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

Abstract

The invention discloses a seismic waveform inversion model construction method, a seismic waveform inversion model gradient shaping method, equipment and a program product. The method comprises the following steps: firstly, constructing an initial model; dividing seismological observation shot gather data into sub shot gather data groups; then filtering processing is carried out on the sub-shot gather data set and the seismic wavelets by using a preset frequency band; performing wave equation forward modeling processing by using the initial model and the filtered seismic wavelets, and obtaining a parameter gradient of a target function to model parameters by using the filtered sub-shot gather data set and a forward modeling result; and performing Fourier series expansion on the parameter gradient, intercepting a Fourier series coefficient of a finite term, reconstructing the parameter gradient by using fast Fourier inversion, and performing updating iteration on the model by using the reconstructed parameter gradient until an iteration stop condition is met, thereby obtaining a final inversion model. According to the method, the original low-wave-number component in the parameter gradient can be kept while the interference of the high-wave-number component in the parameter gradient of the seismic inversion model is effectively suppressed.

Description

Technical Field

[0001] The present invention relates to the technical field of seismic waveform inversion, and in particular to a seismic waveform inversion model construction, 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 achieved through local optimization iterative update. When doing local optimization, it is necessary to calculate the model parameter gradient of the objective function to the model. The model parameter gradient contains high-frequency / high-wavenumber disturbances that affect the model update.

[0003] In order to suppress the high-frequency / high-wavenumber disturbances in the model parameter gradient that affect the model update, the existing technology usually uses Gaussian smoothing to smooth the model parameter gradient. This smoothing method does not distinguish between low-wavenumber and high-wavenumber components, but smoothes all components simultaneously, so that the interference of high-wavenumber components is suppressed while the low-wavenumber components are also suppressed to a certain extent, that is, the value of the low-wavenumber component is reduced, which makes the update amount of the model smaller, so that more iterations 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-oriented smoothing method, which requires estimating the inclination angle first, and the calculation of the inclination angle takes extra time, which in turn increases the calculation time.

[0005] Therefore, it is urgent to invent an efficient seismic waveform inversion model gradient shaping method so that the reconstructed model parameter gradient can effectively suppress the disturbance of high wavenumber components while maintaining the original low wavenumber components in the model parameter gradient. Summary of the invention

[0006] In view of this, an embodiment of the present invention provides a seismic waveform inversion model construction, gradient shaping method, device and 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 from the following detailed description, or may be learned in part by practice of the present invention.

[0008] In order to achieve the above purpose, the embodiment of the present invention provides the following technical solutions:

[0009] According to a first aspect of an embodiment of the present invention, a method for constructing a seismic waveform inversion model is provided, the method comprising:

[0010] Build an initial model;

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

[0012] 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;

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

[0014] 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;

[0015] 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;

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

[0017] 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.

[0018] Further, the parameter gradient is subjected to Fourier series expansion processing, a finite number of Fourier series coefficients are intercepted from the Fourier series expansion result, and the parameter gradient is reconstructed using an inverse fast Fourier transform, including:

[0019] 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;

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

[0021] 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.

[0022] Further, the parameter gradient of the objective function to the model parameter is obtained by using the filtered sub-shot collection data set and the forward modeling result, including:

[0023] Using the filtered sub-shot collection data set and the forward modeling result, a corresponding wave field residual is calculated;

[0024] According to the wave field residual, an objective function corresponding to the initial model is obtained;

[0025] 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.

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

[0027] 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.

[0028] Furthermore, the preset frequency band includes a low frequency band, a middle frequency band and a high frequency band.

[0029] Furthermore, the model parameter is a speed parameter.

[0030] According to a second aspect of an embodiment of the present invention, a seismic waveform inversion model gradient shaping method is provided, the method comprising:

[0031] Fourier series expansion is performed on the model parameter gradient in the seismic waveform inversion model. A finite number of Fourier series coefficients are extracted from the Fourier series expansion result, and the parameter gradient is reconstructed using the inverse fast Fourier transform.

[0032] Furthermore, Fourier series expansion processing is performed on the model parameter gradient in the seismic waveform inversion model, and the Fourier series coefficients of a finite term are intercepted in the Fourier series expansion result, and the parameter gradient is reconstructed using the fast Fourier inverse transform, including:

[0033] 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;

[0034] 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;

[0035] A fast inverse Fourier transform 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.

[0036] According to a third aspect of an embodiment of the present invention, a device is provided, the device comprising: 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 seismic waveform inversion model construction method as described in any of the above items or a seismic waveform inversion model gradient shaping method as described in any of the above items.

[0039] According to a fourth aspect of an embodiment of the present invention, a computer program product is provided, the computer program product comprising a computer program stored on a non-transitory computer-readable storage medium, the computer program comprising program instructions, which, when executed by a computer, enable the computer to implement the steps of a seismic waveform inversion model construction method as described in any one of the above items or a seismic waveform inversion model gradient shaping method as described in any one of the above items.

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

[0041] The embodiment of the present invention shapes and smoothes the gradient of the inversion model parameters through Fourier series expansion, which can suppress high-wavenumber interference while effectively retaining the original low-wavenumber component of the gradient, which is helpful to obtain a high-precision inversion model; at the same time, the embodiment of the present invention uses Fourier forward transform and inverse transform to respectively realize Fourier coefficient estimation and gradient reconstruction, which has high computational efficiency, can effectively save computing time and improve computing efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] In order to more clearly illustrate the implementation methods of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for the implementation methods or the description of the prior art. Obviously, the drawings in the following description are only exemplary, and for ordinary technicians in this field, other implementation drawings can be derived from the provided drawings without creative work.

[0043] Figure 1 A schematic diagram of a flow chart of a method for constructing a seismic waveform inversion model provided by an embodiment of the present invention;

[0044] Figure 2 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 A schematic diagram showing a comparison between a seismic waveform inversion theoretical model and an initial model provided in an embodiment of the present invention;

[0046] Figure 4 A schematic diagram of comparing model parameter gradients under different smoothing methods provided in an embodiment of the present invention;

[0047] Figure 5 A schematic diagram showing a comparison of gradient curves under different smoothing methods provided in an embodiment of the present invention;

[0048] Figure 6 A schematic diagram for comparing seismic waveform inversion models under different smoothing methods provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0049] In order to enable those skilled in the art to better understand the scheme of the present invention, the technical scheme in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should 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 inclusions. For example, a process, method, system, product or apparatus comprising a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to these processes, methods, products or apparatus.

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

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

[0053] like Figure 1 As shown, the seismic waveform inversion model construction method according to the 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] refer to Figure 2 The seismic waveform inversion model construction method provided by the embodiment of the present invention specifically includes:

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

[0056] Figure 3 The figure shows the comparison between the seismic waveform inversion theoretical model constructed based on velocity parameters and the initial model, where: Figure 3 (a) is the theoretical model, Figure 3 (b) is the initial model, the horizontal axis is distance (Distance), the vertical axis is depth (Depth), and the depth represents the velocity (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 include:

[0059] 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.

[0060] The embodiment of the present invention divides the seismic observation data into sub-shot gather data groups and uses less shot gather data to invert the model, which can reduce the demand for computer hardware and effectively improve the computing efficiency.

[0061] In step S300, for each sub-shot collection data group, the sub-shot collection data group and the corresponding seismic wavelet are filtered using a preset frequency band to obtain a filtered sub-shot collection data group and a filtered seismic wavelet.

[0062] Specifically, the above preset frequency bands include a low frequency band, a middle frequency band and a high frequency band.

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

[0064] In step S500, the parameter gradient of the objective function with respect to the model parameters is obtained using the filtered sub-shot collection data set and the forward modeling results.

[0065] Specifically, the above steps include:

[0066] First, the corresponding wave field residual is calculated using the filtered sub-shot data set and the forward modeling results;

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

[0068] Then the objective function is used to simulate the return wave field;

[0069] Finally, the parameter gradient of the objective function to the model parameters is calculated based on the simulation results.

[0070] Preferably, the above-mentioned model parameters are model speed parameters.

[0071] In step S600, Fourier series expansion processing is performed on the parameter gradient, a finite number of Fourier series coefficients are intercepted from the Fourier series expansion result, and the parameter gradient is reconstructed using inverse fast Fourier transform.

[0072] Specifically, the above steps include:

[0073] Firstly, the parameter gradient is subjected to Fourier series expansion processing to obtain a Fourier series expansion result, wherein the Fourier coefficients in the Fourier series expansion result are obtained by fast Fourier transform calculation;

[0074] Then, according to the above preset frequency band, a finite number of Fourier series coefficients are intercepted from the Fourier series expansion result, wherein the preset frequency band of the filter is positively correlated with the number of Fourier series coefficients intercepted. If the filter frequency band is a high frequency band, more Fourier series coefficients are intercepted.

[0075] Finally, a fast inverse 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 reconstructed model parameter gradient to obtain the reconstructed parameter gradient.

[0076] Figure 4 The figure shows the gradient comparison of model parameters 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 of (0.2, 0.1). Figure 4 (c) is the model parameter gradient after smoothing using a Gaussian smoothing factor of (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 horizontal axis is distance (Distance), the vertical axis is depth (Depth), and the depth represents the gradient (Gradient).

[0077] Figure 5 The figure shows the comparison of gradient curves under different smoothing methods, where: Figure 5 (a) corresponds to Figure 4 The gradient curve of the position of line segment A in Figure 5 (b) corresponds to Figure 4 The gradient curve of the position of line segment B in Figure 5 The solid line in the figure is the model parameter gradient without smoothing, the single dotted line is the gradient curve after smoothing with a Gaussian smoothing factor of (0.2, 0.1), the double dotted line is the gradient curve after smoothing with a Gaussian smoothing factor of (0.35, 0.1), the dotted line is the gradient curve after gradient shaping using the Fourier series method provided by the present invention, the horizontal axis is the distance (Distance), and the vertical axis is the gradient value (Gradient Values).

[0078] The embodiment of the present invention realizes the reconstruction of the model parameter gradient through the fast Fourier transform and inverse transform. The reconstructed model parameter gradient not only maintains the original low-wavenumber component in the gradient, but also effectively suppresses the disturbance interference of the high-wavenumber component, and has the advantage of high computational efficiency.

[0079] Next, in step S700, the model is optimized using the reconstructed parameter gradient to obtain a model update step size.

[0080] In step S800, the model is updated and iterated according to the above-mentioned model update step size until the model meets the iteration stop condition, thereby obtaining an iteratively completed inversion model.

[0081] Figure 6 The figure shows the comparison of seismic waveform inversion models under different smoothing methods, where: Figure 6 (a) is the seismic waveform inversion model obtained by gradient smoothing using Gaussian smoothing. Figure 6 (b) is a seismic waveform inversion model obtained by iteration after gradient shaping using the Fourier series method provided by the present invention, wherein the horizontal axis is distance (Distance), the vertical axis is depth (Depth), and the depth represents velocity (Velocity).

[0082] The embodiment of the present invention uses the sub-shot collection data groups of different filtering frequency bands to repeat the above process to iterate the inversion model, and finally constructs an iteratively completed seismic waveform inversion model.

[0083] In addition, an embodiment of the present invention further provides a seismic waveform inversion model gradient shaping method, the method comprising:

[0084] In the process of updating and iterating the seismic waveform inversion model, the model parameter gradient in the seismic waveform inversion model is subjected to Fourier series expansion processing, the Fourier series coefficients of a finite number of items are intercepted in the Fourier series expansion result, and the parameter gradient is reconstructed using the fast Fourier inverse transform to obtain the reconstructed model parameter gradient.

[0085] Specifically, the above steps include:

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

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

[0088] Finally, the Fourier series coefficients are processed by inverse fast Fourier transform, and the inverse Fourier transform result is used as the approximate value of the gradient of the reconstructed model parameters to obtain the gradient of the reconstructed model parameters.

[0089] In addition, an 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 seismic waveform inversion model construction method as described above or a seismic waveform inversion model gradient shaping method as described above.

[0090] In addition, an embodiment of the present invention also provides a computer program product, which includes computer program instructions, and when the computer program instructions are executed by a processor, they implement the steps of a seismic waveform inversion model construction method as described above or a seismic waveform inversion model gradient shaping method as described above.

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

[0092] The embodiment of the present invention shapes and smoothes the gradient of the inversion model parameters through Fourier series expansion, which can suppress high-wavenumber interference while effectively retaining the original low-wavenumber component of the gradient, which is helpful to obtain a high-precision inversion model; at the same time, the embodiment of the present invention uses Fourier forward transform and inverse transform to respectively realize Fourier coefficient estimation and gradient reconstruction, which has high computational efficiency, can effectively save computing time and improve computing efficiency.

[0093] In the embodiment of the present invention, the processor may be an integrated circuit chip with signal processing capability. 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 gates or transistor logic devices, or discrete hardware components. The methods, steps, and logic block diagrams disclosed in the embodiments of the present invention may be implemented or executed. The general-purpose processor may be a microprocessor or the processor may be any conventional processor, etc. The steps of the method disclosed in the embodiment of the present invention may be directly embodied as being executed by a hardware decoding processor, or may be executed by a combination of hardware and software modules in a decoding processor. The software module may be located in a mature storage medium in the art such as a random access memory, a flash memory, a read-only memory, a programmable read-only memory, or an electrically erasable programmable memory, a register, 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, a volatile memory or a non-volatile memory, or may include both volatile and non-volatile memories. Among them, the non-volatile memory can 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 can 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 (DDRSDRAM), enhanced synchronous dynamic random access memory (ESDRAM), synchronous link dynamic random access memory (SLDRAM) and direct memory bus random access memory (Direct Rambus RAM, DRRAM).The storage medium described in the embodiment of the present invention is intended to include but is not limited to these and any other suitable types of memory. Those skilled in the art should be aware 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 the software is applied, the corresponding function 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, wherein the communication medium includes any medium that is convenient for transmitting a computer program from one place to another. The storage medium can be any available medium that a general or special-purpose computer can access. Although the present invention has been described in detail above with general descriptions and specific embodiments, it is obvious to those skilled in the art that some modifications or improvements can be made to it on the basis of the present invention. Therefore, these modifications or improvements made on the basis of not departing from the spirit of the present invention all belong to the scope of protection claimed in the present invention.

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: Fourier series expansion is performed on the model parameter gradient in the seismic waveform inversion model. A finite number of Fourier series coefficients are extracted from the Fourier series expansion result, and the parameter gradient is reconstructed using the inverse fast Fourier 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.

Images