A fast calculation method and device for scattered electromagnetic field based on random matrix approximation

Abstract

The application discloses a fast calculation method and device for scattered electromagnetic field based on random matrix approximation, and belongs to the field of fast modeling of scattered field. The method comprises the following steps: precalculating an incident field vector and a reciprocal incident field vector; generating a Gaussian random matrix matched with the column number of a to-be-determined scattered response matrix; performing linear superposition on the incident field vector to obtain a synthetic incident field vector, and constructing a random projection matrix according to the scattered field vector of an equivalent current vector at a receiving point; performing linear superposition on the reciprocal incident field vector to obtain a reciprocal synthetic incident field vector, and constructing a projection coefficient matrix according to the response of a reciprocal equivalent current vector at a transmitting source; and calculating a complete scattered response matrix based on the product of an orthogonal basis matrix and the projection coefficient matrix. In the application, a large-scale geophysical electromagnetic complex scene can be adapted, higher calculation precision and stable convergence are achieved, and the reconstruction of the complete scattered response matrix can be completed at a lower relative error level.

Description

Technical Field

[0001] This application belongs to the field of rapid modeling of scattered fields, and specifically relates to a method and apparatus for rapid calculation of scattered electromagnetic fields based on random matrix approximation. Background Technology

[0002] In geophysical electromagnetic exploration, multiple-transmitter-multiple-receiver (MTMR) configurations are frequently employed simultaneously. For example, in controlled-source electromagnetic methods for the ocean, a towed horizontal electric dipole source works in conjunction with a seabed receiving array; in well-to-ground electromagnetic methods, multiple in-well transmitters are used in conjunction with surface or in-well receiving arrays for joint observation; in air-to-ground coordinated electromagnetic systems, airborne and ground coils act as transmitters, while multiple receiving arrays sample synchronously. Such MTMR configurations can improve exploration efficiency and enhance source-target coupling, but they also lead to a large number of repetitive forward modeling calculations under source-receiver combinations. For sensitivity analysis, parameter scanning, and inversion problems, this computational cost is further amplified.

[0003] In existing methods for solving scattering fields in three-dimensional layered media, the Volume Integral Equation (VIE) method offers high accuracy and broad applicability due to its reliance on discrete anomalous regions and its ability to naturally incorporate the Green's function of the layered medium. While techniques such as the Fast Multipole Method, Fast Fourier Transform (FFT), and layered matrix methods have been developed to improve the efficiency of single-step VIE solutions, iterative methods in MTMR configurations typically still require solving for each emission source individually; if the number of sources is large, the computation time increases approximately linearly with the number of sources. On the other hand, while direct methods can theoretically be reused after a single matrix decomposition, the VIE impedance matrix is ​​dense, making conventional direct decomposition too costly and unsuitable for large-scale three-dimensional problems in layered media.

[0004] Therefore, there is an urgent need to propose a fast method for calculating the three-dimensional scattered electromagnetic field of MTMR that is applicable to layered media backgrounds, can handle various transmission / reception types, can significantly reduce the number of three-dimensional forward modeling steps, and maintains high accuracy. Summary of the Invention

[0005] The embodiments of this disclosure provide a method and apparatus for fast calculation of scattered electromagnetic fields based on random matrix approximation, which aims to solve one or more of the above-mentioned problems and other potential problems.

[0006] According to a first aspect of this disclosure, a fast calculation method for scattered electromagnetic fields based on random matrix approximation is provided. The method includes pre-calculating the incident field vectors of all emission sources in the anomalous body region in a three-dimensional scattering model of the target exploration scene, and pre-calculating the reciprocal incident field vectors of virtual sources of all receiving points in the anomalous body region.

[0007] Set the target rank and generate a Gaussian random matrix that matches the number of columns of the scattering response matrix to be determined. The column of the scattering response matrix characterizes the scattering response of a source at all receiving points, and the row characterizes the scattering response of a receiving component to all sources.

[0008] The columns of the Gaussian random matrix are used as weighting coefficients to linearly superimpose the incident field vectors to obtain the synthetic incident field vector. The equivalent current vector is obtained by solving the volume integral equation of the synthetic incident field vector. A random projection matrix is ​​constructed based on the scattered field vector of the equivalent current vector at the receiving point.

[0009] The random projection matrix is ​​decomposed by QR to obtain an orthogonal basis matrix. The rows of the conjugate transpose of the orthogonal basis matrix are used as weighting coefficients to linearly superimpose the reciprocal incident field vectors to obtain the reciprocal composite incident field vector. The reciprocal equivalent current vector is obtained by solving the volume integral equation of the reciprocal composite incident field vector. The projection coefficient matrix is ​​constructed based on the response of the reciprocal equivalent current vector in the emission source. QR decomposition is to split a matrix into the product of an orthogonal basis matrix Q and an upper triangular matrix R.

[0010] The complete scattering response matrix is ​​calculated based on the product of the orthogonal basis matrix and the projection coefficient matrix.

[0011] According to a second aspect of this disclosure, a fast calculation device for scattered electromagnetic fields based on random matrix approximation is provided. The device includes a pre-calculation module configured in a three-dimensional scattering model of a target exploration scene to pre-calculate the incident field vectors of all emission sources in the anomalous body region and to pre-calculate the reciprocal incident field vectors of virtual sources at all receiving points in the anomalous body region.

[0012] The Gaussian random matrix generation module is configured to set a target rank and generate a Gaussian random matrix that matches the number of columns of the scattering response matrix to be determined. The column of the scattering response matrix characterizes the scattering response of a source at all receiving points, and the row characterizes the scattering response of a receiving component to all sources.

[0013] The random projection matrix construction module is configured to use each column of the Gaussian random matrix as a weighting coefficient to linearly superimpose the incident field vector to obtain the synthetic incident field vector. The equivalent current vector is obtained by solving the volume integral equation of the synthetic incident field vector. The random projection matrix is ​​constructed based on the scattered field vector of the equivalent current vector at the receiving point.

[0014] The projection coefficient matrix construction module is configured to perform QR decomposition on the random projection matrix to obtain an orthogonal basis matrix. The rows of the conjugate transpose of the orthogonal basis matrix are used as weighting coefficients to linearly superimpose the reciprocal incident field vectors to obtain the reciprocal composite incident field vector. The reciprocal equivalent current vector is obtained by solving the volume integral equation on the reciprocal composite incident field vector. The projection coefficient matrix is ​​constructed based on the response of the reciprocal equivalent current vector in the emission source. The QR decomposition is to split a matrix into the product of an orthogonal basis matrix Q and an upper triangular matrix R.

[0015] The scattering response matrix calculation module is configured to calculate the complete scattering response matrix based on the product of the orthogonal basis matrix and the projection coefficient matrix.

[0016] According to a third aspect of this disclosure, an electronic device is provided, including one or more processors and a memory associated with the one or more processors, the memory being used to store program instructions that, when read and executed by the one or more processors, perform a method provided according to a first scheme.

[0017] According to a fourth aspect of this disclosure, a computer program product is provided, including a computer program that, when executed by a processor, implements the method provided according to the first aspect.

[0018] The solution provided in this specification transforms the three-dimensional scattering field calculation problem under a multi-transmitter, multi-receiver configuration from the traditional exhaustive solution mode of per-transmitter or per-receiver point into a low-rank matrix reconstruction problem. This eliminates the need to explicitly construct the complete scattering response matrix, reducing the number of three-dimensional solutions, improving computational efficiency, and effectively lowering the cost of engineering applications. Simultaneously, it transforms the abstract matrix operations in random matrix approximation into a physically meaningful process of weighted incident field superposition, equivalent current solution, and scattering field calculation. By constructing the projection coefficient matrix using the electromagnetic reciprocity principle, the method can seamlessly integrate with existing volume fractional equation solvers, providing a clear implementation path and facilitating engineering deployment. Thus, this solution is adaptable to complex large-scale geophysical electromagnetic scenarios, possesses high computational accuracy and stable convergence, and can reconstruct the complete scattering response matrix with a low relative error level. Attached Figure Description

[0019] The above and other features, advantages, and aspects of the embodiments of this disclosure will become more apparent from the accompanying drawings and the following detailed description. In the drawings, the same or similar reference numerals denote the same or similar elements, wherein:

[0020] Figure 1 A flowchart illustrating a fast calculation method for scattered electromagnetic fields based on random matrix approximation according to some embodiments of this disclosure is shown.

[0021] Figure 2A schematic diagram illustrating the principle of a fast calculation method for scattered electromagnetic fields based on random matrix approximation according to some embodiments of this disclosure is shown.

[0022] Figure 3 A schematic diagram of the configuration of a three-dimensional scattering model according to some embodiments of the present disclosure is shown;

[0023] Figure 4 A schematic flowchart illustrating the solution of the single-emission source scattering field according to some embodiments of this disclosure is shown;

[0024] Figure 5 The following diagram illustrates matrix row evaluation based on the reciprocity principle, representing some embodiments of this disclosure.

[0025] Figure 6 A schematic diagram of the process for approximate reconstruction of a random matrix according to some embodiments of this disclosure is shown;

[0026] Figure 7 A schematic diagram illustrating the principle of parallel implementation of some embodiments of this disclosure is shown;

[0027] Figure 8 A schematic diagram of the structure of a fast calculation device for scattered electromagnetic fields based on random matrix approximation according to some embodiments of the present disclosure is shown;

[0028] Figure 9 A schematic block diagram of an electronic device according to some embodiments of the present disclosure is shown. Detailed Implementation

[0029] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions in the embodiments of this specification will be clearly and completely described below with reference to the corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application.

[0030] The terms “comprising” and “having”, and any variations thereof, in this specification, claims, and the foregoing drawings are intended to cover a non-exclusive inclusion. For example, a process, method, system, product, or apparatus that includes a series of steps or units is not limited to the steps or units listed, but may optionally include steps or units not listed, or may optionally include other steps or units inherent to such process, method, product, or apparatus. Depending on the context, the word “if” as it applies herein may be interpreted as “when”, “in response to determination”, or “in response to detection”.

[0031] As mentioned earlier, existing methods for solving the scattering field in three-dimensional layered media are difficult to apply to large-scale three-dimensional problems in layered media. This application considers that in the MTMR problem, the scattering responses of all emission sources at all receiving points naturally constitute a "scattering response matrix." The formation of this matrix involves three physical processes: the emission source generates an incident field within the anomalous body, an equivalent current is formed within the anomalous body, and the equivalent current generates a scattering field at the receiving point. Since the Green's function in layered media decays with distance, and the responses of adjacent emission sources are strongly correlated, this response matrix typically exhibits significant low-rank characteristics. Therefore, if the entire matrix can be reconstructed using its low-rank property without explicitly filling it column-by-column or row-by-row, it is expected to significantly reduce the overall cost of MTMR forward modeling.

[0032] Figure 1 A flowchart illustrating a fast calculation method 100 for scattered electromagnetic fields based on random matrix approximation, according to some embodiments of this disclosure, is shown. Method 100 can be executed by a terminal, which may include, but is not limited to, mobile phones, tablets, desktop computers, servers, etc. Figure 1 As shown, in method 100, step 102 can pre-calculate the incident field vectors of all emission sources in the anomalous body region and the reciprocal incident field vectors of virtual sources of all receiving points in the anomalous body region in the three-dimensional scattering model of the target exploration scene.

[0033] In this embodiment, the overall working principle of the method can be described as follows: Figure 2 As shown, a three-dimensional scattering model is first constructed based on the actual exploration scenario. This model includes a layered background medium, at least one subsurface anomaly, multiple emission sources, and multiple receiver points. The model construction and configuration process can be implemented manually in existing modeling software. Specific configuration methods can be as follows: Figure 3 As shown. The layered background medium can be configured with electromagnetic parameters such as conductivity and permeability for each layer according to actual geological conditions; the underground anomaly is located at any depth within the layered background medium, and its electromagnetic parameters differ from those of the background medium; the emission source can be any one or more combinations of electric dipoles, magnetic dipoles, or electric bipolar sources, and can be deployed on the surface, in the air, or in a well according to exploration requirements; the receiving point can record one or more of the x, y, and z components of the electric or magnetic field, and the receiving array composed of the receiving points can be deployed at any location on the surface, in a well, on the seabed, or in the air.

[0034] like Figure 4 As shown, in the traditional process of solving the complete volume integral equation for the scattered field generated by a single emission source, for any emission source, the incident field within the anomalous body region is first calculated based on the Green's function of the layered medium:

[0035]

[0036] in, The second-order electric Green's function of the current source in a layered dielectric background. and These represent the locations of the target point and the source point, respectively. For the current distribution of the emission source, This is the region of origin for the launch.

[0037] Then, the total field and equivalent current inside the anomalous body are solved. It is the incident field and scattered field The sum, that is:

[0038]

[0039] The scattered field is:

[0040]

[0041] in, Describing an abnormal body, the equivalent current satisfies , This represents the difference in conductivity between the anomalous medium and the background medium.

[0042] Therefore, inside the anomalous body, we have:

[0043]

[0044] By solving this volume integral equation, the total internal field can be obtained. With equivalent current Then the scattered field at the receiving point can be obtained. .

[0045] The solution equations for discretizing the incident field, total field (equivalent current), and scattered field can be written as:

[0046]

[0047] in, The source-to-target coupling matrix, The discrete volume integral equation matrix, The target-to-receiver coupling matrix, , , and express , , , The corresponding discrete vector. Therefore, the scattered field corresponding to a single emission source can be expressed as:

[0048]

[0049] The above method requires source-by-source calculation, which is quite complex. This application first pre-calculates only the incident field of the emission source in the anomalous body region to obtain the incident field vector and stores the incident field vector.

[0050] like Figure 5 As shown, in the traditional solution of scattered fields point by point, when each row of the matrix corresponds to a certain receiving component (i.e., field component) of a receiving point in response to the scattered field response of all emission sources, the electromagnetic reciprocity principle can be used to evaluate the matrix row by row:

[0051]

[0052] in, The inner product is defined as follows: . and They represent the power supply. and magnetic source The generated electric and magnetic fields; and and This indicates that it is powered by a power source. and magnetic source The resulting electric and magnetic fields. The integration region V corresponds to the region where the source is located.

[0053] When only considering the electric field at the receiving point, the case of the electric emission source can be simplified to:

[0054]

[0055] in, for The area where it is located for Location. Virtual source at the receiving point. (in The polarization direction of the virtual point power source. (Given the spatial location of the virtual point power source at the receiving end), the above formula is transformed into:

[0056]

[0057] because The properties of functions can be further transformed into:

[0058]

[0059] Thus, a certain field component at the receiving point The evaluation is transformed into: placing a reciprocal source at the receiver location. The reciprocal field is calculated at each emission source point using VIE. Then, for the source distribution function Integration. This is equivalent to simultaneously finding the results from multiple sources at the same receiving point. The field value at that location. The same applies to magnetic emission sources.

[0060] Similarly, if the calculation is performed exactly as described above, the computation is quite complex. This application will first pre-calculate the reciprocal incident field of the virtual source at the receiving point in the anomalous body region to obtain the reciprocal incident field vector and store the reciprocal incident field vector.

[0061] In method 100, step 104 can set the target rank and generate a Gaussian random matrix that matches the number of columns of the scattering response matrix to be determined. The columns of the scattering response matrix characterize the scattering field response of an emission source at all receiving points, and the rows characterize the scattering field response of a receiving component to all emission sources.

[0062] In this embodiment, the scattered field responses generated by all emitters at all receiver points can be integrated into a two-dimensional scattering response matrix. For the case of three electric field components, the three electric field components at each receiver point are treated as independent row elements; the same applies to the case of three magnetic field components. Each column of this matrix corresponds to the scattered field response of an emitter at all receiver points and all receiver components, and each row corresponds to the scattered field response of a specific receiver component (i.e., field component) at a receiver point to all emitters. For the case of three electric field components, the matrix elements can be defined as follows:

[0063]

[0064] in, Indicates the first The launch source is at the The scattered electric field generated at each receiving position and Let represent three orthogonal unit vectors in the Cartesian coordinate system. This indicates the sequence number corresponding to the three directions.

[0065] After the scattering response matrix is ​​constructed, the values ​​of its matrix elements have not yet been solved, so further processing is needed to determine the complete scattering response matrix. Because the Green's function in the layered medium decays rapidly with distance, the coupling matrix from the emitter to the anomalous body and the coupling matrix from the anomalous body to the receiver both exhibit significant low-rank properties. Consequently, the scattering response matrix formed by combining these two coupling matrices with the volume fractional equation matrix also exhibits low-rank properties, meaning its effective rank is much smaller than its number of rows and columns. Therefore, a low-rank approximation method can be used to reconstruct the complete scattering response matrix by calculating only a small number of matrix elements, without explicitly calculating all elements of the matrix.

[0066] Specifically, a random matrix approximation method will be used for reconstruction calculations, such as... Figure 6As shown, for a given matrix A to be approximated (i.e., the target scattering response matrix that is ultimately desired, assuming the size is...), Given a preset target rank k, generate a Gaussian random matrix. .

[0067] In method 100, step 106 can use each column of the Gaussian random matrix as a weighting coefficient to linearly superimpose the incident field vector to obtain a synthetic incident field vector. The equivalent current vector is obtained by solving the volume integral equation of the synthetic incident field vector. A random projection matrix is ​​constructed based on the scattered field vector of the equivalent current vector at the receiving point.

[0068] In this embodiment, since the original matrix A is not explicitly constructed, ordinary matrix-vector multiplication cannot be performed directly. For the random vectors of each column of the Gaussian random matrix... ,have:

[0069]

[0070] in, Represents the first... List, Representing vectors The Each element. Combining the column response expression, the above formula can be written as:

[0071]

[0072] This means that as long as the incident field vectors of all emission sources in the target region (i.e., the anomalous body region) are pre-calculated and stored, then according to... The coefficients are weighted and superimposed to form a new synthetic incident field vector. Then, a VIE solution is performed again to obtain the final vector. Therefore, the random projection matrix Each column can be obtained through "weighted incident field construction - equivalent current solution - scattered field calculation". This process can be summarized as follows: first construct the impedance matrix, then calculate the incident fields of all physical sources, and then form a weighted incident field, solve the equivalent current and calculate the scattered field for each random sample column in sequence.

[0073] In method 100, step 108 can perform QR decomposition on the random projection matrix to obtain an orthogonal basis matrix. Using the rows of the conjugate transpose of the orthogonal basis matrix as weighting coefficients, the reciprocal incident field vectors are linearly superimposed to obtain a reciprocal composite incident field vector. The reciprocal equivalent current vector is obtained by solving the volume integral equation on the reciprocal composite incident field vector. The projection coefficient matrix is ​​constructed based on the response of the reciprocal equivalent current vector at the emission source. The QR decomposition is to split a matrix into the product of an orthogonal basis matrix Q and an upper triangular matrix R.

[0074] In this embodiment, the random projection matrix Y can be decomposed into an orthogonal basis matrix Q using methods such as Householder transformation or Gram-Schmidt orthogonalizing process. Next, the projection coefficient matrix needs to be calculated. ,for The Okay, there are:

[0075]

[0076] in, For each column of Q The conjugate transpose of . for The The complex conjugate of each element Represents the first... OK.

[0077] In combination with the above Figure 5 The reciprocity row-wise evaluation shown can be rewritten as evaluating all reciprocal incident field vectors by row. The weights are superimposed to form a new reciprocal composite incident field vector, and then the projection result for that row is obtained through a reciprocal VIE solution. Therefore, Similarly, obtaining the values ​​does not require explicitly constructing matrix rows, but only requires pre-calculating the reciprocal incident field vectors and performing weighted superposition.

[0078] In method 100, step 110 can calculate the complete scattering response matrix based on the product of the orthogonal basis matrix and the projection coefficient matrix.

[0079] In this embodiment, after obtaining the orthogonal basis matrix and the projection coefficient matrix, the complete scattering response matrix can be obtained by multiplying the two. This calculation method transforms the MTMR three-dimensional scattering field problem from an "exhaustive solution per emitter / receiver point" to a "low-rank matrix reconstruction problem," significantly reducing the number of three-dimensional solutions. Traditional column-based construction methods require N three-dimensional solutions; row-based reciprocal construction requires M solutions or even more in the case of three components. However, with this method, the total number of solutions is reduced to only (M+N) incident field calculations, 2k equivalent current calculations, 2k scattered field calculations, and one QR decomposition.

[0080] In one possible implementation, the method further includes:

[0081] Perform singular value decomposition on the projection coefficient matrix and calculate the reconstruction error under the current target rank;

[0082] In response to a reconstruction error exceeding the error threshold, the target rank is adjusted and the Gaussian random matrix, random projection matrix, and projection coefficient matrix are repeatedly calculated until the reconstruction error is no greater than the error threshold.

[0083] In this embodiment, a combination of stopping error and true error is used to control the reconstruction accuracy. Specifically, the reconstruction error at the current target rank is determined by approximating the singular values ​​of the reduced-dimensional projection coefficient matrix. If the reconstruction error exceeds the error threshold, the target rank is adjusted (the initial target rank is generally small, so it can be increased by a preset magnitude or value), and the aforementioned calculation process is repeated until the reconstruction error is no greater than the error threshold, satisfying the convergence condition. This method eliminates the need for Singular Value Decomposition (SVD) on the complete large matrix, saving costs.

[0084] In one possible implementation, the incident field vector and the reciprocal incident field vector are pre-computed in parallel, and the random projection matrix and the projection coefficient matrix are computed in parallel.

[0085] In this embodiment, as Figure 7 As shown, in the entire processing of the method in this application, the calculation processes of the incident fields of different emission sources are independent of each other, and the calculation processes of the incident fields of different reciprocal virtual sources are also independent of each other, and can be simultaneously distributed to multiple computing cores for execution. Since the calculation of the k columns of the random projection matrix is ​​independent of each other, and the calculation of the k rows of the projection coefficient matrix is ​​independent of each other, they will also be executed simultaneously. In addition, as needed, the VIE solution process corresponding to a single synthetic incident field can also be performed in grid-level parallelism, further accelerating the single VIE solution.

[0086] The above scheme can be verified through various experiments.

[0087] Experiment 1: Reciprocity Verification. A three-layer background model was constructed, with the conductivity of the three layers being respectively... The conductivity values ​​are 0.04 and 0.01 S / m, and the intermediate layer thickness is 50 m. Two anomalies of different scales are set: the top center coordinates of target 1 are (0,−55,15), the size is 50x50x20 m, the grid number is 16x16x4, and the conductivity is 1 S / m; the top center coordinates of target 2 are (10,50,20), the size is 50x25x20 m, the grid number is 16x8x4, and the conductivity is 0.5 S / m.

[0088] Five types of transmit-receive combinations are set up: 1) electric dipole transmit-electric field receive; 2) magnetic dipole transmit-magnetic field receive; 3) electric dipole transmit-magnetic field receive; 4) magnetic dipole transmit-electric field receive; 5) electric bipolar line source transmit-electric field receive. In each case, the dipole transmitter is polarized in x, y, and z directions at each location; the line source is polarized in the x direction; and the receiver records three components. The dipole sources are distributed on a grid of (−200:10:200,−200:10:200,5m), and the line sources extend 10m along the x direction from the same starting point; the receiving point is located on the same xy grid, with z=1m. The first four cases have a total of 5043 transmitters and 5043 field components, while the fifth case has 1681 transmitters and 5043 field components.

[0089] The calculation results show that the relative errors between the direct VIE and the reciprocal method are approximately 0.71%, 0.45%, 0.45%, 0.58%, and 0.55%, respectively. This demonstrates that the reciprocal row recovery method adopted in this application can accurately replace the traditional row-by-row evaluation process.

[0090] Experiment 2: Benchmark MTMR-RMA Validation. Based on the model in Experiment 1, this experiment further validates the ability of this application to reconstruct the complete MTMR response matrix. Three cases are considered: electric dipole-electric field, magnetic dipole-magnetic field, and electric bipolar source-electric field. For each case, 100 independent experiments with different Gaussian random matrices are conducted, and the rank required to achieve different error levels is calculated.

[0091] The results show that when the target error is about 2%, the electric dipole-electric field case requires about 54–59 rank units, corresponding to a total of about 108–118 three-dimensional solutions to reconstruct the 5043×5043 response matrix; the magnetic dipole-magnetic field case requires about 36–40 rank units, corresponding to a total of about 72–80 three-dimensional solutions; and the line source-electric field case requires about 46–50 rank units, corresponding to a total of about 92–100 three-dimensional solutions. The serial / parallel time comparison shows that: in the case of electric dipoles, the method of this application requires approximately 92.5s / 16.5s, while the direct VIE method requires 1815s / 238.3s, and the reciprocal method requires 1770s / 233.3s; in the case of magnetic dipoles, the method of this application requires 120.2s / 16.4s, while the direct method requires 1971s / 256.0s, and the reciprocal method requires 2002s / 246.8s; in the case of line sources, the method of this application requires 576.2s / 60.8s, while the direct method requires 1033s / 124.9s, and the reciprocal method requires 8714s / 1819s.

[0092] Experiment 3: Verification of a Multi-Scale Complex Model. A multi-scale electromagnetic model in mid-air was constructed. The transmitting array consisted of 21x21 magnetic dipoles, each with three polarizations, distributed over a range of [missing information]. The receiver array consists of 41x41 receiver points located in the z=30m plane; the operating frequency is 900Hz.

[0093] Comparing the results of the method in this application with those of direct MTMR-VIE, the relative errors of the three representative emission source positions are 1.92%, 1.87%, and 1.85%, respectively. The total runtime of the complete system is approximately 832 s, while that of direct MTMR-VIE is approximately 27246 s, and that of the reciprocal construction method is approximately 54389 s, representing speedups of approximately 30 times and 60 times, respectively.

[0094] Experiment 4: Controlled-source Electromagnetic (CSEM) Model Experiment in the Ocean. A controlled-source electromagnetic model of the ocean was constructed. The transmitting array consisted of 21x21 line sources, each 100m in length, distributed over a range of [missing information]. The receiver array consists of 41x41 receiver points located in the same area on the z=990m plane; the operating frequency is 0.25Hz.

[0095] The results show that the relative errors of the three representative emission source positions are approximately 1.97%, 1.93%, and 1.89%, respectively. The total computation time of the complete system is approximately 225 s, while that of direct MTMR-VIE is approximately 17862 s and that of the reciprocal method is approximately 176958 s, representing speedups of approximately 80 times and 786 times, respectively.

[0096] Figure 8 A schematic diagram of the structure of a fast calculation device 800 for scattered electromagnetic fields based on random matrix approximation according to some embodiments of this disclosure is shown. The various embodiments in this specification are described in a progressive manner, and the same or similar parts between the various embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, for the device embodiments, since they are basically similar to the method embodiments, the description is relatively simple, and relevant parts can be referred to the description of the method embodiments. Figure 8 As shown, the device 800 includes a pre-calculation module 801, which is configured in the three-dimensional scattering model of the target exploration scene to pre-calculate the incident field vectors of all emission sources in the anomalous body region, and to pre-calculate the reciprocal incident field vectors of the virtual sources of all receiving points in the anomalous body region.

[0097] The Gaussian random matrix generation module 802 is configured to set a target rank and generate a Gaussian random matrix that matches the number of columns of the scattering response matrix to be determined. The column of the scattering response matrix characterizes the scattering field response of a source at all receiving points, and the row characterizes the scattering field response of a receiving component to all sources.

[0098] The random projection matrix construction module 803 is configured to use each column of the Gaussian random matrix as weighting coefficients to linearly superimpose the incident field vector to obtain the synthetic incident field vector, and then solve the volume integral equation of the synthetic incident field vector to obtain the equivalent current vector. The random projection matrix is ​​constructed based on the scattered field vector of the equivalent current vector at the receiving point.

[0099] The projection coefficient matrix construction module 804 is configured to perform QR decomposition on the random projection matrix to obtain an orthogonal basis matrix. The rows of the conjugate transpose of the orthogonal basis matrix are used as weighting coefficients to linearly superimpose the reciprocal incident field vectors to obtain the reciprocal composite incident field vector. The reciprocal equivalent current vector is obtained by solving the volume integral equation on the reciprocal composite incident field vector. The projection coefficient matrix is ​​constructed based on the response of the reciprocal equivalent current vector in the emission source. The QR decomposition is to split a matrix into the product of the orthogonal basis matrix Q and the upper triangular matrix R.

[0100] The scattering response matrix calculation module 805 is configured to calculate the complete scattering response matrix based on the product of the orthogonal basis matrix and the projection coefficient matrix.

[0101] In one possible implementation, the three-dimensional scattering model includes a layered background medium, an underground anomaly, multiple emission sources, and multiple receiving points.

[0102] In one possible implementation, the pre-calculation module 801 is further configured to pre-calculate the incident field vectors of all emission sources in the anomalous body region based on the layered medium Green's function; and to pre-calculate the reciprocal incident field vectors of all virtual sources with the same polarization direction corresponding to all receiving points in the anomalous body region based on the electromagnetic reciprocity principle.

[0103] In one possible implementation, the apparatus further includes a target rank adjustment module configured to perform singular value decomposition on the projection coefficient matrix, calculate the reconstruction error under the current target rank, and adjust the target rank and repeatedly calculate the Gaussian random matrix, random projection matrix and projection coefficient matrix in response to the reconstruction error being greater than an error threshold until the reconstruction error is not greater than the error threshold.

[0104] In one possible implementation, the random projection matrix construction module 803 is further configured to use the synthetic incident field vector as excitation to solve the discrete volume integral equation and obtain the equivalent current vector; the projection coefficient matrix construction module 804 is further configured to use the reciprocal synthetic incident field vector as excitation to solve the discrete volume integral equation and obtain the reciprocal equivalent current vector.

[0105] In one possible implementation, the incident field vector and the reciprocal incident field vector are pre-computed in parallel, and the random projection matrix and the projection coefficient matrix are computed in parallel.

[0106] In the above embodiments, implementation can be achieved, in whole or in part, through software, hardware, firmware, or any combination thereof. When implemented in software, it can be implemented, in whole or in part, as a computer program product. A computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the flow or function according to the embodiments of this specification is generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in or transmitted through a computer-readable storage medium. The computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, fiber optic, Digital Subscriber Line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that integrates one or more available media. The available media can be magnetic media (e.g., floppy disks, hard disks, magnetic tapes), optical media (e.g., Digital Versatile Discs (DVDs)), or semiconductor media (e.g., Solid State Disks (SSDs)).

[0107] Figure 9 A block diagram of an electronic device 900 that can implement various embodiments of the present disclosure is shown. For example... Figure 9 As shown, the electronic device 900 includes a processor 910, a disk drive 920, an input / output interface 930, a network interface 940, and a memory 950. The processor 910, disk drive 920, input / output interface 930, network interface 940, and memory 950 can communicate with each other via a communication bus 960.

[0108] The processor 910 can be implemented using a general-purpose CPU, microprocessor, application-specific integrated circuit (ASIC), or one or more integrated circuits to execute relevant programs in order to implement the technical solution provided in this application.

[0109] The memory 950 can be implemented in the form of ROM (Read Only Memory), RAM (Read Access Memory), static memory, dynamic storage devices, etc. The memory 950 can store the operating system 951 used to control the operation of the electronic device 900, and the basic input / output system (BIOS) 952 used to control the low-level operations of the electronic device 900. Additionally, it can store a web browser 953, a data storage management system 954, etc. In summary, when the technical solution provided in this application is implemented through software or firmware, the relevant program code is stored in the memory 950 and is called and executed by the processor 910.

[0110] The input / output interface 930 is used to connect input / output modules to enable information input and output. Input / output modules can be configured as components within the device (not shown in the figure) or externally connected to the device to provide corresponding functions. Input devices may include keyboards, mice, touchscreens, microphones, various sensors, etc., while output devices may include displays, vibrators, indicator lights, etc.

[0111] Network interface 940 is used to connect a communication module (not shown in the figure) to enable communication and interaction between the device and other devices. The communication module can communicate via wired means (such as USB, Ethernet cable, etc.) or wireless means (such as mobile network, WIFI, Bluetooth, etc.).

[0112] Bus 960 includes a pathway for transmitting information between various components of the device, such as processor 910, disk drive 920, input / output interface 930, network interface 940, and memory 950.

[0113] It should be noted that although the above-described device only shows the processor 910, disk drive 920, input / output interface 930, network interface 940, memory 950, bus 960, etc., in specific implementations, the device may also include other components necessary for normal operation. Furthermore, those skilled in the art will understand that the above-described device may only include the components necessary for implementing the method of this application, and does not necessarily include all the components shown in the figures.

[0114] The program code used to implement the methods of this disclosure may be written in any combination of one or more programming languages. This program code may be provided to a processor or controller of a general-purpose computer, special-purpose computer, or other programmable data processing apparatus, such that when executed by the processor or controller, the program code causes the functions / operations specified in the flowcharts and / or block diagrams to be implemented. The program code may be executed entirely on a machine, partially on a machine, as a standalone software package partially on a machine and partially on a remote machine, or entirely on a remote machine or server.

[0115] In the context of this disclosure, a machine-readable medium can be a tangible medium that may contain or store a program for use by or in conjunction with an instruction execution system, apparatus, or device. A machine-readable medium can be a machine-readable signal medium or a machine-readable storage medium. Machine-readable media can be, but is not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatus, or devices, or any suitable combination of the foregoing. More specific examples of machine-readable storage media include electrical connections based on one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination of the foregoing. Furthermore, although operations are depicted in a specific order, this should be understood as requiring that such operations be performed in the specific order shown or in sequential order, or requiring that all illustrated operations be performed to achieve the desired result. In certain environments, multitasking and parallel processing may be advantageous. Similarly, while several specific implementation details are included in the foregoing discussion, these should not be construed as limiting the scope of this disclosure. Certain features described in the context of individual embodiments may also be implemented in combination in a single implementation. Conversely, various features described in the context of a single implementation may also be implemented individually or in any suitable sub-combination in multiple implementations.

[0116] Although the subject matter has been described using language specific to structural features and / or methodological logic, it should be understood that the subject matter defined in the appended claims is not necessarily limited to the specific features or actions described above. Rather, the specific features and actions described above are merely illustrative examples of implementing the claims.

Claims

1. A fast calculation method for scattered electromagnetic fields based on random matrix approximation, characterized in that, The method includes: In the three-dimensional scattering model of the target exploration scenario, the incident field vectors of all emission sources in the anomalous body region are pre-calculated, as are the reciprocal incident field vectors of the virtual sources of all receiving points in the anomalous body region. Set the target rank and generate a Gaussian random matrix that matches the number of columns of the scattering response matrix to be determined. The columns of the scattering response matrix characterize the scattering field response of a source at all receiving points, and the rows characterize the scattering field response of a receiving component to all sources. The columns of the Gaussian random matrix are used as weighting coefficients to linearly superimpose the incident field vector to obtain a synthetic incident field vector. The equivalent current vector is obtained by solving the volume integral equation of the synthetic incident field vector. A random projection matrix is ​​constructed based on the scattered field vector of the equivalent current vector at the receiving point. The random projection matrix is ​​decomposed into a QR decomposition to obtain an orthogonal basis matrix. The rows of the conjugate transpose of the orthogonal basis matrix are used as weighting coefficients to linearly superimpose the reciprocal incident field vectors to obtain a reciprocal composite incident field vector. The reciprocal equivalent current vector is obtained by solving the volume integral equation of the reciprocal composite incident field vector. The projection coefficient matrix is ​​constructed based on the response of the reciprocal equivalent current vector in the emission source. The QR decomposition is to split a matrix into the product of an orthogonal basis matrix Q and an upper triangular matrix R. The complete scattering response matrix is ​​calculated based on the product of the orthogonal basis matrix and the projection coefficient matrix.

2. The method for fast calculation of scattered electromagnetic fields based on random matrix approximation according to claim 1, characterized in that, The three-dimensional scattering model includes a layered background medium, underground anomalies, multiple emission sources, and multiple receiving points.

3. The method for fast calculation of scattered electromagnetic fields based on random matrix approximation according to claim 1, characterized in that, The pre-calculation of the incident field vectors of all transmitting sources in the anomalous body region, and the pre-calculation of the reciprocal incident field vectors of the virtual sources at all receiving points in the anomalous body region, include: Based on the Green's function of the layered medium, the incident field vectors of all emission sources in the anomalous body region are pre-calculated. Based on the principle of electromagnetic reciprocity, the reciprocal incident field vector of the virtual source with the same polarization direction at all receiving points in the anomalous body region is pre-calculated.

4. The method for fast calculation of scattered electromagnetic fields based on random matrix approximation according to claim 1, characterized in that, The method further includes: Perform singular value decomposition on the projection coefficient matrix and calculate the reconstruction error under the current target rank; In response to the reconstruction error being greater than the error threshold, the target rank is adjusted and the Gaussian random matrix, random projection matrix, and projection coefficient matrix are repeatedly calculated until the reconstruction error is no greater than the error threshold.

5. The method for fast calculation of scattered electromagnetic fields based on random matrix approximation according to claim 1, characterized in that, The step of solving the volume integral equation of the synthesized incident field vector to obtain the equivalent current vector includes: Using the synthetic incident field vector as an excitation, the discrete volume integral equation is solved to obtain the equivalent current vector; The step of solving the volume integral equation of the reciprocal composite incident field vector to obtain the reciprocal equivalent current vector includes: Using the reciprocal composite incident field vector as excitation, the discrete volume integral equation is solved to obtain the reciprocal equivalent current vector.

6. The method for fast calculation of scattered electromagnetic fields based on random matrix approximation according to claim 1, characterized in that, The incident field vector and the reciprocal incident field vector are pre-calculated in parallel, and the random projection matrix and the projection coefficient matrix are calculated in parallel.

7. A fast calculation device for scattered electromagnetic fields based on random matrix approximation, characterized in that, The device includes: The pre-calculation module is configured in the three-dimensional scattering model of the target exploration scene to pre-calculate the incident field vectors of all emission sources in the anomalous body region, and to pre-calculate the reciprocal incident field vectors of the virtual sources of all receiving points in the anomalous body region. The Gaussian random matrix generation module is configured to set a target rank and generate a Gaussian random matrix that matches the number of columns of the scattering response matrix to be determined. The columns of the scattering response matrix characterize the scattering field response of a source at all receiving points, and the rows characterize the scattering field response of a receiving component to all sources. The random projection matrix construction module is configured to use each column of the Gaussian random matrix as weighting coefficients to linearly superimpose the incident field vector to obtain a synthetic incident field vector, and then solve the volume integral equation of the synthetic incident field vector to obtain an equivalent current vector. The random projection matrix is ​​constructed based on the scattered field vector of the equivalent current vector at the receiving point. The projection coefficient matrix construction module is configured to perform QR decomposition on the random projection matrix to obtain an orthogonal basis matrix, use the rows of the conjugate transpose of the orthogonal basis matrix as weighting coefficients to linearly superimpose the reciprocal incident field vectors to obtain a reciprocal composite incident field vector, solve the volume integral equation of the reciprocal composite incident field vector to obtain a reciprocal equivalent current vector, and construct the projection coefficient matrix based on the response of the reciprocal equivalent current vector at the emission source. The QR decomposition is to split a matrix into the product of an orthogonal basis matrix Q and an upper triangular matrix R. The scattering response matrix calculation module is configured to calculate the complete scattering response matrix based on the product of the orthogonal basis matrix and the projection coefficient matrix.

8. An electronic device, characterized in that, include: One or more processors, and a memory associated with the one or more processors, the memory being used to store program instructions that, when read and executed by the one or more processors, perform the steps of the fast calculation method for scattered electromagnetic fields based on random matrix approximation according to any one of claims 1-6.

9. A computer program product, characterized in that, The method includes a computer program that, when executed by a processor, implements a fast calculation method for scattered electromagnetic fields based on random matrix approximation according to any one of claims 1-6.

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