A two-dimensional magnetotelluric inversion method and system based on implicit neural network

Abstract

The present invention relates to the field of magnetotelluric inversion technology, and in particular to a magnetotelluric two-dimensional inversion method and system based on an implicit neural network, the method comprising: obtaining measured data and a model to be inverted; meshing the model to be inverted to obtain grid coordinate parameters, and determining receiver coordinate parameters; inputting the grid coordinate parameters into the implicit neural network to obtain an intermediate conductivity model; inputting the intermediate conductivity model, grid coordinate parameters, receiver coordinate parameters, and the frequency or period of measured data into a forward algorithm to obtain theoretical data; calculating a total loss term; training an implicit neural network according to the total loss term to obtain an optimal implicit neural network; inputting the grid coordinate parameters into the optimal implicit neural network to obtain a conductivity model of an underground medium. The present invention has a low dependence on an initial model, and can effectively avoid the problem of local minima through a deep learning optimization algorithm, thereby revealing a more accurate abnormal body boundary.

Description

Technical Field

[0001] The present invention relates to the technical field of magnetotelluric inversion, and in particular to a two-dimensional magnetotelluric inversion method and system based on an implicit neural network. Background Art

[0002] Magnetotelluric (MT) is a geophysical exploration method that uses natural electromagnetic fields to detect underground electrical structures to obtain information about underground geological structures. At present, traditional inversion methods mainly include linear inversion methods and nonlinear inversion methods. Linear inversion methods mainly include Occam method, fast relaxation method, Gauss-Newton method, linear conjugate gradient method and other inversion methods, and nonlinear inversion methods mainly include machine learning, simulated annealing method, particle swarm optimization algorithm, Bayesian inversion, artificial bee colony algorithm and other inversion methods. Linear inversion methods have their unique advantages, such as low computing resource requirements, fast processing speed and clear boundary identification, but due to the nonlinear nature of the inversion problem, the linearized iteration method of linear inversion methods often leads to excessive dependence on the initial model and may fall into a local optimal solution. Compared with linear methods, nonlinear inversion algorithms reduce dependence on the initial model and can theoretically obtain the global optimal solution, but when dealing with high-dimensional inversion problems or large data calculations, they still face the challenges of low inversion accuracy and slow calculation speed.

[0003] Deep Learning (DL), as an important branch of machine learning, is being applied by more and more scholars in the field of MT inversion. At present, the application of DL in MT inversion mainly adopts data-driven supervised learning. Although supervised learning can efficiently map the correspondence of data sets, it takes a lot of time to produce high-quality data sets, and the quality of the data set directly affects the inversion accuracy and generalization ability of the network.

[0004] In the prior art, from the perspective of deep learning theory, convolutional neural networks are often used as deep learning networks. This is mainly because the input of the network is data (i.e., apparent resistivity and phase), and the output is a conductivity model. The data points and the conductivity model points are not one-to-one corresponding. It is necessary to use a convolution layer to extract information from the data and then deconvolve it back to the conductivity model. This method is applied in geophysical inversion, making the inversion process lack of interpretability. From the perspective of deep learning learning methods, data-driven supervised learning methods are often used. This requires the establishment of a data set consisting of apparent resistivity, phase, and a conductivity model output by the network. By training the network, an end-to-end mapping relationship between the network input and output is established, thereby realizing deep learning inversion. This training method takes a lot of time to build a data set, and the accuracy of the network inversion depends on the quality of the data set. It lacks physical information constraints and has poor generalization ability.

[0005] Therefore, the present invention aims to solve these problems by introducing implicit neural network and neural derivative regularization into MT inversion to reduce the dependence on the initial model and improve the accuracy of the inversion results. Summary of the invention

[0006] In view of the defects in the prior art, the present invention provides a two-dimensional magnetotelluric inversion method and system based on an implicit neural network. The specific technical solution is as follows:

[0007] In a first aspect, the present invention provides a two-dimensional magnetotelluric inversion method based on an implicit neural network, the method comprising:

[0008] Step S1, obtaining measured data and a model to be inverted;

[0009] Step S2, gridding the model to be inverted to obtain grid original coordinate parameters; standardizing the grid original coordinate parameters to obtain grid coordinate parameters, and determining receiver coordinate parameters from the grid coordinate parameters;

[0010] Step S3, inputting the grid coordinate parameters into an implicit neural network, and obtaining an intermediate conductivity model based on an output result of the implicit neural network;

[0011] Step S4, inputting the intermediate conductivity model, grid coordinate parameters, receiver coordinate parameters, and the frequency or period of the measured data into a magnetotelluric forward algorithm to obtain theoretical data;

[0012] Step S5, calculating the data loss term between the theoretical data and the measured data; obtaining an initial model loss term according to the gradient information between the intermediate conductivity model and the grid coordinate parameters retained by automatic differentiation, and multiplying the initial model loss term by a regularization factor to obtain a model loss term; and adding the data loss term and the model loss term to obtain a total loss term;

[0013] Step S6, repeatedly iteratively training the implicit neural network according to the total loss term to obtain an optimal implicit neural network;

[0014] Step S7, inputting the grid coordinate parameters into the optimal implicit neural network to obtain the conductivity model of the underground medium.

[0015] In a possible implementation, the implicit neural network is an MLPs neural network framework using a Sine activation function.

[0016] In a possible implementation, the intermediate conductivity model is obtained based on the output result of the implicit neural network, specifically: prior information is added to the output result of the implicit neural network and the power series of e is taken to obtain the intermediate conductivity model, and the calculation formula is:

[0017] ,

[0018] in, m represents the intermediate conductivity model, represents the output of the implicit neural network, m 0 Represents prior information.

[0019] In a possible implementation, the magnetotelluric forward algorithm is a magnetotelluric two-dimensional finite difference algorithm based on Maxwell's equations under the pytorch framework.

[0020] In a possible implementation, the measured data includes a measured apparent resistivity and a measured phase, and the theoretical data includes a theoretical apparent resistivity and a theoretical phase.

[0021] In a possible implementation, the calculating of the data loss term between the theoretical data and the measured data is specifically as follows:

[0022] The theoretical apparent resistivity and the measured apparent resistivity are logarithmized with a base of 10 to obtain the pre-processed theoretical apparent resistivity and the pre-processed measured apparent resistivity. The calculation formula is:

[0023] ,

[0024] ,

[0025] in, Indicates i The preprocessed theoretical apparent resistivity of each node, Indicates i The theoretical apparent resistivity of each node is Indicates i The preprocessed measured apparent resistivity of each node, Indicates i The measured apparent resistivity of each node;

[0026] The theoretical phase and the measured phase are respectively converted into arcs to obtain a preprocessed theoretical phase and a preprocessed measured phase, and the calculation formula is:

[0027] ,

[0028] ,

[0029] in, Indicates i The preprocessing theoretical phase of nodes, Indicates i The theoretical phase of each node, Indicates i The preprocessed measured phase of each node, Indicates i The measured phase of each node;

[0030] The data loss term between the theoretical data and the measured data is calculated based on the preprocessed theoretical apparent resistivity, the preprocessed measured apparent resistivity, the preprocessed theoretical phase, and the preprocessed measured phase. The calculation formula is:

[0031] ,

[0032] ,

[0033] ,

[0034] in, L d represents the data loss term, represents the apparent resistivity loss term, represents the phase loss term, n Indicates the total number of nodes in the inversion result.

[0035] In a possible implementation, the calculation formula of the initial model loss term is:

[0036] ,

[0037] in, L m represents the initial model loss term, m i Indicates the intermediate conductivity model i The conductivity value of each node, y i and z i Respectively represent i The horizontal and vertical coordinates of each node, n Indicates the total number of nodes in the inversion result.

[0038] In a possible implementation, the regularization factor is expressed as follows:

[0039] ,

[0040] in, represents the regularization factor, represents the initial coefficient, l d0 indicates that the initial data fit is poor, l m0 indicates that the initial model fit is poor, Indicates the change ratio, epoch Indicates the number of iterations.

[0041] In a possible implementation, step S6 is specifically: substituting the total loss term into the Adam optimizer, back-propagating the total loss term gradient through the gradient back-propagation mechanism of the Adam optimizer's automatic differentiation, updating the training parameters of the implicit neural network according to a preset learning rate, repeating steps S3-S5, training the implicit neural network by minimizing the objective function, until the maximum number of training times is reached or the total loss term converges, and the neural representation network at this time is the optimal implicit neural network;

[0042] The expression of the minimization objective function is:

[0043] ,

[0044] in, represents the training parameters of the implicit neural network, R represents the receiver coordinate parameter matrix, represents the magnetotelluric forward algorithm, represents an implicit neural network, x represents the grid coordinate parameters, d Represents the measured data, m A conductivity model representing the subsurface medium.

[0045] In a second aspect, the present invention provides a two-dimensional magnetotelluric inversion system based on an implicit neural network, the system comprising:

[0046] A data acquisition module, configured to acquire measured data and a model to be inverted;

[0047] A grid generation module is configured to perform grid generation on the model to be inverted to obtain grid original coordinate parameters; perform standardization processing on the grid original coordinate parameters to obtain grid coordinate parameters, and determine receiver coordinate parameters from the grid coordinate parameters;

[0048] An intermediate conductivity model acquisition module is configured to input the grid coordinate parameters into an implicit neural network, and obtain an intermediate conductivity model based on an output result of the implicit neural network;

[0049] A theoretical data acquisition module is configured to input the intermediate conductivity model, grid coordinate parameters, receiver coordinate parameters, and the frequency or period of measured data into a magnetotelluric forward algorithm to obtain theoretical data;

[0050] A total loss term acquisition module is configured to calculate a data loss term between the theoretical data and the measured data; obtain an initial model loss term according to the gradient information between the intermediate conductivity model and the grid coordinate parameter retained by automatic differentiation, and multiply the initial model loss term by a regularization factor to obtain a model loss term; and add the data loss term and the model loss term to obtain a total loss term;

[0051] An iteration module is configured to repeatedly iteratively train the implicit neural network according to the total loss term to obtain an optimal implicit neural network;

[0052] The conductivity model acquisition module is configured to input the grid coordinate parameters into the optimal implicit neural network to obtain the conductivity model of the underground medium.

[0053] Compared with the prior art, the present invention has the following beneficial effects:

[0054] (1) Compared with the convolutional neural network in the prior art, the present invention uses the implicit neural network for deep learning based on the implicit neural network representation theory, calculates the conductivity of the corresponding position through the spatial coordinates, and takes the continuous function that characterizes the conductivity model as the search target. It can characterize the conductivity parameters of the underground medium in the continuous domain with higher accuracy and efficiency.

[0055] (2) Compared with the data-driven supervised learning method used in the prior art, the present invention adopts a physics-driven learning method, relying on the finite difference magnetotelluric forward modeling algorithm based on the Maxwell equations written in the pytorch framework for forward modeling. In each iteration, only the loss between the output result of the current network (i.e., theoretical data) and the measured data is required to train the network. This training method first saves the time cost of constructing the data set, and the magnetotelluric forward modeling algorithm can provide physical information constraints for the network, making the results more credible and having better generalization ability in the face of different measured data.

[0056] (3) The MLPs neural network framework of the present invention adopts the Sine activation function, which utilizes the periodic characteristics of the sine function and can effectively learn the high-frequency components and high-order derivative information in the data. Compared with the traditional non-periodic activation function, the Sine activation function has a faster convergence speed and a more powerful fine structure characterization ability. It has significant advantages in processing high-frequency details of images and scenes, and can more accurately capture and represent complex geometric shapes and appearance features.

[0057] (4) The present invention introduces a model loss term into the loss term. The model loss term does not need to rely on a priori models, and the intermediate conductivity model required by the model loss term can use automatic differentiation to retain the gradients of the intermediate conductivity model and the spatial coordinates with respect to the gradients in the y and z directions, thereby improving the boundary accuracy of the anomaly in the inversion results.

[0058] (5) The first output of the implicit neural network of the present invention is a random initial model containing prior information, which reduces the dependence on the initial model. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0060] Figure 1 A schematic diagram of a flow chart of a two-dimensional magnetotelluric inversion method based on an implicit neural network provided in an embodiment of the present invention;

[0061] Figure 2 The measured data diagram provided by the embodiment of the present invention, wherein the left diagram is a measured apparent resistivity diagram, and the right diagram is a measured phase diagram;

[0062] Figure 3 The Mare2dEM inversion result in the prior art provided by the embodiment of the present invention;

[0063] Figure 4 An inversion result of a two-dimensional magnetotelluric inversion method based on an implicit neural network disclosed in the present invention provided in an embodiment of the present invention;

[0064] Figure 5 A real conductivity model diagram provided by an embodiment of the present invention;

[0065] Figure 6 A structural block diagram of a two-dimensional magnetotelluric inversion system based on an implicit neural network provided in an embodiment of the present invention;

[0066] Figure 7 A schematic diagram of the structure of an electronic device provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0067] The following embodiments of the technical solution of the present invention are described in detail in conjunction with the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and are therefore only used as examples, and cannot be used to limit the protection scope of the present invention.

[0068] It should be noted that, unless otherwise specified, the technical terms or scientific terms used in the present invention should have the common meanings understood by those skilled in the art to which the present invention belongs.

[0069] Reference to "embodiments" herein means that a particular feature, structure, or characteristic described in conjunction with the embodiments may be included in at least one embodiment of the present invention. The appearance of the phrase in various places in the specification does not necessarily refer to the same embodiment, nor is it an independent or alternative embodiment that is mutually exclusive with other embodiments. It is explicitly and implicitly understood by those skilled in the art that the embodiments described herein may be combined with other embodiments.

[0070] The method of the present invention reduces the dependence of the inversion algorithm on the initial model, increases the accuracy of the inversion result, and eliminates the problem of supervised learning requiring a lot of time and effort to construct a huge sample set during the inversion process.

[0071] See also Figure 1 , is a flow chart of a two-dimensional magnetotelluric inversion method based on an implicit neural network provided by an embodiment of the present invention. Figure 1 As shown, the method includes:

[0072] Step S1, obtaining measured data and the model to be inverted.

[0073] The measured data is stored in the form of one file for one receiver, and the file contains the frequency information of the magnetotelluric signal collected by the corresponding receiver, the coordinate position and relative position of the receiver, and various magnetotelluric data.

[0074] Step S2, gridding the model to be inverted to obtain grid original coordinate parameters; standardizing the grid original coordinate parameters to obtain grid coordinate parameters, and determining receiver coordinate parameters from the grid coordinate parameters.

[0075] Preferably, the specific method of grid division can be adjusted according to the scale of the underground medium, the burial depth of the target body and the forward modeling method.

[0076] Specifically, the grid coordinate parameters are underground space coordinate parameters of the model constructed according to the frequency, coordinate and other information in the measured data, including the horizontal direction y and the vertical direction z.

[0077] The normalizing the original grid coordinate parameters is specifically: normalizing the original grid coordinate parameters to limit the original grid coordinate parameters to a range of [-1, 1].

[0078] In a specific embodiment, the model to be inverted is gridded, with a total of 84 layers in the vertical direction, the first 10 layers are air layers, the thickness of the 11th to 20th layers is 50m, and the thickness of each subsequent layer is 1.07 times the thickness of the previous layer. The total depth of the model to be inverted is about 210km; there are a total of 128 grid units in the horizontal direction, the inversion core area is the middle 100 grid units, the width of each grid unit is 500m, and there are 14 expansion grid units on each side of the model. The grid width is 1.2 times the width of the previous grid, and the expansion area on one side extends about 29.1km.

[0079] Step S3, inputting the grid coordinate parameters into an implicit neural network, and obtaining an intermediate conductivity model based on an output result of the implicit neural network.

[0080] Preferably, the implicit neural network is an MLPs neural network framework using a Sine activation function. The size of the MLPs neural network framework is [2,256,256,256,256,1], where '2' is the input layer size, '256' is the hidden layer size, and '1' is the output layer size; the activation function is a Sine function; and the parameters of the network are randomly initialized.

[0081] The intermediate conductivity model is obtained based on the output result of the implicit neural network, specifically, the intermediate conductivity model is obtained by adding prior information to the output result of the implicit neural network and taking the power series of e, and the calculation formula is:

[0082] ,

[0083] in, m represents the intermediate conductivity model, represents the output of the implicit neural network, m 0 Represents prior information.

[0084] It should be noted that the intermediate conductivity model is a random model obtained by random initialization network calculation, and is not a model of the underground medium.

[0085] Step S4, inputting the intermediate conductivity model, grid coordinate parameters, receiver coordinate parameters, and the frequency or period of the measured data into a magnetotelluric forward algorithm to obtain theoretical data.

[0086] In an embodiment of the present invention, the magnetotelluric forward modeling algorithm is a magnetotelluric two-dimensional finite difference algorithm based on Maxwell's equations under the pytorch framework, which not only enables the gradient calculated by deep learning to be transferred back from theoretical data to the intermediate conductivity model, but also improves the accuracy and applicability of the forward modeling compared to forward modeling using deep learning methods.

[0087] In a specific embodiment, 35 receiving points are set in the model to be inverted, distributed in the range of -25.5km~25.5km, and the interval between each receiving point is 1.5km. The theoretical data of 32 frequencies in the range of 0.001~100Hz are calculated, and the theoretical data include theoretical apparent resistivity and theoretical phase.

[0088] Step S5, calculating the data loss term between the theoretical data and the measured data; obtaining the initial model loss term according to the gradient information between the intermediate conductivity model and the grid coordinate parameters retained by automatic differentiation, and multiplying the initial model loss term by the regularization factor to obtain the model loss term; and adding the data loss term and the model loss term to obtain the total loss term.

[0089] It should be noted that the measured data include the measured apparent resistivity and the measured phase, and the theoretical data include the theoretical apparent resistivity and the theoretical phase.

[0090] The calculation of the data loss term between the theoretical data and the measured data is specifically as follows:

[0091] The theoretical apparent resistivity and the measured apparent resistivity are logarithmized with a base of 10 to obtain the pre-processed theoretical apparent resistivity and the pre-processed measured apparent resistivity. The calculation formula is:

[0092] ,

[0093] ,

[0094] in, Indicates i The preprocessed theoretical apparent resistivity of each node, Indicates i The theoretical apparent resistivity of each node is Indicates i The preprocessed measured apparent resistivity of each node, Indicates i The measured apparent resistivity of each node.

[0095] The theoretical phase and the measured phase are respectively converted into arcs to obtain a preprocessed theoretical phase and a preprocessed measured phase, and the calculation formula is:

[0096] ,

[0097] ,

[0098] in, Indicates i The preprocessing theoretical phase of nodes, Indicates i The theoretical phase of each node, Indicates i The preprocessed measured phase of each node, Indicates i The measured phase of each node.

[0099] The data loss term between the theoretical data and the measured data is calculated based on the preprocessed theoretical apparent resistivity, the preprocessed measured apparent resistivity, the preprocessed theoretical phase, and the preprocessed measured phase. The calculation formula is:

[0100] ,

[0101] ,

[0102] ,

[0103] in, L d represents the data loss term, represents the apparent resistivity loss term, represents the phase loss term, n Indicates the total number of nodes in the inversion result.

[0104] See also Figure 2 , which is a measured data diagram provided by an embodiment of the present invention, wherein the left figure is a measured apparent resistivity diagram, and the right figure is a measured phase diagram. In this embodiment, key processing is performed on the theoretical data and the measured data, respectively, to enhance the comparability of the data and the accuracy of the analysis. Specifically, the theoretical apparent resistivity and the measured apparent resistivity are logarithmized with a base of 10, and the theoretical phase and the measured phase are radianized. The benefits of this processing method are mainly reflected in two aspects: First, the logarithmic transformation helps to reveal the potential characteristics of the apparent resistivity data, reduces the difference between high and low values, thereby avoiding the masking of low-order data by high-order data, making subtle changes in the data more obvious, and facilitating observation and analysis. Second, due to the large difference in the original scale between the apparent resistivity and the phase, direct comparison may be misleading. By converting the two data to the same scale, the difference between them can be more fairly evaluated. This standardized processing ensures the rationality of the error calculation and makes the results more accurate and reliable.

[0105] Furthermore, the calculation formula of the initial model loss term is:

[0106] ,

[0107] in, L m represents the initial model loss term, m i Indicates the intermediate conductivity model i The conductivity value of each node, y i and z i Respectively represent i The horizontal and vertical coordinates of each node, n Indicates the total number of nodes in the inversion result.

[0108] Furthermore, the expression of the regularization factor is as follows:

[0109] ,

[0110] in, represents the regularization factor, represents the initial coefficient, l d0 indicates that the initial data fit is poor, l m0 indicates that the initial model fit is poor, Indicates the change ratio, epoch Indicates the number of iterations.

[0111] Preferably, the initial coefficient of the regularization factor is is 0.001, the coefficient of variation is 0.9995.

[0112] Step S6, iteratively train the implicit neural network according to the total loss term to obtain the optimal implicit neural network. Specifically, the total loss term is substituted into the Adam optimizer, and the gradient of the total loss term is back-propagated through the gradient back-propagation mechanism of the Adam optimizer's automatic differentiation, and the training parameters of the implicit neural network are updated according to the preset learning rate, and steps S3-S5 are repeated to train the implicit neural network by minimizing the objective function until the maximum number of training times is reached or the total loss term converges, and the neural representation network at this time is the optimal implicit neural network.

[0113] Furthermore, the expression of the minimization objective function is:

[0114] ,

[0115] in, represents the training parameters of the implicit neural network, R represents the receiver coordinate parameter matrix, represents the magnetotelluric forward algorithm, represents an implicit neural network, x represents the grid coordinate parameters, d Represents the measured data, m A conductivity model representing the subsurface medium.

[0116] Preferably, the learning rate is 1e-4 and the maximum number of training times is 2000. epoch , the total loss term converges to the point that the total loss term drops to a certain threshold and tends to be stable.

[0117] Step S7, inputting the grid coordinate parameters into the optimal implicit neural network to obtain the conductivity model of the underground medium.

[0118] Through this embodiment, the present invention demonstrates a two-dimensional magnetotelluric inversion method based on an implicit neural network. This method uses implicit neural representation to continuously describe the underground resistivity distribution. This method has little dependence on the initial model and can effectively avoid the problem of local minima through a deep learning optimization algorithm.

[0119] See also Figure 3 , which is the Mare2dEM inversion result in the prior art provided by the embodiment of the present invention; see Figure 4 , which is the inversion result of a two-dimensional magnetotelluric inversion method based on an implicit neural network disclosed in the present invention, combined with Figure 3 and Figure 4 It can be seen that under the condition of the total loss term constraint of neural derivative regularization, compared with the prior art, the two-dimensional magnetotelluric inversion method based on implicit neural network disclosed in the present invention can reveal more accurate abnormal body boundaries. Figure 5 , which is a real conductivity model diagram provided by an embodiment of the present invention, combined with Figure 3-Figure 5 It can be seen that compared with the prior art, the result of the two-dimensional magnetotelluric inversion method based on implicit neural network disclosed in the present invention is more accurate.

[0120] It should be emphasized that the technical solution of the present invention is not limited by the above specific embodiments, and technical adjustments and deformations are allowed as needed, and these adjustments and deformations are included in the technical scope of the present invention. This makes the present invention have broad application prospects and value in the fields of geophysical exploration and magnetotelluric inversion.

[0121] Corresponding to the above-mentioned embodiment, the present invention also provides a two-dimensional magnetotelluric inversion system based on an implicit neural network.

[0122] See also Figure 6 , is a structural block diagram of a two-dimensional magnetotelluric inversion system based on an implicit neural network provided by an embodiment of the present invention. Figure 6 As shown, the system mainly includes the following modules:

[0123] A data acquisition module, configured to acquire measured data and a model to be inverted;

[0124] A grid generation module is configured to perform grid generation on the model to be inverted to obtain grid original coordinate parameters; perform standardization processing on the grid original coordinate parameters to obtain grid coordinate parameters, and determine receiver coordinate parameters from the grid coordinate parameters;

[0125] An intermediate conductivity model acquisition module is configured to input the grid coordinate parameters into an implicit neural network, and obtain an intermediate conductivity model based on an output result of the implicit neural network;

[0126] A theoretical data acquisition module is configured to input the intermediate conductivity model, grid coordinate parameters, receiver coordinate parameters, and the frequency or period of measured data into a magnetotelluric forward algorithm to obtain theoretical data;

[0127] A total loss term acquisition module is configured to calculate a data loss term between the theoretical data and the measured data; obtain an initial model loss term according to the gradient information between the intermediate conductivity model and the grid coordinate parameter retained by automatic differentiation, and multiply the initial model loss term by a regularization factor to obtain a model loss term; and add the data loss term and the model loss term to obtain a total loss term;

[0128] An iteration module is configured to repeatedly iteratively train the implicit neural network according to the total loss term to obtain an optimal implicit neural network;

[0129] The conductivity model acquisition module is configured to input the grid coordinate parameters into the optimal implicit neural network to obtain the conductivity model of the underground medium.

[0130] It should be pointed out that the specific contents involved in the embodiments of the present invention can be found in the description of the above method embodiments, and for the sake of brevity, they will not be repeated here.

[0131] Corresponding to the above embodiment, an embodiment of the present invention further provides an electronic device.

[0132] See also Figure 7 , is a schematic diagram of the structure of an electronic device provided by an embodiment of the present invention. Figure 7As shown, the electronic device may include: a processor, a memory and a communication unit. These components communicate via one or more buses. Those skilled in the art will appreciate that the electronic device structure may be a bus structure or a star structure, and may include more or fewer components than those described above, or a combination of certain components, or different component arrangements.

[0133] The communication unit is used to establish a communication channel so that the electronic device can communicate with other devices.

[0134] The processor is the control center of the electronic device. It uses various interfaces and lines to connect the various parts of the entire electronic device. It runs or executes software programs and / or modules stored in the memory, and calls the data stored in the memory to perform various functions of the electronic device and / or process data. The processor can be composed of an integrated circuit (IC), for example, it can be composed of a single packaged IC, or it can be composed of multiple packaged ICs with the same or different functions. For example, the processor can only include a central processing unit (CPU). In an embodiment of the present invention, the CPU can be a single computing core or multiple computing cores.

[0135] Memory, used to store the execution instructions of the processor. The memory can be implemented by any type of volatile or non-volatile storage device or a combination of them, such as static random access memory (SRAM), electrically erasable programmable read-only memory (EEPROM), erasable programmable read-only memory (EPROM), programmable read-only memory (PROM), read-only memory (ROM), magnetic memory, flash memory, magnetic disk or optical disk.

[0136] When the execution instructions in the memory are executed by the processor, the electronic device is enabled to execute part or all of the steps in the above method embodiments.

[0137] Corresponding to the above embodiment, the embodiment of the present invention further provides a computer-readable storage medium, wherein the computer-readable storage medium may store a program, wherein when the program is running, the device where the computer-readable storage medium is located may be controlled to execute some or all of the steps in the above method embodiment. In a specific implementation, the computer-readable storage medium may be a magnetic disk, an optical disk, a read-only memory (ROM) or a random access memory (RAM).

[0138] Corresponding to the above embodiment, an embodiment of the present invention further provides a computer program product, which includes executable instructions. When the executable instructions are executed on a computer, the computer executes part or all of the steps in the above method embodiment.

[0139] In the embodiments of the present invention, "at least one" refers to one or more, and "more than one" refers to two or more. "And / or" describes the association relationship of associated objects, indicating that three relationships may exist. For example, A and / or B may represent the existence of A alone, the existence of A and B at the same time, and the existence of B alone. A and B may be singular or plural. The character " / " generally indicates that the previous and subsequent associated objects are in an "or" relationship. "At least one of the following" and similar expressions refer to any combination of these items, including any combination of single or plural items. For example, at least one of a, b and c may be represented by: a, b, c, ab, ac, bc or abc, where a, b, c may be single or multiple.

[0140] Those skilled in the art will appreciate that the various units and algorithm steps described in the embodiments disclosed herein can be implemented in a combination of electronic hardware, computer software, and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of the present invention.

[0141] Those skilled in the art can clearly understand that, for the convenience and brevity of description, the specific working processes of the systems, devices and units described above can refer to the corresponding processes in the aforementioned method embodiments and will not be repeated here.

[0142] In several embodiments provided by the present invention, if any function is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention is essentially or the part that contributes to the prior art or the part of the technical solution can be embodied in the form of a software product, and the computer software product is stored in a storage medium, including a number of instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM), random access memory (RAM), disk or optical disk, etc., various media that can store program codes.

[0143] The above is only a specific embodiment of the present invention. Any person skilled in the art can easily think of changes or substitutions within the technical scope disclosed by the present invention, which should be included in the protection scope of the present invention. The protection scope of the present invention shall be based on the protection scope of the claims.

Claims

1. A two-dimensional magnetotelluric inversion method based on implicit neural network, characterized in that: The method comprises: Step S1, obtaining measured data and a model to be inverted; Step S2, gridding the model to be inverted to obtain grid original coordinate parameters; standardizing the grid original coordinate parameters to obtain grid coordinate parameters, and determining receiver coordinate parameters from the grid coordinate parameters; Step S3, inputting the grid coordinate parameters into an implicit neural network, and obtaining an intermediate conductivity model based on an output result of the implicit neural network; Step S4, inputting the intermediate conductivity model, grid coordinate parameters, receiver coordinate parameters, and the frequency or period of the measured data into a magnetotelluric forward algorithm to obtain theoretical data; Step S5, calculating the data loss term between the theoretical data and the measured data; obtaining an initial model loss term according to the gradient information between the intermediate conductivity model and the grid coordinate parameters retained by automatic differentiation, and multiplying the initial model loss term by a regularization factor to obtain a model loss term; and adding the data loss term and the model loss term to obtain a total loss term; Step S6, repeatedly iteratively training the implicit neural network according to the total loss term to obtain an optimal implicit neural network; Step S7, inputting the grid coordinate parameters into the optimal implicit neural network to obtain a conductivity model of the underground medium; The implicit neural network is an MLPs neural network framework using a Sine activation function; the magnetotelluric forward algorithm is a magnetotelluric two-dimensional finite difference algorithm based on Maxwell's equations under a pytorch framework.

2. The magnetotelluric two-dimensional inversion method based on implicit neural network according to claim 1, characterized in that: The intermediate conductivity model is obtained based on the output result of the implicit neural network, specifically: adding prior information to the output result of the implicit neural network and taking the power series of e to obtain the intermediate conductivity model, and the calculation formula is: ， in, m represents the intermediate conductivity model, represents the output of the implicit neural network, m 0 Represents prior information.

3. The magnetotelluric two-dimensional inversion method based on implicit neural network according to claim 1, characterized in that: The measured data include measured apparent resistivity and measured phase, and the theoretical data include theoretical apparent resistivity and theoretical phase.

4. The method for two-dimensional magnetotelluric inversion based on implicit neural network according to claim 3, characterized in that: The data loss term between the theoretical data and the measured data is calculated as follows: The theoretical apparent resistivity and the measured apparent resistivity are logarithmized with a base of 10 to obtain the preprocessed theoretical apparent resistivity and the preprocessed measured apparent resistivity. The calculation formula is: ， ， in, Indicates i The preprocessed theoretical apparent resistivity of each node, Indicates i The theoretical apparent resistivity of each node is Indicates i The preprocessed measured apparent resistivity of each node, Indicates i The measured apparent resistivity of each node; The theoretical phase and the measured phase are respectively converted into arcs to obtain a preprocessed theoretical phase and a preprocessed measured phase, and the calculation formula is: ， ， in, Indicates i The preprocessing theoretical phase of nodes, Indicates i The theoretical phase of each node, Indicates i The preprocessed measured phase of each node, Indicates i The measured phase of each node; The data loss term between the theoretical data and the measured data is calculated based on the preprocessed theoretical apparent resistivity, the preprocessed measured apparent resistivity, the preprocessed theoretical phase, and the preprocessed measured phase. The calculation formula is: ， ， ， in, L d represents the data loss term, represents the apparent resistivity loss term, represents the phase loss term, n Indicates the total number of nodes in the inversion result.

5. The magnetotelluric two-dimensional inversion method based on implicit neural network according to claim 1, characterized in that: The calculation formula of the initial model loss term is: ， in, L m represents the initial model loss term, m i Indicates the intermediate conductivity model i The conductivity value of each node, y i and z i Respectively represent i The horizontal and vertical coordinates of each node, n Indicates the total number of nodes in the inversion result.

6. The magnetotelluric two-dimensional inversion method based on implicit neural network according to claim 1, characterized in that: The expression of the regularization factor is as follows: ， in, represents the regularization factor, represents the initial coefficient, l d0 indicates that the initial data fit is poor, l m0 indicates that the initial model fit is poor, Indicates the change ratio, epoch Indicates the number of iterations.

7. The two-dimensional magnetotelluric inversion method based on implicit neural network according to claim 1, characterized in that: Step S6 is specifically: substituting the total loss term into the Adam optimizer, back-propagating the total loss term gradient through the gradient back-propagation mechanism of the Adam optimizer's automatic differentiation, updating the training parameters of the implicit neural network according to the preset learning rate, repeating steps S3-S5, training the implicit neural network by minimizing the objective function, until the maximum number of training times is reached or the total loss term converges, and the neural representation network at this time is the optimal implicit neural network; The expression of the minimization objective function is: ， in, represents the training parameters of the implicit neural network, R represents the receiver coordinate parameter matrix, represents the magnetotelluric forward algorithm, represents an implicit neural network, x represents the grid coordinate parameters, d Represents the measured data, m A conductivity model representing the subsurface medium.

8. A two-dimensional magnetotelluric inversion system based on implicit neural network, characterized in that: The system comprises: A data acquisition module, configured to acquire measured data and a model to be inverted; A grid generation module is configured to perform grid generation on the model to be inverted to obtain grid original coordinate parameters; perform standardization processing on the grid original coordinate parameters to obtain grid coordinate parameters, and determine receiver coordinate parameters from the grid coordinate parameters; An intermediate conductivity model acquisition module is configured to input the grid coordinate parameters into an implicit neural network, and obtain an intermediate conductivity model based on an output result of the implicit neural network; A theoretical data acquisition module is configured to input the intermediate conductivity model, grid coordinate parameters, receiver coordinate parameters, and the frequency or period of measured data into a magnetotelluric forward algorithm to obtain theoretical data; A total loss term acquisition module is configured to calculate a data loss term between the theoretical data and the measured data; obtain an initial model loss term according to the gradient information between the intermediate conductivity model and the grid coordinate parameter retained by automatic differentiation, and multiply the initial model loss term by a regularization factor to obtain a model loss term; and add the data loss term and the model loss term to obtain a total loss term; An iteration module is configured to repeatedly iteratively train the implicit neural network according to the total loss term to obtain an optimal implicit neural network; A conductivity model acquisition module is configured to input the grid coordinate parameters into the optimal implicit neural network to obtain a conductivity model of the underground medium; The implicit neural network is an MLPs neural network framework using a Sine activation function; the magnetotelluric forward algorithm is a magnetotelluric two-dimensional finite difference algorithm based on Maxwell's equations under a pytorch framework.

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