Finite difference contrast source inversion method and device based on hyper-memory mixed conjugate gradient method, electronic equipment and medium
By updating the contrast source and contrast using the super-memory hybrid conjugate gradient method, the problems of high computational cost and slow convergence speed in the finite difference contrast source inversion algorithm are solved, achieving high accuracy and speed in the inversion model.
Patent Information
- Application Number
- CN202410477635.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-04-19
- Publication Date
- 2025-10-24
AI Technical Summary
Among existing full waveform inversion methods, the finite difference comparison source inversion algorithm suffers from high computational cost and slow convergence speed, especially when optimizing with Newton's method, which consumes a lot of memory.
The super-memory hybrid conjugate gradient method is adopted. The initial contrast source and contrast are obtained through wavefield backpropagation, the super-memory gradient is constructed, and the contrast source and contrast are updated using the conjugate gradient method, which reduces the amount of computation and improves the convergence speed.
Without increasing computational load, the accuracy and convergence speed of the inversion model were improved, the computational load was reduced, and the inversion efficiency was increased.
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Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the field of seismic data inversion velocity modeling, more particularly, to a finite difference contrast source inversion method based on hypermemory mixed conjugate gradient method, device, electronic equipment and medium. BACKGROUND
[0002] With the continuous deepening of exploration, the exploration target tends to be complex, so a more accurate subsurface profile is needed, and the acquisition of the accurate subsurface profile needs a more accurate velocity model. Full waveform inversion is a method for efficiently reconstructing complex subsurface structures, which uses the kinematics and dynamics information of seismic waves, uses the wave equation satisfied by seismic waves as a carrier, and inverts the subsurface physical parameters for oil reservoir development. Full waveform inversion can be performed in the time domain or in the frequency domain. At present, the full waveform inversion optimization algorithm is mainly divided into gradient method and Newton method. The Newton method converges faster than the gradient method, but the calculation amount and memory requirement are large. In the inversion process, the nonlinear conjugate gradient method and the Gauss-Newton method are mainly used. In each iteration optimization, multiple forward calculations are needed, which greatly increases the calculation amount. Van den Berg and Kleinman (1997) started from the inverse scattering theory and proposed an integral contrast source (IECSI) inversion method. This method only needs to perform one full forward calculation in the iteration optimization process, which improves the inversion efficiency. Abubakar et al (2008, 2009) further expanded the contrast source inversion algorithm and proposed a finite difference contrast source inversion (FDCSI), and applied the method to seismic wave data inversion based on the acoustic wave equation. Although the FDCSI algorithm has fast calculation speed, but the convergence speed of the optimization objective function using the conventional conjugate gradient is slow, and the Newton method can speed up the convergence speed but has the problems of calculation amount and memory consumption.
[0003] Therefore, it is necessary to develop a finite difference contrast source inversion method based on hypermemory mixed conjugate gradient method, device, electronic equipment and medium.
[0004] The information disclosed in the background section of the present application is only intended to deepen the understanding of the general background of the present application, and should not be regarded as acknowledging or implying in any form that the information constitutes prior art known to those skilled in the art. SUMMARY
[0005] The present application proposes a finite difference contrast source inversion method based on hypermemory mixed conjugate gradient method, device, electronic equipment and medium, which can accelerate the convergence of the objective function without increasing the calculation amount, reduce the calculation amount, and improve the model accuracy obtained by inversion.
[0006] In a first aspect, the embodiments of the present disclosure provide a finite difference contrast source inversion method based on an ultra-memory mixed conjugate gradient method, comprising:
[0007] An initial contrast source and contrast are obtained by wave field back propagation, and a data equation and a state equation are obtained by forward propagation;
[0008] A target functional is obtained according to the data equation and the state equation;
[0009] According to the target functional, a contrast source gradient is calculated using a Fréchet derivative, and then an ultra-memory gradient is constructed;
[0010] The ultra-memory gradient is used as a new gradient, and the contrast source, the total wave field and the contrast are updated by a conjugate gradient method to complete one iteration update;
[0011] The above steps are repeated to update and invert, and a final velocity model is obtained.
[0012] As a specific implementation of the embodiments of the present disclosure, the data equation is:
[0013]
[0014] Where j represents the excitation point number, A b represents an operator related to the background model, M S represents a mapping matrix of the data domain.
[0015] As a specific implementation of the embodiments of the present disclosure, the state equation is:
[0016]
[0017] Where j represents the excitation point number, A b represents an operator related to the background model, M D represents a mapping matrix of the inversion space.
[0018] As a specific implementation of the embodiments of the present disclosure, the target functional is:
[0019]
[0020] Where C S (W j ) and C D (W j ,χ) are data equation errors and state equation errors, respectively, is an observed scattered wave record.
[0021] As a specific implementation of the embodiments of the present disclosure, the ultra-memory gradient is:
[0022]
[0023] wherein, M is a positive integer, N unstable is the number of iterations when instability occurs.
[0024] As a specific implementation manner of the embodiment of the present disclosure, the total wave field is updated as:
[0025]
[0026] The contrast is updated as:
[0027]
[0028] As a specific implementation manner of the embodiment of the present disclosure, the final velocity model is:
[0029]
[0030] wherein, c and k are respectively a velocity and a wave number of the model, c b and k b are respectively a velocity and a wave number of the background model, and D is an inversion target domain.
[0031] In a second aspect, the embodiment of the present disclosure further provides a device for contrast source inversion based on a super-memory hybrid conjugate gradient method finite difference, comprising:
[0032] A forward modeling module, which obtains an initial contrast source and contrast by wave field back propagation, and obtains a data equation and a state equation by forward modeling;
[0033] A target functional module, which obtains a target functional according to the data equation and the state equation;
[0034] A calculation module, which calculates a contrast source gradient by using a Fréchet derivative according to the target functional, and further constructs a super-memory gradient;
[0035] An updating module, which takes the super-memory gradient as a new gradient, updates the contrast source by a conjugate gradient method, updates the total wave field and the contrast, and completes one iteration update;
[0036] An iteration module, which repeats the above steps to perform update iteration and inversion, and obtains a final velocity model.
[0037] As a specific implementation manner of the embodiment of the present disclosure, the data equation is:
[0038]
[0039] wherein, j represents a firing point number, A bdenotes the operator related to the background model, M S denotes the mapping matrix of the data domain.
[0040] As a specific implementation manner of the embodiment of the present disclosure, the state equation is:
[0041]
[0042] wherein j denotes the excitation point number, A b denotes the operator related to the background model, M D denotes the mapping matrix of the inversion space.
[0043] As a specific implementation manner of the embodiment of the present disclosure, the target functional is:
[0044]
[0045] wherein C S (W j ) and C D (W j ,χ) are respectively the data equation error and the state equation error, is the observed scattered wave record.
[0046] As a specific implementation manner of the embodiment of the present disclosure, the hyper-memory gradient is:
[0047]
[0048] wherein, the memory degree M is a positive integer, N unstable is the iteration number when instability occurs.
[0049] As a specific implementation manner of the embodiment of the present disclosure, the updated total wave field is:
[0050]
[0051] The updated contrast is:
[0052]
[0053] As a specific implementation manner of the embodiment of the present disclosure, the final velocity model is:
[0054]
[0055] wherein c and k are respectively the velocity and the wave number of the model, c b and k b are respectively the velocity and the wave number of the background model, and D is the inversion target domain.
[0056] In a third aspect, the present disclosure also provides an electronic device, comprising:
[0057] a memory storing executable instructions;
[0058] a processor running the executable instructions in the memory to implement the finite difference contrast source inversion method based on the hypermemory hybrid conjugate gradient method.
[0059] In a fourth aspect, the present disclosure also provides a computer readable storage medium storing a computer program, which, when executed by a processor, implements the finite difference contrast source inversion method based on the hypermemory hybrid conjugate gradient method.
[0060] The method and device of the present application have other characteristics and advantages, which will be apparent from or will be set forth in more detail in the accompanying drawings and the following detailed description, which together serve to explain certain principles of the present application. BRIEF DESCRIPTION OF DRAWINGS
[0061] The above and other objects, features and advantages of the present application will become more apparent from the following detailed description when taken in conjunction with the accompanying drawings, in which like reference characters refer to like parts throughout the figures, and in which:
[0062] Figure 1 A flowchart showing the steps of the finite difference contrast source inversion method based on the hypermemory hybrid conjugate gradient method is shown.
[0063] Figure 2 A flowchart showing the steps of the finite difference contrast source inversion method based on the hypermemory hybrid conjugate gradient method according to one embodiment of the present application is shown.
[0064] Figure 3 A schematic diagram showing a true velocity model according to one embodiment of the present application is shown.
[0065] Figure 4 A schematic diagram showing a background velocity model according to one embodiment of the present application is shown.
[0066] Figure 5 A schematic diagram showing a conventional conjugate gradient method inversion result according to one embodiment of the present application is shown.
[0067] Figure 6 A schematic diagram showing a hypermemory hybrid conjugate gradient method inversion result according to one embodiment of the present application is shown.
[0068] Figure 7a andFigure 7b A comparison diagram of the inversion velocity curve of the conventional conjugate gradient method (CG) and the hypermemory mixed conjugate gradient method (SHMCG) is shown at the transverse coordinates X = 1250 and 1375.
[0069] Figure 8 A diagram of the 9Hz target function inversion convergence curve of the conventional conjugate gradient method and the hypermemory mixed conjugate gradient method is shown.
[0070] Figure 9 A block diagram of a finite difference contrast source inversion device based on the hypermemory mixed conjugate gradient method according to an embodiment of the present application is shown.
[0071] Explanation of reference signs:
[0072] 201, forward modeling module; 202, target functional module; 203, calculation module; 204, update module; 205, iteration module. DETAILED DESCRIPTION
[0073] The preferred embodiments of the present application will be described in more detail below. Although the preferred embodiments of the present application are described below, it should be understood that the present application can be implemented in various forms and should not be limited by the embodiments set forth herein.
[0074] In order to understand the scheme and effects of the embodiments of the present application, five specific application examples are given below. Those skilled in the art should understand that the examples are only for the convenience of understanding the present application, and any specific details thereof are not intended to limit the present application in any way.
[0075] Example 1
[0076] Figure 1 A flowchart showing the steps of the finite difference contrast source inversion method based on the hypermemory mixed conjugate gradient method is shown.
[0077] As Figure 1 shown, the finite difference contrast source inversion method based on the hypermemory mixed conjugate gradient method includes: step 101, obtaining an initial contrast source and contrast by wave field back propagation, and obtaining a data equation and a state equation by forward modeling; step 102, obtaining a target functional according to the data equation and the state equation; step 103, using the Fréchet derivative to calculate the contrast source gradient according to the target functional, and then constructing a hypermemory gradient; step 104, using the hypermemory gradient as a new gradient, updating the contrast source by the conjugate gradient method, updating the total wave field and the contrast, and completing one iteration update; step 105, repeating the above steps for update iteration and inversion to obtain a final velocity model.
[0078] In one example, the data equation is:
[0079]
[0080] where j denotes the excitation point number, A b denotes the operator related to the background model, M S denotes the mapping matrix of the data domain.
[0081] In one example, the state equation is:
[0082]
[0083] where j denotes the excitation point number, A b denotes the operator related to the background model, M D denotes the mapping matrix of the inversion space.
[0084] In one example, the objective functional is:
[0085]
[0086] where C S (W j ) and C D (W j ,χ) are the data equation error and the state equation error, respectively, is the observed scattered wave record.
[0087] In one example, the hyper-memory gradient is:
[0088]
[0089] where, the memory degree M is a positive integer, N unstable is the iteration number when instability occurs.
[0090] In one example, the updated total wavefield is:
[0091]
[0092] The updated contrast is:
[0093]
[0094] In one example, the final velocity model is:
[0095]
[0096] where c, k are the velocity and wave number of the model, respectively, c b , k b are the velocity and wave number of the background model, respectively, and D is the inversion target domain.
[0097] Figure 2 A flowchart showing the steps of a finite difference contrast source inversion method based on a super memory hybrid conjugate gradient method according to an embodiment of the present invention is shown.
[0098] Specifically, if Figure 2 As shown, the frequency domain matrix expression of the two-dimensional acoustic wave equation is:
[0099] HU=-S(ω,r s ) (1)
[0100] Where U is the frequency domain single frequency wave field, H is the coefficient matrix of the equation, S is the source term, r S is the source coordinate, and ω is the angular frequency.
[0101] The scattered wave field is defined by the relationship between the total wave field and the incident wave field as follows:
[0102] U sct =U tol -U inc (2)
[0103] Where U tol is the total wave field in the frequency domain, U sct and U bac are the scattered wave field and the background wave field respectively.
[0104] The contrast χ is introduced as follows:
[0105]
[0106] Where c, k and c b 、k b are the velocity and wave number of the model and background model respectively, and D is the inversion target domain.
[0107] The data equation and state equation are as follows:
[0108]
[0109]
[0110] Where, j represents the excitation point number, A b Represents the operator related to the background model, M S and M D Represent the mapping matrices of the data domain and inversion space respectively.
[0111] In equations (4) and (5), when χ is known, It is a forward process, and it is known that Obtaining χ is an inversion process.
[0112] The comparison sources are introduced as follows:
[0113]
[0114] Then, equations (4) and (5) can be changed into:
[0115]
[0116]
[0117] The objective function is established according to equations (7) and (8) as follows:
[0118]
[0119] In the equation, C S (W j ) and C D (W j ,χ) are the data equation error and the state equation error, respectively, is the observed scattered wave record. It can be seen from the objective function that the objective function has two unknowns, the contrast source W j and the contrast χ. The inversion is to constantly update the contrast source W j and the contrast χ.
[0120] The gradient of the contrast source W j is calculated by using the Fréchet derivative,
[0121]
[0122]
[0123] In the equation, M S* and M D* are the conjugate transposes of A b , M S and M D , is the complex conjugate.
[0124] The contrast source W j is updated by using the conventional PR conjugate gradient method, and the PR search direction is as follows:
[0125]
[0126] The update formula of the contrast source W j is as follows:
[0127]
[0128] In the equation, is the update step, and the updated contrast source W j,nThe optimal step size is given by n-1 ,W j,n ) can be obtained as follows:
[0129]
[0130] The updated contrast source W j,n is obtained by using (15) to update the total wavefield The contrast χ is updated by using (16) to complete one iteration, as follows:
[0131]
[0132]
[0133] The initial contrast source and contrast are given by the wavefield back-propagation method, as follows:
[0134]
[0135]
[0136]
[0137] where and M S* are the adjoint operators of A b and M S , respectively.
[0138] The super-memory hybrid conjugate gradient (SMHCG) method has the characteristics of small memory consumption, fast calculation speed, and super-linear convergence. The accurate gradient is very important for the convergence of the objective function. The steepest descent method only uses the current gradient, and the conventional conjugate gradient method only uses the gradient information of the previous and current steps. The super-memory conjugate gradient method uses the information of the updated direction of the previous steps and the current gradient information to reconstruct a new gradient direction. In this paper, the super-memory conjugate gradient method is used to update the contrast source, and the contrast is updated by using (15) and (16).
[0139] The super-memory gradient is as follows:
[0140]
[0141] where M is a positive integer, and N unstable is the iteration number when instability occurs.
[0142] The super-memory gradient is used as a new gradient to update the contrast source by using the conjugate gradient method, as follows:
[0143]
[0144]
[0145] The optimal step is calculated in the same way as the conventional PR conjugate gradient method As follows:
[0146]
[0147] Finally, the contrast source is updated by using equation (22) and the total wave field is updated by using equation (15) Then, the contrast χ is updated by using equation (16) to complete one iteration.
[0148] Therefore, the steps of the method for data inversion are as follows:
[0149] ①The initial contrast source W is obtained by wave field back propagation j,0 and the contrast χ0.
[0150] ②The forward is performed by using equations (4) and (5) respectively to obtain the data equation and the state equation.
[0151] ③The contrast source is introduced to obtain equations (7) and (8) and the target functional (9).
[0152] ④The contrast source W j gradient is obtained by using the Fréchet derivative according to the data of the target functional.
[0153] ⑤The super-memory gradient is constructed by using equation (20).
[0154] ⑥The super-memory gradient is taken as a new gradient to update the contrast source by using the conjugate gradient method.
[0155] ⑦The total wave field and the contrast are updated by using equations (15) and (16) to complete one iteration.
[0156] ⑧The steps of ②-⑦ are repeated to continuously update and iterate until the condition is met.
[0157] ⑨The steps of ②-⑤ are repeated to perform inversion.
[0158] ⑩The final velocity model is obtained by using equation (3).
[0159] Example 2
[0160] Figure 3 A schematic diagram of a real velocity model according to one embodiment of the application is shown.
[0161] Figure 4 A schematic diagram of a background velocity model according to one embodiment of the application is shown.
[0162] Figure 5A schematic diagram of a conventional conjugate gradient method inversion result is shown according to one embodiment of the present application.
[0163] Figure 6 A schematic diagram of a super-memory hybrid conjugate gradient method inversion result is shown according to one embodiment of the present application.
[0164] Figure 7a And Figure 7b A schematic diagram of a comparison of inversion velocity curves of a conventional conjugate gradient method (CG) and a super-memory hybrid conjugate gradient method (SHMCG) at X = 1250 and 1375 is shown.
[0165] Figure 8 A schematic diagram of a conventional conjugate gradient method and a super-memory hybrid conjugate gradient method target function 9Hz inversion convergence curves is shown.
[0166] Figure 3 For a real velocity model to be subjected to a numerical experiment, the longitudinal depth is 1225m, the lateral distance is 2500m, the lateral discretization is 100 grids, the longitudinal discretization is 49 grids, the grid spacing is 25m, 101 geophones are distributed on the grid points on the upper surface of the model, the source spacing is 100m, and the 7 frequencies are selected for inversion (2, 3, 4, 6, 9, 13, 18Hz), each frequency is iterated 50 times, and the inversion result is shown in Figure 5 And Figure 6 From Figure 5 , Figure 6 and Figure 7a , Figure 7b , it can be seen that the inversion results of the conventional conjugate gradient method and the super-memory hybrid conjugate gradient method are basically consistent, but the details of the super-memory hybrid conjugate gradient method inversion result are slightly better. From Figure 8 , it can be seen that the super-memory hybrid conjugate gradient method converges faster, the target function residual is smaller, and the accuracy is higher. From the experiment, it can be proved that, compared with the conventional conjugate gradient method, when the same residual accuracy is selected, the super-memory hybrid conjugate gradient method has fewer iteration calculation times, and the calculation convergence efficiency is higher.
[0167] Example 3
[0168] Figure 9 A block diagram of a super-memory hybrid conjugate gradient method finite difference contrast source inversion device is shown according to one embodiment of the present application.
[0169] As shown in Figure 9 , the super-memory hybrid conjugate gradient method finite difference contrast source inversion device comprises:
[0170] The forward modeling module 201 obtains initial contrast source and contrast by wave field back propagation, and obtains data equation and state equation by forward modeling;
[0171] The objective functional module 202 obtains objective functional according to the data equation and the state equation;
[0172] The calculation module 203 calculates the contrast source gradient by using the Fréchet derivative according to the objective functional, and further constructs the hyper-memory gradient;
[0173] The update module 204 updates the contrast source by the conjugate gradient method with the hyper-memory gradient as the new gradient, updates the total wave field and the contrast, and completes one iteration update;
[0174] The iteration module 205 repeats the above steps to perform update iteration and inversion, and obtains the final velocity model.
[0175] In one example, the data equation is:
[0176]
[0177] Wherein, j represents the number of excitation points, A b represents an operator related to the background model, M S represents the mapping matrix of the data domain.
[0178] In one example, the state equation is:
[0179]
[0180] Wherein, j represents the number of excitation points, A b represents an operator related to the background model, M D represents the mapping matrix of the inversion space.
[0181] In one example, the objective functional is:
[0182]
[0183] Wherein, C S (W j ) and C D (W j ,χ) are data equation error and state equation error respectively, is the observed scattered wave record.
[0184] In one example, the hyper-memory gradient is:
[0185]
[0186] Wherein, The memory M is a positive integer, N unstable is the iteration number when instability occurs.
[0187] In one example, the total wave field is updated as:
[0188]
[0189] The contrast is updated as:
[0190]
[0191] In one example, the final velocity model is:
[0192]
[0193] where c, k are the velocity, wave number of the model, c b , k b are the velocity, wave number of the background model, and D is the inversion target domain.
[0194] Example 4
[0195] The present disclosure provides an electronic device, comprising: a memory storing executable instructions; a processor running the executable instructions in the memory to implement the above-mentioned finite difference contrast source inversion method based on the hyper-memory mixed conjugate gradient method.
[0196] The electronic device according to the embodiments of the present disclosure comprises a memory and a processor.
[0197] The memory is configured to store non-transitory computer-readable instructions. Specifically, the memory can include one or more computer program products, which can 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), cache memory, and / or the like. The non-volatile memory may, for example, include read-only memory (ROM), hard disk, flash memory, and / or the like.
[0198] The processor can be a central processing unit (CPU) or other form of processing unit having data processing and / or instruction execution capabilities, and can control other components in the electronic device to perform desired functions. In one embodiment of the present disclosure, the processor is configured to run the computer-readable instructions stored in the memory.
[0199] Those skilled in the art will understand that, in order to solve the technical problem of how to obtain a good user experience effect, the present embodiment can also include well-known structures such as a communication bus, an interface, and the like, which should also be included in the protection scope of the present disclosure.
[0200] Detailed description of the present embodiment can refer to the corresponding description in the foregoing embodiments, which will not be repeated here.
[0201] Example 5
[0202] The computer readable storage medium of the embodiments of the present disclosure stores a computer program, and the computer program is executed by a processor to implement the finite difference contrast source inversion method based on the hypermemory mixed conjugate gradient method.
[0203] The computer readable storage medium of the embodiments of the present disclosure stores a computer program, and the computer program is executed by a processor to implement the finite difference contrast source inversion method based on the hypermemory mixed conjugate gradient method.
[0204] The computer readable storage medium includes, but is not limited to, optical storage media (such as CD-ROM and DVD), magneto-optical storage media (such as MO), magnetic storage media (such as magnetic tape or mobile hard disk), media with built-in rewritable non-volatile memory (such as memory card), and media with built-in ROM (such as ROM cartridge).
[0205] Those skilled in the art should understand that the above description of the embodiments of the present application is only for the purpose of exemplarily illustrating the beneficial effects of the embodiments of the present application, and is not intended to limit the embodiments of the present application to any examples given.
[0206] The above has described the embodiments of the present application, and the above description is exemplary, not exhaustive, and is not limited to the disclosed embodiments. Many modifications and changes are obvious to those skilled in the art without departing from the scope and spirit of the described embodiments.
Claims
1. A finite-difference contrast source inversion method based on the hypermemory mixed conjugate gradient method, characterized in that, The method comprises the steps of: obtaining initial contrast sources and contrasts by wave field back propagation, and obtaining data equations and state equations by forward propagation; obtaining a target functional according to the data equations and the state equations; calculating contrast source gradients by using Fréchet derivatives according to the target functional, and then constructing hyper-memory gradients; updating the contrast sources by using the hyper-memory gradients as new gradients through a conjugate gradient method, updating total wave fields and contrasts, and completing one iteration update; repeating the above steps to perform update iteration and inversion, and obtaining a final velocity model.
2. The finite-difference contrast-source inversion method based on the hypermemory mixed conjugate gradient method of claim 1, wherein, The data equations are: where j denotes the index of the excitation point, A b denotes an operator related to the background model, M S denotes a mapping matrix of the data domain.
3. The finite-difference contrast-source inversion method based on the hypermemory mixed conjugate gradient method of claim 1, wherein, The state equations are: where j denotes the index of the excitation point, A b denotes an operator related to the background model, M D denotes the mapping matrix of the inversion space.
4. The finite-difference contrast-source inversion method based on the hypermemory- mixed conjugate gradient method of claim 1, wherein, The target functional is: where C S (W j ) and C D (W j ,χ) are the data equation error and the state equation error, respectively, is the observed scattered wave record.
5. The finite-difference contrast-source inversion method based on the hypermemory mixed conjugate gradient method of claim 1, wherein, The hyper-memory gradients are: wherein, M is a positive integer, N unstable is the number of iterations at which instability occurs.
6. The finite-difference contrast-source inversion method based on the hypermemory- mixed conjugate gradient method of claim 1, wherein, The updated total wave fields are: The updated contrasts are:
7. The finite-difference contrast-source inversion method based on the hypermemory- mixed conjugate gradient method of claim 1, wherein, The final velocity model is: where c, k are the velocity, wave number of the model, respectively b c b k are the velocity, wave number of the background model, respectively, and D is the domain of inversion.
8. An apparatus for finite difference contrast source inversion based on the hypermemory mixed conjugate gradient method, characterized in that, The method comprises the steps of: a forward propagation module, which obtains initial contrast sources and contrasts by wave field back propagation, and obtains data equations and state equations by forward propagation; a target functional module, which obtains a target functional according to the data equations and the state equations; a calculation module, which calculates contrast source gradients by using Fréchet derivatives according to the target functional, and then constructs hyper-memory gradients; an update module, which updates the contrast sources by using the hyper-memory gradients as new gradients through a conjugate gradient method, updates total wave fields and contrasts, and completes one iteration update; an iteration module, which repeats the above steps to perform update iteration and inversion, and obtains a final velocity model.
9. An electronic device, comprising: The electronic device comprises: a memory, which stores executable instructions; a processor, which runs the executable instructions in the memory to implement the hyper-memory hybrid conjugate gradient method based finite difference contrast source inversion method in any one of claims 1-7.
10. A computer readable storage medium characterized by, The computer readable storage medium stores a computer program, which is executed by a processor to implement the hyper-memory hybrid conjugate gradient method based finite difference contrast source inversion method in any one of claims 1-7.