Anisotropy parameter full waveform inversion method based on undulating ground surface and related equipment

Abstract

The application provides a kind of anisotropy parameter full waveform inversion method based on relief surface and related equipment, the method comprises: establishing relief surface model;According to relief surface model, anisotropic wave equation is converted from Cartesian coordinate system to curved coordinate system, the solution of anisotropic wave equation is determined, and the forward modeling of seismic wave is realized;The difference between the solution of anisotropic wave equation of seismic wave in relief surface model and actual observation wave field is residual error, the solution of reverse propagation anisotropic wave equation is solved with residual error as source, and the objective function of relief surface is determined;Determine the gradient equation of objective function relative to unknown parameter;According to the solution of anisotropic wave equation in Cartesian coordinate system and the solution of anisotropic wave equation of residual error as source reverse propagation, the inversion gradient of anisotropic parameter is determined;According to the solution of anisotropic wave equation of relief surface model, actual observation wave field and the gradient inversion of anisotropic parameter, the anisotropic parameter is calculated.

Description

Technical Field

[0001] This application relates to the field of surface exploration technology, and in particular to a method and related equipment for full waveform inversion of anisotropic parameters based on undulating surfaces. Background Technology

[0002] Full waveform inversion (FWI) derives high-resolution velocity models by minimizing the differences between observed and simulated seismic waveforms. Traditional refraction and reflection tomography techniques utilize only the travel time information of seismic data. However, seismic amplitude and phase carry a wealth of information about subsurface structures. FWI uses this additional information from seismic waveforms to invert subsurface parameters. It directly solves the two-way wave equation, providing a superior method for establishing high-resolution velocity fields, especially for complex geological models. However, existing FWI algorithms are only applicable to acoustic or elastic media and do not consider the influence of surface undulations and media anisotropy on the inversion parameters. The methods for calculating the inversion gradient matrix are not suitable for stratigraphic models with undulating surfaces. Summary of the Invention

[0003] In view of this, the purpose of this application is to propose a full waveform inversion method and related equipment for anisotropic parameters based on undulating surfaces to solve the above problems or at least partially solve the above problems.

[0004] To achieve the above objectives, a first aspect of this application provides a method for full waveform inversion of anisotropic parameters based on undulating surfaces, comprising:

[0005] Obtain a model of undulating terrain;

[0006] Based on the undulating surface model, the anisotropic wave equation is transformed from the Cartesian coordinate system to the curvilinear coordinate system to determine the solution of the anisotropic wave equation, thereby realizing the forward modeling of seismic waves.

[0007] The difference between the solution of the anisotropic wave equation of the seismic wave on the undulating surface model and the actual observed wave field is determined as the residual. The solution of the backpropagation anisotropic wave equation is solved using the residual as the source, and the objective function of the undulating surface is determined based on the residual.

[0008] Based on the objective function, determine the gradient equation of the objective function with respect to the unknown parameters;

[0009] Based on the solution of the anisotropic wave equation in the Cartesian coordinate system and the solution of the anisotropic wave equation backpropagating from the residual as the source, the inversion gradient of the anisotropic parameter is determined using the gradient equation.

[0010] Based on the solution of the anisotropic wave equation of the undulating surface model, the anisotropic parameters are calculated by gradient inversion of the actual observed wavefield and the anisotropic parameters.

[0011] Optionally, based on the undulating surface model, the anisotropic wave equation is transformed from the Cartesian coordinate system to the curvilinear coordinate system to determine the solution of the anisotropic wave equation, thereby realizing the forward modeling of seismic waves, including:

[0012] Determine the anisotropic wave equation in the Cartesian coordinate system within the time domain;

[0013] Determine the free surface boundary conditions in the Cartesian coordinate system based on the anisotropic wave equation in the Cartesian coordinate system.

[0014] Determine the mapping relationship between the grid points in the physical space of the Cartesian coordinate system and the grid points in the computational space of the curvilinear coordinate system;

[0015] Based on the mapping relationship, the anisotropic wave equation and the undulating surface boundary conditions within the curvilinear coordinate system are determined.

[0016] Optionally, the difference between the solution of the anisotropic wave equation of the seismic wave on the undulating surface model and the actual observed wavefield is determined as the residual. The solution of the backpropagation anisotropic wave equation is solved using the residual as the source, and the objective function is determined based on the residual, including:

[0017] Determine the location of the seismic source and detector of the undulating surface model;

[0018] Based on the location of the seismic source and detector of the undulating surface model, determine the solution of the anisotropic wave equation conjectured by the undulating surface model.

[0019] Determine the location of the actual seismic source and detector;

[0020] The observed wavefield is determined based on the actual observed source and detector locations;

[0021] The objective function is determined by using the residual between the solution of the anisotropic wave equation predicted by the undulating surface model and the actual observed wave field.

[0022] Optionally, the objective function is expressed as:

[0023]

[0024] Among them, u cal (x s ,x r ,t) represents the solution to the anisotropic wave equation of the undulating surface model, u obs (x s ,x r (t) represents the actual observed wave field, x sIndicates the location of the earthquake source in the undulating surface model, x r The x represents the location of the detector in the undulating terrain model. s1 Indicates the actual observed location of the earthquake source, x r1 The actual position of the detector observed, where t represents time.

[0025] Optionally, based on the objective function, the gradient of the objective function with respect to the unknown parameters is determined, including:

[0026] Based on the objective function, the solution of the anisotropic wave equation propagated from the residual source is determined using the method of reverse wave field propagation with residual source.

[0027] Based on the solution of the anisotropic wave equation backpropagated from the residual source, the gradient equation of the objective function with respect to the unknown parameters is determined.

[0028] Optionally, based on the solution of the anisotropic wave equation in the Cartesian coordinate system and the solution of the anisotropic wave equation backpropagated from the residual as the source, the inversion gradient of the anisotropic parameter is determined using the gradient equation, including:

[0029] Based on the solution of the anisotropic wave equation in the Cartesian coordinate system, determine the perturbation of each anisotropic parameter and the displacement perturbation.

[0030] Determine the Green's function equation for the displacement perturbation;

[0031] Based on the Green's function equation of the displacement disturbance, determine the amount of displacement disturbance caused by the anisotropic parameter disturbance;

[0032] Based on the gradient equation of the objective function with respect to the unknown parameters, the partial derivatives of the objective function with respect to the anisotropic parameters are determined by using the partial derivatives of the displacement perturbation with respect to the anisotropic parameters.

[0033] The gradient of the objective function with respect to the anisotropic parameters is determined based on the partial derivative of the objective function with respect to the anisotropic parameters.

[0034] Optional, also includes:

[0035] Based on the mapping relationship between the grid points in the physical space of the Cartesian coordinate system and the grid points in the computational space of the curvilinear coordinate system, the displacement disturbance generated by the anisotropic parameters in the curvilinear coordinate system is determined.

[0036] The gradient values ​​of the anisotropic parameters in the curvilinear coordinate system are determined based on the displacement disturbances generated by the anisotropic parameters.

[0037] A second aspect of this application provides an anisotropic parameter full waveform inversion device based on undulating surfaces, comprising:

[0038] The acquisition module is used to acquire undulating terrain models.

[0039] The forward modeling module is used to transform the anisotropic wave equation from the Cartesian coordinate system to the curvilinear coordinate system based on the undulating surface model, determine the solution of the anisotropic wave equation, and realize the forward modeling simulation of seismic waves.

[0040] The objective function module is used to determine the residual as the difference between the solution of the anisotropic wave equation of the seismic wave on the undulating surface model and the actual observed wave field. The residual is used as the source to solve the solution of the backpropagation anisotropic wave equation, and the objective function of the undulating surface is determined based on the residual.

[0041] The gradient equation module is used to determine the gradient equation of the objective function with respect to the unknown parameters based on the objective function.

[0042] The anisotropic parameter inversion gradient module determines the gradient of the anisotropic parameter based on the solution of the anisotropic wave equation in the Cartesian coordinate system and the solution of the anisotropic wave equation backpropagated from the residual.

[0043] An anisotropic parameter inversion module is used to calculate the anisotropic parameters based on the solution of the anisotropic wave equation of the undulating surface model, the actual observed wavefield, and the gradient inversion of the anisotropic parameters. A third aspect of this application provides an electronic device including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the program, implements the method described in the first aspect.

[0044] A fourth aspect of this application provides a non-transitory computer-readable storage medium storing computer instructions for causing a computer to perform the method described in the first aspect.

[0045] As can be seen from the above, the anisotropic parameter full-waveform inversion method and related equipment based on undulating surfaces provided in this application realizes the transformation of the anisotropic wave equation from the Cartesian coordinate system to the curvilinear coordinate system by solving the anisotropic wave equation in the curvilinear coordinate system. Forward modeling is achieved by solving the anisotropic wave equation in the curvilinear coordinate system, and the objective function is minimized using the conjugate gradient method. A gradient calculation method for inverting the anisotropic parameters of the strata containing undulating surfaces is constructed using the perturbation method. Finally, the gradient of the anisotropic parameters is numerically calculated using the wavefield solution of the seismic wave forward modeling with undulating surfaces in the curvilinear coordinate system and the solution of the anisotropic wave equation propagating backward with residuals as the source. Ultimately, the inversion calculation of anisotropic parameters is achieved. This application realizes the inversion of anisotropic parameters of undulating surfaces by considering the influence of undulating surfaces and medium anisotropy on the inversion parameters. Attached Figure Description

[0046] To more clearly illustrate the technical solutions in this application or related technologies, the drawings used in the description of the embodiments or related technologies will be briefly introduced below. Obviously, the drawings described below are only embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0047] Figure 1 This is a flowchart of the full waveform inversion method for anisotropic parameters based on undulating terrain according to an embodiment of this application;

[0048] Figure 2 This is a schematic diagram illustrating the mapping relationship between the Cartesian coordinate system and the curvilinear coordinate system in an embodiment of this application.

[0049] Figure 3 This is a gradient flowchart for determining anisotropy parameters according to an embodiment of this application;

[0050] Figure 4 This is a schematic diagram of the anisotropic parameter full waveform inversion device based on undulating terrain according to an embodiment of this application;

[0051] Figure 5 This is a schematic diagram of an electronic device according to an embodiment of this application. Detailed Implementation

[0052] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with specific embodiments and the accompanying drawings.

[0053] It should be noted that, unless otherwise defined, the technical or scientific terms used in the embodiments of this application should have the ordinary meaning understood by one of ordinary skill in the art to which this application pertains. The terms "first," "second," and similar terms used in the embodiments of this application do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed after the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are only used to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0054] As described in the background section above, this application considers the anisotropic parameters of undulating surfaces and addresses the inversion problem of anisotropic parameters of elastic anisotropic media with undulating surfaces, thereby solving the problems of surface undulation and stratigraphic anisotropy.

[0055] refer to Figure 1 The diagram shown is a flowchart of a full waveform inversion method for anisotropic parameters based on undulating surfaces provided in this application. The method includes:

[0056] S101. Obtain the undulating terrain model.

[0057] In this application, the undulating surface model is pre-established, which can be an initial undulating surface model established by pre-collecting the corresponding parameters of known undulating surfaces and using the corresponding parameters for training.

[0058] S102. Based on the undulating surface model, the anisotropic wave equation is transformed from the Cartesian coordinate system to the curvilinear coordinate system to determine the solution of the anisotropic wave equation and realize the forward modeling of seismic waves.

[0059] In step S102, the anisotropic wave equation in the Cartesian coordinate system in the time domain is first determined as follows:

[0060]

[0061]

[0062] Based on the anisotropic wave equation in the Cartesian coordinate system, the free surface boundary conditions in the Cartesian coordinate system are determined as follows:

[0063]

[0064] In the above formula, ρ is the density of the medium, u is the lateral displacement of the seismic wave, v is the longitudinal displacement of the seismic wave, and c 11 c 13 c 33 c 44 n is the anisotropy parameter of the medium. x n z Let x and y represent the directions of the interior normal in the Cartesian coordinate system, respectively. z These represent the horizontal and vertical coordinates of the Cartesian coordinate system, respectively.

[0065] Determine the mapping relationship between grid points in the physical space of the Cartesian coordinate system and grid points in the computational space of the curvilinear coordinate system.

[0066] refer to Figure 2As shown, for undulating surfaces, this embodiment uses a boundary-consistent grid to describe the free surface and suppress anthropogenic scattered waves, achieved through the transformation between curvilinear computational space and Cartesian physical space. The mapping relationship between grid points (x,z) in the Cartesian coordinate system and grid points (q,r) in the curvilinear coordinate system is x = x(q,r) and z = z(q,r). Then, according to the chain rule, the spatial derivative in the Cartesian coordinate system obtained from the curvilinear coordinate system is:

[0067]

[0068]

[0069] Where, q x q z r x r z For metric derivatives, respectively represent and

[0070] Based on the mapping relationship, the anisotropic wave equation and the undulating surface boundary conditions within the curvilinear coordinate system are determined.

[0071] Based on the above mapping relationship, the anisotropic wave equation in the curvilinear coordinate system is expressed as:

[0072]

[0073]

[0074] In the above formula, and These represent the partial derivatives in the q and r directions, respectively, in the curvilinear coordinate system.

[0075] The boundary conditions for undulating terrain are expressed as follows:

[0076]

[0077]

[0078] In the above formula, u q u r v q v r Let represent the partial derivatives of u and v in the q and r directions, respectively.

[0079] By solving the anisotropic wave equation in a curvilinear coordinate system, a forward wavefield simulation of seismic waves with undulating surfaces is performed in the time domain. Using known topographic and medium conditions, the anisotropic parameters are determined by calculating the anisotropic wave equation, simulating the process of seismic waves reaching the ground from the hypocenter. Here, by comparing the response of the undulating surface model—that is, the predicted data—with the actual data, the differences between the predicted and actual data can be clearly identified.

[0080] S103. Determine the difference between the solution of the anisotropic wave equation of the seismic wave model on the undulating surface and the actual observed wave field as the residual. Use the residual as the source to solve the solution of the backpropagation anisotropic wave equation, and determine the objective function of the undulating surface based on the residual.

[0081] In this embodiment, the main purpose is to solve the problem of full waveform inversion of anisotropic parameters by constructing an objective function for undulating terrain.

[0082] Least squares is a standard regression method used to approximate the solution of an overdetermined system. Using least squares, the objective function for undulating terrain is determined based on the residuals:

[0083]

[0084] Where T denotes the transpose of the matrix, introduced into the equation for simplification. The seismic response recorded by the detector is d, and the unknown parameter to be inverted is m. The relationship between the two can be expressed as a nonlinear function F, then d = F(m). The residual Δd is defined as the solution F(m) of the anisotropic wave equation of the undulating surface model and the actual observed wavefield d. obs The difference between them, i.e., Δd = F(m) - d obs .

[0085] In the above formula, ||Δd|| 2 Let L2 represent the residual.

[0086] Specifically, step S103 includes,

[0087] Determine the location of the seismic source and detector of the undulating surface model;

[0088] Based on the location of the seismic source and the detector of the undulating surface model, the wave field predicted by the undulating surface model is determined.

[0089] Determine the location of the actual seismic source and detector;

[0090] The actual observed wave field is determined based on the actual observed source and detector locations;

[0091] The objective function is determined by using the difference between the wave field predicted by the undulating surface model and the actual observed wave field as the residual.

[0092] The objective function in the L2 norm form described above can be expressed as:

[0093]

[0094] Among them, u cal (x s ,x r ,t) represents the solution to the anisotropic wave equation of the undulating surface model, u obs (x s ,x r (t) represents the actual observed wave field, x s Indicates the location of the earthquake source in the undulating surface model, x r The x represents the location of the detector in the undulating terrain model. s1 Indicates the actual observed location of the earthquake source, x r1 The actual position of the detector observed, where t represents time.

[0095] S104. Based on the objective function, determine the gradient equation of the objective function with respect to the unknown parameters.

[0096] Specifically, step S104 includes,

[0097] Based on the objective function, the solution of the anisotropic wave equation of the gradient back propagation of the residual source is determined by using the method of back propagation of the residual source back field.

[0098] Based on the solution of the anisotropic wave equation backpropagated from the residual source, the gradient equation of the objective function with respect to the unknown parameters is determined.

[0099] In this embodiment, the inversion problem is solved by minimizing the objective function E(c), using the gradient method to minimize the objective function, and iteratively updating the undulating surface model data m[c] in the opposite direction to E(c). 11 ,c 13 ,c 33 ,c 44 It can be determined that the unknown parameters include anisotropic parameters.

[0100]

[0101] Where n is the number of iterations and α is the step size. During the inversion iteration, the backpropagation gradient needs to be explicitly defined; the gradient of the objective function can be expressed as:

[0102]

[0103] Where i represents the earthquake record, mj This represents the data that needs to be inverted. Since the Jacobian matrix J is difficult to calculate, a method using the residual as the source for back-propagation of the wave field is employed. Multiple forward calculations are performed to obtain the solution to the anisotropic wave equation for back-propagation of the residual source. The gradient of the objective function can be expressed as:

[0104]

[0105] Where c represents the parameters in the data to be inverted.

[0106] The gradient equation of the objective function with respect to the unknown parameters is obtained as follows:

[0107]

[0108] In some embodiments, after iteratively updating the data of the undulating surface model using the gradient method in the opposite direction of the objective function through the above embodiments, it is also necessary to calculate the step size of the iterative update. According to the gradient inversion method, we obtain:

[0109] p (k) =m (k+1) -m (k) (12a)

[0110]

[0111]

[0112] Where, p (k) m represents the difference between the unknown parameters in the k-th and (k+1)-th iterations. (k+1) and m (k) Let q represent the unknown parameters obtained from the (k+1)th and kth calculations, respectively. (k) This represents the difference between the objective function at the k-th and (k+1)-th iterations. and Let α represent the values ​​of the objective function obtained in the (k+1)th and kth calculations, respectively. (k) This is the step size for the update iteration.

[0113] S105. Based on the solution of the anisotropic wave equation in the Cartesian coordinate system and the solution of the anisotropic wave equation propagating backward from the residual, the inversion gradient of the anisotropic parameters is determined using the gradient equation.

[0114] Specifically, refer to Figure 3 As shown, step S105 includes:

[0115] S301. Based on the solution of the anisotropic wave equation in the Cartesian coordinate system, determine the amount of displacement disturbance caused by the anisotropic parameter disturbance.

[0116] Using formulas (1a) and (1b), with the anisotropic parameter c 11 For example, determine the anisotropy parameter c. 11 The disturbance is δc 11 =c′ 11 -c 11 The resulting displacement disturbances are δu = u' - u and δv = v' - v. Applying a new parameter, namely the anisotropic disturbance c′ generated by the wave field disturbance... 11 Substituting the horizontal wave field disturbance u' and the vertical wave field disturbance v' generated by the wave field disturbance into the second-order wave equation in Cartesian coordinates, we obtain:

[0117]

[0118]

[0119] Substituting equations (13a) and (13b) into the anisotropic wave equations (1a) and (1b) in the Cartesian coordinate system, the displacement disturbance becomes:

[0120]

[0121]

[0122] S302. Determine the Green's function equation for the displacement disturbance.

[0123] Specifically, determine detector X g The Green's function equation for the horizontal displacement perturbation u is:

[0124]

[0125] Where Ω represents the entire computational domain, and T n This represents the total travel time. For formula (15), add and subtract... The displacement perturbation equation with Green's function is obtained as follows:

[0126]

[0127] When δc 11 As u'-u→0, the horizontal displacement disturbance δu becomes:

[0128]

[0129] S303. Based on the Green's function equation of the displacement disturbance, determine the amount of displacement disturbance caused by the anisotropic parameter disturbance.

[0130] Specifically, assuming the strata are as follows Figure 2The grid in the shown curvilinear coordinate system is uniform, and the number of grids in the entire computational domain is N. p Then in the computational domain N p In the anisotropy parameter c 11 The disturbance amount of the horizontal displacement caused by the disturbance is:

[0131]

[0132] S304. Based on the gradient equation of the objective function with respect to the unknown parameters, the partial derivative of the objective function with respect to the anisotropic parameters is determined by using the partial derivative of the displacement perturbation with respect to the anisotropic parameters.

[0133] Specifically, based on the gradient equation of the objective function with respect to the position parameters, the gradient of the unknown parameters is determined by the partial derivative of the objective function with respect to the unknown parameters. For the anisotropic parameters included in the unknown parameters, the horizontal displacement with respect to the anisotropic parameter c is determined. 11 The partial derivative is:

[0134]

[0135] The objective function with respect to the anisotropic parameter c 11 The partial derivative is:

[0136]

[0137] Among them, u * This represents the horizontal displacement of the wave field backpropagation, and its source is the horizontal displacement residual uu. d .

[0138] Compared to other anisotropic parameters, the objective function is more effective for anisotropic parameters c. 44 The derivation is more complex, involving the anisotropic parameter c. 44 The disturbance is δc 44 =c' 44 -c 44 Similarly, the resulting displacement disturbances are δu = u' - u and δv = v' - v. Substituting these into the second-order wave equation in Cartesian coordinates, we obtain:

[0139]

[0140]

[0141] Subtracting equations (1a) and (1b) from equations (23a) and (23b) determines that the displacement disturbance becomes:

[0142]

[0143]

[0144] The displacements u and v with Green's function become:

[0145]

[0146]

[0147] Displacements u and v with respect to anisotropic parameter c 44 The partial derivative is:

[0148]

[0149]

[0150] The objective function with respect to the anisotropic parameter c 44 The partial derivative is:

[0151]

[0152] Displacements u and v with respect to anisotropic parameter c 13 and c 33 It can be deduced similarly as follows:

[0153]

[0154]

[0155]

[0156]

[0157] The objective function with respect to the anisotropic parameter c 13 and c 33 The partial derivative is:

[0158]

[0159]

[0160] S305. Based on the partial derivatives of the objective function with respect to the anisotropic parameters, determine the inversion gradient of the objective function with respect to the anisotropic parameters. Specifically,

[0161] c 11 c 13 c 33 and c 44 The gradient is:

[0162]

[0163]

[0164]

[0165]

[0166] In some embodiments, the method further includes:

[0167] Based on the mapping relationship between the grid points in the physical space of the Cartesian coordinate system and the grid points in the computational space of the curvilinear coordinate system, the displacement disturbance generated by the anisotropic parameters in the curvilinear coordinate system is determined.

[0168] The gradient values ​​of the anisotropic parameters in the curvilinear coordinate system are determined based on the displacement disturbances generated by the anisotropic parameters.

[0169] Specifically, for undulating surfaces, this embodiment uses a boundary-consistent grid to describe the free surface and suppress anthropogenic scattered waves, achieved through a transformation between curvilinear computational space and Cartesian physical space. The mapping relationship between grid points (x,z) in the Cartesian coordinate system and grid points (q,r) in the curvilinear coordinate system is x = x(q,r) and z = z(q,r). Then, according to the chain rule, the spatial derivative in the Cartesian coordinate system obtained from the curvilinear coordinate system is:

[0170]

[0171]

[0172] Where, q x q z r x r z For metric derivatives, respectively represent and These metric derivatives can be expressed as

[0173]

[0174]

[0175] In the formula, z r , z q x r and x q They represent The transformation Jacobi J is:

[0176] J = x q z r -x r z q (33)

[0177] When calculating the gradient, a small perturbation can be given to derive the solution, using the anisotropic parameter c. 11 For example, the displacement disturbance it generates at all grid points is:

[0178]

[0179] S106. Based on the solution of the anisotropic wave equation of the undulating surface model, the anisotropic parameters are calculated by gradient inversion of the actual observed wave field and the anisotropic parameters.

[0180] In a curvilinear coordinate system, the objective function is sensitive to the anisotropic parameter c. 11 c 13 c 33 and c 44 The partial derivative is:

[0181]

[0182]

[0183]

[0184]

[0185] The specific values ​​of the gradient of the anisotropic parameters are obtained.

[0186] Then, repeat the above steps to update the undulating surface model until the termination loop condition is met.

[0187] It should be noted that the method in this embodiment can be executed by a single device, such as a computer or server. The method can also be applied in a distributed scenario, where multiple devices cooperate to complete the task. In such a distributed scenario, one of these devices may execute only one or more steps of the method in this embodiment, and the multiple devices will interact with each other to complete the method described.

[0188] It should be noted that the above description describes some embodiments of this application. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recorded in the claims can be performed in a different order than that shown in the above embodiments and still achieve the desired result. Furthermore, the processes depicted in the drawings do not necessarily require a specific or sequential order to achieve the desired result. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0189] Based on the same technical concept, and corresponding to any of the above embodiments, this application also provides an anisotropic parameter full waveform inversion device based on undulating terrain.

[0190] refer to Figure 4 The anisotropic parameter full waveform inversion device based on undulating terrain includes:

[0191] Module 41 is used to acquire the undulating surface model;

[0192] The forward modeling module 42 is used to transform the anisotropic wave equation from the Cartesian coordinate system to the curvilinear coordinate system based on the undulating surface model, determine the solution of the anisotropic wave equation, and realize the forward modeling simulation of seismic waves.

[0193] Objective function module 43 is used to determine the difference between the solution of the anisotropic wave equation of the seismic wave in the undulating surface model and the actual observed wave field as the residual, to solve the solution of the backpropagation anisotropic wave equation using the residual as the source, and to determine the objective function of the undulating surface based on the residual.

[0194] The gradient equation module 44 is used to determine the gradient equation of the objective function with respect to the unknown parameters based on the objective function.

[0195] Anisotropic parameter inversion gradient module 45 is used to determine the gradient of the anisotropic parameter based on the solution of the anisotropic wave equation in the Cartesian coordinate system and the solution of the anisotropic wave equation backpropagated from the residual.

[0196] The anisotropic parameter inversion module 46 is used to calculate the anisotropic parameters based on the solution of the anisotropic wave equation of the undulating surface model, the actual observed wave field, and the gradient inversion of the anisotropic parameters.

[0197] For ease of description, the above devices are described in terms of function, divided into various modules. Of course, in implementing this application, the functions of each module can be implemented in one or more software and / or hardware.

[0198] The apparatus of the above embodiments is used to implement the corresponding anisotropic parameter full waveform inversion method based on undulating surface in any of the foregoing embodiments, and has the beneficial effects of the corresponding method embodiments, which will not be repeated here.

[0199] Based on the same technical concept, corresponding to the methods of any of the above embodiments, this application also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the full waveform inversion method for anisotropic parameters based on undulating terrain as described in any of the above embodiments.

[0200] Figure 5This embodiment illustrates a more specific hardware structure of an electronic device, which may include a processor 1010, a memory 1020, an input / output interface 1030, a communication interface 1040, and a bus 1050. The processor 1010, memory 1020, input / output interface 1030, and communication interface 1040 are interconnected internally via the bus 1050.

[0201] The processor 1010 can be implemented using a general-purpose CPU (Central Processing Unit), microprocessor, application-specific integrated circuit (ASIC), or one or more integrated circuits, and is used to execute relevant programs to implement the technical solutions provided in the embodiments of this specification.

[0202] The memory 1020 can be implemented in the form of ROM (Read Only Memory), RAM (Random Access Memory), static storage device, dynamic storage device, etc. The memory 1020 can store the operating system and other applications. When the technical solutions provided in the embodiments of this specification are implemented by software or firmware, the relevant program code is stored in the memory 1020 and is called and executed by the processor 1010.

[0203] The input / output interface 1030 is used to connect input / output modules to realize information input and output. Input / output modules can be configured as components within the device (not shown in the figure) or externally connected to the device to provide corresponding functions. Input devices may include keyboards, mice, touchscreens, microphones, various sensors, etc., while output devices may include displays, speakers, vibrators, indicator lights, etc.

[0204] The communication interface 1040 is used to connect a communication module (not shown in the figure) to enable communication between this device and other devices. The communication module can communicate via wired means (such as USB, Ethernet cable, etc.) or wireless means (such as mobile network, WIFI, Bluetooth, etc.).

[0205] Bus 1050 includes a pathway for transmitting information between various components of the device, such as processor 1010, memory 1020, input / output interface 1030, and communication interface 1040.

[0206] It should be noted that although the above-described device only shows the processor 1010, memory 1020, input / output interface 1030, communication interface 1040, and bus 1050, in specific implementations, the device may also include other components necessary for normal operation. Furthermore, those skilled in the art will understand that the above-described device may only include the components necessary for implementing the embodiments of this specification, and not necessarily all the components shown in the figures.

[0207] The electronic devices described above are used to implement the corresponding anisotropic parameter full waveform inversion method based on undulating terrain in any of the foregoing embodiments, and have the beneficial effects of the corresponding method embodiments, which will not be repeated here.

[0208] Based on the same technical concept, corresponding to the methods of any of the above embodiments, this application also provides a non-transitory computer-readable storage medium storing computer instructions for causing the computer to execute the anisotropic parameter full waveform inversion method based on undulating terrain as described in any of the above embodiments.

[0209] The computer-readable medium of this embodiment includes permanent and non-permanent, removable and non-removable media, and information storage can be implemented by any method or technology. Information can be computer-readable instructions, data structures, program modules, or other data. Examples of computer storage media include, but are not limited to, phase-change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, CD-ROM, digital versatile optical disc (DVD) or other optical storage, magnetic tape, magnetic magnetic disk storage or other magnetic storage devices, or any other non-transfer medium that can be used to store information accessible by a computing device.

[0210] The computer instructions stored in the storage medium of the above embodiments are used to cause the computer to execute the anisotropic parameter full waveform inversion method based on undulating surface as described in any of the above embodiments, and have the beneficial effects of the corresponding method embodiments, which will not be repeated here.

[0211] Those skilled in the art should understand that the discussion of any of the above embodiments is merely exemplary and is not intended to imply that the scope of this application (including the claims) is limited to these examples; within the framework of this application, the technical features of the above embodiments or different embodiments can also be combined, the steps can be implemented in any order, and there are many other variations of different aspects of the embodiments of this application as described above, which are not provided in the details for the sake of brevity.

[0212] Additionally, to simplify the description and discussion, and to avoid obscuring the embodiments of this application, the well-known power / ground connections to integrated circuit (IC) chips and other components may or may not be shown in the provided drawings. Furthermore, the apparatus may be shown in block diagram form to avoid obscuring the embodiments of this application, and this also takes into account the fact that the details of the implementation of these block diagram apparatuses are highly dependent on the platform on which the embodiments of this application will be implemented (i.e., these details should be fully understood by those skilled in the art). While specific details (e.g., circuits) have been set forth to describe exemplary embodiments of this application, it will be apparent to those skilled in the art that the embodiments of this application can be implemented without these specific details or with variations thereof. Therefore, these descriptions should be considered illustrative rather than restrictive.

[0213] Although this application has been described in conjunction with specific embodiments thereof, many substitutions, modifications, and variations of these embodiments will be apparent to those skilled in the art from the foregoing description. For example, other memory architectures (e.g., dynamic RAM (DRAM)) may be used with the embodiments discussed.

[0214] The embodiments of this application are intended to cover all such substitutions, modifications, and variations that fall within the broad scope of the appended claims. Therefore, any omissions, modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the embodiments of this application should be included within the protection scope of this application.

Claims

1. A method for full waveform inversion of anisotropic parameters based on undulating terrain, characterized in that, include: Obtain a model of undulating terrain; Based on the undulating surface model, the anisotropic wave equation is transformed from the Cartesian coordinate system to the curvilinear coordinate system to determine the solution of the anisotropic wave equation, thereby realizing the forward modeling of seismic waves. This includes: determining the anisotropic wave equation in the Cartesian coordinate system in the time domain; determining the free surface boundary conditions in the Cartesian coordinate system based on the anisotropic wave equation in the Cartesian coordinate system; determining the mapping relationship between the grid points in the physical space of the Cartesian coordinate system and the grid points in the computational space of the curvilinear coordinate system; and determining the anisotropic wave equation and the undulating surface boundary conditions in the curvilinear coordinate system based on the mapping relationship. The residual is determined by comparing the solution of the anisotropic wave equation of the undulating surface model with the actual observed wavefield. The residual is used as the source to solve the backpropagation anisotropic wave equation, and the objective function of the undulating surface is determined based on the residual. This process includes: determining the locations of the seismic source and geophone in the undulating surface model; determining the solution of the anisotropic wave equation of the undulating surface model based on the locations of the seismic source and geophone; determining the locations of the actual observed seismic source and geophone; determining the actual observed wavefield based on the locations of the actual observed seismic source and geophone; and using the residual as the difference between the solution of the anisotropic wave equation of the undulating surface model and the actual observed wavefield to determine the objective function. Based on the objective function, determine the gradient equation of the objective function with respect to the unknown parameters; Based on the solutions to the anisotropic wave equation in the Cartesian coordinate system and the solutions to the anisotropic wave equation propagated back from the residuals, the inversion gradient of the anisotropic parameters is determined using the gradient equation. This includes: determining the perturbations and displacement perturbations of each anisotropic parameter based on the solutions to the anisotropic wave equation in the Cartesian coordinate system; determining the Green's function equation for the displacement perturbation; determining the amount of displacement perturbation caused by the anisotropic parameter perturbation based on the Green's function equation for the displacement perturbation; determining the partial derivative of the objective function with respect to the anisotropic parameters using the partial derivatives of the displacement perturbation with respect to the anisotropic parameters based on the gradient equation of the objective function with respect to the unknown parameters; and determining the inversion gradient of the objective function with respect to the anisotropic parameters based on the partial derivatives of the objective function with respect to the anisotropic parameters. Based on the solution of the anisotropic wave equation of the undulating surface model, the anisotropic parameters are calculated by inverting the actual observed wavefield and the inversion gradient of the anisotropic parameters.

2. The method according to claim 1, characterized in that, The objective function is expressed as: ， in, This represents the solution to the anisotropic wave equation for the undulating surface model. This represents the actually observed wave field. This indicates the location of the earthquake source in the undulating terrain model. This indicates the location of the geophone in the undulating terrain model. Indicates the actual observed location of the earthquake source. The actual location of the detector observed. Indicates time.

3. The method according to claim 1, characterized in that, Based on the objective function, determine the gradient of the objective function with respect to the unknown parameters, including: Based on the objective function, the solution of the anisotropic wave equation propagated from the residual source is determined using the method of reverse wave field propagation with residual source. Based on the solution of the anisotropic wave equation backpropagated from the residual source, the gradient equation of the objective function with respect to the unknown parameters is determined.

4. The method according to claim 1, characterized in that, Also includes: Based on the mapping relationship between the grid points in the physical space of the Cartesian coordinate system and the grid points in the computational space of the curvilinear coordinate system, the displacement disturbance generated by the anisotropic parameters in the curvilinear coordinate system is determined. The gradient values ​​of the anisotropic parameters in the curvilinear coordinate system are determined based on the displacement disturbances generated by the anisotropic parameters.

5. A device for inverting the full waveform of anisotropic parameters based on undulating terrain, characterized in that, include: The acquisition module is used to acquire undulating terrain models. The forward modeling module is used to transform the anisotropic wave equation from the Cartesian coordinate system to the curvilinear coordinate system based on the undulating surface model, determine the solution of the anisotropic wave equation, and realize the forward modeling simulation of seismic waves. This includes: determining the anisotropic wave equation in the Cartesian coordinate system within the time domain; determining the free surface boundary conditions in the Cartesian coordinate system based on the anisotropic wave equation; determining the mapping relationship between grid points in the physical space of the Cartesian coordinate system and grid points in the computational space of the curvilinear coordinate system; and determining the anisotropic wave equation and the undulating surface boundary conditions in the curvilinear coordinate system based on the mapping relationship. The objective function module is used to determine the residual as the difference between the solution of the anisotropic wave equation of the seismic wave on the undulating surface model and the actual observed wavefield. The residual is used as the source to solve the solution of the backpropagation anisotropic wave equation, and the objective function of the undulating surface is determined based on the residual. This includes: determining the locations of the seismic source and geophones of the undulating surface model; determining the solution of the anisotropic wave equation of the undulating surface model based on the locations of the seismic source and geophones; determining the locations of the actually observed seismic source and geophones; determining the actually observed wavefield based on the locations of the actually observed seismic source and geophones; and using the difference between the solution of the anisotropic wave equation of the undulating surface model and the actually observed wavefield as the residual to determine the objective function. The gradient equation module is used to determine the gradient equation of the objective function with respect to the unknown parameters based on the objective function. The anisotropic parameter inversion gradient module is used to determine the inversion gradient of the anisotropic parameters using the gradient equation based on the solution of the anisotropic wave equation in the Cartesian coordinate system and the solution of the anisotropic wave equation backpropagated from the residual. This includes: determining the perturbation and displacement perturbation of each anisotropic parameter based on the solution of the anisotropic wave equation in the Cartesian coordinate system; determining the Green's function equation for the displacement perturbation; determining the amount of displacement perturbation caused by the anisotropic parameter perturbation based on the Green's function equation for the displacement perturbation; determining the partial derivative of the objective function with respect to the anisotropic parameters using the partial derivative of the displacement perturbation with respect to the anisotropic parameters based on the gradient equation of the objective function with respect to the unknown parameters; and determining the inversion gradient of the objective function with respect to the anisotropic parameters based on the partial derivative of the objective function with respect to the anisotropic parameters. The anisotropic parameter inversion module is used to calculate the anisotropic parameters based on the solution of the anisotropic wave equation of the undulating surface model, the actual observed wave field, and the gradient inversion of the anisotropic parameters.

6. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the method as described in any one of claims 1 to 4.

7. A non-transitory computer-readable storage medium storing computer instructions, characterized in that, The computer instructions are used to cause the computer to perform the method as described in any one of claims 1 to 4.

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