Controllable Source Electromagnetic Three-Dimensional Inversion Method Based on Anisotropic Media

Abstract

This invention relates to the field of controlled-source electromagnetic inversion technology, and more particularly to a controlled-source electromagnetic three-dimensional inversion method based on anisotropic media. Based on the method defined by Tikhonov, this invention constructs an anisotropic objective function for the inversion model from observational data, without requiring additional construction or the use of independent preconditioning operators, thus effectively improving the efficiency of anisotropic inversion calculations. Furthermore, this invention first takes the natural logarithm of the model conductivity before inversion, effectively avoiding the problem of negative conductivity values ​​during the inversion process, thereby ensuring the physical rationality of the inversion results. Simultaneously, this invention effectively suppresses the multiple solutions in anisotropic inversion through forward and inversion grid decoupling technology, improving the reliability of anisotropic inversion.

Description

Technical Field

[0001] This invention relates to the field of controlled-source electromagnetic inversion technology, and in particular to a controlled-source electromagnetic three-dimensional inversion method based on anisotropic media. Background Technology

[0002] Controlled-source electromagnetic methods (CSEs) are an important approach in deep geophysical exploration. Their core principle involves exciting the subsurface medium with an artificial source and acquiring electromagnetic response characteristics using receivers deployed on the surface, in wells, in the ocean, and in the air, thereby inverting the electrical structure of the subsurface medium. Due to its advantages such as large exploration depth, strong anti-interference capability, and high resolution, this method has been widely applied in the exploration of mineral resources and oil and gas energy.

[0003] After years of development, three-dimensional controlled-source electromagnetic (CME) inversion technology has matured, and significant progress has been made in gradient-based deterministic inversion methods. In past CME exploration, electric field components aligned with the source direction and magnetic field components perpendicular to the source direction were typically acquired and utilized for three-dimensional inversion. However, the potential of other electromagnetic components in improving inversion resolution has not been fully explored. Meanwhile, conductivity anisotropy is widespread in the crust and upper mantle, significantly impacting the response characteristics of CME observation data. Using isotropic conductivity models to generate predictive data to fit observation results may lead to severe geological interpretation biases. Furthermore, multi-parameter inversion considering anisotropy significantly exacerbates the ambiguity of inversions, and traditional inversion algorithms cannot effectively recover the model information contained in CME data. In complex geological environments, the reliability of inversions is low, making it difficult to meet the needs of inverting wide-coverage and high-density CME datasets.

[0004] Therefore, it is necessary to provide a new controllable source electromagnetic three-dimensional inversion method based on anisotropic media to solve the above-mentioned technical problems. Summary of the Invention

[0005] The main objective of this invention is to provide a controllable source electromagnetic three-dimensional inversion method based on anisotropic media that can effectively suppress the multiple solutions of anisotropic inversion and improve the reliability of anisotropic inversion.

[0006] To achieve the above objectives, the present invention proposes a controllable source electromagnetic three-dimensional inversion method based on anisotropic media, comprising the following steps:

[0007] S1: Collect controlled-source electromagnetic data from the exploration area as observation data. Let the current inversion model be The prior model is Number of iterations According to the current inversion model and prior models Construct a preconditioned model ;

[0008] S2: Based on the method defined by Tikhonov, construct an anisotropic objective function for the inversion model of the th inversion iteration according to the observed data ;

[0009] S3: Calculate the inversion model parameters of the th inversion iteration through the forward and inverse grid decoupling technology and in combination with the anisotropic objective function

[0010] S4: Calculate the root mean square fitting difference RMS of the inversion model according to the inversion model parameters of the th inversion iteration. If RMS < M or > Q times, then perform preconditioned inverse processing on to obtain the inversion model of the th inversion iteration, output , otherwise enter S5, where: M is the set threshold, and Q is the total number of set iterations;

[0011] S5: Update the inversion model to obtain the inversion model of the th inversion iteration , and return to step S2. Specifically:

[0012] S5.1: Solve the gradient of the anisotropic objective function with respect to the inversion model based on the anisotropic objective function;

[0013] S5.2: Calculate the update step size and search direction based on the anisotropic objective function and the gradient, and update the inversion model using the update step size and search direction to obtain the inversion model of the th inversion iteration;

[0014] S5.3: Call the adjustment step size formula to adjust the update step size, let , and return to step S3.

[0015] Optionally, S2 includes:

[0016] S2.1: Based on the method defined by Tikhonov, construct the initial objective function of the inversion model, and the specific expression is as follows:

[0017] ;

[0018] where, Representation Model The forward modeling results; Update during inversion. , , , The models are respectively exist x , y , z Model conductivity in the direction, , , The models are respectively exist x , y , z The natural logarithm of the model conductivity in the direction; Represents the prior model; Represents the regularization factor; The data covariance matrix representing anisotropy is consistent with the form of isotropic media; The model covariance matrix represents the anisotropy.

[0019] S2.2, Perform data fitting on the initial objective function to obtain the data-fitted objective function. The specific formula is as follows:

[0020] ;

[0021] in: For anisotropic models, smoothing constraints are used.

[0022] S2.3, Model-based The objective function after fitting the data Rewriting the initial objective function yields information about the inversion model. Anisotropic objective function The specific formula is as follows:

[0023] ;

[0024] in: , for The inverse of the square root; Representation Model The forward modeling results, .

[0025] Optionally, the inversion model parameters in S3 include reference frequency model parameters and other frequency model parameters, with the reference frequencies being the median sorted from low to high; S3 specifically includes:

[0026] An adaptive algebraic multi-resolution grid method is adopted to generate corresponding forward modeling grids based on the initial grid according to different frequencies, and to perform forward modeling calculations to obtain the electric field and its adjoint electric field at different frequencies.

[0027] The forward modeling grid at the reference frequency is used as the reference grid for joint inversion. The electric field and its adjoint electric field at the reference frequency are used to calculate the first electric field on the reference grid. Reference frequency model parameters for the next inversion iteration;

[0028] The electric field at other frequencies and its accompanying electric field are used to calculate the electric field on the reference grid. Other frequency model parameters in the next inversion iteration.

[0029] Optionally, the electric field at other frequencies and its accompanying electric field can be used to calculate the electric field on the reference grid. Other frequency model parameters for the next inversion iteration include:

[0030] The electric field and its adjoint electric field at other frequencies are recovered to the electric field on the initial grid using the algebraic multi-resolution grid method. and accompanying electric field ;

[0031] The inverse of the interpolation matrix constructed using the reference frequency and the electric field and accompanying electric field Multiplying yields the electric fields of other frequencies mapped onto the reference grid. and accompanying electric field ;

[0032] Using the electric field on the reference grid and accompanying electric field The calculation yields the first [number] on the reference grid. Other frequency model parameters in the next inversion iteration.

[0033] Optionally, in S3, the electric field and accompanying electric field The specific calculation formula is as follows:

[0034] ;

[0035] in: , , These are the inverses of the interpolation matrices for levels 1, 2, and 3, respectively. The total interpolation matrix is ​​constructed by inverting the multi-level interpolation matrix;

[0036] The specific calculation formulas for the reference frequency model parameters and other frequency model parameters are as follows:

[0037] ;

[0038] ;

[0039] in: For reference frequency model parameters, The electric field at the reference frequency, The accompanying electric field at the reference frequency; For other frequency model parameters, For electric fields at other frequencies, For the accompanying electric field at other frequencies; Represents a mapping operator, including transformation operators. .

[0040] Optionally, S5.1 includes:

[0041] S5.1.1. Take the partial derivative of the anisotropic objective function with respect to the inversion model parameters to obtain the gradient calculation formula, as follows:

[0042] ;

[0043] Where: real represents the operation of taking the real part of a complex number; for The square root of; This is the transpose of the sensitivity matrix for anisotropic conductivity; for The reverse;

[0044] S5.1.2, Let vector Calculate the product of the transpose of the sensitivity matrix and the vector;

[0045] S5.1.3, Transpose the sensitivity matrix and this vector Substituting the product into the gradient calculation formula in S5.1.1, we obtain the gradient of the anisotropic objective function with respect to the inversion model.

[0046] Optionally, in S5.1.1, for the triaxial anisotropic medium model, the gradient calculation formula is further expressed as:

[0047] ;

[0048] in: , and Objective function representing anisotropy right x Directional model conductivity , y Directional model conductivity and z Directional model conductivity The partial derivatives;

[0049] For isotropic medium models x , y , z Model parameters in three directions ,have Within the framework of the triaxial anisotropic medium model, the gradient calculation formula is further expressed as:

[0050] ;

[0051] in: , , The models are respectively Along x , y , z Edge conductivity in three directions; ;

[0052] For an inversion model where the model conductivity is equal in any two directions, then... x Directional model conductivity and y-direction model conductivity For example, The formula for calculating the gradient is further expressed as:

[0053] ;

[0054] in, This represents the conductivity corresponding to the horizontal model. This represents the conductivity in the vertical direction.

[0055] Alternatively, for isotropic media, the mapping relationship of conductivity from edge to element is reversed. The specific calculation formula is as follows:

[0056] ;

[0057] in, To realize a transpose operator for conductivity from edge to grid cell conductivity; It is a diagonalized angular frequency matrix. , It is the identity matrix; It is a diagonal matrix. The volume vector of the model unit. This represents the electric field obtained by solving the forward equation.

[0058] Optionally, S5.1.2 specifically includes:

[0059] ① Based on the forward modeling formula, the adjoint equation is obtained by adjusting the right-hand side of the forward modeling equation using the nonlinear conjugate gradient method and the adjoint forward modeling technique. The specific formula is as follows:

[0060] ;

[0061] in: Represents the double curl operator; Indicates the imaginary part. ; Represents angular frequency. , For frequency parameters; Represents the magnetic permeability in a vacuum. , Represents the conductivity tensor, corresponding to the model Discrete; Indicates the accompanying electric field; This indicates the transpose of the interpolation matrix; This indicates a poor data fit.

[0062] ② Based on the adjoint equation, the algebraic multi-resolution grid method is used to obtain the linear equation system of the adjoint equation, and the specific formula is as follows:

[0063] ;

[0064] in: The coefficient matrix representing the forward equation; Represents a multi-resolution interpolation matrix; Represents a square matrix. Indicates the accompanying electric field at multiple resolutions; This is the right-hand side term of the above adjoint equation;

[0065] ③ Combining the BiCGSTAB iterative algorithm, the linear equations of the adjoint equation are solved to obtain the multi-resolution adjoint electric field. ;

[0066] ④ Based on the multi-resolution accompanying electric field The transpose of the sensitivity matrix for calculating anisotropic conductivity and this vector The product of is given by the following formula:

[0067] ;

[0068] in: This is the inversion of the mapping relationship of conductivity from edge to element, where edge and element represent the mesh edge and mesh element used for the discrete model, respectively.

[0069] Optionally, in S5.1.2, for triaxial anisotropic media, the mapping relationship of conductivity from edge to element is reversed. The specific calculation formula is as follows:

[0070] ;

[0071] ;

[0072] ;

[0073] in: , and They are respectively x , y , z The directional conductivity mapping from edge to cell is reversed; for x The transpose operator of directional conductivity from edge to mesh cell conductivity. The dimension is , Indicates the number of model units. express x The number of directional unit edges; express Along x Electric field components in the direction, Indicates along x A vector of direction; and They represent Along y and z Electric field components in the direction, and They represent along y and z A vector of direction; and They are respectively y and z The transpose operator of directional conductivity from edge to mesh cell conductivity. and The dimensions are respectively and , and express y direction and z The number of directional unit edges.

[0074] The technical solution of this invention is based on a method defined by Tikhonov, according to observation data. Constructing an inversion model The anisotropic objective function does not require additional construction or independent preconditioning operators, thus effectively improving the efficiency of anisotropic inversion calculation. Furthermore, this invention first takes the natural logarithm of the model conductivity before inversion, effectively avoiding the problem of negative conductivity values ​​during the inversion process, thereby ensuring the physical rationality of the inversion results. At the same time, this invention effectively suppresses the multiple solutions of anisotropic inversion through forward and inversion grid decoupling technology, improving the reliability of anisotropic inversion. Attached Figure Description

[0075] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the structures shown in these drawings without creative effort.

[0076] Figure 1 This is a flowchart illustrating the controllable source electromagnetic three-dimensional inversion method based on anisotropic media in an embodiment of the present invention.

[0077] Figure 2 This is a schematic diagram of the decoupling process of the forward and inverse meshes in an embodiment of the present invention;

[0078] Figure 3 This is a schematic diagram comparing the actual model and inversion results of horizontal and vertical resistivity in a horizontal slice in an embodiment of the present invention;

[0079] Figure 4 This is a schematic diagram comparing the actual model and inversion results of horizontal and vertical resistivity in a vertical slice in an embodiment of the present invention.

[0080] The realization of the objective, functional features and advantages of the present invention will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0081] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0082] It should be noted that all directional indications (such as up, down, left, right, front, back, etc.) in the embodiments of the present invention are only used to explain the relative positional relationship and movement of each component in a certain specific posture (as shown in the figure). If the specific posture changes, the directional indication will also change accordingly.

[0083] Furthermore, in this invention, descriptions involving "first," "second," etc., are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this invention, "a plurality of" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0084] In this invention, unless otherwise explicitly specified and limited, the terms "connection," "fixed," etc., should be interpreted broadly. For example, "fixed" can mean a fixed connection, a detachable connection, or an integral part; it can mean a mechanical connection or an electrical connection; it can mean a direct connection or an indirect connection through an intermediate medium; it can mean the internal communication of two components or the interaction between two components, unless otherwise explicitly limited. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0085] Furthermore, the technical solutions of the various embodiments of the present invention can be combined with each other, but only if they are based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such combination of technical solutions does not exist and is not within the scope of protection claimed by the present invention.

[0086] This invention proposes a controllable source electromagnetic three-dimensional inversion method based on anisotropic media that can effectively suppress the multiple solutions of anisotropic inversion and improve the reliability of anisotropic inversion.

[0087] See Figure 1 The controllable source electromagnetic three-dimensional inversion method based on anisotropic media in this embodiment includes the following steps:

[0088] S1: Collect controlled-source electromagnetic data from the exploration area as observation data. Let the current inversion model be The prior model is Number of iterations =1; based on the current inversion model and prior models Constructing a preconditioning model ;

[0089] S2: A method based on Tikhonov's definition, based on observation data. Building about the Inversion model of the second inversion iteration Anisotropic objective function;

[0090] S2 includes:

[0091] S2.1 Constructing the initial objective function of the inversion model based on the method defined by Tikhonov. The specific expression is as follows:

[0092] ;

[0093] in, Representation Model The forward modeling results; Update during inversion. , , , The models are respectively exist x , y , z Model conductivity in the direction, , , The models are respectively exist x , y , z The natural logarithm of the model conductivity in the direction; Represents the prior model; Represents the regularization factor; The data covariance matrix representing anisotropy is consistent with the form of isotropic media; The model covariance matrix represents the anisotropy.

[0094] S2.2, Perform data fitting on the initial objective function to obtain the data-fitted objective function. The specific formula is as follows:

[0095] ;

[0096] in: For anisotropic models, smoothing constraints are used.

[0097] S2.3, Model-based The objective function after fitting the data Rewriting the initial objective function yields information about the inversion model. Anisotropic objective function The specific formula is as follows:

[0098] ;

[0099] in: , for The inverse of the square root; Representation Model The forward modeling results, .

[0100] S3: Calculate the first... Inversion model parameters for the next inversion iteration;

[0101] like Figure 2 As shown, the inversion model parameters in S3 include reference frequency model parameters and other frequency model parameters, with the reference frequencies being the median sorted from low to high; S3 specifically includes:

[0102] An adaptive algebraic multi-resolution grid method is adopted to generate corresponding forward modeling grids based on the initial grid according to different frequencies, and to perform forward modeling calculations to obtain the electric field and its adjoint electric field at different frequencies.

[0103] The forward modeling grid at the reference frequency is used as the reference grid for joint inversion. The electric field and its adjoint electric field at the reference frequency are used to calculate the first electric field on the reference grid. Reference frequency model parameters for the next inversion iteration;

[0104] The electric field at other frequencies and its accompanying electric field are used to calculate the electric field on the reference grid. The other frequency model parameters for the next inversion iteration are as follows:

[0105] The electric field and its adjoint electric field at other frequencies are recovered to the electric field on the initial grid using the algebraic multi-resolution grid method. and accompanying electric field ;

[0106] The inverse of the interpolation matrix constructed using the reference frequency and the electric field and accompanying electric field Multiplying yields the electric fields of other frequencies mapped onto the reference grid. and accompanying electric field ;

[0107] In S3, the electric field and accompanying electric field The specific calculation formula is as follows:

[0108] ;

[0109] in: , , These are the inverses of the interpolation matrices for levels 1, 2, and 3, respectively. The total interpolation matrix is ​​constructed by inverting the multi-level interpolation matrix;

[0110] The specific calculation formulas for the reference frequency model parameters and other frequency model parameters are as follows:

[0111] ;

[0112] ;

[0113] Where: is the reference frequency model parameter, is the electric field at the reference frequency, is the adjoint electric field at the reference frequency; is the other frequency model parameter, is the electric field at the other frequency, is the adjoint electric field at the other frequency; represents the mapping operator, including the transformation operator ;

[0114] Using the electric field and the adjoint electric field on the reference grid, calculate the other frequency model parameter for the th inversion iteration on the reference grid.

[0115] S4: Calculate the root mean square fitting difference RMS of the inversion model according to the inversion model parameters of the th inversion iteration. If RMS < M or > Q times, then perform the inverse process of preconditioning on to obtain the inversion model for the th inversion iteration, output = , otherwise enter S5, where: M is the set threshold, and Q is the set number of iterations;

[0116] S5: Update the inversion model to obtain the inversion model for the th inversion iteration, and return to step S2. Specifically:

[0117] S5.1. Solve the gradient of the anisotropic objective function with respect to the inversion model based on the anisotropic objective function;

[0118] The above S5.1 includes:

[0119] S5.1.1. Take the partial derivative of the anisotropic objective function with respect to the inversion model parameters to obtain the calculation formula for the gradient, specifically as follows:

[0120] ;

[0121] where: real represents the operation of taking the real part of a complex number; is the square root of; This is the transpose of the sensitivity matrix for anisotropic conductivity; for The reverse;

[0122] In S5.1.1, for the triaxial anisotropic medium model, the gradient calculation formula is further expressed as:

[0123] ;

[0124] in: , and Objective function representing anisotropy right x Directional model conductivity , y Directional model conductivity and z Directional model conductivity The partial derivatives;

[0125] For isotropic medium models x , y , z Model parameters in three directions ,have Within the framework of the triaxial anisotropic medium model, the gradient calculation formula is further expressed as:

[0126] ;

[0127] in: , , The models are respectively Along x , y , z Edge conductivity in three directions; ;

[0128] For an inversion model where the model conductivity is equal in any two directions, then... x Directional model conductivity and y-direction model conductivity For example, The formula for calculating the gradient is further expressed as:

[0129] ;

[0130] in, This represents the conductivity corresponding to the horizontal model. This represents the conductivity in the vertical direction.

[0131] For isotropic media, the mapping of conductivity from edge to element is reversed. The specific calculation formula is as follows:

[0132] ;

[0133] in, To realize a transpose operator for conductivity from edge to grid cell conductivity; It is a diagonalized angular frequency matrix. , It is the identity matrix; It is a diagonal matrix. The volume vector of the model unit. This represents the electric field obtained by solving the forward equation.

[0134] S5.1.2, Let vector Calculate the product of the transpose of the sensitivity matrix and the vector;

[0135] Specifically, S5.1.2 includes:

[0136] ① Based on the forward modeling formula, the adjoint equation is obtained by adjusting the right-hand side terms of the forward modeling equation using the nonlinear conjugate gradient method and the adjoint forward modeling technique. The specific formula is as follows:

[0137] ;

[0138] in: Represents the double curl operator; Indicates the imaginary part. ; Represents angular frequency. , For frequency parameters; Represents the magnetic permeability in a vacuum. , Represents the conductivity tensor, corresponding to the model Discrete; Indicates the accompanying electric field; This indicates the transpose of the interpolation matrix; Indicates poor data fit;

[0139] ② Based on the adjoint equation, the algebraic multi-resolution grid method is used to obtain the linear equation system of the adjoint equation, and the specific formula is as follows:

[0140] ;

[0141] in: The coefficient matrix representing the forward equation; Represents a multi-resolution interpolation matrix; Represents a square matrix. Indicates the accompanying electric field at multiple resolutions; This is the right-hand side term of the above adjoint equation;

[0142] ③ Combining the BiCGSTAB iterative algorithm, the linear equations of the adjoint equation are solved to obtain the multi-resolution adjoint electric field. ;

[0143] ④ Based on the multi-resolution accompanying electric field The sensitivity matrix transpose for calculating anisotropic conductivity and the vector The product of is given by the following formula:

[0144] ;

[0145] in: This is the inversion of the mapping relationship of conductivity from edge to element, where edge and element represent the mesh edge and mesh element used for the discrete model, respectively.

[0146] S5.1.3, Transpose the sensitivity matrix and this vector Substituting the product into the gradient calculation formula in S5.1.1, we obtain the gradient of the anisotropic objective function with respect to the inversion model.

[0147] In S5.1.2, for triaxial anisotropic media, the mapping relationship of conductivity from edge to element is reversed. The specific calculation formula is as follows:

[0148] ;

[0149] ;

[0150] ;

[0151] in: , and They are respectively x , y , z The directional conductivity mapping from edge to cell is reversed; for x The transpose operator of directional conductivity from edge to mesh cell conductivity. The dimension is , Indicates the number of model units. express x The number of directional unit edges; express Along x Electric field components in the direction, Indicates along x A vector of direction; and They represent Along y and z Electric field components in the direction, and They represent along y and z A vector of direction; and They are respectively y and z The transpose operator of directional conductivity from edge to mesh cell conductivity. and The dimensions are respectively and , and express y direction and z The number of directional unit edges.

[0152] S5.2. Based on the anisotropic objective function and gradient calculation, update the step size and search direction, and use the update step size and search direction to update the inversion model. Get the first Inversion model of the second inversion iteration ;

[0153] S5.3, Call the step size adjustment formula to adjust and update the step size, let Return to step S3.

[0154] See Figure 3 The electric field at the observation point was calculated using a real model and used to simulate the electric field collected in the field. A 3% Gaussian random error was added to the observed value, with an initial model value of 0.02 S / m. The simulation area is: x and y The z-axis ranges from -14 to 14 km, and the z-axis ranges from -150 km to 30 km; the air layer extends from -150 km to 0 km and has an electrical conductivity of 10. -10 S / m; the background conductivity underground is 0.02 S / m, and there are two anomalies (i.e., two cubes) with conductivity of 0.2 S / m and 0.02 S / m respectively. S / m, the two anomalies are 600 m long, 600 m wide, and 400 m thick, with a top burial depth of 100 m and a bottom burial depth of 500 m; the model region is divided into 40×40×40 small cuboid units. Observation points: -1 km to 1 km, 20 survey lines, 20 survey points per line, totaling 400 survey points; the frequency is set at [0.1, 250] Hz, with a total of 9 frequencies. Through this example, we will consider the inversion data type under line source: The launch source along x The directional arrangement is such that the center of the transmitter is at (0, -5000, 0), and the length of the transmitter is 600 meters.

[0155] First, by Figure 3 and Figure 4 It can be seen that in the inversion of resistivity in the horizontal direction It can effectively identify the location, morphology, and resistivity values ​​of low-resistivity anomalies. The difference in inversion results between high-resistivity and low-resistivity (two anomalies) reflects the differences in sensitivity and resolution of controlled-source electromagnetic detection (CSEM) technology for different electrical anomalies. Good inversion results were also achieved in the vertical resistivity inversion, closely resembling the actual model. Simultaneously, it was observed that... x and z Non-uniform anomalies appeared in the uniform half-space background region of the orientation. This is because the predicted data generated by the complex three-dimensional construction model was used to fit the anisotropic observation data.

[0156] This embodiment also includes a readable storage medium storing computer program instructions, which, when executed by a processor, implement the controllable source electromagnetic three-dimensional inversion method based on anisotropic media as described above.

[0157] It should be noted that the device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Furthermore, in the accompanying drawings of the device embodiments provided by this invention, the connection relationships between modules indicate that they have communication connections, which can be specifically implemented as one or more communication buses or signal lines. Those skilled in the art can understand and implement this without any creative effort.

[0158] This embodiment also includes an electronic device, comprising: at least one processor, at least one memory, and computer program instructions stored in the memory, wherein the computer program instructions are executed by the processor to perform the controllable source electromagnetic three-dimensional inversion method based on anisotropic media as described above.

[0159] For example, the computer program may be divided into one or more modules / units, which are stored in the memory and executed by the processor to complete the present invention. The one or more modules / units may be a series of computer program instruction segments capable of performing a specific function, which describe the execution process of the computer program in the electronic device.

[0160] The electronic device can be a mobile phone, desktop computer, laptop, handheld computer, cloud server, or other computing device. The electronic device may include, but is not limited to, processors and memory. For example, the electronic device may also include input / output devices, network access devices, buses, etc.

[0161] The processor can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor can be a microprocessor or any conventional processor. The processor is the control center of the electronic device, connecting all parts of the electronic device via various interfaces and lines.

[0162] The memory can be used to store the computer program and / or modules. The processor implements the computer program by running or executing the computer program and / or modules stored in the memory, and by calling data stored in the memory. The memory may mainly include a program storage area and a data storage area. The program storage area may store the operating system, at least one application program required for a function (such as sound playback function, image playback function, etc.), etc.; the data storage area may store data created according to the use of the mobile phone (such as audio data, phonebook, etc.). In addition, the memory may include high-speed random access memory, and may also include non-volatile memory, such as hard disk, memory, plug-in hard disk, smart media card (SMC), secure digital card (SD) card, flash card, at least one disk storage device, flash memory device, or other volatile solid-state storage device.

[0163] If the modules / units integrated in the electronic device are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments of the present invention can also be implemented by a computer program instructing related hardware. The computer program can be stored in a readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include: any entity or device capable of carrying the computer program code, recording media, USB flash drives, portable hard drives, magnetic disks, optical disks, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc. It should be noted that the content included in the computer-readable medium can be appropriately added or removed according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, computer-readable media do not include electrical carrier signals and telecommunication signals.

[0164] The above description is only a preferred embodiment of the present invention and does not limit the scope of the present invention. All equivalent structural transformations made under the inventive concept of the present invention using the contents of the present invention specification and drawings, or direct / indirect applications in other related technical fields, are included within the protection scope of the present invention.

Claims

1. A controllable source electromagnetic three-dimensional inversion method based on anisotropic media, characterized in that, Includes the following steps: S1: Collect controlled-source electromagnetic data from the exploration area as observation data. Let the current inversion model be The prior model is Number of iterations According to the current inversion model and prior models Constructing a preconditioning model ; S2: A method based on Tikhonov's definition, based on observation data. Building about the Inversion model of the second inversion iteration Anisotropic objective function; S2 includes: S2.1 Constructing the initial objective function of the inversion model based on the method defined by Tikhonov. The specific expression is as follows: ； in, Representation Model The forward modeling results; Update during inversion. , , , The models are respectively exist x , y , z Model conductivity in the direction, , , The models are respectively exist x , y , z The natural logarithm of the model conductivity in the direction; Represents the prior model; Represents the regularization factor; The data covariance matrix representing anisotropy is consistent with the form of isotropic media; The model covariance matrix represents the anisotropy. S2.2, Perform data fitting on the initial objective function to obtain the data-fitted objective function. The specific formula is as follows: ； in: For anisotropic models, smoothing constraints are used. S2.3, Model-based The objective function after fitting the data Rewriting the initial objective function yields information about the inversion model. Anisotropic objective function The specific formula is as follows: ； in: , for The inverse of the square root; Representation Model The forward modeling results, ; S3: Calculate the first... Inversion model parameters for the next inversion iteration; S4: Calculate the root mean square fitting error RMS of the inversion model according to the inversion model parameters of the -th inversion iteration. If RMS < M or > Q times, then perform preconditioned inverse processing on to obtain the inversion model of the -th inversion iteration, output ; otherwise, enter S5, where: M is the set threshold, and Q is the total number of set iterations;​​​​ S5: Inversion Model Update to get the first Inversion model of the second inversion iteration And return to step S2, which is: S5.1 Solving for the gradient of the anisotropic objective function with respect to the inversion model based on the anisotropic objective function; S5.

2. Based on the anisotropic objective function and gradient calculation, update the step size and search direction, and use the update step size and search direction to update the inversion model. Get the first Inversion model of the second inversion iteration ; S5.3, Call the step size adjustment formula to adjust and update the step size, let Return to step S3.

2. The controllable source electromagnetic three-dimensional inversion method based on anisotropic media according to claim 1, characterized in that, The inversion model parameters in S3 include reference frequency model parameters and other frequency model parameters, with the reference frequencies arranged in ascending order of median. Specifically, S3 includes: An adaptive algebraic multi-resolution grid method is adopted to generate corresponding forward modeling grids based on the initial grid according to different frequencies, and to perform forward modeling calculations to obtain the electric field and its adjoint electric field at different frequencies. The forward modeling grid at the reference frequency is used as the reference grid for joint inversion. The electric field and its adjoint electric field at the reference frequency are used to calculate the first electric field on the reference grid. Reference frequency model parameters for the next inversion iteration; The electric field at other frequencies and its accompanying electric field are used to calculate the electric field on the reference grid. Other frequency model parameters in the next inversion iteration.

3. The controllable source electromagnetic three-dimensional inversion method based on anisotropic media according to claim 2, characterized in that, The electric field at other frequencies and its accompanying electric field are used to calculate the electric field on the reference grid. Other frequency model parameters for the next inversion iteration include: The electric field and its adjoint electric field at other frequencies are recovered to the electric field on the initial grid using the algebraic multi-resolution grid method. and accompanying electric field ; The inverse of the interpolation matrix constructed using the reference frequency and the electric field and accompanying electric field Multiplying yields the electric fields of other frequencies mapped onto the reference grid. and accompanying electric field ; Using the electric field on the reference grid and accompanying electric field The calculation yields the first [number] on the reference grid. Other frequency model parameters in the next inversion iteration.

4. The controllable source electromagnetic three-dimensional inversion method based on anisotropic media according to claim 3, characterized in that, In S3, the electric field and accompanying electric field The specific calculation formula is as follows: ； in: , , These are the inverses of the interpolation matrices for levels 1, 2, and 3, respectively. The total interpolation matrix is ​​constructed by inverting the multi-level interpolation matrix; The specific calculation formulas for the reference frequency model parameters and other frequency model parameters are as follows: ； ； in: For reference frequency model parameters, The electric field at the reference frequency, The accompanying electric field at the reference frequency; For other frequency model parameters, For electric fields at other frequencies, For the accompanying electric field at other frequencies; Represents a mapping operator, including transformation operators. .

5. The controllable source electromagnetic three-dimensional inversion method based on anisotropic media according to any one of claims 2 to 4, characterized in that, S5.1 includes: S5.1.

1. Take the partial derivative of the anisotropic objective function with respect to the inversion model parameters to obtain the gradient calculation formula, as follows: ； Where: real represents the operation of taking the real part of a complex number; for The square root of; This is the transpose of the sensitivity matrix for anisotropic conductivity; for The reverse; S5.1.2, Let vector Calculate the product of the transpose of the sensitivity matrix and the vector; S5.1.3, Transpose the sensitivity matrix and this vector Substituting the product into the gradient calculation formula in S5.1.1, we obtain the gradient of the anisotropic objective function with respect to the inversion model.

6. The controllable source electromagnetic three-dimensional inversion method based on anisotropic media according to claim 5, characterized in that, In S5.1.1, for the triaxial anisotropic medium model, the gradient calculation formula is further expressed as: ； in: , and Objective function representing anisotropy right x Directional model conductivity , y Directional model conductivity and z Directional model conductivity The partial derivatives; For isotropic medium models x , y , z Model parameters in three directions ,have Within the framework of the triaxial anisotropic medium model, the gradient calculation formula is further expressed as: ； in: , , The models are respectively Along x , y , z Edge conductivity in three directions; ; For an inversion model where the model conductivity is equal in any two directions, then... x Directional model conductivity and y-direction model conductivity For example, The formula for calculating the gradient is further expressed as: ； in, This represents the conductivity corresponding to the horizontal model. This represents the conductivity in the vertical direction.

7. The controllable source electromagnetic three-dimensional inversion method based on anisotropic media according to claim 6, characterized in that, For isotropic media, the mapping of conductivity from edge to element is reversed. The specific calculation formula is as follows: ； in, To realize a transpose operator for conductivity from edge to grid cell conductivity; It is a diagonalized angular frequency matrix. , It is the identity matrix; It is a diagonal matrix. The volume vector of the model unit. This represents the electric field obtained by solving the forward equation.

8. The controllable source electromagnetic three-dimensional inversion method based on anisotropic media according to claim 7, characterized in that, Specifically, S5.1.2 includes: ① Based on the forward modeling formula, the adjoint equation is obtained by adjusting the right-hand side terms of the forward modeling equation using the nonlinear conjugate gradient method and the adjoint forward modeling technique. The specific formula is as follows: ； in: Represents the double curl operator; Indicates the imaginary part. ; Represents angular frequency. , For frequency parameters; Represents the magnetic permeability in a vacuum. , Represents the conductivity tensor, corresponding to the model Discrete; Indicates the accompanying electric field; This indicates the transpose of the interpolation matrix; Indicates poor data fit; ② Based on the adjoint equation, the algebraic multi-resolution grid method is used to obtain the linear equation system of the adjoint equation, and the specific formula is as follows: ； in: The coefficient matrix representing the forward equation; Represents a multi-resolution interpolation matrix; Represents a square matrix. Indicates the accompanying electric field at multiple resolutions; This is the right-hand side term of the above adjoint equation; ③ Combining the BiCGSTAB iterative algorithm, the linear equations of the adjoint equation are solved to obtain the multi-resolution adjoint electric field. ; ④ Based on the multi-resolution accompanying electric field The sensitivity matrix transpose for calculating anisotropic conductivity and the vector The product of is given by the following formula: ； in: This is the inversion of the mapping relationship of conductivity from edge to element, where edge and element represent the mesh edge and mesh element used for the discrete model, respectively.

9. The controllable source electromagnetic three-dimensional inversion method based on anisotropic media according to claim 8, characterized in that, In S5.1.2, for triaxial anisotropic media, the mapping relationship of conductivity from edge to element is reversed. The specific calculation formula is as follows: ； ； ； in: , and They are respectively x , y , z The directional conductivity mapping from edge to cell is reversed; for x The transpose operator of directional conductivity from edge to mesh cell conductivity. The dimension is , Indicates the number of model units. express x The number of directional unit edges; express Along x The electric field component in the direction, Indicates along x A vector of direction; and They represent Along y and z The electric field component in the direction, and They represent along y and z A vector of direction; and They are respectively y and z The transpose operator of directional conductivity from edge to mesh cell conductivity. and The dimensions are respectively and , and express y direction and z The number of directional unit edges.

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