave

-S-wave Ss - Sandstone
Ls - Limestone
---P-wave
- \
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$+___
--9_
--4- LS
---------

OL I I 1 I I
0 1 2 3 4 5
Ol
0 1 2 3 4 5 6
Differential pressure in psi . 10m3
Differential pressure in kpsi

FIG. 10. Reciprocal velocity rate of change with porosity [B in

FIG. 9. Standard deviation, from regression analysis fits of equation (3)], from regression analysis fits of equation (3) to
equation (3) to measured values, versus differential pressure. measured values, versus differential pressure.

standard deviation is appreciably more (Table 2). Correlation smallest rate of change with porosity. The rate of change of
coefficients for sandstone are significantly greater than those limestone S-wave is slightly less than that of sandstone P-wave
for limestone, approaching unity at high pressures. Standard reciprocal velocities.
deviations listed in Table 2 are plotted versus differential pres- The curve derived from equation (2), the time average equa-
sure in Figure 9. These decrease nonlinearly with increasing tion, with V, equal to quartz and calcite velocities (Table 1) and
pressure, the largest decrease occurring as the pressure is in- a water velocity I’,, of 1.43 km/s, is shown (dashed line) in
creased from the initial value of 500 to 2000 psi. Thus, equation Figures 7 and 8, respectively. This equation, of course, only
(3) becomes an appreciably more accurate representation of applies to P-waves. The time-average curve on the plot of
measured velocities and porosities as pressure increases. sandstone values (Figure 7) appears to correspond to a differ-
In accordance with equation (3), reciprocal velocity at zero ential pressure between 500 and 2000 psi. The time-average
porosity, which is the constant A, should be nearly invariant curve on the plot of limestone values (Figure 8) does not
with pressure. Values of A given in Table 2 generally decrease conform to those from the fit of equation (3).
with increasing pressure, the largest overall decrease being in Reciprocal velocity versus differential pressure curves at con-
the S-wave sandstone (4.9 percent) and limestone (7.8 percent) stant porosities of 0 to .3 at .05 intervals derived from equation
values. It is likely that the larger reduction in S-wave, relative to (3) with constants from Table 2, are plotted in Figures 11 and
that in P-wave, values of A is due to the larger standard 12 for sandstone and limestone, respectively. The larger rate of
deviations. Average values of A are given in Table 2 with the change of sandstone S-wave reciprocal velocity with increasing
corresponding reciprocal velocity of quartz for sandstone and porosity (Figure 10) is responsible for the much greater separa-
calcite for limestone. Average values of A are slightly less than tion of the sandstone S-wave curves in Figure 11 relative to that
quartz reciprocal velocities in the case of sandstone and slightly of the limestone S-wave curves in Figure 12 as well as to that of
greater than calcite reciprocal velocities in the case of lime- the P-wave curves in both figures. Thus, sandstone S-wave
stone. Reciprocal quartz and calcite velocities are indicated in reciprocal velocities appear to offer the best potential for poros-
Figures 7 and 8, respectively. ity determination. By contrast, limestone P-wave reciprocal
As noted previously, the constant B in equation (3), which velocity (Figure 12) is least sensitive to porosity variation.
expresses reciprocal velocity rate of change with porosity, de- These observations could also have been made by inspection of
pends upon differential pressure as well as other rock proper- the reciprocal velocity rate of change with porosity versus
ties. Values of B given in Table 2 and plotted versus differential differential pressure curves in Figure 10.
pressure in Figure 10 decrease nonlinearly with increasing pres- In well logging and in seismic surveying, certain errors are
sure. The largest decrease occurs between 500 and about 2000 common to S- and P-wave velocity determinations, such as
psi. Sandstone S-wave reciprocal velocities exhibit the greatest those due to well diameter changes in the former and to near-
rate of change; limestone P-wave reciprocal velocities, the surface effects in the latter. Thus, the difference in S- and
 1194 Domenico

Reciprccalvelccity (1lV) in pseclm Reciprocalvelacity UIVI in ps%im

500 MO I
I Porosity'
I I I
Porosity'
I I
0 .l .2 .3
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- S-wave
--- P-wave
-S-wave
---P-wave

6 I,#:
“,- 500

FIG. 11. Sandstone reciprocal velocity versus differential pres- FIG. 12. Limestone reciprocal velocity versus differential pres-
sure curves at constant porosities from 0 to 0.3 at 0.05 intervals, sure curves, derived from equation (3) with constants from
derived from equation (3) with constants from Table 2. Table 2.

Difference [$ - $1 in pseclm Difference

II$,-f P
in rseclm

100 MO 300 0 100 2w 3

’
Porosity ’
I Poorosiv
, 0
0 .05 .lO .I5 .al .25 .3U . 10 .20 .30

1 1

&(f:
‘ I fr
h 5
c C

Q 5
2x 2g

3
3

- -i - I’li, ; , ~, ,
2lxl 300 100 200 34

FIG. 14. Difference in limestone S- and P-wave reciprocal veloc- FIG. 13. Difference in sandstone S- and P-wave reciprocal ve-
ities versus differential pressure curves at constant porosities, locities versus differential pressure curves at constant poros-
derived from equation (3) with constants from Table 2. ities, derived from equation (3) with constants from Table 2.
 Rock Lithology and Porosity from V, and V, 1195

P-wave reciprocal velocities may be a more reliable indication porosity variation, the rate of change with porosity being more
of porosity than is each reciprocal velocity alone. This differ- than twice that of sandstone P-wave and limestone S- and
ence is plotted versus differential pressure, again at constant P-wave reciprocal velocities. Limestone P-wave reciprocal ve-
porosities from 0 to 0.3, in Figures 13 and 14 for sandstone and locity is least sensitive to porosity variation. Thus, it appears
limestone, respectively. As would be expected, sandstone re- that S-wave velocity will be useful in definiton of sandstone
ciprocal velocity difference is much more sensitive to porosity porosity. Unfortunately, limestone S-wave reciprocal velocity is
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variation than is limestone reciprocal velocity difference. slightly less sensitive than sandstone P-wave reciprocal velocity
The foregoing analysis indicates that sandstone S-wave re- to porosity variation. Consequently, it will be somewhat less
ciprocal velocity is more sensitive to porosity variation, the rate useful in detection of limestone porosity than sandstone
of change (Figure 10) being about 2.5 times that of sandstone P-wave velocity has been in detection of sandstone porosity.
P-wave reciprocal velocity and from 2 to 5 times that of both
limestone reciprocal velocities. Limestone P-wave reciprocal
ACKNOWLI%)GMENTS
velocity is least sensitive to porosity variation. Differential pres-
sure (depth) does not have a pronounced effect on the sensitivi- The author expresses his appreciation to the late G. R.
ty of reciprocal velocity to porosity changes (Figures 11 and 12) Pickett who graciously supplied his laboratory velocity and
above about 1000 psi (below a depth of about 600 m). Finally, porosity measurements on water-saturated sandstone and lime-
the difference in sandstone S-wave and P-wave reciprocal ve- stone cores. The author also is indebted to his assistant, Jana
locities (Figure 13) appears to be an effective indication of Walker, for computations and construction of graphs, and to
porosity. On the other hand, the difference in limestone recipro- Amoco Production Company for permission to publish this
cal velocities (Figure 14) likely cannot be used to estimate work.
porosity, except possibly at shallow depths.

REFERENCES
CONCLUSIONS
Anderson,0. L., and Lieberman, R. C., 1966. Sound velocities in rocks
Previous and ongoing developments in S-wave data acqui- and minerals: VESIAC state-of-the-art report no. 788.5-4-X, Univ. of
Michigan,
sition equipment and techniques require parallel efforts to uti- Cherry: J. T., and Waters, K. H., 1968, Shear-wave recording using
lize such data effectively in petroleum exploration. contmuous signal methods, Part I-Early development: Geophys-
ics, 33,229-239.
This study indicates that gross lithology likely is separable by
Erickson, E. L, Miller, D. E., and Waters, K. H.. 1968. Shear-wave
Poisson’s ratio or, equivalently, by the ratio of P- to S-wave recording using continuous signal methods, Part II--Later experi-
velocity. The principal factor separating sandstone from lime- mentation : Geophysics, 33,24&2.54.
Hicks, W. G., and Berry. J. E., 1956, Fluid saturation of rocks from
stone appears to be difference in quartz and calcite Poisson’s velocity logs: Geophysics, 21,739 754.
ratio. The substantially higher S-wave reciprocal velocity of Ogura, K., Nakanishi, S., and Mortta, K., 1980, Development of the
quartz results in a Poisson’s ratio of less than two-tenths that of suspension S-wave logging system: OYO Corporation Report No. 2,
20 p.
calcite. Pickett, G. R., 1963, Acoustic character logs and their applications in
Fits by regression analysis of the equation I/V = A + B$ to formation evaluation: J. of Petr. Tech., June, 6599667.
laboratory measured S- and P-wave velocities (V) and poros- Toksoz. M. N., Cheng, C. H., and Timur. A., 1976, Velocities of seismic
waves in porous rocks: Geophysics, 41,62 I-645.
ities (+) demonstrate that the sensitivity of reciprocal velocity Wyllie, M. R. J.. Gregory. A. R.. and Gardner, G. H. F., 1956, Elastic
to porosity variation (as indicated by B) does not decrease wave velocities in heterogeneous and porous media: Geophysics, 21,
41-70.
substantially with increasing depth at depths below about 600 -~~~ 1958, An experimental inve\tiation of factors affecting elastic
m. Sandstone S-wave reciprocal velocity is most sensitive to wave velocities in porous media: ( jeophysics, 23,459-493.