Three-dimensional inversion methods, systems, media, products and equipment for transient electromagnetic data

Abstract

The present invention belongs to the field of geophysical exploration technology. A method, system, medium, product and equipment for three-dimensional inversion of transient electromagnetic data are provided, and three-dimensional regularized inversion is performed with the objective function of minimizing the sum of the product of the model constraint term and the regularization parameter and the data fitting term; the acquisition of the sensitivity matrix in the gradient of the objective function includes: solving the three-dimensional forward electromagnetic field full discrete equation to obtain the forward field, constructing the adjoint forward electromagnetic field full discrete equation whose coefficient matrix is ​​a low-order tridiagonal matrix, solving the adjoint forward electromagnetic field full discrete equation to obtain the calculated adjoint field, and obtaining the sensitivity matrix according to the forward field and the adjoint field. The present invention uses a direct splitting strategy to decompose the coupled electromagnetic field, and reconstructs the large sparse matrix into a series of low-order tridiagonal matrices. Whether it is the forward process or the sensitivity calculation, it only needs to solve the low-order tridiagonal matrix, which significantly speeds up the three-dimensional inversion speed.

Description

Technical Field

[0001] The present invention relates to the field of geophysical exploration technology, and in particular to a method, system, medium, product and equipment for three-dimensional inversion of transient electromagnetic data. Background Art

[0002] The statements in this section merely provide background art related to the present invention and do not necessarily constitute prior art.

[0003] The time-domain transient electromagnetic method (TEM) collects the electromagnetic response after the excitation source is turned off, which ensures that the data is not interfered by the primary field and is completely derived from geological anomalies. At present, TEM has been widely used in many fields such as engineering exploration, mineral resource survey, groundwater resource exploration, geothermal energy detection, etc. In practical applications, the interpretation of TEM data usually relies on apparent resistivity imaging and one-dimensional inversion technology. However, there is no unified definition of apparent resistivity and it is mainly used for qualitative analysis. One-dimensional inversion technology can restore a reasonable resistivity distribution in areas with flat terrain and layered strata. However, in the real world, strata are often not always horizontally layered, especially in areas with complex terrain or variable underground structures, and one-dimensional inversion may misinterpret the data in these areas. In contrast, three-dimensional inversion technology can more accurately reveal the underground geological conditions.

[0004] The three-dimensional inversion of TEM data can be solved directly in the time domain. Although the explicit finite-difference time-domain (FDTD) method can be used to deal with the forward modeling problem of three-dimensional TEM, the time step of this method is strictly limited by the Courant-Friedrichs-Lewy (CFL) condition, and the three-dimensional forward modeling speed is very time-consuming, which in turn limits the convergence speed of the three-dimensional inversion. Therefore, the three-dimensional TEM inversion technology based on the explicit FDTD method has not been further developed.

[0005] In geophysical three-dimensional forward modeling, the backward Euler method is popular because of its unconditional stability. This method is more flexible in the choice of time step. Compared with the explicit method, it reduces the number of linear equations that need to be solved, thereby shortening the simulation time. The efficient solution of the forward problem makes fast three-dimensional inversion possible. Despite this, the significant consumption of computing time is still one of the main challenges faced by three-dimensional inversion technology in practical applications. When processing transient electromagnetic data, traditional three-dimensional inversion technology involves the processing of large sparse matrices. In the process of forward modeling and sensitivity matrix calculation, whether it is an iterative or direct solution method, it is computationally intensive and very time-consuming. Summary of the invention

[0006] In order to address the deficiencies of the prior art, the present invention provides a method, system, medium, product and equipment for three-dimensional inversion of transient electromagnetic data, which uses a direct splitting strategy to decompose the coupled electromagnetic field and reconstructs large sparse matrices into a series of low-order tridiagonal matrices. Whether it is a forward modeling process or a sensitivity calculation, it only needs to solve the low-order tridiagonal matrix, which significantly speeds up the three-dimensional inversion speed.

[0007] In order to achieve the above object, the present invention adopts the following technical solution:

[0008] In a first aspect, the present invention provides a three-dimensional inversion method for transient electromagnetic data.

[0009] A three-dimensional inversion method for transient electromagnetic data includes the following processes:

[0010] Acquire time-domain transient electromagnetic data;

[0011] According to time-domain transient electromagnetic data, three-dimensional regularized inversion is performed with the product of the model constraint term and the regularization parameter and the sum of the data fitting term as the objective function; the sensitivity matrix in the gradient of the objective function is obtained, including:

[0012] Solve the three-dimensional forward electromagnetic field full discrete equation to obtain the forward field, construct an adjoint forward equation whose coefficient matrix is ​​a low-order tridiagonal matrix, solve the adjoint forward equation to obtain the adjoint field, and obtain a sensitivity matrix based on the forward field and the adjoint field.

[0013] In a second aspect, the present invention provides a three-dimensional inversion system for transient electromagnetic data.

[0014] A transient electromagnetic data three-dimensional inversion system, using the transient electromagnetic data three-dimensional inversion method described in the first aspect of the present invention, comprises a GPU and a CPU communicating with each other:

[0015] The GPU is used for the calculation of the three-dimensional forward electromagnetic field full discrete equation and the adjoint forward electromagnetic field full discrete equation, and the CPU is used for other processes in the three-dimensional inversion except the calculation of the three-dimensional forward electromagnetic field full discrete equation and the adjoint forward electromagnetic field full discrete equation.

[0016] In a third aspect, the present invention provides a computer device, comprising: a processor and a computer-readable storage medium;

[0017] a processor adapted to execute a computer program;

[0018] A computer-readable storage medium, wherein a computer program is stored in the computer-readable storage medium, and when the computer program is executed by the processor, the three-dimensional inversion method for transient electromagnetic data as described in the first aspect of the present invention is implemented.

[0019] In a fourth aspect, the present invention provides a computer-readable storage medium storing a computer program, wherein the computer program is suitable for being loaded by a processor and executing the three-dimensional inversion method for transient electromagnetic data as described in the first aspect of the present invention.

[0020] In a fifth aspect, the present invention provides a computer program product, which includes a computer program. When the computer program is executed by a processor, it implements the three-dimensional inversion method of transient electromagnetic data as described in the first aspect of the present invention.

[0021] Compared with the prior art, the present invention has the following beneficial effects:

[0022] 1. The present invention innovatively designs a three-dimensional inversion method, system, medium, product and equipment for transient electromagnetic data. It uses a direct splitting strategy to decompose the coupled electromagnetic field and reconstructs the large sparse matrix into a series of low-order tridiagonal matrices. Whether it is the forward modeling process or the sensitivity calculation, it only needs to solve the low-order tridiagonal matrix, which significantly speeds up the three-dimensional inversion speed.

[0023] 2. In order to further accelerate the three-dimensional inversion, the present invention calculates the three-dimensional forward electromagnetic field full discrete equations and the adjoint forward electromagnetic field full discrete equations on the GPU. All forward fields and adjoint fields are directly read from the GPU memory, thereby eliminating the need to pass through the host memory. This not only speeds up the solution of the forward and adjoint forward equations, but also reduces the data transmission time when calculating the gradient of the objective function.

[0024] Advantages of additional aspects of the present invention will be given in part in the following description, and in part will become obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] The accompanying drawings in the specification, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0026] Figure 1 A flowchart of fast three-dimensional inversion of BEDS-FDTD transient electromagnetic data provided in Example 1 of the present invention;

[0027] Figure 2 The L-shaped low-resistance body model excited by a large loop provided in Example 1 of the present invention;

[0028] Figure 3 A three-dimensional inversion model of an L-shaped low-resistance body model excited by a large loop source provided in Example 1 of the present invention;

[0029] Figure 4A slice of the inversion model provided in Example 1 of the present invention on the xy plane;

[0030] Figure 5 A slice of the inversion model provided in Example 1 of the present invention on the xz plane;

[0031] Figure 6 A slice of the inversion model provided in Example 1 of the present invention on the yz plane;

[0032] Figure 7 A schematic diagram of a computer device provided in Example 2 of the present invention. DETAILED DESCRIPTION

[0033] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0034] It should be noted that the following detailed descriptions are exemplary and are intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present invention belongs.

[0035] In the absence of conflict, the embodiments of the present invention and the features of the embodiments may be combined with each other.

[0036] Embodiment 1:

[0037] This implementation proposes a three-dimensional inversion method for transient electromagnetic data, which uses a direct splitting strategy to decompose the coupled electromagnetic field and reconstructs a large sparse matrix into a series of low-order tridiagonal matrices; subsequently, by quickly processing these low-order tridiagonal matrices, the three-dimensional TEM forward modeling speed can be significantly accelerated. In order to achieve fast three-dimensional inversion, the forward modeling problem in the present invention is still solved using the BEDS-FDTD algorithm; in addition, based on the characteristics of the forward equation, the adjoint forward control equation whose coefficient matrix is ​​a low-order tridiagonal matrix is ​​derived; in the inversion algorithm proposed by the present invention, whether it is the forward process or the sensitivity calculation, it is only necessary to solve the low-order tridiagonal matrix; at the same time, in order to further accelerate the three-dimensional TEM inversion, GPU parallel technology is used; the inversion of the algorithm of the present invention on synthetic models and measured data shows that compared with traditional methods, the inversion time is greatly shortened while maintaining the accuracy of the inversion results.

[0038] Specifically, the three-dimensional inversion method of transient electromagnetic data includes the following contents:

[0039] S101: Establish the three-dimensional forward electromagnetic field fully discrete equation.

[0040] The BEDS-FDTD algorithm can reduce the order of large sparse matrices and reconstruct them into a series of low-order tridiagonal matrices. The Maxwell equations in the time domain can be written as:

[0041] (1a);

[0042] (1b);

[0043] In the formula, and represent the electric field and magnetic field respectively, represents the curl operator, , , are magnetic permeability, dielectric constant, and electrical conductivity, respectively. is the source current density, is the position vector, Represents time.

[0044] In this implementation, the derivatives of the field with respect to time and space are approximated using first-order backward Euler and first-order central difference methods, respectively.

[0045] Equations 1a and 1b can be restated as:

[0046] (2a);

[0047] (2b);

[0048] In the formula, is the coordinate direction, satisfying the cyclic shift property, Indicates along The first-order central difference operator in the direction, , , , is the time step, At time n+1, The electric field in the direction of At time n, The electric field in the direction of and Respectively indicate along The first-order central difference operator along the direction The first-order central difference operator in the direction, express n +1 time edge The source current density in the direction, express n +1 time edge Direction of the magnetic field, express n The edge of time Direction of the magnetic field, is the edge at time n+1 Direction of the electric field.

[0049] Equations (2a) and (2b) can be rewritten as:

[0050] (3);

[0051] Where I is the identity matrix, , represents the field on the nth time track, represents the field on the n+1th time track, is the source term of the n+1th time channel, , , , ;

[0052] Where M is the operator matrix:

[0053] (4);

[0054] Substitute the above matrix into formula (3) and introduce the virtual electric field ,available:

[0055] (5a);

[0056] (5b);

[0057] (5c);

[0058] in, is the electric field source term at time n+1, For along The virtual electric field in the direction, is the electric field at the n+1th moment.

[0059] Applying the matrix M to equations (5a), (5b), and (5c) yields:

[0060] (6a);

[0061] (6b);

[0062] (6c);

[0063] in, For along The electric field source term at time n+1 in the direction.

[0064] The unconditionally stable backward Euler method is used, which allows for flexible selection of the time step and improves computational efficiency. The emission current waveform is considered, the waveform response is calculated, and the modified trapezoidal waveform is used as the current waveform. In addition, we assume that the tangential electric field at infinity is zero as a boundary condition.

[0065] S201: Find the minimum value of the objective function.

[0066] The three-dimensional regularized inversion problem of TEM data is solved by minimizing the following objective function:

[0067] (7);

[0068] In the formula, is the data fitting term, is the model constraint, is the electrical parameter vector of the model space (in this application, it is the model conductivity), is the initial model electrical parameter vector determined based on prior geological information; d is the observed data, is the model vector The forward response of is a diagonal weighted matrix consisting of the inverse of the uncertainty of each reference data, is the model smoothing matrix, which consists of the second-order difference operator, is the regularization parameter used to balance and .

[0069] The L-BFGS method is used to solve the TEM data inversion problem. This method has the advantage of low memory requirements. By taking the derivative of the parameter m of the objective function, the gradient of the objective function is obtained as:

[0070] (8);

[0071] In the formula, is the model found at the kth iteration, , for The time sensitivity matrix, is the regularization factor, is the roughness matrix, is the model vector The forward response of .

[0072] When the regularization parameter changes, restart the L-BFGS algorithm and use the last result and regularization parameter as the new initial model and initial regularization parameter.

[0073] S301: Solve the sensitivity matrix.

[0074] To calculate , the forward problem can be written as:

[0075] (9);

[0076] In the formula, is the field vector in the BEDS-FDTD algorithm, including the virtual electric field, electric field and magnetic field at all times, is the coefficient matrix, is the source term. By taking the derivative of both sides of equation (9) with respect to m, we can obtain:

[0077] (10);

[0078] For TEM, the data usually collected is the magnetic field response ; Then, the sensitivity matrix J can be expressed as:

[0079] (11);

[0080] In the formula, , is the interpolation matrix in space and time, and is the spatial interpolation matrix that maps the electric field at the edge of the unit to the observed data position, is the time interpolation matrix from the computational time trace to the observed data time trace.

[0081] According to formula (10), With vector The product can be written as:

[0082] (12);

[0083] In the formula, , , we can get:

[0084] (13);

[0085] Solving equation (13) is called the adjoint forward process. The calculation method of is as follows: First, r and the forward field x are obtained by solving the forward equation; then, the adjoint field is calculated by equation (13): ; Finally, substitute x and v into equation (12) to calculate .

[0086] From equation (13), it can be seen that the coefficient matrices of the forward modeling equations need to be concatenated in the process of calculating the sensitivity matrix. When these small matrices are combined into a larger matrix, we are faced with the problem of dealing with large sparse matrices in the adjoint forward modeling. To circumvent this problem, the present invention derives a fully discrete equation for the electromagnetic field adjointly forward modeling, whose coefficient matrix is ​​also a low-order tridiagonal matrix, which greatly speeds up the solution speed of the adjoint forward modeling.

[0087] S401: Construct the fully discrete equations accompanying the forward electromagnetic field.

[0088] The original forward equation has many terms, including the coefficient and , in addition, the model parameters are in the denominators of both coefficients. When , not only will more fields be involved, but the calculation process will also become more complicated. Therefore, it is imperative to simplify the forward equations. Both sides of equations (5a) and (5b) are divided by Then, transform the two equations into:

[0089] (14a);

[0090] (14b);

[0091] In the formula, the solution of the magnetic field is still equation 5c. After the above transformation, , no longer contains model parameters, because Located in its numerator rather than in the denominator, another coefficient The derivatives of the model parameters can be easily found.

[0092] Equations (14a), (14b) and (5c) can be expressed as:

[0093] (15);

[0094] In the formula, P is the new differential operator matrix, x is n +1 time to be calculated electromagnetic field vector, Represents the time interval from time n to time n+1, unknown vector for , Equivalent to the previous .

[0095] Specifically, they include:

[0096] (16);

[0097] Unlike matrix K, matrix P is an operator matrix whose elements are all calculation operators rather than specific coefficients. Considering that the solution process from time n-1 to time n still involves the field at time n, relevant operators must be added to matrix P. Move the last two rows of operators in the original matrix P to the left by three positions to obtain new two rows of operators, and fill the empty positions with zero matrices. Then the new matrix is:

[0098] (17);

[0099] Without considering the spurious source, the adjoint forward equation can be written as:

[0100] (18);

[0101] In the formula, yes The transpose of , along with the field vector for .Will Substituting into equation (18), we can obtain:

[0102] (19a);

[0103] (19b);

[0104] (19c);

[0105] (19d);

[0106] (19e).

[0107] The purpose of the present invention is to establish the correlation between the adjoint fields at time n and time n+1. However, equations (19d) and (19e) only involve the adjoint fields at time n+1. Therefore, equations (19d) and (19e) are discarded and only the first three equations are retained. Considering that the adjoint forward modeling of TEM is an inverse process in time, after adjusting the position of the adjoint field in the equation, a pseudo source is added to the equation. The pseudo source is added by placing the point source (residual r) at the position of the observed data on the corresponding time channel. After applying and simplifying the matrix M, it can be obtained:

[0108] (20a);

[0109] (20b);

[0110] (20c).

[0111] in, express The edge of time The accompanying electric field in the direction of Indicates along The accompanying electric field at time n+1 in the direction of Indicates along The accompanying electric field at time n+1 in the direction of Indicates along Direction The accompanying magnetic field at all times, For along Direction The accompanying magnetic field at all times, For along Direction The accompanying magnetic field at all times, express The edge of time The accompanying electric field in the direction of express The edge of time The accompanying electric field in the direction of express The edge of time The accompanying electric field in the direction of For along Direction The accompanying magnetic field at all times, for The edge of time The pseudo electric field source term in the direction.

[0112] Equations (20a), (20b), and (20c) constitute the governing equations for the adjoint forward modeling, and these equations are solved in sequence to obtain the adjoint fields. The coefficient matrices of equations (20a) and (20c) are low-order tridiagonal matrices. Therefore, there is no need to solve large sparse matrices in the adjoint process, similar to the forward process. Since these special matrices can be solved efficiently using fast algorithms, the overall inversion process can be significantly accelerated.

[0113] Through the above calculation, we can get , the search direction can be calculated according to the following formula:

[0114] (twenty one)

[0115] In the formula, For the k The search direction of the is the Hessian matrix.

[0116] In this implementation, the entire inversion process includes: (1) forward modeling the current model to obtain the electromagnetic field response at the observation point; (2) calculating the root mean square error of the data fitting term in combination with the observed data; (3) calculating the sensitivity matrix and gradient through adjoint forward modeling; (4) calculating the incremental equation in combination with the Hessian matrix and obtaining a new geoelectric model. The specific GPU parallel computing strategy is as follows: Figure 1 As shown in FIG. 1 , the specific process of the BEDS-FDTD fast three-dimensional inversion algorithm flow is shown.

[0117] The three-dimensional inversion process of TEM data is very time-consuming, and it is very effective to improve the inversion efficiency through the hardware platform. In view of this, the present implementation method provides a three-dimensional inversion system for transient electromagnetic data, and the high-performance computing on the hardware platform can be divided into two main branches: the central processing unit (CPU) and the GPU. In the GPU, the chip area is mainly occupied by numerous computing cores, while in the CPU, the computing cores only occupy a small part of the area. Under the same chip area, the GPU will have more computing cores. In addition, GPU threads are lightweight and low-cost for thread creation, destruction, and switching. All of these lead to the GPU showing its natural advantages as a high-performance computing accelerator. When dealing with problems of the same size, the computational efficiency of the GPU solver is dozens of times that of the CPU solver. In the L-BFGS inversion framework, multiple forward modeling and adjoint forward modeling are required to calculate the gradient of the objective function. In order to accelerate the 3D inversion, forward modeling, adjoint forward modeling and Jacobian matrix calculation can be performed on the GPU. The forward modeling is implemented based on formulas (6a), (6b) and (6c), which have the characteristics of different field decomposition decoupling and low-order tridiagonal matrix; the adjoint forward modeling is implemented based on formulas (20a), (20b) and (20c), which have the characteristics of different field decomposition decoupling and low-order tridiagonal matrix. The steps of "calculating time step → updating model conductivity → calculating objective function, updating Jacobian matrix → calculating root mean square error → calculating search direction" are performed on the CPU. This method not only accelerates the solution of forward and adjoint forward equations, but also reduces data transfer time when calculating the gradient of the objective function. This is because all forward and adjoint fields are read directly from the GPU memory, thus avoiding reading through the host memory.

[0118] This implementation provides the following comprehensive model examples:

[0119] L-shaped low-resistance body model, such as Figure 2 Model system shown is AMD EPYC Rome, 2.6GHz CPU, 96GB RAM, Tesla A100, 40GB graphics card.

[0120] The resistivity of air is Ω·m, the resistivity of the earth is 200Ω·m. A 500m×500m loop frame (marked with a red line) is placed on the ground as an excitation source. 100m below the loop, there is an L-shaped object with a resistivity of 10Ω·m (the area within the purple line). The number of cells in the x, y and z directions is 71×71×85 (a total of 428,485 cells). A 20-meter uniform grid is used in the core area, and the size of the cells is gradually increased with a certain proportional factor outside the core area. The size of the entire model satisfies the Dirichlet boundary condition. For this model, the origin of the coordinate system is located at the center of the loop. The receivers are evenly distributed in the loop with a spacing of 40m. A total of 11×11=121 receiving points are set, and the positions of these receiving points are represented by white balls. We start from logarithmically equal intervals. seconds~ The data of 28 time channels are extracted from the forward response of 100 s (after the current is turned off). All data are contaminated with 3% Gaussian noise to simulate the observed data. For the inversion of this model, we use data.

[0121] Both the initial model and the reference model use a uniform half-space model with a background resistivity of 200Ω·m. The initial regularization parameter is 10, and the regularization parameter in each iteration is calculated according to the "cooling process". When the root mean square (RMS) decreases rapidly, the regularization parameter will remain unchanged in the next iteration. When the root mean square (RMS) decreases slowly, it will be multiplied by a factor less than 1 in the next iteration. The above process is repeated until the regularization parameter drops to a predefined minimum value. For this model, the decay coefficient is 0.1 and the minimum regularization parameter is .

[0122] When the RMS drops to about 1, it can be considered that the inverted data has been sufficiently fitted to the observed data, and the inversion algorithm ends the calculation. For this model, the inversion ends after 52 iterations, including 140 forward modeling and 105 adjoint forward modeling calculations. Since the forward modeling or adjoint forward modeling is very fast in our inversion algorithm, it only takes 6.7 seconds, so the entire inversion process takes less than 30 minutes (1745 seconds). The memory used includes 30.1GB of video memory and 30.5GB of host memory. This result is very impressive, and the three-dimensional inversion of TEM data only takes a few minutes.

[0123] Figure 3 , Figure 4 , Figure 5 and Figure 6The resistivity isosurface (65Ω·m) of the inversion model is plotted for the 3D inversion model (core area) after 52 iterations. It can be seen that the shape and spatial position of the anomaly are well restored. In addition, the electrical characteristics of the anomaly can be clearly distinguished from the background. It is worth noting that in the inversion model, a low-resistance ring surrounds the anomaly, a phenomenon known as the current ring effect.

[0124] Embodiment 2:

[0125] like Figure 7 As shown, this implementation provides an electronic device, which includes a processor 1001, a communication interface 1002, and a computer-readable storage medium 1003. The processor 1001, the communication interface 1002, and the computer-readable storage medium 1003 may be connected via a bus or other means.

[0126] Among them, the communication interface 1002 is used to receive and send data, the computer-readable storage medium 1003 can be stored in the memory of the electronic device, the computer-readable storage medium 1003 is used to store a computer program, the computer program includes program instructions, and the processor 1001 is used to execute the program instructions stored in the computer-readable storage medium 1003.

[0127] The processor 1001 (or CPU (Central Processing Unit)) is the computing core and control core of the electronic device, which is suitable for implementing one or more instructions, and specifically suitable for loading and executing one or more instructions to implement corresponding method processes or corresponding functions.

[0128] The processor 1001 is configured to execute the following process:

[0129] Acquire time-domain transient electromagnetic data;

[0130] According to time-domain transient electromagnetic data, three-dimensional regularized inversion is performed with the product of the model constraint term and the regularization parameter and the sum of the data fitting term as the objective function; the sensitivity matrix in the gradient of the objective function is obtained, including:

[0131] Solve the three-dimensional forward electromagnetic field full discrete equation to obtain the forward field, construct an adjoint forward electromagnetic field full discrete equation whose coefficient matrix is ​​a low-order tridiagonal matrix, solve the adjoint forward electromagnetic field full discrete equation to obtain the calculated adjoint field, and obtain a sensitivity matrix based on the forward field and the adjoint field.

[0132] The specific working process is described in Example 1 and will not be repeated here.

[0133] Embodiment 3:

[0134] This implementation provides a computer-readable storage medium (Memory), which is a memory device in an electronic device for storing programs and data. It is understandable that the computer-readable storage medium here can include both built-in storage media in the electronic device and, of course, extended storage media supported by the electronic device. The computer-readable storage medium provides a storage space that stores the processing system of the electronic device.

[0135] In addition, the storage space also stores one or more instructions suitable for being loaded and executed by the processor, and these instructions may be one or more computer programs (including program codes). It should be noted that the computer-readable storage medium here may be a high-speed RAM memory, or a non-volatile memory, such as at least one disk memory; optionally, it may also be at least one computer-readable storage medium located away from the aforementioned processor.

[0136] In one embodiment, the computer-readable storage medium stores one or more instructions; the processor loads and executes the one or more instructions stored in the computer-readable storage medium to implement the following process:

[0137] Acquire time-domain transient electromagnetic data;

[0138] According to time-domain transient electromagnetic data, three-dimensional regularized inversion is performed with the product of the model constraint term and the regularization parameter and the sum of the data fitting term as the objective function; the sensitivity matrix in the gradient of the objective function is obtained, including:

[0139] Solve the three-dimensional forward electromagnetic field full discrete equation to obtain the forward field, construct an adjoint forward electromagnetic field full discrete equation whose coefficient matrix is ​​a low-order tridiagonal matrix, solve the adjoint forward electromagnetic field full discrete equation to obtain the calculated adjoint field, and obtain a sensitivity matrix based on the forward field and the adjoint field.

[0140] The specific working process is described in Example 1 and will not be repeated here.

[0141] Embodiment 4:

[0142] The present implementation provides a computer program product or a computer program, which includes computer instructions stored in a computer-readable storage medium. A processor of an electronic device reads the computer instructions from the computer-readable storage medium, and the processor executes the computer instructions, so that the electronic device performs the following process:

[0143] Acquire time-domain transient electromagnetic data;

[0144] According to time-domain transient electromagnetic data, three-dimensional regularized inversion is performed with the objective function of minimizing the sum of the product of the model constraint term and the regularization parameter and the data fitting term; the sensitivity matrix in the gradient of the objective function is obtained, including:

[0145] Solve the three-dimensional forward electromagnetic field full discrete equation to obtain the forward field, construct an adjoint forward electromagnetic field full discrete equation whose coefficient matrix is ​​a low-order tridiagonal matrix, solve the adjoint forward electromagnetic field full discrete equation to obtain the calculated adjoint field, and obtain a sensitivity matrix based on the forward field and the adjoint field.

[0146] The specific working process is described in Example 1 and will not be repeated here.

[0147] A person skilled in the art can appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed in 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. A person skilled in the art 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.

[0148] In the above embodiments, it can be implemented in whole or in part by software, hardware, firmware or any combination thereof. When implemented using software, it can be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on the computer, the process or function according to the embodiment of the present application is generated in whole or in part. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable devices. The computer instructions can be stored in a computer-readable storage medium or transmitted through a computer-readable storage medium. The computer instructions can be transmitted from a website site, a computer, a server or a data center to another website site, a computer, a server or a data center by wired (e.g., coaxial cable, optical fiber, digital line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.). The computer-readable storage medium can be any available medium that can be accessed by the computer or a data processing device such as a server, a data center, etc. that includes one or more available media integrated. The available medium can be a magnetic medium (e.g., a floppy disk, a hard disk, a tape), an optical medium (e.g., a DVD), or a semiconductor medium (e.g., a solid-state drive (SSD)), etc.

[0149] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A three-dimensional inversion method for transient electromagnetic data, characterized in that: The process includes: Acquire time-domain transient electromagnetic data; According to the time-domain transient electromagnetic data, a three-dimensional regularized inversion is performed with the product of the model constraint term and the regularization parameter and the sum of the data fitting term as the objective function; The acquisition of the sensitivity matrix in the gradient of the objective function includes: Solve the three-dimensional forward electromagnetic field full discrete equation to obtain the forward field, construct an adjoint forward electromagnetic field full discrete equation whose coefficient matrix is ​​a low-order tridiagonal matrix, solve the adjoint forward electromagnetic field full discrete equation to obtain the calculated adjoint field, and obtain a sensitivity matrix based on the forward field and the adjoint field.

2. The method for three-dimensional inversion of transient electromagnetic data according to claim 1, characterized in that: The objective function includes: ； in, is the data fitting term, is the model constraint, is the model vector, It is a reference model selected based on geophysical information; is the observed data, is the model vector The forward response of is a diagonal weighted matrix consisting of the inverse of the uncertainty of each reference data, is the model smoothing matrix, which consists of the second-order difference operator, is the regularization parameter used to balance and .

3. The three-dimensional inversion method of transient electromagnetic data according to claim 2, characterized in that: The gradient of the objective function is: ； in, is the model vector found at the kth iteration, , is the forward modeling vector, for The time sensitivity matrix, is the model vector The forward response of is the regularization factor, is the roughness matrix.

4. The method for three-dimensional inversion of transient electromagnetic data according to claim 1, characterized in that: Solve the three-dimensional forward electromagnetic field full discrete equation to obtain the forward field, including: ； ； ； in, is the coordinate direction, , satisfying the cyclic shift property, Indicates along The first-order central difference operator in the direction, , , , , , are magnetic permeability, dielectric constant, and electrical conductivity, respectively. is the time step, At time n+1, The electric field in the direction of At time n, The electric field in the direction of and Respectively indicate along The first-order central difference operator along the direction The first-order central difference operator in the direction, express n +1 time edge Direction of the magnetic field, express n The edge of time Direction of the magnetic field, express n The edge of time Direction of the magnetic field, express n The edge of time Direction of the magnetic field, is the edge at time n+1 The electric field in the direction of is the edge at time n The electric field in the direction of For along The virtual electric field in the direction, For along The electric field source term at time n+1 in the direction, For along The virtual electric field in the direction, For along The virtual electric field in the direction, Indicates along Directional central difference operator, Indicates along Directional Central Difference Operator.

5. The method for three-dimensional inversion of transient electromagnetic data according to claim 4, characterized in that: Construct the adjoint forward electromagnetic field full discrete equations with a coefficient matrix of low-order tridiagonal matrix, including: ； ； ； in, express The edge of time The accompanying electric field in the direction of Indicates along The accompanying electric field at time n+1 in the direction of Indicates along The accompanying electric field at time n+1 in the direction of Indicates along Direction The accompanying magnetic field at all times, For along Direction The accompanying magnetic field at all times, For along Direction The accompanying magnetic field at all times, express The edge of time The accompanying electric field in the direction of express The edge of time The accompanying electric field in the direction of express The edge of time The accompanying electric field in the direction of For along Direction The accompanying magnetic field at all times, for The edge of time The pseudo electric field source term in the direction.

6. The three-dimensional inversion method of transient electromagnetic data according to claim 1, characterized in that: According to the positive scene and the accompanying field Get the sensitivity matrix, including: ； in, is the coefficient matrix, is the source term, , , is the interpolation matrix in space and time, and is the spatial interpolation matrix that maps the electric field at the unit prism to the observed data location, is the observed time channel from the time interpolation matrix mapping the field in the calculation, , , is the position vector.

7. A three-dimensional inversion system for transient electromagnetic data, characterized in that: A method for three-dimensional inversion of transient electromagnetic data according to any one of claims 1 to 6, comprising a GPU and a CPU communicating with each other: The GPU is used for the calculation of the three-dimensional forward electromagnetic field full discrete equation and the adjoint forward electromagnetic field full discrete equation, and the CPU is used for other processes in the three-dimensional inversion except the calculation of the three-dimensional forward electromagnetic field full discrete equation and the adjoint forward electromagnetic field full discrete equation.

8. A computer device, characterized in that: include: a processor and a computer readable storage medium; a processor adapted to execute a computer program; A computer-readable storage medium, wherein a computer program is stored in the computer-readable storage medium, and when the computer program is executed by the processor, the three-dimensional inversion method for transient electromagnetic data according to any one of claims 1 to 6 is implemented.

9. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, and the computer program is suitable for being loaded by a processor and executing the three-dimensional inversion method for transient electromagnetic data according to any one of claims 1 to 6.

10. A computer program product, characterized in that The computer program product comprises a computer program, and when the computer program is executed by a processor, the method for three-dimensional inversion of transient electromagnetic data as claimed in any one of claims 1 to 6 is implemented.

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