Earthquake waveform inversion model construction, gradient shaping method, device and program product

Abstract

The present invention discloses a method, device and program product for constructing a seismic waveform inversion model and gradient shaping. The method includes: first constructing an initial model; then dividing seismic observation shot gather data into sub-shot gather data groups; then filtering the sub-shot gather data groups and seismic wavelets using a preset frequency band; performing wave equation forward modeling using the initial model and the filtered seismic wavelets, and obtaining the parameter gradient of the objective function with respect to the model parameters using the filtered sub-shot gather data groups and the forward modeling results; performing Fourier series expansion on the parameter gradient, intercepting the Fourier series coefficients of a finite number of terms, reconstructing the parameter gradient using inverse fast Fourier transform, and updating and iterating the model using the reconstructed parameter gradient until the iteration stop condition is satisfied, thereby obtaining the final inversion model. The present invention can effectively suppress the interference of high wavenumber components in the parameter gradient of the seismic inversion model while maintaining the original low wavenumber components in the parameter gradient.

Description

Technical Field

[0001] The present invention relates to the technical field of seismic waveform inversion, and particularly to a method for constructing a seismic waveform inversion model, a gradient shaping method, a device, and a program product. Background Art

[0002] The seismic full waveform inversion method is an important way to obtain underground model parameters. This method obtains the inversion result by solving the minimum difference between the observed data and the simulated data. This process is realized through local optimization iteration update. When performing local optimization, it is necessary to calculate the gradient of the objective function with respect to the model parameters of the model, and the model parameter gradient contains high-frequency / high-wave number perturbations that affect model update.

[0003] To suppress the high-frequency / high-wave number perturbations that affect model update in the model parameter gradient, the prior art usually uses Gaussian smoothing to smooth the model parameter gradient. This smoothing method does not distinguish between low-wave number and high-wave number components, but smooths all components synchronously, so that while the high-wave number component interference is suppressed, the low-wave number component is also suppressed to a certain extent, that is, the value of the low-wave number component decreases, resulting in a smaller update amount for the model, so that more iteration times are required to obtain a high-precision inversion model, thereby increasing the calculation time and reducing the calculation efficiency.

[0004] The prior art also uses a structure-guided smoothing method. This method requires estimating the dip angle first, and the dip angle calculation takes extra time, thus leading to an increase in the calculation time.

[0005] Therefore, there is an urgent need to invent an efficient method for shaping the gradient of the seismic waveform inversion model, so that the reconstructed model parameter gradient can effectively suppress the high-wave number component perturbation interference while maintaining the original low-wave number component in the model parameter gradient. Summary of the Invention

[0006] In view of this, embodiments of the present invention provide a method for constructing a seismic waveform inversion model, a gradient shaping method, a device, and a program product, which at least partially solve the problems existing in the prior art.

[0007] Other features and advantages of the present invention will become apparent through the following detailed description, or be partially learned through the practice of the present invention.

[0008] To achieve the above object, embodiments of the present invention provide the following technical solutions:

[0009] According to the first aspect of the embodiments of the present invention, a method for constructing a seismic waveform inversion model is provided, and the method includes:

[0010] Construct an initial model;

[0011] Divide the seismic observation shot gather data into at least two sub-shot gather data groups;

[0012] For each subset of shot gather data, filter the subset of shot gather data and the seismic wavelet using a preset frequency band to obtain the filtered subset of shot gather data and the seismic wavelet;

[0013] Perform wave equation forward modeling using the initial model and the filtered seismic wavelet to obtain a forward modeling result;

[0014] Use the filtered subset of shot gather data and the forward modeling result to obtain the parameter gradient of the objective function with respect to the model parameters;

[0015] Perform Fourier series expansion on the parameter gradient, intercept a finite number of Fourier series coefficients in the Fourier series expansion result, and reconstruct the parameter gradient using inverse fast Fourier transform;

[0016] Use the reconstructed parameter gradient to optimize the model to obtain a model update step size;

[0017] Update and iterate the model according to the model update step size until the iteration stop condition is satisfied to obtain an inversion model.

[0018] Further, performing Fourier series expansion on the parameter gradient, intercepting a finite number of Fourier series coefficients in the Fourier series expansion result, and reconstructing the parameter gradient using inverse fast Fourier transform includes:

[0019] Perform Fourier series expansion on the parameter gradient to obtain a Fourier series expansion result, where the Fourier coefficients in the Fourier series expansion result are calculated using fast Fourier transform;

[0020] According to the preset frequency band, intercept a finite number of Fourier series coefficients in the Fourier series expansion result;

[0021] Perform inverse fast Fourier transform processing on the finite number of Fourier series coefficients, and use the inverse Fourier transform result as an approximation of the reconstructed model parameter gradient to obtain the reconstructed parameter gradient.

[0022] Further, using the filtered subset of shot gather data and the forward modeling result to obtain the parameter gradient of the objective function with respect to the model parameters includes:

[0023] Use the filtered subset of shot gather data and the forward modeling result to calculate the corresponding wavefield residual;

[0024] According to the wavefield residual, obtain the objective function corresponding to the initial model;

[0025] Perform backpropagation wavefield simulation using the objective function, and calculate the parameter gradient of the objective function with respect to the model parameters according to the simulation result.

[0026] Further, the seismic observation shot gather data is divided into at least two sub-shot gather data groups, including:

[0027] Randomly divide the seismic observation shot gather data into at least two sub-shot gather data groups according to the preset number of subsets.

[0028] Further, the preset frequency band includes a low frequency band, a medium frequency band, and a high frequency band.

[0029] Further, the model parameter is a velocity parameter.

[0030] According to the second aspect of the embodiments of the present invention, a method for shaping the gradient of a seismic waveform inversion model is provided. The method includes:

[0031] Perform Fourier series expansion processing on the model parameter gradient in the seismic waveform inversion model, intercept a finite number of Fourier series coefficients in the Fourier series expansion result, and reconstruct the parameter gradient using the inverse fast Fourier transform.

[0032] Further, performing Fourier series expansion processing on the model parameter gradient in the seismic waveform inversion model, intercepting a finite number of Fourier series coefficients in the Fourier series expansion result, and reconstructing the parameter gradient using the inverse fast Fourier transform includes:

[0033] Perform Fourier series expansion processing on the model parameter gradient in the seismic waveform inversion model to obtain a Fourier series expansion result, where the Fourier coefficients in the Fourier series expansion result are calculated by the fast Fourier transform;

[0034] Intercept a finite number of Fourier series coefficients in the Fourier series expansion result according to the filtering frequency band of the seismic observation data;

[0035] Perform inverse fast Fourier transform processing on the Fourier series coefficients, and use the inverse Fourier transform result as an approximation of the reconstructed model parameter gradient to obtain the reconstructed model parameter gradient.

[0036] According to the third aspect of the embodiments of the present invention, a device is provided. The device includes: a processor and a memory;

[0037] The memory is used to store one or more program instructions;

[0038] The processor is used to run one or more program instructions to execute the steps of a method for constructing a seismic waveform inversion model or a method for shaping the gradient of a seismic waveform inversion model as described in any one of the above.

[0039] According to a fourth aspect of the embodiments of the present invention, there is provided a computer program product, which includes a computing program stored on a non-transitory computer-readable storage medium. The computer program includes program instructions that, when executed by a computer, cause the computer to implement the steps of a method for constructing a seismic waveform inversion model or a method for shaping the gradient of a seismic waveform inversion model as described in any one of the above.

[0040] The embodiments of the present invention have the following advantages:

[0041] In the embodiments of the present invention, the gradient of the inversion model parameters is shaped and smoothed by Fourier series expansion. While suppressing high-wave number interference, it can effectively retain the original low-wave number components of the gradient, which helps to obtain a high-precision inversion model. At the same time, in the embodiments of the present invention, the Fourier coefficients are estimated and the gradient is reconstructed by means of the forward Fourier transform and the inverse Fourier transform respectively. The calculation efficiency is high, which can effectively save the calculation time and improve the calculation efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only exemplary, and for those of ordinary skill in the art, other implementation drawings can be obtained according to the provided drawings without creative efforts.

[0043] Figure 1 It is a schematic flowchart of a method for constructing a seismic waveform inversion model provided by an embodiment of the present invention;

[0044] Figure 2 It is a schematic block diagram of the principle of a method for constructing a seismic waveform inversion model provided by an embodiment of the present invention;

[0045] Figure 3 It is a schematic comparison diagram of the seismic waveform inversion theoretical model and the initial model provided by an embodiment of the present invention;

[0046] Figure 4 It is a schematic comparison diagram of the model parameter gradients under different smoothing methods provided by an embodiment of the present invention;

[0047] Figure 5 It is a schematic comparison diagram of the gradient curves under different smoothing methods provided by an embodiment of the present invention;

[0048] Figure 6 It is a schematic comparison diagram of the seismic waveform inversion models under different smoothing methods provided by an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0049] To enable those skilled in the art to better understand the solution of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the scope of protection of the present invention.

[0050] It should be noted that the terms "include" and "have" and any variations thereof are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or device that includes a series of steps or units does not necessarily have to be limited to those steps or units clearly listed, but may include other steps or units not clearly listed or inherent to these processes, methods, products, or devices.

[0051] In order to solve the defect that the existing inversion model gradient perturbation suppression method cannot effectively suppress the perturbation interference of high wavenumber components while maintaining the original low wavenumber components in the model parameter gradient, the present invention provides a method for constructing a seismic waveform inversion model and a method for shaping the gradient of a seismic waveform inversion model.

[0052] Figure 1 The figure shows a flowchart of a method for constructing a seismic waveform inversion model according to an embodiment of the present invention.

[0053] As Figure 1 shown, the method for constructing a seismic waveform inversion model according to an embodiment of the present invention may include step S100, step S200, step S300, step S400, step S500, step S600, step S700, and step S800.

[0054] Referring to Figure 2 , the method for constructing a seismic waveform inversion model provided by an embodiment of the present invention specifically includes:

[0055] In step S100, an initial model is constructed.

[0056] Figure 3 The figure shows a comparison diagram of the seismic waveform inversion theoretical model constructed according to the velocity parameter and the initial model, where Figure 3 (a) is the theoretical model, Figure 3 (b) is the initial model, the abscissa is the distance, the ordinate is the depth, and the shade represents the velocity.

[0057] Next, in step S200, the seismic observation shot gather data is divided into at least two sub-shot gather data groups.

[0058] Specifically, the above steps specifically include:

[0059] According to the preset number of subsets, randomly divide the seismic observation shot gather data into at least two sub-shot gather data groups.

[0060] In the embodiment of the present invention, by dividing the seismic observation data into sub-shot gather data groups and using fewer shot gather data to invert the model, the requirement for computer hardware can be reduced, and the calculation efficiency can be effectively improved.

[0061] In step S300, for each sub-shot gather data group, use the preset frequency band to filter the sub-shot gather data group and the corresponding seismic wavelet to obtain the filtered sub-shot gather data group and seismic wavelet.

[0062] Specifically, the above preset frequency band includes a low frequency band, a medium frequency band, and a high frequency band.

[0063] In step S400, use the above initial model and the filtered seismic wavelet to perform wave equation forward modeling to obtain a forward modeling result.

[0064] In step S500, use the above filtered sub-shot gather data group and the above forward modeling result to obtain the parameter gradient of the objective function with respect to the model parameters.

[0065] Specifically, the above steps specifically include:

[0066] First, use the above filtered sub-shot gather data group and the above forward modeling result to calculate the corresponding wave field residual;

[0067] Then, according to the wave field residual, obtain the objective function corresponding to the initial model;

[0068] Then use the objective function to perform backpropagation wave field simulation;

[0069] Finally, calculate the parameter gradient of the objective function with respect to the model parameters according to the simulation result.

[0070] Preferably, the above model parameter is a model velocity parameter.

[0071] In step S600, perform Fourier series expansion processing on the parameter gradient, intercept the Fourier series coefficients of a finite number of terms in the Fourier series expansion result, and use the inverse fast Fourier transform to reconstruct the parameter gradient.

[0072] Specifically, the above steps specifically include:

[0073] First, perform Fourier series expansion processing on the parameter gradient to obtain a Fourier series expansion result, wherein the Fourier coefficients in the above Fourier series expansion result are calculated by the fast Fourier transform;

[0074] Then, according to the above preset frequency band, finite-term Fourier series coefficients are intercepted from the result of Fourier series expansion. Among them, the level of the preset frequency band for filtering is positively correlated with the number of intercepted Fourier series coefficients. If the filtering frequency band is a high-frequency band, a relatively large number of Fourier series coefficients are intercepted.

[0075] Finally, perform an inverse fast Fourier transform on the finite-term Fourier series coefficients, and use the result of the inverse Fourier transform as an approximation of the reconstructed model parameter gradient to obtain the reconstructed parameter gradient.

[0076] Figure 4 The figure shows a comparison diagram of model parameter gradients under different smoothing methods, where Figure 4 (a) is the model parameter gradient without smoothing, Figure 4 (b) is the model parameter gradient after smoothing using a Gaussian smoothing factor with values (0.2, 0.1), Figure 4 (c) is the model parameter gradient after smoothing using a Gaussian smoothing factor with values (0.35, 0.1), Figure 4 (d) is the model parameter gradient after gradient shaping using the Fourier series method provided by the present invention. The abscissa is Distance, the ordinate is Depth, and the shade represents Gradient.

[0077] Figure 5 The figure shows a comparison diagram of gradient curves under different smoothing methods, where Figure 5 (a) corresponds to Figure 4 the gradient curve at the position of line segment A in Figure 5 (b) corresponds to Figure 4 the gradient curve at the position of line segment B in Figure 5 In the solid line is the model parameter gradient without smoothing, the single-dot dashed line is the gradient curve after smoothing using a Gaussian smoothing factor with values (0.2, 0.1), the double-dot dashed line is the gradient curve after smoothing using a Gaussian smoothing factor with values (0.35, 0.1), and the dashed line is the gradient curve after gradient shaping using the Fourier series method provided by the present invention. The abscissa is Distance, and the ordinate is Gradient Values.

[0078] In the embodiment of the present invention, through the forward and inverse fast Fourier transforms, the reconstruction of the model parameter gradient is realized. The reconstructed model parameter gradient not only retains the original low-wave number components in the gradient but also effectively suppresses the perturbation interference of the high-wave number components, and at the same time has the advantage of high calculation efficiency.

[0079] Next, in step S700, the reconstructed parameter gradient is used to optimize the model to obtain the model update step size.

[0080] In step S800, the model is updated iteratively according to the above model update step size until the model meets the iteration stop condition, and an inversion model with completed iteration is obtained.

[0081] Figure 6 The figure shows a comparison diagram of seismic waveform inversion models under different smoothing methods, where Figure 6 (a) is the seismic waveform inversion model obtained by iterative gradient smoothing using Gaussian smoothing, Figure 6 (b) is the seismic waveform inversion model obtained by iterative gradient shaping using the Fourier series method provided by the present invention. The abscissa is distance, the ordinate is depth, and the depth represents velocity.

[0082] In the embodiment of the present invention, the above process is repeated using the sub-shot gather data sets of each different filtering frequency band to update and iterate the inversion model, and finally an inversion model of the seismic waveform with completed iteration is constructed.

[0083] In addition, the embodiment of the present invention also provides a method for shaping the gradient of a seismic waveform inversion model. The above method includes:

[0084] During the update and iteration process of the seismic waveform inversion model, Fourier series expansion processing is performed on the model parameter gradient in the seismic waveform inversion model. A finite number of Fourier series coefficients are intercepted from the Fourier series expansion result, and the inverse fast Fourier transform is used to reconstruct the parameter gradient to obtain the reconstructed model parameter gradient.

[0085] Specifically, the above steps include:

[0086] First, Fourier series expansion processing is performed on the model parameter gradient in the seismic waveform inversion model to obtain the Fourier series expansion result, where the Fourier coefficients in the above Fourier series expansion result are calculated by the fast Fourier transform;

[0087] Then, according to the filtering frequency band of the seismic observation data, a finite number of Fourier series coefficients are intercepted from the Fourier series expansion result;

[0088] Finally, inverse fast Fourier transform processing is performed on the Fourier series coefficients, and the inverse Fourier transform result is used as an approximation of the reconstructed model parameter gradient to obtain the reconstructed model parameter gradient.

[0089] In addition, the embodiment of the present invention also provides a device, which includes: a processor and a memory; the memory is used to store one or more program instructions; the processor is used to run one or more program instructions to execute the steps of a method for constructing a seismic waveform inversion model or a method for shaping the gradient of a seismic waveform inversion model as described above.

[0090] In addition, an embodiment of the present invention further provides a computer program product, which includes computer program instructions. When the computer program instructions are executed by a processor, the steps of a method for constructing a seismic waveform inversion model or a method for shaping the gradient of a seismic waveform inversion model as described above are implemented.

[0091] The method for constructing a seismic waveform inversion model, the method for shaping the gradient, the device and the program product provided by the embodiment of the present invention have at least the following advantages:

[0092] In the embodiment of the present invention, the gradient of the inversion model parameters is shaped and smoothed by Fourier series expansion, which can suppress high wavenumber interference while effectively retaining the original low wavenumber components of the gradient, helping to obtain a high-precision inversion model. At the same time, in the embodiment of the present invention, the Fourier coefficient estimation and gradient reconstruction are respectively realized by means of the forward Fourier transform and the inverse Fourier transform, with high calculation efficiency, which can effectively save calculation time and improve calculation efficiency.

[0093] In an embodiment of the present invention, the processor may be an integrated circuit chip with signal processing capabilities. The processor may be a general-purpose processor, a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components. It can implement or execute the various methods, steps, and logic block diagrams disclosed in the embodiments of the present invention. The general-purpose processor may be a microprocessor or the processor may also be any conventional processor, etc. The steps of the method disclosed in combination with the embodiments of the present invention may be directly embodied as being executed by a hardware decoding processor, or executed by a combination of hardware and software modules in the decoding processor. The software module may be located in a mature storage medium in the art such as random access memory, flash memory, read-only memory, programmable read-only memory, or electrically erasable programmable memory, registers, etc. The processor reads the information in the storage medium and completes the steps of the above method in combination with its hardware. The storage medium may be a memory, for example, it may be a volatile memory or a non-volatile memory, or may include both volatile and non-volatile memories. Among them, the non-volatile memory may be a read-only memory (ROM), a programmable read-only memory (PROM), an erasable programmable read-only memory (EPROM), an electrically erasable programmable read-only memory (EEPROM), or a flash memory. The volatile memory may be a random access memory (RAM), which is used as an external cache. By way of example but not limitation, many forms of RAM are available, such as static random access memory (SRAM), dynamic random access memory (DRAM), synchronous dynamic random access memory (SDRAM), double data rate synchronous dynamic random access memory (DDR SDRAM), enhanced synchronous dynamic random access memory (ESDRAM), synchlink dynamic random access memory (SLDRAM), and direct rambus random access memory (DRRAM).The storage media described in the embodiments of the present invention are intended to include, but are not limited to, these and any other suitable types of memories. Those skilled in the art should be able to realize that in one or more of the above examples, the functions described in the present invention can be implemented by a combination of hardware and software. When applying software, the corresponding functions can be stored in a computer-readable medium or transmitted as one or more instructions or codes on a computer-readable medium. Computer-readable media include computer storage media and communication media, where communication media include any medium that facilitates the transfer of a computer program from one place to another. The storage medium can be any available medium accessible by a general-purpose or special-purpose computer. Although the present invention has been described in detail with general descriptions and specific embodiments above, modifications or improvements can be made based on the present invention, which are obvious to those skilled in the art. Therefore, these modifications or improvements made without departing from the spirit of the present invention all fall within the scope of the present invention claimed.

Claims

1. A method for constructing a seismic waveform inversion model, characterized in that: The method comprises: Build an initial model; Dividing the seismic observation shot gather data into at least two sub-shot gather data groups; For each sub-shot collection data group, filtering the sub-shot collection data group and the seismic wavelet is performed using a preset frequency band to obtain a filtered sub-shot collection data group and a seismic wavelet; Using the initial model and the filtered seismic wavelet to perform wave equation forward modeling to obtain a forward modeling result; Using the filtered sub-shot collection data set and the forward modeling result, a parameter gradient of an objective function to a model parameter is obtained; Performing Fourier series expansion processing on the parameter gradient, intercepting a finite number of Fourier series coefficients in the Fourier series expansion result, and reconstructing the parameter gradient using inverse fast Fourier transform; Use the reconstructed parameter gradient to optimize the model and obtain the model update step size; The model is updated and iterated according to the model update step size until an iteration stop condition is met to obtain an inversion model.

2. A method for constructing a seismic waveform inversion model according to claim 1, characterized in that: Performing Fourier series expansion processing on the parameter gradient, intercepting the Fourier series coefficients of a finite term in the Fourier series expansion result, and reconstructing the parameter gradient using inverse fast Fourier transform, including: Performing Fourier series expansion processing on the parameter gradient to obtain a Fourier series expansion result, wherein the Fourier coefficients in the Fourier series expansion result are calculated by fast Fourier transform; According to the preset frequency band, extracting a finite number of Fourier series coefficients from the Fourier series expansion result; The inverse fast Fourier transform is performed on the finite-term Fourier series coefficients, and the inverse Fourier transform result is used as the approximate value of the gradient of the reconstructed model parameters to obtain the reconstructed parameter gradient.

3. A method for constructing a seismic waveform inversion model according to claim 1, characterized in that: Using the filtered sub-shot collection data set and the forward modeling result, the parameter gradient of the objective function to the model parameter is obtained, including: Using the filtered sub-shot collection data set and the forward modeling result, a corresponding wave field residual is calculated; According to the wave field residual, an objective function corresponding to the initial model is obtained; The objective function is used to simulate the return wave field, and the parameter gradient of the objective function to the model parameter is calculated according to the simulation result.

4. A method for constructing a seismic waveform inversion model according to claim 1, characterized in that: The seismic observation shot gather data are divided into at least two sub-shot gather data groups, including: The seismic observation shot gather data are randomly divided into at least two sub-shot gather data groups according to the preset number of subsets.

5. A method for constructing a seismic waveform inversion model according to claim 2, characterized in that: The preset frequency bands include a low frequency band, a middle frequency band and a high frequency band.

6. A method for constructing a seismic waveform inversion model according to claim 1, characterized in that: The model parameter is a speed parameter.

7. A seismic waveform inversion model gradient shaping method, characterized in that: The method comprises: A Fourier series expansion process is performed on the model parameter gradients in the seismic waveform inversion model constructed by the seismic waveform inversion model construction method described in any one of claims 1 to 6, a finite number of Fourier series coefficients are truncated from the Fourier series expansion result, and the parameter gradients are reconstructed using a fast Fourier inverse transform.

8. A seismic waveform inversion model gradient shaping method as claimed in claim 7, characterized in that: The Fourier series expansion processing is performed on the model parameter gradient in the seismic waveform inversion model, and the Fourier series coefficients of the finite items are intercepted in the Fourier series expansion result, and the parameter gradient is reconstructed using the fast Fourier inverse transform, including: Performing Fourier series expansion processing on the model parameter gradient in the seismic waveform inversion model to obtain a Fourier series expansion result, wherein the Fourier coefficients in the Fourier series expansion result are calculated by fast Fourier transform; According to the filtering frequency band of the seismic observation data, truncating the Fourier series coefficients of a finite number of items in the Fourier series expansion result; A fast inverse Fourier transform process is performed on the Fourier series coefficients, and the inverse Fourier transform result is used as an approximate value of the gradient of the reconstructed model parameter to obtain the gradient of the reconstructed model parameter.

9. A device, characterized in that: The device comprises: a processor and a memory; The memory is used to store one or more program instructions; The processor is used to run one or more program instructions to execute the steps of a seismic waveform inversion model construction method as described in any one of claims 1 to 6 or a seismic waveform inversion model gradient shaping method as described in any one of claims 7 to 8.

10. A computer program product, characterized in that The computer program product includes computer program instructions, which, when executed by a processor, implement the steps of a seismic waveform inversion model construction method as described in any one of claims 1 to 6 or a seismic waveform inversion model gradient shaping method as described in any one of claims 7 to 8.

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