Full waveform inversion method and device based on matched filtering approximate Hessian

Abstract

The invention relates to the technical field of seismic velocity modeling, and particularly discloses a full waveform inversion method and device based on matched filtering approximate Hessian, and the method comprises the steps: constructing a filter, and solving an approximate Hessian operator through the filter; a filter is matched through Gabor; a filter matched with Gabor acts on inversion, and a matched filtering full-waveform inversion iteration solution formula is established; and performing full-waveform inversion based on an iterative solution formula to obtain a final inversion result. According to the method, the approximate Hessian matrix is solved through matched filtering, observation seismic records and simulation seismic records are enabled to be well matched, an amplitude adjustment effect is achieved, modeling truncation illusion generated when conventional full-waveform inversion is limited and seismic data are lost can be well solved, false structures are effectively prevented from being generated in the model, and the method is suitable for large-scale popularization and application. And the precision of full-waveform inversion modeling and the iterative convergence efficiency are improved.

Description

Technical Field

[0001] This invention relates to the field of seismic velocity modeling technology, specifically to a full waveform inversion method and apparatus based on matched filtering approximation of Hessian. Background Technology

[0002] Full waveform inversion is one of the most accurate inversion methods currently available. In full waveform inversion, the Hessian operator is the second derivative of the objective functional with respect to the model parameters. Directly calculating the accurate Hessian matrix is ​​computationally intensive. Traditional full waveform inversion is limited by the computational burden and often uses gradient-based methods to avoid directly solving for the Hessian matrix, or uses Newton-based methods that linearize the Hessian matrix.

[0003] The linearized Hessian operator is derived as follows:

[0004] H a =G T G;

[0005] Where G is the seismic wave forward modeling operator;

[0006] The Gauss-Newton equations based on linear Hessian matrices are expressed as follows:

[0007]

[0008] Where m represents parameters of the Earth medium model, such as velocity or elastic parameters, and d... obs To observe earthquake data, k is the number of iterations.

[0009] However, when the number of detectors is limited, the observed seismic data d obs In cases where there are gaps and seismic traces are sparse, conventional full-waveform inversion modeling based on approximate Hessian operators can produce truncation artifacts, affecting the accuracy of velocity modeling.

[0010] Based on this technical background, this invention studies a full waveform inversion method and apparatus based on matched filtering approximation of Hessian. Summary of the Invention

[0011] To address the shortcomings of existing technologies, this invention provides a full waveform inversion method and apparatus based on matched filtering approximate Hessian. This method solves for the approximate Hessian matrix through matched filtering, enabling a better match between observed seismic records and simulated seismic records. It also has an amplitude adjustment function, effectively solving the modeling truncation artifacts caused by limited detectors and missing seismic data in conventional full waveform inversion. This effectively avoids the generation of false structures in the model and improves the accuracy and iterative convergence efficiency of full waveform inversion modeling.

[0012] To achieve the above objectives, a first aspect of the present invention provides a full waveform inversion method based on matched filtering approximation of Hessian, comprising:

[0013] Construct a filter and solve for the approximate Hessian operator using the filter;

[0014] The filter is matched using Gabor;

[0015] The Gabor-matched filter is applied to the inversion process to establish an iterative solution formula for the full waveform inversion of the matched filter.

[0016] The final inversion result is obtained by performing a full waveform inversion based on the iterative solution formula.

[0017] A second aspect of the present invention provides a full waveform inversion apparatus based on matched filtering approximation of Hessian, comprising:

[0018] The operator solving module is used to construct filters and solve for approximate Hessian operators through the filters.

[0019] A matching module is used to match the filter using Gabor;

[0020] The formula establishment module is used to apply the Gabor-matched filter to the inversion and establish the iterative solution formula for the full waveform inversion of the matched filter.

[0021] The inversion module is used to perform full waveform inversion based on the iterative solution formula to obtain the final inversion result.

[0022] A third aspect of the present invention provides an electronic device, the electronic device comprising:

[0023] Memory, which stores executable instructions;

[0024] A processor that executes the executable instructions in the memory to implement the full waveform inversion method based on matched filter approximation Hessian as described in the first aspect.

[0025] A fourth aspect of the present invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the full waveform inversion method based on matched filtering approximation Hessian as described in the first aspect.

[0026] The beneficial effects of this invention include:

[0027] The full waveform inversion method proposed in this invention, based on matched filtering approximate Hessian, solves the approximate Hessian matrix through matched filtering, which enables a better match between observed seismic records and simulated seismic records. It also has an amplitude adjustment function, which can effectively solve the modeling truncation artifacts caused by limited detectors and missing seismic data in conventional full waveform inversion. It effectively avoids the generation of false structures in the model and improves the accuracy and iterative convergence efficiency of full waveform inversion modeling.

[0028] Other features and advantages of the present invention will be described in detail in the following detailed description section. Attached Figure Description

[0029] The above and other objects, features and advantages of the present invention will become more apparent from the more detailed description of exemplary embodiments of the invention in conjunction with the accompanying drawings.

[0030] Figure 1 This is a flowchart illustrating the full waveform inversion method based on matched filtering approximation of Hessian proposed in this invention.

[0031] Figure 2 This is a schematic diagram of the actual velocity model in a specific implementation of the full waveform inversion method based on matched filtering approximation Hessian proposed in this invention.

[0032] Figure 3 This is a schematic diagram of the initial velocity model in a specific implementation of the full waveform inversion method based on matched filtering approximation Hessian proposed in this invention.

[0033] Figure 4 This is a schematic diagram of the conventional method for calculating the Hessian matrix (1 shot) in a specific implementation of the full waveform inversion method based on matched filtering approximation of Hessian proposed in this invention.

[0034] Figure 5 This is a schematic diagram illustrating the calculation of the Hessian matrix (1 shot) by the method of the present invention in a specific implementation of the full waveform inversion method based on matched filtering approximation of Hessian proposed in this invention.

[0035] Figure 6 This is a schematic diagram of the conventional full waveform inversion result in a specific implementation of the full waveform inversion method based on matched filtering approximation Hessian proposed in this invention.

[0036] Figure 7 This is a schematic diagram of the full waveform inversion result of the method proposed in this invention, based on the matched filter approximation Hessian. Detailed Implementation

[0037] Preferred embodiments of the invention will now be described in more detail. While preferred embodiments of the invention are described below, it should be understood that the invention can be implemented in various forms and should not be limited to the embodiments set forth herein.

[0038] This invention provides a full waveform inversion method based on matched filtering approximation of Hessian, such as... Figure 1 As shown, it includes:

[0039] Construct a filter and solve for the approximate Hessian operator using the filter;

[0040] Through Gabor matched filter;

[0041] By applying the Gabor-matched filter to the inversion, an iterative solution formula for the full waveform inversion of the matched filter is established.

[0042] The final inversion result is obtained by performing full waveform inversion based on the iterative solution formula.

[0043] In this invention, the approximate Hessian matrix is ​​solved by matched filtering, which makes the observed seismic records and simulated seismic records better matched and has an amplitude adjustment function. It can better solve the modeling truncation artifact caused by the limited detector and missing seismic data in conventional full waveform inversion, effectively avoid the generation of false structures in the model, and improve the accuracy and iterative convergence efficiency of full waveform inversion modeling.

[0044] According to the present invention, the relational formula used to construct the filter is:

[0045]

[0046] Where G is the seismic wave forward modeling operator, F is the filter, m is the Earth medium model parameter, and d obs To observe earthquake data.

[0047] According to the present invention, the formula used to solve the approximate Hessian operator by means of a filter is as follows:

[0048]

[0049] F≈H -1 ;

[0050] Where H is the Hessian operator.

[0051] According to the present invention, the Gabor matched filter includes:

[0052] The unsteady seismic trace is decomposed into time windows to obtain the local steady-state signal;

[0053] Solving the filter based on the local steady-state signal.

[0054] According to the present invention, the formula used to decompose unsteady seismic traces into time windows to obtain local steady-state signals is as follows:

[0055]

[0056] Among them, l t τ is the time window length, τ is the center time of the time window, and s is the local steady-state signal.

[0057] According to the present invention, the formula used to solve the filter based on the local steady-state signal is as follows:

[0058]

[0059] Where ω is the angular frequency, Indicates conjugate.

[0060] Preferably, the formula for the full waveform inversion iteration of the matched filter is:

[0061]

[0062] According to the present invention, k is the iteration number, m (k+1) This is the final inversion result.

[0063] The present invention will be described in more detail below through embodiments.

[0064] Example 1:

[0065] like Figure 1 As shown in the figure, this embodiment proposes a full waveform inversion method based on matched filtering approximation of Hessian. The specific steps are as follows:

[0066] Step 1: Derivation of the Hessian matrix for matched filtering;

[0067] This embodiment designs a matched filter F to eliminate the modeling truncation artifact caused by the conventional approximation of the Hessian matrix; F satisfies:

[0068]

[0069] Where, d * To complete the earthquake observation record,

[0070] This filter F needs to match the recorded residual terms, that is,

[0071]

[0072] Then, F≈H -1 ;

[0073] Step 2: Set the matching filter;

[0074] This embodiment uses a Gabor matched filter;

[0075] The non-steady-state seismic traces are decomposed into time windows to obtain local steady-state signals.

[0076]

[0077] Among them, l t τ represents the time window length, and τ represents the center time of the time window;

[0078] The solution to the filter is:

[0079]

[0080] Where ω is the angular frequency, Indicates conjugate.

[0081] Step 3: Apply the filter to the inversion and establish the iterative solution formula for the matched filter full waveform inversion:

[0082]

[0083] Step 4: Use the iterative solution formula from step 3 to perform full waveform inversion and obtain the final inversion result m. (k+1) .

[0084] In this embodiment, the following is used: Figure 2 The model shown was used for method testing. The model size was 301 grid points in the horizontal direction and 131 grid points in the vertical direction. The grid spacing in both directions was 20m. The seismic source and detectors were set on the upper surface of the model. There were a total of 30 seismic sources with a shot spacing of 200m and a detector spacing of 160m. The maximum offset distance was 4000m. Figure 3 This serves as the initial model for full waveform inversion. Figure 4 The approximate Hessian matrix for a single shot is calculated using conventional methods. Figure 5 This is the approximate Hessian matrix for a single shot calculated by the method of this invention; Figure 6 The results are from a standard full-waveform inversion. Due to the limited number of detectors and the lack of seismic traces, a grid-like artifact is caused at the location indicated by the arrow in the inversion results. Figure 7 The inversion results obtained using the method of this invention can be seen by comparison. Figure 7 The inversion results are in better agreement with the actual model, the model accuracy is higher, and there are no grid-like artifacts. The experiments demonstrate that the method of the present invention can effectively obtain a high-precision velocity model.

[0085] Example 2:

[0086] This embodiment provides a full waveform inversion method based on matched filtering approximation of Hessian, such as... Figure 1 As shown, it includes:

[0087] Construct a filter and solve for the approximate Hessian operator using the filter;

[0088] Through Gabor matched filter;

[0089] By applying the Gabor-matched filter to the inversion, an iterative solution formula for the full waveform inversion of the matched filter is established.

[0090] The final inversion result is obtained by performing full waveform inversion based on the iterative solution formula;

[0091] In this embodiment, the relation used to construct the filter is:

[0092]

[0093] Where G is the seismic wave forward modeling operator, F is the filter, m is the Earth medium model parameter, and d obs To observe earthquake data;

[0094] In this embodiment, the formula used to solve for the approximate Hessian operator through a filter is:

[0095]

[0096] F≈H -1 ;

[0097] Where H is the Hessian operator;

[0098] In this embodiment, the Gabor matched filter includes:

[0099] The unsteady seismic trace is decomposed into time windows to obtain the local steady-state signal;

[0100] Solving the filter based on the local steady-state signal;

[0101] In this embodiment, the formula used to decompose the unsteady seismic trace into a time window form to obtain the local steady-state signal is:

[0102]

[0103] Among them, l t τ is the time window length, τ is the center time of the time window, and s is the local steady-state signal;

[0104] In this embodiment, the formula used to solve the filter based on the local steady-state signal is:

[0105]

[0106] Where ω is the angular frequency, Indicates conjugate.

[0107] In this embodiment, the formula for the full waveform inversion iteration of the matched filter is:

[0108]

[0109] In this embodiment, k is the iteration number, m (k+1) This is the final inversion result.

[0110] Example 3:

[0111] This embodiment provides a full waveform inversion device based on matched filtering approximation of Hessian, including:

[0112] The operator solving module is used to construct filters and solve for approximate Hessian operators through the filters.

[0113] Matching module, used to match Gabor filters;

[0114] The formula establishment module is used to apply the Gabor matched filter to the inversion and establish the iterative solution formula for the full waveform inversion of the matched filter;

[0115] The inversion module is used to perform full waveform inversion based on iteratively solved formulas to obtain the final inversion result.

[0116] In this embodiment, the relation used to construct the filter is:

[0117]

[0118] Where G is the seismic wave forward modeling operator, F is the filter, m is the Earth medium model parameter, and d obs To observe earthquake data;

[0119] In this embodiment, the formula used to solve for the approximate Hessian operator through a filter is:

[0120]

[0121] F≈H -1 ;

[0122] Where H is the Hessian operator;

[0123] In this embodiment, the Gabor matched filter includes:

[0124] The unsteady seismic trace is decomposed into time windows to obtain the local steady-state signal;

[0125] Solving the filter based on the local steady-state signal;

[0126] In this embodiment, the formula used to decompose the unsteady seismic trace into a time window form to obtain the local steady-state signal is:

[0127]

[0128] Among them, l t τ is the time window length, τ is the center time of the time window, and s is the local steady-state signal;

[0129] In this embodiment, the formula used to solve the filter based on the local steady-state signal is:

[0130]

[0131] Where ω is the angular frequency, Indicates conjugate.

[0132] In this embodiment, the formula for the full waveform inversion iteration of the matched filter is:

[0133]

[0134] In this embodiment, k is the iteration number, m (k+1) This is the final inversion result.

[0135] Example 4:

[0136] This invention provides an electronic device including a memory and a processor, comprising:

[0137] Memory, which stores executable instructions;

[0138] The processor executes executable instructions in memory to implement a full waveform inversion method based on matched filtering approximation of Hessian.

[0139] This memory is used to store non-transitory computer-readable instructions. Specifically, the memory may include one or more computer program products, which may include various forms of computer-readable storage media, such as volatile memory and / or non-volatile memory. The volatile memory may, for example, include random access memory (RAM) and / or cache memory. The non-volatile memory may, for example, include read-only memory (ROM), hard disk, flash memory, etc.

[0140] The processor may be a central processing unit (CPU) or other form of processing unit with data processing capabilities and / or instruction execution capabilities, and may control other components in the electronic device to perform desired functions. In one embodiment of the invention, the processor is used to execute computer-readable instructions stored in the memory.

[0141] Those skilled in the art should understand that, in order to solve the technical problem of how to achieve a good user experience, this embodiment may also include well-known structures such as communication buses and interfaces, and these well-known structures should also be included within the protection scope of this invention.

[0142] For a detailed description of this embodiment, please refer to the corresponding descriptions in the foregoing embodiments, which will not be repeated here.

[0143] Example 5:

[0144] This invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements a full waveform inversion method based on matched filtering approximation of Hessian.

[0145] A computer-readable storage medium according to embodiments of the present invention stores non-transitory computer-readable instructions. When these non-transitory computer-readable instructions are executed by a processor, all or part of the steps of the methods described in the foregoing embodiments of the present invention are performed.

[0146] The aforementioned computer-readable storage media include, but are not limited to: optical storage media (e.g., CD-ROM and DVD), magneto-optical storage media (e.g., MO), magnetic storage media (e.g., magnetic tape or portable hard drive), media with built-in rewritable non-volatile memory (e.g., memory card), and media with built-in ROM (e.g., ROM cartridge).

[0147] The full waveform inversion method based on matched filtering approximate Hessian proposed in the embodiments of the present invention solves the approximate Hessian matrix by matched filtering, so that the observed seismic records and simulated seismic records are well matched, and it has an amplitude adjustment function. It can effectively solve the modeling truncation artifact caused by the limited number of detectors and missing seismic data in conventional full waveform inversion, effectively avoid the generation of false structures in the model, and improve the accuracy and iterative convergence efficiency of full waveform inversion modeling.

[0148] The various embodiments of the present invention have been described above. These descriptions are exemplary and not exhaustive, nor are they limited to the disclosed embodiments. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments.

Claims

1. A full waveform inversion method based on matched filtering approximation of Hessian, characterized in that, include: Construct a filter and solve for the approximate Hessian operator using the filter; The filter is matched using Gabor; The Gabor-matched filter is applied to the inversion process to establish an iterative solution formula for the full waveform inversion of the matched filter. The final inversion result is obtained by performing a full waveform inversion based on the iterative solution formula.

2. The method according to claim 1, characterized in that, The relation used to construct the filter is: Where G is the seismic wave forward modeling operator, F is the filter, m is the Earth medium model parameter, and d obs To observe earthquake data; The formula used to solve for the approximate Hessian operator through the filter is: F≈H -1 ; Where H is the Hessian operator.

3. The method according to claim 2, characterized in that, The filter is matched using Gabor: The unsteady seismic trace is decomposed into time windows to obtain the local steady-state signal; The filter is solved based on the local steady-state signal.

4. The method according to claim 3, characterized in that, The formula used to decompose unsteady seismic traces into time-window form to obtain local steady-state signals is: Among them, l t τ is the time window length, τ is the center time of the time window, and s is the local steady-state signal.

5. The method according to claim 4, characterized in that, The formula used to solve the filter based on the local steady-state signal is: Where ω is the angular frequency, Indicates conjugate.

6. The method according to claim 5, characterized in that, The formula for the full waveform inversion iterative solution of the matched filter is as follows:

7. The method according to claim 6, characterized in that, k is the number of iterations, m (k+1) This is the final inversion result.

8. A full waveform inversion device based on matched filtering approximation of Hessian, characterized in that, include: The operator solving module is used to construct filters and solve for approximate Hessian operators through the filters. A matching module is used to match the filter using Gabor; The formula establishment module is used to apply the Gabor-matched filter to the inversion and establish the iterative solution formula for the full waveform inversion of the matched filter. The inversion module is used to perform full waveform inversion based on the iterative solution formula to obtain the final inversion result.

9. An electronic device, characterized in that, The electronic device includes: Memory, which stores executable instructions; A processor that executes the executable instructions in the memory to implement the full waveform inversion method based on matched filter approximation Hessian according to any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the full waveform inversion method based on matched filter approximation Hessian as described in any one of claims 1-7.

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