Wavelet extension-based full-waveform inversion wave field reconstruction method and device

Abstract

The invention relates to the technical field of seismic data processing, and particularly discloses a full-waveform inversion wave field reconstruction method and device based on wavelet extension, and the method comprises the steps: carrying out the wave field simulation through seismic wavelets, and obtaining a simulated seismic record; calculating a wave field residual error based on the simulated seismic record; performing deconvolution operation on the wave field residual error to obtain a deconvolution operation result; performing wave field back propagation on a deconvolution operation result and summing each channel to generate an extended wavelet corresponding to a residual wave field; and performing wave field propagation by using the extended wavelets to form a reconstructed wave field, thereby obtaining a final wave field. According to the method, the extended seismic wavelets are obtained through deconvolution, back propagation and summation of the wave field residuals, the extended seismic wavelets are used for reconstructing the nonlinear wave field, the problem that full-waveform inversion is prone to falling into a local extremum due to linearization of seismic wave numerical simulation in conventional full-waveform inversion is solved, and inversion reliability is improved.

Description

Technical Field

[0001] This invention relates to the field of seismic data processing technology, specifically to a method and apparatus for full-waveform inversion wavefield reconstruction based on wavelet extension. Background Technology

[0002] Full waveform inversion is currently the most advanced technique in seismic data processing and modeling. This technique employs a numerical simulation method for seismic waves based on the wave equation, offering high computational accuracy and adaptability to complex tectonic velocity modeling and seismic imaging. However, in practical applications, this method is limited by computational efficiency and storage constraints, typically relying on the Born approximation. This assumption simplifies the full waveform inversion from a nonlinear problem to a linear one. When multiple minima exist, the inversion results become trapped in local minima, leading to failure. Therefore, it is necessary to mitigate the linear approximation characteristics of the Born approximation and fully consider the solution of nonlinear problems during the inversion process.

[0003] Based on this technical background, this invention studies a method and apparatus for full waveform inversion wavefield reconstruction based on wavelet extension. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a method and apparatus for full-waveform inversion wavefield reconstruction based on wavelet extension. This method obtains an extended seismic wavelet through deconvolution of the wavefield residuals and backpropagation and summation. The extended seismic wavelet is then used to reconstruct the nonlinear wavefield, reducing the problem of full-waveform inversion easily getting trapped in local extrema due to the linearization of seismic wave numerical simulation in conventional full-waveform inversion, thereby improving the reliability of the inversion.

[0005] To achieve the above objectives, a first aspect of the present invention provides a full-waveform inversion wavefield reconstruction method based on wavelet extension, comprising:

[0006] Wavefield simulation was performed using seismic wavelets to obtain simulated seismic records;

[0007] Based on the simulated seismic record, the wavefield residuals were calculated;

[0008] The wavefield residual is deconvolved to obtain the deconvolution result;

[0009] The deconvolution result is backpropagated into the wave field and the sum of each trace is performed to generate the extended wavelet corresponding to the remaining wave field.

[0010] The propagation of the wave field using the extended wavelet forms a reconstructed wave field, which in turn yields the final wave field.

[0011] A second aspect of the present invention provides a full-waveform inversion wavefield reconstruction apparatus based on wavelet spreading, comprising:

[0012] The wavefield simulation module is used to simulate the wavefield using seismic wavelets to obtain simulated seismic records.

[0013] The wavefield residual calculation module is used to calculate the wavefield residual based on the simulated seismic record;

[0014] The deconvolution operation module is used to perform deconvolution operation on the wavefield residual to obtain the deconvolution operation result;

[0015] The summation module is used to backpropagate the deconvolution operation result into the wave field and sum the results of each trace to generate the extended wavelet corresponding to the remaining wave field.

[0016] The reconstructed wavefield forming module is used to propagate the wavefield using the extended wavelet to form a reconstructed wavefield, thereby obtaining the final wavefield.

[0017] A third aspect of the present invention provides an electronic device, the electronic device comprising:

[0018] Memory, which stores executable instructions;

[0019] A processor that executes the executable instructions in the memory to implement the full waveform inversion wavefield reconstruction method based on wavelet extension as described in the first aspect.

[0020] 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 wavefield reconstruction method based on wavelet extension described in the first aspect.

[0021] The beneficial effects of this invention include:

[0022] The wavefield reconstruction method based on wavelet extension proposed in this invention obtains the extended seismic wavelet through the deconvolution of the wavefield residuals and backpropagation and summation. The extended seismic wavelet is used to reconstruct the nonlinear wavefield, which reduces the problem of the full waveform inversion easily getting trapped in local extrema caused by the linearization of seismic wave numerical simulation in conventional full waveform inversion, and improves the reliability of the inversion.

[0023] Other features and advantages of the present invention will be described in detail in the following detailed description section. Attached Figure Description

[0024] 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.

[0025] Figure 1 This is a schematic diagram of the process of the full waveform inversion wavefield reconstruction method based on wavelet extension proposed in this invention.

[0026] Figure 2 This is a flowchart illustrating a specific implementation of the wavelet extension-based full-waveform inversion wavefield reconstruction method proposed in this invention.

[0027] Figure 3 This is a schematic diagram illustrating the application effect of a specific implementation of the wavelet extension-based full waveform inversion wavefield reconstruction method proposed in this invention. Detailed Implementation

[0028] 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.

[0029] This invention provides a full-waveform inversion wavefield reconstruction method based on wavelet extension, such as... Figure 1 As shown, it includes:

[0030] Wavefield simulation was performed using seismic wavelets to obtain simulated seismic records;

[0031] Calculate wavefield residuals based on simulated seismic records;

[0032] The wavefield residual is deconvolved to obtain the deconvolution result.

[0033] The deconvolution result is backpropagated into the wave field, and the traces are summed to generate the extended wavelet corresponding to the remaining wave field.

[0034] The wave field is propagated using the extended wavelet to form a reconstructed wave field, which in turn yields the final wave field.

[0035] In this invention, an extended seismic wavelet is obtained by deconvolution of the wavefield residuals and backpropagation and summation. The extended seismic wavelet is used to reconstruct the nonlinear wavefield, which reduces the problem of the full waveform inversion easily getting trapped in local extrema caused by the linearization of the numerical simulation of seismic waves in conventional full waveform inversion, and improves the reliability of the inversion.

[0036] According to the present invention, wavefield simulation is performed using seismic wavelets, and the equations used to simulate seismic records are obtained as follows:

[0037] A(m)u=b,d=Pu;

[0038] Where A(m)u=b is the wave equation, u is the simulated wave field, b is the source wavelet, m is the underground model, d is the simulated seismic record, and P is the observation system.

[0039] According to the present invention, the formula used to calculate the wavefield residuals based on simulated seismic records is as follows:

[0040] δd=dd obs ;

[0041] Where, d obs This represents the actual earthquake record, and δd is the wavefield residual.

[0042] According to the present invention, the expression for reconstructing the wave field is:

[0043] A(m)u e =b+δb e ;

[0044] Where, δb e To extend the wavelet, u e This is the final wave field.

[0045] According to the present invention, the final wave field includes both linear and nonlinear wave fields;

[0046] The way to convert nonlinearity to linearity is as follows:

[0047] The objective function is expanded using a second-order Taylor expansion to obtain the second-order Taylor expansion.

[0048] Under the linear Born approximation condition, the third term of the second-order Taylor expansion is discarded.

[0049] Preferably, the expression for the objective function is:

[0050]

[0051] The second-order Taylor expansion is:

[0052]

[0053] According to the present invention, the linear Born approximation condition is:

[0054] δd=Lδm.

[0055] The present invention will be described in more detail below through embodiments.

[0056] Example 1:

[0057] like Figure 2 As shown, this embodiment proposes a full-waveform inversion wavefield reconstruction method based on wavelet extension, which introduces extended source wavelets to avoid the local extremum problem introduced by linearization;

[0058] The objective function for full waveform inversion based on wavefield error is:

[0059] A(m)u=b;

[0060] Where A(m)u=b is the wave equation, u is the simulated wave field, b is the source wavelet, and m is the subsurface model, representing the propagation velocity of seismic waves in the subsurface. Pu=d yields the simulated seismic record, where P is the observation system, and d is the... obs This is an actual earthquake record. The objective functional is expanded using Taylor, and only the second-order terms are taken, resulting in the following form:

[0061]

[0062] Under the linear Born approximation condition, δd = Lδm, the objective function discards the third term, and the inversion problem simplifies to a linearization problem, δm k+1 =[L T L] -1 δd * It is prone to getting trapped in local extrema;

[0063] The specific steps of this method are as follows:

[0064] Step 1: Calculate the simulated earthquake record using the equations A(m)u=b and d=Pu;

[0065] Step 2: Using the formula δd = dd obs Calculate the wavefield residual;

[0066] Step 3: Deconvolve the wavefield residuals to obtain δd e ;

[0067] Step 4: δd e Perform backpropagation of the wavefield and sum the results of each trace to generate the extended wavelet δb corresponding to the residual wavefield. e ;

[0068] Step 4: Utilizing the extended wavelet δb e Propagation of the wave field is carried out to form a reconstructed wave field A(m)u e =b+δb e The wave field u obtained at this time e It includes both linear and nonlinear wave fields.

[0069] In this embodiment, Figure 3 To illustrate the application effect of this invention, in the figure (a) is the actual wave field, (b) is the wave field obtained by using the Born approximation linearization, and (c) is the wave field obtained by this invention. As can be seen from the figure, when using the Born linear approximation, the obtained wave field only contains the wave field information of a single strong reflection, which is very different from the actual wave field. Using this wave field for full waveform inversion is prone to getting trapped in local extrema. The wave field obtained by this invention is similar to the actual wave field, containing both the main single reflection and multi-level scattering wave fields, thus ensuring that the full waveform inversion tends to the global optimal solution.

[0070] Example 2:

[0071] This embodiment provides a full-waveform inversion wavefield reconstruction method based on wavelet extension, such as... Figure 1 As shown, it includes:

[0072] Wavefield simulation was performed using seismic wavelets to obtain simulated seismic records;

[0073] Calculate wavefield residuals based on simulated seismic records;

[0074] The wavefield residual is deconvolved to obtain the deconvolution result.

[0075] The deconvolution result is backpropagated into the wave field, and the traces are summed to generate the extended wavelet corresponding to the remaining wave field.

[0076] The wave field is propagated using the extended wavelet to form a reconstructed wave field, and thus the final wave field is obtained.

[0077] In this embodiment, wavefield simulation is performed using seismic wavelets, and the equations used to simulate seismic records are obtained as follows:

[0078] A(m)u=b,d=Pu;

[0079] Where A(m)u=b is the wave equation, u is the simulated wave field, b is the source wavelet, m is the underground model, d is the simulated seismic record, and P is the observation system;

[0080] In this embodiment, the formula used to calculate the wavefield residual based on the simulated seismic record is as follows:

[0081] δd=dd obs ;

[0082] Where, d obs This is the actual earthquake record, where δd is the wavefield residual;

[0083] In this embodiment, the expression for reconstructing the wave field is:

[0084] A(m)u e =b+δb e ;

[0085] Where, δb e To extend the wavelet, u e For the final wave field;

[0086] In this embodiment, the final wave field includes both linear and nonlinear wave fields;

[0087] The way to convert nonlinearity to linearity is as follows:

[0088] The objective function is expanded using a second-order Taylor expansion to obtain the second-order Taylor expansion.

[0089] Under the linear Born approximation condition, the third term of the second-order Taylor expansion is discarded;

[0090] In this embodiment, the expression for the objective function is:

[0091]

[0092] The second-order Taylor expansion is:

[0093]

[0094] In this embodiment, the linear Born approximation condition is:

[0095] δd=Lδm.

[0096] Example 3:

[0097] This embodiment provides a full-waveform inversion wavefield reconstruction device based on wavelet spreading, including:

[0098] The wavefield simulation module is used to simulate the wavefield using seismic wavelets to obtain simulated seismic records.

[0099] The wavefield residual calculation module is used to calculate wavefield residuals based on simulated seismic records.

[0100] The deconvolution module is used to perform deconvolution operations on the wavefield residuals to obtain the deconvolution results.

[0101] The summation module is used to backpropagate the wavefield of the deconvolution operation result and sum the traces to generate the extended wavelet corresponding to the remaining wavefield.

[0102] The reconstructed wavefield forming module is used to propagate the wavefield using the extended wavelet to form a reconstructed wavefield, thereby obtaining the final wavefield.

[0103] In this embodiment, wavefield simulation is performed using seismic wavelets, and the equations used to simulate seismic records are obtained as follows:

[0104] A(m)u=b,d=Pu;

[0105] Where A(m)u=b is the wave equation, u is the simulated wave field, b is the source wavelet, m is the underground model, d is the simulated seismic record, and P is the observation system;

[0106] In this embodiment, the formula used to calculate the wavefield residual based on the simulated seismic record is as follows:

[0107] δd=dd obs ;

[0108] Where, d obs This is the actual earthquake record, where δd is the wavefield residual;

[0109] In this embodiment, the expression for reconstructing the wave field is:

[0110] A(m)u e =b+δb e ;

[0111] Where, δb e To extend the wavelet, u e For the final wave field;

[0112] In this embodiment, the final wave field includes both linear and nonlinear wave fields;

[0113] The way to convert nonlinearity to linearity is as follows:

[0114] The objective function is expanded using a second-order Taylor expansion to obtain the second-order Taylor expansion.

[0115] Under the linear Born approximation condition, the third term of the second-order Taylor expansion is discarded;

[0116] In this embodiment, the expression for the objective function is:

[0117]

[0118] The second-order Taylor expansion is:

[0119]

[0120] In this embodiment, the linear Born approximation condition is:

[0121] δd=Lδm.

[0122] Example 4:

[0123] This invention provides an electronic device including a memory and a processor, comprising:

[0124] Memory, which stores executable instructions;

[0125] The processor executes executable instructions in memory to implement a full-waveform inversion wavefield reconstruction method based on wavelet extension.

[0126] 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.

[0127] 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.

[0128] 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.

[0129] For a detailed description of this embodiment, please refer to the corresponding descriptions in the foregoing embodiments, which will not be repeated here.

[0130] Example 5:

[0131] This invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements a full-waveform inversion wavefield reconstruction method based on wavelet extension.

[0132] 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.

[0133] 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).

[0134] The wavefield reconstruction method based on wavelet extension proposed in the embodiments of the present invention obtains the extended seismic wavelet through the deconvolution of the wavefield residuals and backpropagation and summation. The extended seismic wavelet is used to reconstruct the nonlinear wavefield, which reduces the problem of the full waveform inversion easily getting trapped in local extrema caused by the linearization of seismic wave numerical simulation in conventional full waveform inversion, and improves the reliability of the inversion.

[0135] 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 wavefield reconstruction method based on wavelet spreading, characterized in that, include: Wavefield simulation was performed using seismic wavelets to obtain simulated seismic records; Based on the simulated seismic record, the wavefield residuals were calculated; The wavefield residual is deconvolved to obtain the deconvolution result; The deconvolution result is backpropagated into the wave field and the sum of each trace is performed to generate the extended wavelet corresponding to the remaining wave field. The propagation of the wave field using the extended wavelet forms a reconstructed wave field, which in turn yields the final wave field.

2. The method according to claim 1, characterized in that, Wavefield simulation using seismic wavelets yields the following equations for simulating seismic records: A(m)u=b,d=Pu; Where A(m)u=b is the wave equation, u is the simulated wave field, b is the source wavelet, m is the underground model, d is the simulated seismic record, and P is the observation system.

3. The method according to claim 2, characterized in that, Based on the simulated seismic record, the formula used to calculate the wavefield residual is: δd=d-d obs ; Where, d obs This represents the actual earthquake record, and δd is the wavefield residual.

4. The method according to claim 3, characterized in that, The expression for the reconstructed wave field is: A(m)u e =b+δb e ; Where, δb e To extend the wavelet, u e This is the final wave field.

5. The method according to claim 4, characterized in that, The final wavefield includes both linear and nonlinear wavefields; The method for converting nonlinearity to linearity is as follows: The objective function is expanded using a second-order Taylor expansion to obtain the second-order Taylor expansion. Under the linear Born approximation condition, the third term of the second-order Taylor expansion is discarded.

6. The method according to claim 5, characterized in that, The expression for the objective function is: The second-order Taylor expansion is:

7. The method according to claim 6, characterized in that, The linear Born approximation condition is: δd=Lδm.

8. A full-waveform inversion wavefield reconstruction device based on wavelet spreading, characterized in that, include: The wavefield simulation module is used to simulate the wavefield using seismic wavelets to obtain simulated seismic records. The wavefield residual calculation module is used to calculate the wavefield residual based on the simulated seismic record; The deconvolution operation module is used to perform deconvolution operation on the wavefield residual to obtain the deconvolution operation result; The summation module is used to backpropagate the deconvolution operation result into the wave field and sum the results of each trace to generate the extended wavelet corresponding to the remaining wave field. The reconstructed wavefield forming module is used to propagate the wavefield using the extended wavelet to form a reconstructed wavefield, thereby obtaining the final wavefield.

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 wavefield reconstruction method based on wavelet extension 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 wavefield reconstruction method based on wavelet extension as described in any one of claims 1-7.

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