Anisotropic medium pure acoustic wave least square reverse time migration method

Abstract

The invention provides an anisotropic medium pure acoustic wave least square reverse time migration method, and relates to the field of data processing and oil and gas geophysical exploration, and the method comprises the steps: calculating an anisotropic medium pure acoustic wave equation demigration operator; determining an anisotropic medium pure acoustic wave equation adjoint equation and a parameter disturbance gradient formula; solving an anisotropic medium pure acoustic wave equation demigration operator and an adjoint equation; determining an anisotropic medium pure acoustic wave equation Hessian matrix and vector product formula; calculating a model parameter disturbance gradient and a Gaussian-Newton gradient precondition; and iteratively updating the speed and the anisotropic parameter disturbance model. Through Gaussian-Newton Hessian operator gradient preconditions, crosstalk of disturbance of different model parameters is suppressed, a speed and anisotropy parameter disturbance model is established, an efficient and accurate imaging analysis tool is provided for seismic exploration and acquisition in a complex area, the migration imaging effect of anisotropic medium seismic data is improved, and the method is suitable for the seismic exploration and acquisition of the complex area. And the imaging precision and the convergence speed of the pure acoustic wave least square reverse time migration of the anisotropic medium are improved.

Description

Technical Field

[0001] The present application relates to the technical fields of data processing and oil and gas geophysical exploration, and in particular to a pure acoustic least squares reverse time migration method for anisotropic media. Background Art

[0002] As exploration progresses, oil and gas exploration targets become increasingly complex, posing new challenges to existing seismic exploration methods. Migration imaging is a critical technical step in seismic exploration observation system design and seismic data processing. Optimizing acquisition parameters through imaging analysis can improve the exploration of target layers. Migration imaging is also an effective means of acquiring subsurface structures and structures. Reverse time migration, based on the two-way wave equation, has no inclination restrictions and can image any steeply dipping interface, offering higher accuracy than Cauchhof integral migration and one-way wave migration. However, reverse time migration uses the adjoint of the forward operator to approximate its inverse operator, and satisfactory imaging cannot be achieved when seismic data is incomplete (e.g., noisy, band-limited, or missing). Prior art offers least squares reverse time migration as a linear waveform inversion method. By iteratively updating the reflection coefficient / model parameter perturbation profile based on the inversion concept, the quality of seismic data migration imaging can be further improved.

[0003] Anisotropic media are media whose physical properties (such as absorbance, refractive index, conductivity, and tensile strength) vary with direction. This is the opposite of isotropic media and is commonly found in materials such as crystals and wood. In the exploration field, anisotropy is ubiquitous in subsurface media. The directional arrangement of underground rocks, minerals, and fractures causes the propagation velocity of seismic waves to vary along different directions (creating anisotropy). The assumption of isotropic media is increasingly inadequate for exploration in complex areas. Therefore, achieving high-precision seismic imaging in anisotropic media has become crucial for the exploration of deep, deepwater, and unconventional oil and gas reservoirs.

[0004] In addition, most of the above-mentioned existing least squares reverse time migration methods have the following problems: (1) Based on the isotropy assumption, the anisotropic characteristics of seismic waves cannot be considered; (2) Based on the assumption of elastic anisotropy, it is difficult to deal with the coupling problem of longitudinal waves and fast and slow shear waves, and the calculation is large; (3) Based on the pseudo-acoustic anisotropy assumption, it is impossible to completely eliminate the interference of shear wave artifacts, and the stability is poor. However, pure acoustic anisotropic least squares reverse time migration can effectively overcome the above problems. The method has moderate computational complexity and speed, is well suited for the design of acquisition observation systems, and has broad application prospects. Compared with isotropic media, anisotropic media involve more model parameters (such as velocity and Thomsen anisotropy parameters), and the crosstalk between different parameter perturbations seriously affects the accuracy and convergence of reverse time migration. Summary of the Invention

[0005] This application presents a pure acoustic wave least squares reverse time migration method for anisotropic media.

[0006] In a first aspect, the present application provides a pure acoustic least squares reverse time migration method for anisotropic media, the method comprising: Calculate the back-migration operator of the pure acoustic wave equation in anisotropic media; Determine the adjoint equation of the pure acoustic wave equation in anisotropic media and the parameter perturbation gradient formula; Solve the anti-migration operator and adjoint equation of the pure acoustic wave equation in anisotropic media; Determine the Hessian matrix and vector product formula of the pure acoustic wave equation in anisotropic media; Calculate model parameter perturbation gradients and Gauss-Newton gradient preconditioners; Iteratively update the velocity and anisotropy parameter perturbation model.

[0007] Optionally, the anisotropic medium pure acoustic wave equation demigration operator is calculated in the following manner, including: The pure acoustic wave equations for VTI vertical transverse isotropic and anisotropic media are as follows: (1) in, For TRON, are model parameters, is the source term; (2) in, is the propagation velocity in the direction of the symmetry axis, and is the Thomsen anisotropy parameter, For time, and is the spatial coordinate, Represents matrix or vector transpose; Based on the Born approximation, the seismic wave field and model parameters are split into background components and disturbance components. Formula (1) becomes: (3) in, is the background wave field, To disturb the wave field, is the background parameter, is the disturbance parameter; Expanding formula (3) using Taylor series yields: (4) in, (5) (6) (7) The background wave field and background parameters also satisfy the wave equation shown in formula (1): (8) Subtracting formula (8) from formula (3) and ignoring the high-order terms of wave field perturbations and parameter perturbations yields: (9) In order to eliminate the velocity dimension, the relative change of velocity is used to express the image of velocity, such as expression (10): (10) Formula (10) can be rewritten as: (11) Among them, formulas (8) and (11) are the back migration operators of the pure acoustic wave equation of VTI anisotropic media, that is, the perturbation wave field is calculated by perturbing the known model parameters: .

[0008] Optionally, the adjoint equation of the pure acoustic wave equation in anisotropic medium and the parameter perturbation gradient formula are determined in the following manner, including: Establish the minimization objective function: (12) in, To simulate the disturbance wave field, To observe the disturbance wave field, is the calculation area, is the maximum recording time, is the detection point projection operator; The Lagrange multiplier method is used to solve this constrained optimization problem, and the objective function becomes: (13) in, For the accompanying wave field; By integrating formula (13) by parts and assuming that the wave fields at the initial, final and boundary locations are zero, we can obtain: (14) make The adjoint equation of the pure acoustic wave equation in VTI anisotropic media can be obtained: (15) Based on the chain rule Derive the gradient of the objective function with respect to the perturbation of the model parameters: (16) (17) (18) in, .

[0009] Optionally, the demigration operator and adjoint equation of the pure acoustic wave equation for anisotropic media are solved in the following manner, including: High-order regular grid finite differences are used to quickly solve the hyperbolic differential equations in formulas (8), (11) and (15). The mixed partial derivatives in the x and z directions are approximated by finite differences along the two directions respectively. The fast Poisson equation is used to solve the Poisson equation with constant coefficients in formulas (8), (11) and (15) efficiently.

[0010] Optionally, the Hessian matrix and vector product formula of the pure acoustic wave equation of the anisotropic medium are determined in the following manner, including: In the discrete case, the model parameter perturbation , the gradient of the objective function with respect to the perturbation of the model parameters and Hessian matrix Respectively expressed as: (19) (20) (twenty one) (twenty two) Where, N is the discrete grid dimension; gradient Represents the first-order derivative of the objective function with respect to the model parameter perturbation, the Hessian matrix represents the second-order derivative of the objective function with respect to the model parameter disturbance, and the relationship between the two is shown in expression (23): (twenty three) Construct a new objective function F as shown in expression (24): (twenty four) Where x is an arbitrary column vector of dimension 3N, (25) Based on formulas (23) and (24), we can obtain: (26) In the continuous case, the derivative formula (24) of the objective function with respect to the model parameter perturbation becomes: (27) in, ( ) is an arbitrary function related to the spatial position; Based on the Lagrange multiplier method, the derivative formula of the objective function F with respect to the model parameter disturbance is derived, and formula (27) becomes: (28) in, ( )、 and is the Lagrange multiplier function; Formula (28) can be simplified as: (29) make , , (30) Formula (29) degenerates into: (31) By integrating formula (31) by parts and assuming that the wave fields at the initial, final and boundary locations are zero, we can obtain: (32) make and We can get: (33) (34) Based on the chain rule Derive the gradient of the new objective function with respect to the perturbation of the model parameters: (35) (36) (37) in, , in the discrete case, the gradient of F with respect to the model parameter perturbation m is the product of the Hessian matrix H and any vector x.

[0011] Optionally, the model parameter perturbation gradient and Gauss-Newton gradient precondition are calculated as follows, including: According to formulas (8) and (11), the de-migration operator is numerically solved in the forward direction of time to obtain the background wave field and disturbed wave fields ; According to formula (15), numerically solve the adjoint equation in reverse time to obtain the adjoint wave field Based on formulas (16) to (18), calculate the gradient of the objective function with respect to the model parameter perturbation ( ); Gradient of the perturbation of model parameters using Hessian operator Perform preconditioning: (38) in, is the inverse of the Hessian matrix, is the gradient of the model perturbation parameter after preconditioning; It is difficult to directly calculate and store the Hessian matrix or its inverse matrix. The inversion operation in formula (38) is converted into the following linear equation solution problem: (39) The steps for solving the system of equations shown in formula (38) using the conjugate gradient method are: (1) Given an initial value , , and ; (2) Calculate the Hessian matrix using formulas (8), (30), (33), (34), (35)-(37) With vector The product of ; (3) Calculation and : and ; (4) Update and : 、 、 、 ; (5) Repeat steps (2) to (4) until the maximum number of iterations is reached, and output the final model perturbation parameter gradient .

[0012] Optionally, the velocity and anisotropy parameter perturbation model is iteratively updated in the following manner, including: Based on the preconditioned gradient , the velocity and anisotropy parameter perturbation model is updated, and the iterative steps are repeated until the convergence conditions are met. The updated formula is as follows: (40) in, is the number of iterations, Perturb the model parameters for the current and next iterations, Perturb the model for the next iteration’s model parameters, is the iteration step size.

[0013] In a second aspect, the present application shows an electronic device, comprising: a processor, a memory, and a computer program stored in the memory and executable on the processor, wherein the computer program implements any of the above methods when executed by the processor.

[0014] In a third aspect, the present application provides a computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, the method described in any one of the above items is implemented.

[0015] In a fourth aspect, the present application illustrates a computer program product. When instructions in the computer program product are executed by a processor of an electronic device, the electronic device implements any of the methods described above.

[0016] The technical solution provided by this application may have the following beneficial effects: By employing a novel truncated Gauss-Newton Hessian operator gradient preconditioner to suppress crosstalk between different model parameter perturbations, a reliable velocity and anisotropy parameter perturbation model is established. This provides an efficient and accurate imaging analysis tool for seismic exploration acquisition design in complex areas, improves the imaging effect of seismic data migration in anisotropic media, and enhances the imaging accuracy and convergence rate of pure acoustic least-squares reverse time migration in anisotropic media. Furthermore, this application can obtain precise velocity and anisotropy parameter perturbation models, helping to improve the quality of seismic data migration imaging in complex geological conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 A flow chart of the pure acoustic least squares reverse time migration method for anisotropic media provided in this application; Figure 2 Schematic diagram of the Hess VTI model provided in this application under the speed v parameter; Figure 3 The Hess VTI model provided in this application has anisotropic parameters The schematic diagram below; Figure 4 The Hess VTI model provided in this application has anisotropic parameters The schematic diagram below; Figure 5 Velocity perturbation using conventional least squares reverse time migration results for the Hess VTI model Schematic diagram of; Figure 6 Anisotropic parameter perturbations of the Hess VTI model using conventional least squares reverse time migration results Schematic diagram of; Figure 7 Anisotropic parameter perturbations of the Hess VTI model using conventional least squares reverse time migration results Schematic diagram of; Figure 8 Velocity perturbation for the Hess VTI model using the least squares reverse time migration results provided in this application Schematic diagram of; Figure 9 Anisotropic parameter perturbation for the Hess VTI model using the least squares reverse time migration results provided in this application Schematic diagram of; Figure 10 Anisotropic parameter perturbation for the Hess VTI model using the least squares reverse time migration results provided in this application Schematic diagram of; Figure 11 A block diagram of an electronic device provided in this application; Figure 12 This is a block diagram of another electronic device provided by this application. DETAILED DESCRIPTION

[0018] The following will be combined with the drawings in the embodiments of this application to clearly and completely describe the technical solutions in the embodiments of this application. Obviously, the embodiments described are part of the embodiments of this application, not all of them. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0019] This application, in the fields of data processing and oil and gas geophysical exploration, relates to a method for reverse time migration using pure acoustic least squares in anisotropic media. This method can be applied to seismic acquisition design and high-precision imaging of seismic data under complex geological conditions, enabling the acquisition of velocity and anisotropic parameter perturbation profiles. The following describes a detailed description of the method for reverse time migration using pure acoustic least squares in anisotropic media provided in this application. Example 1 Reference Figure 1 , is a flow chart of a method for pure acoustic least squares reverse time migration in anisotropic media provided in this application, the method comprising: Step S101: Calculate the inverse migration operator of the pure acoustic wave equation for anisotropic media; Step S102: determining the adjoint equation of the pure acoustic wave equation of the anisotropic medium and the parameter perturbation gradient formula; Step S103: solving the anisotropic medium pure acoustic wave equation de-migration operator and adjoint equation; Step S104: determining the Hessian matrix and vector product formula of the pure acoustic wave equation of the anisotropic medium; Step S105: Calculate the model parameter perturbation gradient and Gauss-Newton gradient precondition; Step S106: Iteratively update the velocity and anisotropy parameter perturbation model.

[0020] This application employs a novel truncated Gauss-Newton Hessian operator gradient preconditioner to suppress crosstalk between different model parameter perturbations, establishing reliable velocity and anisotropy parameter perturbation models. This provides an efficient and accurate imaging analysis tool for seismic exploration acquisition design in complex areas, improves the imaging of seismic data migration in anisotropic media, and enhances the imaging accuracy and convergence rate of pure acoustic least-squares reverse-time migration in anisotropic media. Furthermore, this application can obtain precise velocity and anisotropy parameter perturbation models, helping to improve the quality of seismic data migration imaging in complex geological conditions.

[0021] For the sake of clarity, the specific process of each step in the first embodiment is described separately.

[0022] In step S101, the de-migration operator of the pure acoustic wave equation for anisotropic media is calculated in the following manner, including: The pure acoustic wave equations for VTI vertical transverse isotropic and anisotropic media are as follows: (1) in, For TRON, are model parameters, is the source term; (2) Among them, see Figures 2 to 4 , is the propagation velocity in the direction of the symmetry axis, and is the Thomsen anisotropy parameter, For time, and is the spatial coordinate, Represents matrix or vector transpose; Based on the Born approximation, the seismic wave field and model parameters are split into background components and disturbance components. Formula (1) becomes: (3) in, is the background wave field, To disturb the wave field, is the background parameter, is the disturbance parameter; Expanding formula (3) using Taylor series yields: (4) in, (5) (6) (7) The background wave field and background parameters also satisfy the wave equation shown in formula (1): (8) Subtracting formula (8) from formula (3) and ignoring the high-order terms of wave field perturbations and parameter perturbations yields: (9) In order to eliminate the velocity dimension, the relative change of velocity is used to express the image of velocity, such as expression (10): (10) Formula (10) can be rewritten as: (11) Among them, formulas (8) and (11) are the back migration operators of the pure acoustic wave equation of VTI anisotropic media, that is, the perturbation wave field is calculated by perturbing the known model parameters: It should be noted that under the Born approximation assumption, the background wave field and They can be regarded as direct waves and single reflected waves respectively.

[0023] In step S102, the adjoint equation of the pure acoustic wave equation of the anisotropic medium and the parameter perturbation gradient formula are determined in the following manner, including: Establish the minimization objective function: (12) in, To simulate the disturbance wave field, To observe the disturbance wave field, is the calculation area, is the maximum recording time, is the detection point projection operator; The Lagrange multiplier method is used to solve this constrained optimization problem, and the objective function becomes: (13) in, For the accompanying wave field; By integrating formula (13) by parts and assuming that the wave fields at the initial, final and boundary locations are zero, we can obtain: (14) make The adjoint equation of the pure acoustic wave equation in VTI anisotropic media can be obtained: (15) Based on the chain rule Derive the gradient of the objective function with respect to the perturbation of the model parameters: (16) (17) (18) in, .

[0024] In step S103, the de-migration operator and adjoint equation of the pure acoustic wave equation for anisotropic media are solved in the following manner, including: High-order regular grid finite differences are used to quickly solve the hyperbolic differential equations in formulas (8), (11) and (15), and the mixed partial derivatives in the x and z directions are approximated by finite differences along the two directions respectively. The fast Poisson equation is used to solve the constant coefficient Poisson equation in formulas (8), (11) and (15). The solver efficiently solves the Poisson equation, which has higher computational efficiency than the pseudo-spectral method.

[0025] In step S104, the Hessian matrix and vector product formula of the pure acoustic wave equation of the anisotropic medium are determined in the following manner, including: In the discrete case, the model parameter perturbation , the gradient of the objective function with respect to the perturbation of the model parameters and Hessian matrix Respectively expressed as: (19) (20) (twenty one) (twenty two) Where, N is the discrete grid dimension; gradient Represents the first-order derivative of the objective function with respect to the model parameter perturbation, the Hessian matrix represents the second-order derivative of the objective function with respect to the model parameter disturbance, and the relationship between the two is shown in expression (23): (twenty three) Construct a new objective function F as shown in expression (24): (twenty four) Where x is an arbitrary column vector of dimension 3N, (25) Based on formulas (23) and (24), we can obtain: (26) It should be noted that formula (26) shows that the product operation of the Hessian matrix and any vector can be converted into the derivative operation of the objective function F with respect to the model parameter perturbation m.

[0026] In the continuous case, the derivative formula (24) of the objective function with respect to the model parameter perturbation becomes: (27) in, ( ) is an arbitrary function related to the spatial position; It should be noted that due to the model parameter perturbation gradient ( ) is obtained by formula (16)-(18), simulating the disturbance wave field and accompanying wave fields By solving the de-migration operator shown in formula (11) and the adjoint equation shown in formula (5), formulas (11), (15) and (16) to (18) serve as constraints for the derivative operation of F.

[0027] Based on the Lagrange multiplier method, the derivative formula of the objective function F with respect to the model parameter disturbance is derived, and formula (27) becomes: (28) in, ( )、 and is the Lagrange multiplier function; Formula (28) can be simplified as: (29) make , (30) Formula (29) degenerates into: (31) By integrating formula (31) by parts and assuming that the wave fields at the initial, final and boundary locations are zero, we can obtain: (32) make and We can get: (33) (34) Based on the chain rule Derive the gradient of the new objective function with respect to the perturbation of the model parameters: (35) (36) (37) in, , in the discrete case, the gradient of F with respect to the model parameter perturbation m is the product of the Hessian matrix H and any vector x.

[0028] It should be noted that Equations (35) to (37) provide the gradient formulas for the new objective function F with respect to the model parameter perturbation in the continuous case. In the discrete case, the calculation can be performed by simply substituting the wave fields and parameters at different grid points. From Equation (26), it can be seen that the gradient of F with respect to the model parameter perturbation m in the discrete case is the product of the Hessian matrix H and an arbitrary vector x.

[0029] In step S105, the model parameter perturbation gradient and Gauss-Newton gradient precondition are calculated in the following manner, including: According to formulas (8) and (11), the de-migration operator is numerically solved in the forward direction of time to obtain the background wave field and disturbed wave fields ; According to formula (15), numerically solve the adjoint equation in reverse time to obtain the adjoint wave field Based on formulas (16) to (18), calculate the gradient of the objective function with respect to the model parameter perturbation ( ); Gradient of the perturbation of model parameters using Hessian operator Perform preconditioning: (38) in, is the inverse of the Hessian matrix, is the gradient of the model perturbation parameter after preconditioning; It is difficult to directly calculate and store the Hessian matrix or its inverse matrix. The inversion operation in formula (38) is converted into the following linear equation solution problem: (39) The steps for solving the system of equations shown in formula (38) using the conjugate gradient method are: (1) Given an initial value , , and ; (2) Calculate the Hessian matrix using formulas (8), (30), (33), (34), (35)-(37) With vector The product of ; (3) Calculation and : and ; (4) Update and : 、 、 、 ; (5) Repeat steps (2) to (4) until the maximum number of iterations is reached, and output the final model perturbation parameter gradient . Preferably, the maximum number of iterations can be set to 5.

[0030] It should be noted that the above process does not require analytical calculation of the Hessian matrix or its inverse matrix. The Gauss-Newton preconditioning of the perturbation parameter gradient is achieved by performing the product (Hx) operation of the Hessian matrix and the vector multiple times.

[0031] In step S106, the velocity and anisotropy parameter perturbation models are iteratively updated in the following manner, including: Based on the preconditioned gradient , the velocity and anisotropy parameter perturbation model is updated, and the iterative steps are repeated until the convergence condition is met (such as the value of the objective function is less than a certain threshold). The updated formula is as follows: (40) in, is the number of iterations, Perturb the model parameters for the current and next iterations, Perturb the model parameters for the next iteration, is the iteration step length.

[0032] In one implementation, the iteration step size may be obtained by linear search or parabola fitting.

[0033] This application proposes a new least-squares reverse-time migration method for pure acoustic waves in anisotropic media. The de-migration operator for the pure acoustic wave equation in anisotropic media is derived based on the Born approximation. The adjoint equation and parameter perturbation gradient formula for the pure acoustic wave equation in anisotropic media are derived using the Lagrange multiplier method. The de-migration operator and adjoint equation for the pure acoustic wave equation in anisotropic media are efficiently solved using finite differences and a fast Poisson solver. The Hessian matrix and vector product formula for the pure acoustic wave equation in anisotropic media are derived based on the Lagrange multiplier method. The model parameter perturbation gradient is calculated and Gauss-Newton gradient preprocessing is performed. The velocity and anisotropic parameter perturbation model are iteratively updated.

[0034] This application adopts the truncated Gauss-Newton inversion algorithm to alleviate the crosstalk effect of perturbations of different model parameters in anisotropic media, which helps to improve the convergence rate and imaging accuracy of pure acoustic least squares reverse time migration in anisotropic media, thereby improving the quality of oil and gas exploration under complex geological conditions.

[0035] See Figures 2 to 4 ,Hess VTI model is used below to verify the effectiveness of the pure acoustic least squares reverse time migration method for anisotropic media proposed in this application.

[0036] Specifically, the model was divided into 630 × 218 grid points with a grid size of 15.0 m × 15.0 m, a time step of 1.5 ms, and a maximum recording time of 3.0 s. The source used a Ricker wavelet with a dominant frequency of 15.0 Hz. Sixty-three shots and 630 receivers were evenly distributed on the surface, with a shot spacing of 150 m and a trace spacing of 15 m. Conventional pure acoustic least-squares reverse-time migration for anisotropic media requires eight forward modeling iterations per iteration (two forward continuations of the background and perturbation wavefields; one backward continuation of the accompanying wavefield; one reconstruction of the background wavefield; and four iterations of the iterative step size calculation). However, the proposed pure acoustic least-squares reverse-time migration method for anisotropic media requires 28 forward modeling iterations per iteration (eight for conventional methods; four iterations per iteration for the gradient Hessian operator preconditioning, and five iterations per iteration).

[0037] It should be noted that the computational effort required for 35 iterations of the conventional method and 10 iterations of the method of the present application is the same (both are 280 forward modelings). Figures 5 to 7 The results of 35 iterations of the conventional least squares reverse time migration method are given. As can be seen from the figure, the image of the velocity perturbation is better than the image of the anisotropy parameter perturbation.

[0038] Figures 8 to 10 Results from 10 iterations of the least-squares reverse time migration method presented in this application are presented. Low-frequency noise in the anisotropic parameter perturbation results is effectively suppressed, and event continuity is significantly improved. Compared with conventional methods, the velocity perturbation images obtained using this method exhibit improved interface focus and reduced ghosting.

[0039] The above results show that by adopting the new truncated Gauss-Newton inversion method, the pure acoustic least squares reverse time migration method for anisotropic media proposed in this application can provide high-quality velocity and anisotropy parameter perturbation models, significantly improving the accuracy and resolution of seismic data migration imaging in anisotropic media.

[0040] It should be noted that for the method embodiments, for simplicity of description, they are all expressed as a series of action combinations, but those skilled in the art should be aware that this application is not limited by the order of the actions described, because according to this application, certain steps can be performed in other orders or simultaneously. Secondly, those skilled in the art should also be aware that the embodiments described in this specification are all optional embodiments, and the actions involved are not necessarily required by this application.

[0041] Example 2 Optionally, an embodiment of the present application also provides an electronic device, comprising: a processor, a memory, and a computer program stored in the memory and runnable on the processor. When the computer program is executed by the processor, the various processes of the above-mentioned method embodiment are implemented and the same technical effect can be achieved. To avoid repetition, it will not be repeated here.

[0042] The present application also provides a computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, the various processes of the above-described method embodiments are implemented and the same technical effects are achieved. To avoid repetition, the details are not described here. The computer-readable storage medium may be, for example, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk.

[0043] Figure 11 This application provides a block diagram of an electronic device 800. For example, the electronic device 800 may be a mobile phone, a computer, a digital broadcast terminal, a messaging device, a game console, a tablet device, a medical device, a fitness device, a personal digital assistant, etc.

[0044] Reference Figure 11 , the electronic device 800 may include one or more of the following components: a processing component 802 , a memory 804 , a power component 806 , a multimedia component 808 , an audio component 810 , an input / output (I / O) interface 812 , a sensor component 814 , and a communication component 816 .

[0045] The processing component 802 generally controls the overall operation of the electronic device 800, such as operations associated with display, phone calls, data communications, camera operation, and recording operations. The processing component 802 may include one or more processors 820 to execute instructions to perform all or part of the steps of the above-described method. In addition, the processing component 802 may include one or more modules to facilitate interaction between the processing component 802 and other components. For example, the processing component 802 may include a multimedia module to facilitate interaction between the multimedia component 808 and the processing component 802.

[0046] The memory 804 is configured to store various types of data to support operations on the device 800. Examples of such data include instructions for any application or method operating on the electronic device 800, contact data, phone book data, messages, images, videos, etc. The memory 804 can be implemented by any type of volatile or non-volatile storage device, or a combination thereof, such as static random access memory (SRAM), electrically erasable programmable read-only memory (EEPROM), erasable programmable read-only memory (EPROM), programmable read-only memory (PROM), read-only memory (ROM), magnetic memory, flash memory, magnetic disk, or optical disk.

[0047] The power supply component 806 provides power to the various components of the electronic device 800. The power supply component 806 may include a power management system, one or more power supplies, and other components associated with generating, managing, and distributing power to the electronic device 800.

[0048] The multimedia component 808 includes a screen that provides an output interface between the electronic device 800 and the user. In some embodiments, the screen may include a liquid crystal display (LCD) and a touch panel (TP). If the screen includes a touch panel, it may be implemented as a touch screen to receive input signals from the user. The touch panel includes one or more touch sensors to sense touches, slides, and gestures on the touch panel. The touch sensors can not only sense the boundaries of a touch or slide action, but also detect the duration and pressure associated with the touch or slide action. In some embodiments, the multimedia component 808 includes a front-facing camera and / or a rear-facing camera. When the device 800 is in an operating mode, such as a capture mode or a video mode, the front-facing camera and / or the rear-facing camera can receive external multimedia data. Each front-facing camera and the rear-facing camera can have a fixed optical lens system or have focal length and optical zoom capabilities.

[0049] The audio component 810 is configured to output and / or input audio signals. For example, the audio component 810 includes a microphone (MIC) that is configured to receive external audio signals when the electronic device 800 is in an operating mode, such as a call mode, a recording mode, and a voice recognition mode. The received audio signals may be further stored in the memory 804 or transmitted via the communication component 816. In some embodiments, the audio component 810 also includes a speaker for outputting audio signals.

[0050] I / O interface 812 provides an interface between processing component 802 and peripheral interface modules, such as a keyboard, click wheel, buttons, etc. These buttons may include, but are not limited to, a home button, volume buttons, a start button, and a lock button.

[0051] The sensor assembly 814 includes one or more sensors for providing various aspects of status assessment for the electronic device 800. For example, the sensor assembly 814 can detect the open / closed state of the device 800, the relative positioning of components, such as the display and keypad of the electronic device 800. The sensor assembly 814 can also detect changes in the position of the electronic device 800 or a component of the electronic device 800, the presence or absence of user contact with the electronic device 800, the orientation or acceleration / deceleration of the electronic device 800, and temperature changes of the electronic device 800. The sensor assembly 814 may include a proximity sensor configured to detect the presence of nearby objects without any physical contact. The sensor assembly 814 may also include a light sensor, such as a CMOS or CCD image sensor, for use in imaging applications. In some embodiments, the sensor assembly 814 may also include an accelerometer, a gyroscope sensor, a magnetic sensor, a pressure sensor, or a temperature sensor.

[0052] The communication component 816 is configured to facilitate wired or wireless communication between the electronic device 800 and other devices. The electronic device 800 can access a wireless network based on a communication standard, such as WiFi, a carrier network (such as 2G, 3G, 4G or 5G), or a combination thereof. In an exemplary embodiment, the communication component 816 receives a broadcast signal or broadcast operation information from an external broadcast management system via a broadcast channel. In an exemplary embodiment, the communication component 816 also includes a near field communication (NFC) module to facilitate short-range communication. For example, the NFC module can be implemented based on radio frequency identification (RFID) technology, infrared data association (IrDA) technology, ultra-wideband (UWB) technology, Bluetooth (BT) technology, and other technologies.

[0053] In an exemplary embodiment, the electronic device 800 may be implemented by one or more application-specific integrated circuits (ASICs), digital signal processors (DSPs), digital signal processing devices (DSPDs), programmable logic devices (PLDs), field programmable gate arrays (FPGAs), controllers, microcontrollers, microprocessors, or other electronic components to perform the above methods.

[0054] In an exemplary embodiment, a non-transitory computer-readable storage medium including instructions is also provided, such as a memory 804 including instructions. The instructions can be executed by the processor 820 of the electronic device 800 to perform the above method. For example, the non-transitory computer-readable storage medium can be a ROM, a random access memory (RAM), a CD-ROM, a magnetic tape, a floppy disk, an optical data storage device, etc.

[0055] Example 3 Figure 12 This is a block diagram of another electronic device 1900 provided in the present application. For example, the electronic device 1900 can be provided as a server.

[0056] Reference Figure 12 The electronic device 1900 includes a processing component 1922, which further includes one or more processors, and a memory resource represented by a memory 1932 for storing instructions executable by the processing component 1922, such as an application. The application stored in the memory 1932 may include one or more modules, each corresponding to a set of instructions. In addition, the processing component 1922 is configured to execute the instructions to perform the above-described method.

[0057] The electronic device 1900 may further include a power supply component 1926 configured to perform power management of the electronic device 1900, a wired or wireless network interface 1950 configured to connect the electronic device 1900 to a network, and an input / output (I / O) interface 1958. The electronic device 1900 may operate based on an operating system stored in the memory 1932, such as Windows Server™, Mac OS X™, Unix™, Linux™, FreeBSD™, or the like.

[0058] Example 4 In a fourth aspect, the present application illustrates a computer program product. When instructions in the computer program product are executed by a processor of an electronic device, the electronic device is enabled to perform the method as described in any one of the above aspects.

[0059] It should be noted that, in this document, the terms "comprises," "includes," or any other variations thereof are intended to encompass non-exclusive inclusion, such that a process, method, article, or apparatus comprising a series of elements includes not only those elements but also other elements not explicitly listed, or elements inherent to such process, method, article, or apparatus. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of other identical elements in the process, method, article, or apparatus comprising the element.

[0060] Through the description of the above embodiments, those skilled in the art can clearly understand that the above-mentioned embodiment methods can be implemented by means of software plus the necessary general hardware platform. Of course, they can also be implemented by hardware, but in many cases the former is a more preferred embodiment. Based on this understanding, the technical solution of this application, or the part that contributes to the existing technology, can be embodied in the form of a software product. This computer software product is stored in a storage medium (such as ROM / RAM, magnetic disk, optical disk), and includes a number of instructions for enabling a terminal (which can be a mobile phone, computer, server, air conditioner, or network device, etc.) to execute the methods described in each embodiment of this application.

[0061] The embodiments of the present application are described above in conjunction with the accompanying drawings, but the present application is not limited to the above-mentioned specific implementation methods. The above-mentioned specific implementation methods are merely illustrative and not restrictive. Under the guidance of this application, ordinary technicians in this field can also make many forms without departing from the purpose of this application and the scope of protection of the claims, all of which are within the protection of this application.

[0062] Those skilled in the art will appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed in the embodiments of this application can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of this application.

[0063] Those skilled in the art will clearly understand that, for the convenience and brevity of description, the specific working processes of the systems, devices and units described above can refer to the corresponding processes in the aforementioned method embodiments and will not be repeated here.

[0064] In the embodiments provided in this application, it should be understood that the disclosed devices and methods can be implemented in other ways. For example, the device embodiments described above are merely schematic. For example, the division of the units is merely a logical function division. In actual implementation, there may be other division methods, such as multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some interfaces, indirect coupling or communication connection of devices or units, which can be electrical, mechanical or other forms.

[0065] The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of these units may be selected to achieve the purpose of this embodiment according to actual needs.

[0066] In addition, each functional unit in each embodiment of the present application may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit.

[0067] If the functions are implemented in the form of software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present application, or the part that contributes to the prior art, or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions for enabling a computer device (which can be a personal computer, server, or network device, etc.) to execute all or part of the steps of the method described in each embodiment of the present application. The aforementioned storage medium includes various media that can store program codes, such as a USB flash drive, a mobile hard disk, a ROM, a RAM, a magnetic disk, or an optical disk.

[0068] The above description is merely a specific embodiment of the present application, but the scope of protection of the present application is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in this application should be included in the scope of protection of the present application. Therefore, the scope of protection of the present application should be based on the scope of protection of the claims.

Claims

1. A pure acoustic least squares reverse time migration method for anisotropic media, characterized by: The method comprises: Calculate the back-migration operator of the pure acoustic wave equation in anisotropic media; Determine the adjoint equation of the pure acoustic wave equation in anisotropic media and the parameter perturbation gradient formula; Solve the anti-migration operator and adjoint equation of the pure acoustic wave equation in anisotropic media; Determine the Hessian matrix and vector product formula of the pure acoustic wave equation in anisotropic media; Calculate model parameter perturbation gradients and Gauss-Newton gradient preconditioners; Iteratively update the velocity and anisotropy parameter perturbation model.

2. The pure acoustic least squares reverse time migration method for anisotropic media according to claim 1, characterized in that: The pure acoustic wave equation demigration operator for anisotropic media is calculated as follows: The pure acoustic wave equations for VTI vertical transverse isotropic and anisotropic media are as follows: (1) in, For TRON, are model parameters, is the source term; (2) in, is the propagation velocity in the direction of the symmetry axis, and is the Thomsen anisotropy parameter, For time, and is the spatial coordinate, Represents matrix or vector transpose; Based on the Born approximation, the seismic wave field and model parameters are split into background components and disturbance components. Formula (1) becomes: (3) in, is the background wave field, To disturb the wave field, is the background parameter, is the disturbance parameter; Expanding formula (3) using Taylor series yields: (4) in, (5) (6) (7) The background wave field and background parameters also satisfy the wave equation shown in formula (1): (8) Subtracting formula (8) from formula (3) and ignoring the high-order terms of wave field perturbations and parameter perturbations yields: (9) In order to eliminate the velocity dimension, the relative change of velocity is used to express the image of velocity, such as expression (10): (10) Formula (10) can be rewritten as: (11) Among them, formulas (8) and (11) are the back migration operators of the pure acoustic wave equation of VTI anisotropic media, that is, the perturbation wave field is calculated by perturbing the known model parameters: .

3. The pure acoustic least squares reverse time migration method for anisotropic media according to claim 1, characterized in that: The adjoint equation of the pure acoustic wave equation in anisotropic media and the parameter perturbation gradient formula are determined in the following manner, including: Establish the minimization objective function: (12) in, To simulate the disturbance wave field, To observe the disturbance wave field, is the calculation area, is the maximum recording time, is the detection point projection operator; The Lagrange multiplier method is used to solve this constrained optimization problem, and the objective function becomes: (13) in, For the accompanying wave field; By integrating formula (13) by parts and assuming that the wave fields at the initial, final and boundary locations are zero, we can obtain: (14) make The adjoint equation of the pure acoustic wave equation in VTI anisotropic media can be obtained: (15) Based on the chain rule Derive the gradient of the objective function with respect to the perturbation of the model parameters: (16) (17) (18) in, .

4. The pure acoustic least squares reverse time migration method for anisotropic media according to claim 1, characterized in that: The demigration operator and adjoint equations of the pure acoustic wave equation in anisotropic media are solved as follows, including: High-order regular grid finite differences are used to quickly solve the hyperbolic differential equations in formulas (8), (11) and (15). The mixed partial derivatives in the x and z directions are approximated by finite differences along the two directions respectively. The fast Poisson equation is used to solve the Poisson equation with constant coefficients in formulas (8), (11) and (15) efficiently.

5. The pure acoustic least squares reverse time migration method for anisotropic media according to claim 1, characterized in that: The Hessian matrix and vector product formula of the pure acoustic wave equation of anisotropic medium are determined in the following manner, including: In the discrete case, the model parameter perturbation , the gradient of the objective function with respect to the perturbation of the model parameters and Hessian matrix Respectively expressed as: (19) (20) (21) (22) Where, N is the discrete grid dimension; gradient Represents the first-order derivative of the objective function with respect to the model parameter perturbation, the Hessian matrix represents the second-order derivative of the objective function with respect to the model parameter disturbance, and the relationship between the two is shown in expression (23): (23) Construct a new objective function F as shown in expression (24): (24) Where x is an arbitrary column vector of dimension 3N, (25) Based on formulas (23) and (24), we can obtain: (26) In the continuous case, the derivative formula (24) of the objective function with respect to the model parameter perturbation becomes: (27) in, ( ) is an arbitrary function related to the spatial position; Based on the Lagrange multiplier method, the derivative formula of the objective function F with respect to the model parameter disturbance is derived, and formula (27) becomes: (28) in, ( )、 and is the Lagrange multiplier function; Formula (28) can be simplified as: (29) make , , (30) Formula (29) degenerates into: (31) By integrating formula (31) by parts and assuming that the wave fields at the initial, final and boundary locations are zero, we can obtain: (32) make and We can get: (33) (34) Based on the chain rule Derive the gradient of the new objective function with respect to the perturbation of the model parameters: (35) (36) (37) in, , in the discrete case, the gradient of F with respect to the model parameter perturbation m is the product of the Hessian matrix H and any vector x.

6. The pure acoustic least squares reverse time migration method for anisotropic media according to claim 1, characterized in that: The model parameter perturbation gradients and Gauss-Newton gradient preconditioners are calculated as follows: According to formulas (8) and (11), the de-migration operator is numerically solved in the forward direction of time to obtain the background wave field and disturbed wave fields ; According to formula (15), numerically solve the adjoint equation in reverse time to obtain the adjoint wave field Based on formulas (16) to (18), calculate the gradient of the objective function with respect to the model parameter perturbation ( ); Gradient of the perturbation of model parameters using Hessian operator Perform preconditioning: (38) in, is the inverse of the Hessian matrix, is the gradient of the model perturbation parameter after preconditioning; It is difficult to directly calculate and store the Hessian matrix or its inverse matrix. The inversion operation in formula (38) is converted into the following linear equation solution problem: (39) The steps for solving the system of equations shown in formula (38) using the conjugate gradient method are: (1) Given an initial value , , and ; (2) Calculate the Hessian matrix using formulas (8), (30), (33), (34), (35)-(37) With vector The product of ; (3) Calculation and : and ; (4) Update and : 、 、 、 ; (5) Repeat steps (2) to (4) until the maximum number of iterations is reached, and output the final model perturbation parameter gradient .

7. The pure acoustic least squares reverse time migration method for anisotropic media according to claim 1, characterized in that: The velocity and anisotropy parameter perturbation model is iteratively updated as follows: Based on the preconditioned gradient , the velocity and anisotropy parameter perturbation model is updated, and the iterative steps are repeated until the convergence conditions are met. The updated formula is as follows: (40) in, is the number of iterations, Perturb the model parameters for the current and next iterations, Perturb the model parameters for the next iteration, is the iteration step length.

8. An electronic device, characterized in that: include: A processor, a memory, and a computer program stored in the memory and executable on the processor, wherein the computer program implements the method according to any one of claims 1 to 7 when executed by the processor.

9. A computer-readable storage medium, characterized in that The computer-readable storage medium stores a computer program, which implements the method according to any one of claims 1 to 7 when executed by a processor.

10. A computer program product, characterized in that When the instructions in the computer program product are executed by a processor of an electronic device, the electronic device implements the method according to any one of claims 1 to 7.

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