CN104730572A - Diffracted wave imaging method and device based on L0 semi-norm - Google Patents
Diffracted wave imaging method and device based on L0 semi-norm Download PDFInfo
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Abstract
The invention discloses a diffracted wave imaging method based on the L0 semi-norm. The method comprises the steps that seismic data with no reflected waves are obtained to be used as input data; discretization is carried out on underground imaging space, any imaging point is selected as the current diffracted imaging point, and a green function of any diffracted imaging point is calculated according to a given speed model and the relation between short points and wave detection points in the input seismic data; other imaging points which are not selected are executed in a loop mode, and other corresponding green functions are calculated until the green functions of all the imaging points in the underground imaging space are obtained; a diffracted wave imaging model based on the L0 semi-norm is built; the homotopy analysis iterative algorithm is used for solving the model, and a diffracted wave imaging result is obtained. The invention further discloses a diffracted wave imaging device based on the L0 semi-norm. By means of the diffracted wave imaging method and device based on the L0 semi-norm, the seismic data imaging resolution ratio can be improved, the diffracted wave imaging signal to noise ratio is increased, and therefore a small-scale geological unit related to reservoir space connectivity can be recognized more easily.
Description
Technical Field
The invention belongs to the technical field of exploration earthquakes, relates to a diffracted wave imaging method based on L0 half norm, and further relates to a diffracted wave imaging device based on L0 half norm.
Background
In the process of exploration and development of oil and gas resources, structural and lithological abnormal bodies such as karst caves, cracks, stratum pinch-out, weathering crust and the like are effectively identified, which is of great importance for reservoir understanding. The small-scale geologic bodies are typically smaller or much smaller in spatial spread than the seismic wavelet wavelength and thus exist in the form of diffracted waves in the seismic data. In the field operation process, the seismic signals received by the detector comprise reflected waves and diffracted waves, and the reflected wave imaging condition assumes an infinite smooth interface, so that the imaging condition can only reflect large-scale geological background generally. In contrast, diffracted waves are a reflection of geological details and are an important information carrier for improving seismic resolution. However, the diffracted energy generated by the geologic body is about 0.1-0.01 times of the reflected energy, is a weak signal, and is often submerged in the reflected wave imaging result, so reflected waves need to be removed, and common methods include signal decomposition such as Harlan transformation (Harlan et at.,1984), Radon transformation (Zhang,2005), plane wave destructive filtering (Taner et al, 2006; Fomel et al, 2006,2007) and the like.
Through patent retrieval and domestic and foreign literature research, the focus of the currently developed diffracted wave imaging method is mostly put on reflected wave removal, and the aim is to highlight diffracted waves by suppressing reflected waves. Such as offset-dip gather reflection subtraction (Klokov and Fomel,2012), focus-ablation-anti-focus (khaidikokokovic et al, 2004), common reflector element superposition (Dell and Gajewski, 2011; Asgedomet al, 2011), multi-focus (Berkovitch et al, 2009), and the like.
The diffracted wave imaging method does not carry out research on diffracted wave imaging operators, and actually, diffraction information has sparse discontinuity in spatial distribution and can be completely described by using a mathematical L0 half norm.
Therefore, the diffraction wave imaging model based on the L0 half norm is constructed according to the Green function, and the model can achieve high-precision and high-signal-to-noise ratio diffraction wave imaging results by restricting the sparsity of diffraction information. Compared with a common diffracted wave imaging method, the diffracted wave imaging method based on the L0 half norm can further ensure the signal-to-noise ratio of imaging data and reduce the multi-solution while improving the seismic signal resolution.
Disclosure of Invention
The invention aims to provide a diffracted wave imaging method based on L0 half-norm, which solves the problem that the signal-to-noise ratio of seismic data cannot be considered while the imaging resolution is improved in the existing diffracted wave imaging technology, and can realize fine depiction of small-scale geological abnormal bodies such as small faults, cracks, karst caves and the like.
Another object of the present invention is to provide a diffracted wave imaging apparatus based on L0 half norm.
The technical scheme adopted by the invention is that the diffracted wave imaging method based on the L0 half norm comprises the following steps:
step 101: acquiring seismic data from which reflected waves are removed as input data;
step 102: discretizing an underground imaging space, selecting any imaging point as a current diffraction imaging point, and calculating a Green function of the any diffraction imaging point according to the relation between a shot point and a demodulator probe in input seismic data and a given velocity model;
step 103: circularly executing other unselected imaging points in the underground imaging space in the step 102, and calculating corresponding Green's functions of the other imaging points until obtaining Green's functions of all imaging points in the underground imaging space;
step 104: constructing a diffracted wave imaging model based on an L0 half-norm according to Green's functions and an initial imaging model of all imaging points of an underground imaging space;
step 105: and solving the model by a homotopy analysis iterative algorithm to obtain a diffracted wave imaging result.
The invention adopts another technical scheme that the diffracted wave imaging device based on the L0 half norm comprises seismic data acquisition modules which are sequentially connected and used for inputting seismic data for removing reflected waves; the diffraction imaging point selection module is used for selecting imaging points from the discretized underground imaging space as Green function calculation positions; the Green function calculation module is used for calculating travel time and amplitude compensation items from a shot point to an earthquake demodulator probe through a diffraction imaging point; the L0 half-norm model construction module is used for constructing a solving model based on the L0 half-norm according to Green functions of all imaging points of the underground space; and the model solving device is used for solving the L0 model constructed by the Green function and the diffraction point model by utilizing the homotopy analysis algorithm to obtain a diffracted wave imaging result.
The method has the beneficial effects that the Green function calculation is carried out on the seismic data with the reflected waves removed, so that an L0 half-norm inversion model is constructed. In general, the solution of the inversion problem is non-unique unless a limit condition is added to narrow the search range, and in the embodiment, the model sparsity is limited in consideration of the discontinuity of diffraction information space, so that the solution model is more consistent with the actual geological condition, and the noise can be suppressed to a certain extent through iterative approximation, and the signal-to-noise ratio of the diffraction wave imaging data is improved. The imaging resolution of seismic data is improved, and the signal-to-noise ratio of diffracted wave imaging is enhanced, so that small-scale geological units related to the spatial connectivity of a reservoir layer can be more easily identified.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
Fig. 2 is a block diagram of the apparatus of the present invention.
The seismic data acquisition module 201, the diffraction imaging point selection module 202, the green function calculation module 203, the half-norm model construction module 204 and the half-norm model construction module L0, and the model solving device 205 are adopted.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
As shown in fig. 1, the diffracted wave imaging method based on L0 half norm provided by the present invention includes the following steps:
step 101: acquiring seismic data from which reflected waves are removed as input data; corresponding seismic data can be pre-stack shot gather seismic data or post-stack seismic data, and a plane wave damage filtering method is adopted in a reflected wave removing method;
step 102: discretizing an underground imaging space, selecting any imaging point as a current diffraction imaging point, and calculating a Green function of the any diffraction imaging point according to the relation between a shot point and a demodulator probe in input seismic data and a given velocity model;
step 103: circularly executing other unselected imaging points in the underground imaging space in the step 102, and calculating corresponding Green's functions of the other imaging points until obtaining Green's functions of all imaging points in the underground imaging space;
step 104: constructing a diffracted wave imaging model based on an L0 half-norm according to Green's functions and an initial imaging model of all imaging points of an underground imaging space;
step 105: and solving the model by a homotopy analysis iterative algorithm to obtain a diffracted wave imaging result.
In the green function calculation method in the steps 102 and 103, travel time from a shot point to a demodulator probe through an imaging point is calculated according to ray tracing, and an amplitude weighting term is stored.
In the step 104, a diffracted wave imaging model based on the L0 half norm is established, which is designed as follows:
wherein min represents minimization, Jα(m) is an objective function, m is a solved diffraction model, and the mathematical notation: ═ denotes that G is green's function, d is seismic data with reflected waves removed, and α is positive
The factor is then changed to a factor,is represented by2The norm of the number of the first-order-of-arrival,is 10A half norm.
By the neighbor method, the above equation can be written as:
wherein Hβ,α(m0M) is Jα(m) approximation formula, m0To the initial model, β is an adjustable regularization parameter, (-) represents the inner product.
The above minimum problem can be solved by a hard threshold operator as follows:
wherein, <math>
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In the step 105, the model solving device is adopted to realize the L0 half-norm model building module, and the iteration process is completed by a homotopy analysis algorithm, and the specific process is as follows:
step 1: inputting Lipschitz parameter beta0Regularization parameter α0And require
β0∈[βmin,βmax]，βmin,βmaxRespectively, the Pethitz parameter beta0Upper and lower limits, initialization parameter, k is 0, ρ ∈ (0,1), and model m is initialized0；
Step 2, setting i to be 0 and mk,0＝mk,βk,0＝βk；
And step 3: <math>
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Carry out betak,i＝min{γβk,i,βmax}，
βk,i+1＝βk,i,i＝i+1；
Returning to the step 3 until | mk,i-mk,i+1||∞≤0
Wherein the termination parameter0Generally is0＝10-1；
And 4, step 4: m isk+1＝mk,i,βk+1＝βk,i,αk+1＝ραk,k＝k+1；
Returning to the step 2 until | mk,i-mk,i+1||∞≤；
Wherein, it is generally 10 ═ c-5；
And 5: outputting the final iteration result, m*＝mk。
Based on the same inventive concept, the invention also provides a diffracted wave imaging device based on the L0 half norm. Since the principle of solving the problem of the diffracted wave imaging device based on the L0 half norm is similar to that of the diffracted wave imaging method based on the L0 half norm, the implementation of the diffracted wave imaging device based on the L0 half norm can be referred to that of the diffracted wave imaging method based on the L0 half norm, and repeated details are omitted. As used hereinafter, the term "unit" or "module" may be a combination of software and/or hardware that implements a predetermined function. Although the means described in the embodiments below are preferably implemented in software, an implementation in hardware, or a combination of software and hardware is also possible and contemplated.
Fig. 2 is a block diagram of a structure of a diffracted wave imaging apparatus based on L0 half norm according to the present invention, which includes a seismic data acquisition module 201, a diffracted imaging point selection module 202, a green function calculation module 203, an L0 norm model construction module 204, and a model solving device 205, which are connected in sequence, and the structure is described below.
A seismic data acquisition module 201 for inputting a seismic data from which reflected waves are removed;
a diffraction imaging point selection module 202, configured to select an imaging point from the discretized underground imaging space as a green function calculation position;
the Green function calculation module 203 is used for calculating travel time and amplitude compensation items from a shot point to an earthquake demodulator probe through a diffraction imaging point;
an L0 half-norm model construction module 204, which constructs a solution model based on L0 half-norm according to the Green's function of all imaging points in the underground space;
the model solving device 205 solves the L0 model constructed by the green function and the diffraction point model by using the homotopy analysis algorithm to obtain the diffracted wave imaging result.
The green function calculation module 203 calculates travel time from a shot point to a demodulator probe through an imaging point according to ray tracing, and stores an amplitude weighting term.
The L0 half-norm model construction module 204 is designed as follows:
wherein min represents minimization, Jα(m) is an objective function, m is a solved diffraction model, the mathematical notation: -represents, defined as, G is a green function, d is seismic data with reflected waves removed, α is a regularization factor,is represented by2The norm of the number of the first-order-of-arrival,is 10A half norm.
By the neighbor method, the above equation can be written as:
wherein Hβ,α(m0M) is Jα(m) approximation formula, m0To the initial model, β is an adjustable regularization parameter, (-) represents the inner product.
The above minimum problem can be solved by a hard threshold operator as follows:
wherein, <math>
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Optionally, the L0 half-norm model building module is implemented by using a model solving device, and the model solving device is iterated
The process is completed by a homotopy analysis algorithm and comprises the following steps:
step 1: inputting Lipschitz parameter beta0Regularization parameter α0And require
β0∈[βmin,βmax]，βmin,βmaxRespectively, the Pethitz parameter beta0Upper and lower limits, initialization parameter, k is 0, ρ ∈ (0,1), initialModel m0；
Step 2, setting i to be 0 and mk,0＝mk,βk,0＝βk；
And step 3: <math>
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βk,i+1＝βk,i,i＝i+1；
Returning to the step 3 until | mk,i-mk,i+1||∞≤0
Wherein the termination parameter0General settings0＝10-1；
And 4, step 4: m isk+1＝mk,i,βk+1＝βk,i,αk+1＝ραk,k＝k+1；
Returning to the step 2 until | mk,i-mk,i+1||∞≤；
Wherein, it is generally 10 ═ c-5；
And 5: outputting the final iteration result, m*＝mk。
In another embodiment, a software is provided, which is used to execute the technical solutions described in the above embodiments and preferred embodiments.
In another embodiment, a storage medium is provided, in which the software is stored, and the storage medium includes but is not limited to: optical disks, floppy disks, hard disks, erasable memory, etc. From the above description, it can be seen that the embodiments of the present invention achieve the following technical effects: a diffracted wave imaging method and device based on L0 half-norm enable a solution model to better accord with actual geological conditions by limiting model sparsity, noise can be suppressed to a certain extent through iterative approximation, signal-to-noise ratio of diffracted wave imaging data is improved, fine depiction of small-scale geological abnormal bodies such as small faults, cracks and karst caves can be achieved through the technology, and the method and device have important application value in oil and gas exploration reservoir research.
Finally, it is to be noted that: the above description is only for the purpose of illustrating the present invention and is not meant to limit the technical solutions described in the present invention; although the present invention has been described in detail in the specification, those skilled in the art can make modifications and equivalents of the present invention, and all technical solutions and modifications thereof without departing from the spirit and scope of the present invention should be covered by the claims of the present invention.
Claims (9)
1. A diffracted wave imaging method based on L0 half norm is characterized by comprising the following steps:
step 101: acquiring seismic data from which reflected waves are removed as input data;
step 102: discretizing an underground imaging space, selecting any imaging point as a current diffraction imaging point, and calculating a Green function of the any diffraction imaging point according to the relation between a shot point and a demodulator probe in input seismic data and a given velocity model;
step 103: circularly executing other unselected imaging points in the underground imaging space in the step 102, and calculating corresponding Green's functions of the other imaging points until obtaining Green's functions of all imaging points in the underground imaging space;
step 104: constructing a diffracted wave imaging model based on an L0 half-norm according to Green's functions and an initial imaging model of all imaging points of an underground imaging space;
step 105: and solving the model by a homotopy analysis iterative algorithm to obtain a diffracted wave imaging result.
2. The method as claimed in claim 1, wherein the seismic data in step 101 is pre-stack shot gather seismic data or post-stack seismic data; the reflected wave removing method adopts a plane wave destructive filtering method.
3. The method for imaging diffracted waves based on L0 half-norm according to claim 1, wherein the Green's function in steps 102 and 103 is calculated by ray tracing from the shot point through the imaging point to the geophone point, and storing the amplitude weighting term.
4. The method as claimed in claim 1, wherein in the step 104, a model of diffracted wave based on L0 half norm is constructed as follows:
wherein min represents minimization, Jα(m) is an objective function, m is a solved diffraction model, the mathematical notation: -represents, defined as, G is a green function, d is seismic data with reflected waves removed, α is a regularization factor,is represented by2The norm of the number of the first-order-of-arrival,is 10A half norm.
By the neighbor method, the above equation is written as:
wherein Hβ,α(m0M) is Jα(m) approximation formula, m0Beta is an adjustable regularization parameter for the initial model, (-) represents the inner product,
the minimum problem can be solved by a hard threshold operator:
wherein, <math>
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5. The diffracted wave imaging method according to claim 1, wherein the iterative algorithm of homotopy analysis in step 105 comprises the following steps:
step 1: inputting Lipschitz parameter beta0Regularization parameter α0And requires β0∈[βmin,βmax]，βmin,βmaxRespectively, the Pethitz parameter beta0Upper and lower limits, initialization parameter, k is 0, ρ ∈ (0,1), and model m is initialized0；
Step 2, setting i to be 0 and mk,0＝mk,βk,0＝βk；
And step 3: m isk,i+1＝Vβk,i(mk,i+1)；
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<mo>|</mo>
<mo>|</mo>
<msup>
<mi>m</mi>
<mrow>
<mi>k</mi>
<mo>,</mo>
<mi>i</mi>
</mrow>
</msup>
<mo>-</mo>
<msup>
<mi>m</mi>
<mrow>
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<mo>+</mo>
<mn>1</mn>
</mrow>
</msup>
<mo>|</mo>
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<mo>,</mo>
</mrow>
</math>
Carry out betak,i＝min{γβk,i,βmax}，mk,i+1＝Tβk,i(mk,i+1)；
βk,i+1＝βk,i,i＝i+1；
Returning to the beginning of the step 3 until | mk,i-mk,i+1||∞≤0；
Wherein the termination parameter0Is composed of0＝10-1；
And 4, step 4: m isk+1＝mk,i,βk+1＝βk,i,αk+1＝ραk,k＝k+1；
Returning to the step 2 until | mk,i-mk,i+1||∞≤；
Wherein is 10-5；
And 5: outputting the final iteration result, m*＝mk。
6. A diffracted wave imaging device based on L0 half norm is characterized by comprising a seismic data acquisition module (201) which is connected in sequence and used for inputting seismic data for removing reflected waves;
a diffraction imaging point selection module (202) for selecting an imaging point from the discretized underground imaging space as a Green function calculation position;
the Green function calculation module (203) is used for calculating travel time and amplitude compensation items from a shot point to an earthquake demodulator probe through a diffraction imaging point;
an L0 half-norm model construction module (204) for constructing a solution model based on L0 half-norm according to Green's functions of all imaging points of the underground space;
and a model solving device (205) for solving the L0 model constructed by the Green function and the diffraction point model by using the homotopy analysis algorithm to obtain a diffracted wave imaging result.
7. The L0 half-norm-based diffracted wave imaging apparatus as claimed in claim 6, wherein the Green's function computation module (203) computes travel time from a shot point to a geophone point through an imaging point according to ray tracing and stores an amplitude weighting term.
8. The diffracted wave imaging apparatus based on L0 half-norm as claimed in claim 6, wherein said L0 half-norm model construction module (204) is designed as follows:
wherein min represents minimization, Jα(m) is an objective function, m is a solved diffraction model, the mathematical notation: -represents, defined as, G is a green function, d is seismic data with reflected waves removed, α is a regularization factor,is represented by2The norm of the number of the first-order-of-arrival,is 10A half norm;
by the neighbor method, the above equation is written as:
wherein Hβ,α(m0M) is Jα(m) approximation formula, m0Beta is an adjustable regularization parameter for the initial model, (-) represents the inner product,
the minimum problem is solved by a hard threshold operator:
wherein, <math>
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<mi>s</mi>
<mi>β</mi>
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<mo>=</mo>
<mi>m</mi>
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<mfrac>
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<mrow>
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<mo>▿</mo>
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</math> [·]irepresenting the ith element of the vector.
9. The diffracted wave imaging apparatus of claim 6, wherein said model solving means (205) is iterative with a homotopy analysis algorithm as follows:
step 1: inputting Lipschitz parameter beta0Regularization parameter α0And requires β0∈[βmin,βmax]，βmin,βmaxRespectively, the Pethitz parameter beta0Upper and lower limits, initialization parameter, k is 0, ρ ∈ (0,1), and model m is initialized0；
Step 2, setting i to be 0 and mk,0＝mk,βk,0＝βk；
And step 3: m isk,i+1＝Vβk,i(mk,i+1)；
When in use <math>
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</math>
Carry out betak,i＝min{γβk,i,βmax}，mk,i+1＝Tβk,i(mk,i+1)；
βk,i+1＝βk,i,i＝i+1；
Returning to the step 3 until | mk,i-mk,i+1||∞≤0
Wherein the termination parameter0Setting up0＝10-1；
And 4, step 4: m isk+1＝mk,i,βk+1＝βk,i,αk+1＝ραk,k＝k+1；
Returning to the step 2 until | mk,i-mk,i+1||∞≤；
Wherein is 10-5；
And 5: outputting the final iteration result, m*＝mk。
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| CN106772592A (en) * | 2016-11-10 | 2017-05-31 | 中国矿业大学(北京) | The analysis method and device of diffracted wave focus energy |
| CN106772593B (en) * | 2016-11-10 | 2018-07-24 | 中国矿业大学(北京) | The imaging method and device of diffracted wave |
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