Transient electromagnetic rapid inversion method based on automatic differentiation

Abstract

The invention discloses a transient electromagnetic rapid inversion method based on automatic differentiation, which belongs to the technical research field of geophysical electromagnetic data processing and analysis, and comprises the following steps of: expressing a transient electromagnetic forward modeling equation and an inversion objective function by using a forward calculation graph realized in an automatic differentiation framework; and the model gradient is accurately and efficiently calculated by using an adaptive moment estimation optimizer and a chain rule so as to update model parameters. According to the invention, an efficient gradient operation method automatic differential is innovatively applied to the transient electromagnetic field, and a self-adaptive moment estimation method which is very adaptive to the automatic differential is used as an optimization algorithm method to carry out the iterative updating of a model. The problem that the rate and the precision are not considered at the same time due to gradient calculation of existing traditional transient electromagnetic inversion is solved. The method has an important application prospect in engineering actual transient electromagnetic exploration.

Description

Technical Field

[0001] The present invention relates to the technical field of geophysical electromagnetic data processing and analysis, and more particularly, to a fast transient electromagnetic inversion method based on automatic differentiation. Background Art

[0002] The transient electromagnetic method is a geophysical exploration method using an artificial field source. By transmitting a pulsed excitation field into the ground through an ungrounded loop source or a grounded wire source, and using coils or grounded electrodes to capture the secondary induced eddy current field in the underground medium, a geophysical detection method for measuring the resistivity of the medium during the intermittent period of the pulsed magnetic field is thus realized. By analyzing the time-varying characteristics of the secondary induced eddy current field, the distribution law of formation resistivity can be studied, and thus related geological problems can be solved. Among them, inverting the resistivity of the underground medium based on the secondary induced eddy current field is one of the key links in transient electromagnetic exploration.

[0003] The core of transient electromagnetic inversion lies in processing and analyzing the collected transient electromagnetic observation data, continuously updating and constructing the physical property parameter model of the underground medium from a given initial geoelectric model, so as to obtain the formation characteristic parameters (such as resistivity, rock layer thickness, etc.) that cannot be directly measured. In inversion, both iterative optimization and global optimization are commonly used model update strategies. The global optimization method has advantages in searching for the global optimal solution, but its computational efficiency is relatively low compared to iterative optimization, and the inversion parameter adjustment is relatively complex. Therefore, iterative optimization is still the preferred method for on-site data processing. In common iterative optimization algorithms, gradient calculation is the core issue. The finite difference method and the adjoint state method are the current main gradient solving methods, but when the model is relatively complex, the electrical interface changes violently, or the number of models is large, the numerical stability of the traditional finite difference-based gradient calculation method will also decrease. And the adjoint state equation in complex media is difficult to derive, and the calculation of the gradient requires the forward and backward propagation of the field, and the calculation cost is also high. At the same time, in order to alleviate the problem that the iterative optimization method is prone to falling into local minima, performing multiple inversions from multiple initial geoelectric models is an effective strategy, but the amount of calculation will also increase accordingly. Therefore, there is an urgent need for a new method that can perform gradient calculation quickly and with high precision, so as to efficiently carry out transient electromagnetic inversion, and improve the application value of the transient electromagnetic method in practical engineering.

[0004] In recent years, automatic differentiation has gradually been regarded as a general method for efficient gradient calculation. In the field of computer science, automatic differentiation is often closely related to "backpropagation" and can be used to calculate the exact gradient of any differentiable function. Unlike gradient calculation based on finite differences, automatic differentiation only requires one forward calculation and one gradient backpropagation to obtain accurate gradients. In the automatic differentiation framework, the arithmetic operations and intermediate results contained in the forward equation are saved in the computational graph, and then the gradient is calculated backtrackingly by applying the chain rule to the computational graph. Once the computational graph of the transient electromagnetic forward equation is correctly constructed using the automatic differentiation framework, the error-free gradient calculation for updating the velocity model can be automatically completed, making the inversion very efficient. In the field of transient electromagnetic inversion, automatic differentiation methods have not yet been well applied.

[0005] Therefore, there is an urgent need to develop an efficient and accurate inversion method that can meet the accuracy requirements while minimizing the time cost, accurately calculate the gradient information, and quickly perform iterative optimization. This method should be able to invert multiple initial geoelectric models in a short time, accurately estimate the geoelectric model parameters, and ensure the reliability of the results. This will provide a new technical means for the rapid processing and reliable interpretation of transient electromagnetic observation data, and significantly enhance the application value of transient electromagnetic technology in real-time inversion of field data. Summary of the invention

[0006] In view of this, the purpose of the present invention is to address the problem that the speed and accuracy of existing transient electromagnetic observation data cannot be taken into account due to the influence of gradient calculation in the inversion, and propose a transient electromagnetic fast inversion method based on automatic differentiation. This method provides an efficient gradient calculation method, which makes the inversion accuracy good and the calculation cost very low.

[0007] To achieve the above object, the present invention adopts the following technical solution: a transient electromagnetic fast inversion method based on automatic differentiation, comprising: Step S1: Based on the automatic differentiation mechanism of the deep learning framework, a forward calculation graph of the transient electromagnetic forward equation is established; Step S2: According to the prior geological information of the inversion target geological body, set an initial geoelectric model, wherein the initial geoelectric model includes resistivity parameters, formation thickness parameters, and formation layer number; Step S3: The initial geoelectric model inputs the forward computation graph and outputs the corresponding Group forward response data; Step S4: Based on the Combine forward modeling response data with transient electromagnetic observation data of the exploration area to construct a transient electromagnetic inversion objective function based on automatic differentiation; Step S5: Use the adaptive moment estimation optimizer to iteratively optimize the inversion objective function, calculate the gradient through automatic differentiation, and update the model parameters. Loop through Step S3 and Step S4 until the convergence condition is met; Step S6: Perform weighted average processing on the resistivity values of the optimized geoelectric model parameters and output the final inverted geoelectric model.

[0008] Furthermore, in Step S1, automatic differentiation includes two steps: forward computation graph construction and backward gradient calculation; The forward computation graph includes the following forward modeling equations: The relationship between the apparent conductivity and the actual conductivity of the equivalent layered geological body is: ; where is the observation time corresponding to the apparent conductivity; is the comprehensive conductivity of each stratum, where is the current stratum number, is the total number of strata; is the Fréchet kernel, expressed as: ; where is the current depth of inversion; is the diffusion depth, determined by the following formula: ; where the scaling factor is 1.04; is the magnetic permeability of free space, with a value of ; is the observation time; since the apparent conductivity is both a parameter of the Fréchet kernel and an unknown quantity of the calculation result, an iterative method needs to be used to solve it. Fixed-point iteration is selected for update iteration: ; The initial value of the iteration is the initially set average layer conductivity, , and the number of iterations is set to 20; substituting into the secondary field equation of the homogeneous half-space model can obtain the transient electromagnetic secondary field response: ; where is the magnitude of the transmitting current; is the radius of the transmitting coil; is the magnetic field strength.

[0009] Further, the method for generating the initial geoelectric model in step S2 includes: Obtain prior information to determine the resistivity range data and formation stratification structure of each formation; Adopt the Monte Carlo sampling method to randomly generate the resistivity values of each formation within the resistivity range according to a uniform distribution, and randomly generate the thickness of each formation to form a combination of resistivity and formation thickness as the initial geoelectric model.

[0010] Further, in step S4, constructing the inversion objective function based on automatic differentiation includes: Define the inversion objective function : ; Among them, represents the error between the data fitting term of the forward response of the initial geoelectric model and the transient electromagnetic observation data in the exploration area ; is order data loss term under the Take 2; is the forward response of the initial geoelectric model, is the model parameter of the current iteration; set the root mean square error as the specific form of the second-order two-norm: ; Among them is the number of interpolation time channels included after preprocessing in the number of measurement points of the transient electromagnetic observation data, is the weight matrix related to the data error, used to measure the influence of the transient electromagnetic observation data under perturbation on the inversion result, represented by the standard deviation , the greater the influence of noise, the smaller the weight ratio, that is is expressed as: ; Among them represents the diagonal matrix operator; Among them represents the model constraint term under the action of the Lagrange factor, is order data loss term under the Take 1, is the initial geoelectric model parameter, use to impose a smoothness constraint matrix on the model: ; Among them, the Lagrange constant . ​​​​​​​​

[0011] Furthermore, the gradient is calculated through automatic differentiation and the model parameters are updated: By inverting the objective function Combined with the forward calculation graph constructed in step S1, the automatic differentiation chain derivation rule is used to update the model parameters. The calculation formula is: .

[0012] Further, the parameter setting of the adaptive moment estimation optimizer in step S5 is: first-order moment attenuation factor The value of is set to 0.9; the second-order moment attenuation factor The value of is set to 0.8.

[0013] Through the above design scheme, compared with the prior art, the present invention has the following beneficial effects: The present invention aims at the problem that the rate and accuracy of transient electromagnetic observation data cannot be taken into account due to the influence of gradient calculation in inversion, and proposes an efficient transient electromagnetic inversion method using error-free gradient calculation automatic differentiation. The present invention uses the calculation graph implemented in the automatic differentiation framework to express the forward modeling of the transient electromagnetic equation and the inversion objective function. By using the chain rule to return the calculation, the model gradient can be calculated very accurately and efficiently for updating the model parameters. In addition, thanks to the improvement in efficiency, the inversion algorithm has the ability to quickly invert multiple sets of initial geoelectric models, thereby reducing the multi-solution of the geoelectric model interpretation and avoiding the inversion result of iterative optimization from falling into the local optimal solution. The present invention innovatively applies an efficient gradient calculation method automatic differentiation in the field of transient electromagnetics, uses the adaptive moment estimation adapted to the automatic differentiation as the optimization algorithm to iteratively update the model, and solves the problem that the rate and accuracy of traditional transient electromagnetic inversion cannot be taken into account. This has important application prospects in actual transient electromagnetic exploration in engineering. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] The accompanying drawings herein are used to provide a further understanding of the present invention and constitute a part of the present application. The exemplary embodiments of the present invention and their descriptions are used to understand the present invention and do not constitute improper limitations of the present invention. In the accompanying drawings: Figure 1 This is a flow chart of the transient electromagnetic fast inversion method based on automatic differentiation; Figure 2 A cross-sectional view of transient electromagnetic observation data provided by an embodiment of the present invention; Figure 3 A resistivity imaging diagram corresponding to the inversion result provided by an embodiment of the present invention; Figure 4 Transient electromagnetic observation data of a random measuring point provided in an example of the present invention and a response curve diagram of the inversion model after using the method of the present invention; Figure 5 It is a comparison chart of resistivity inversion results based on transient electromagnetic observation data; Figure 6 It is a curve graph showing the variation of the inversion time of transient electromagnetic observation data in the examples of the present invention with the number of iterations by the method of the present invention. Specific implementation manners

[0015] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0016] Figure 1 shows a flowchart of a fast transient electromagnetic inversion method based on automatic differentiation. Combining Figure 1 as shown, the fast transient electromagnetic inversion method based on automatic differentiation proposed by the present invention includes the following steps: Step S1: Based on the automatic differentiation mechanism of the deep learning framework, construct a forward computational graph of the transient electromagnetic forward modeling equation under the automatic differentiation framework; Step S2: Set initial geoelectric models within a reasonable range estimated from the inversion target geological body, including different resistivity values, formation thicknesses, and the number of formation layers; Step S3: Combining the forward computational graph in Step S1 above, input the initial geoelectric models in Step S2 into the forward computational graph to obtain forward modeling response data corresponding to the initial geoelectric models; Step S4: Combine the groups of initial geoelectric model forward modeling responses obtained in Step S3 above and the transient electromagnetic observation data of the exploration area to establish a transient electromagnetic inversion objective function under the automatic differentiation framework; Step S5: Use the adaptive moment estimation optimizer (Adam) to iteratively optimize the inversion objective function. If the convergence condition is not met, that is, when the objective function value drops to the final value or the set maximum number of iterations is not reached, calculate the gradient information of each model parameter through automatic differentiation, update the model by backpropagation and generate the corresponding response, and repeat the processes of Step S3 and Step S4 until the convergence condition is met; Step S6: Perform weighted averaging of the resistivity values of the optimized geoelectric model parameters output by the adaptive moment estimation optimizer (Adam) to obtain the final inverted geoelectric model.

[0017] In step S1, automatic differentiation involves two steps: forward computational graph construction and backward gradient calculation. Forward computational graph construction is a way of forward modeling in the automatic differentiation framework. The forward mode is also the process of constructing the computational graph and actual calculation. During the inversion process, when constructing the forward computational graph for the forward modeling calculation, every time an input variable undergoes a calculation operation (such as addition, multiplication, exponentiation, etc.), the automatic differentiation framework records all the involved calculation operations, input variables, and output variables, and organizes them into a computational graph. In this computational graph, each calculation operation is regarded as a "node", and the input and output variables are connected to these nodes through "edges"; therefore, the construction of the computational graph is synchronized with the actual operation process: every time a forward operation is executed, a node is added to the computational graph, and at the same time, the operation and its gradient calculation rule are recorded. Backward gradient calculation starts from the output variable and uses the chain rule along the computational graph to calculate the gradients of each parameter in reverse. Finally, backpropagation accumulates the gradients in reverse along the computational graph from the output layer to the input layer. Specifically, the gradient of each node represents the partial derivative of the inversion objective function with respect to the input tensor of this node, and these gradients are obtained by multiplying the gradients passed from the upstream nodes by the local derivatives of the operation of this node step by step.

[0018] The specific forward computational graph includes the following forward modeling formulas: The relationship between the apparent conductivity and the actual conductivity for the construction of the equivalent layered geological body is: (1); where is the observation time corresponding to the apparent conductivity; is the comprehensive conductivity of each formation, where is the current formation number, is the total number of formations; is the Frechet kernel, which is expressed as: (2); where is the current depth of inversion; is the diffusion depth, which is determined by the following formula: (3); where the scale factor is 1.04; is the magnetic permeability of free space, with a value of ; is the observation time. Since the apparent conductivity serves as both a parameter of the Frechet kernel and an unknown quantity in the calculation result, it needs to be solved by an iterative method. Fixed-point iteration is selected for update iteration: (4); The initial value of the iteration is the average value of the layer conductivity set initially, , set the number of iterations to 20; substitute into the secondary field equation of the homogeneous half-space model to obtain the transient electromagnetic secondary field response: (5); where is the magnitude of the transmitting current; is the radius of the transmitting coil; is the magnetic field strength.

[0019] For step S2, in this example there are 50 groups, that is, 50 groups of initial geoelectric models are input as input variables into the inverted geoelectric model obtained by the present invention. The resistivity of the initial geoelectric model is selected from the known prior information resistivity range data, and 50 groups of geoelectric models are randomly generated according to the uniform distribution by the Monte Carlo Simulation method. At the same time, referring to the prior art, a dynamic variable is introduced to accelerate the exploration of the parameter space, and the gradient information is used to guide the random walk to further improve the algorithm efficiency.

[0020] After obtaining 50 groups of initial geoelectric models, 50 groups of corresponding initial forward responses are obtained according to the constructed forward calculation graph, and they are respectively compared with the transient electromagnetic observation data used in this example Construct 50 groups of inversion objective functions according to formula (1) and simultaneously update and iterate the algorithm according to the obtained gradient information. Select the adaptive moment estimation as the parameter update optimization algorithm. The specific theoretical basis is: Adaptive Moment Estimation (Adam) is an adaptive optimization algorithm that combines the momentum gradient descent method and the RMSProp algorithm. Its core idea is to dynamically adjust the learning rate through the first-order moment estimation (gradient mean) and the second-order moment estimation (mean of the gradient square), so as to adapt to the gradient changes of different parameters. For example, in the th iteration, the gradient is set to by automatic differentiation: (6); where is the first-order moment estimation (momentum term) at the current moment, representing the exponential weighted average of the gradient, used to smooth the gradient direction, is the first-order moment estimation (historical momentum) at the previous moment; is the first-order moment decay factor, representing the decay rate that controls the weight of the historical gradient. In this example, its value is set to 0.9 according to experience. For the second-order moment estimation: (7); where is the second moment estimation at the current moment (adaptive learning rate term), representing the exponentially weighted average of the squared gradient, reflecting the magnitude of gradient change. is the second moment estimation at the previous moment (historical mean of squared gradients). is the second moment decay factor, which also represents the decay rate of controlling the weight of historical gradients. In this example, its value is set to 0.8 according to experience. At the same time, since and are initialized to 0 at the initial moment, the initial bias needs to be eliminated by correction: (8); and represent the weight decay rates of controlling the historical gradient direction for the first moment and the second moment power respectively.

[0021] The corrected first and second moment estimations are closer to the true gradient distribution. Finally, combining the corrected moment estimations, the parameters are updated: (9); where is the model parameter after the th iteration; is the model parameter after the th iteration; is the global learning rate; is a small constant to prevent the denominator from being zero . The adaptive moment estimation method can independently adjust the learning rate for each parameter according to the first and second moment estimations of the gradient: the learning rate decreases when the gradient is large (stable update), and the learning rate increases when the gradient is small (accelerated convergence). The present invention also adopts the early stopping method to stop training in time when the inversion objective function value converges, saving time cost. The tolerance of the early stopping method is set to 100.

[0022] In this example, the transient electromagnetic observation data is input, and the above adaptive moment estimation algorithm is applied to update the objective inversion objective function , specifically expressed as: (10); where the first term of the equation (10) is order data loss term under the is the model parameter of the current iteration. is the forward response of the current model; takes 2, and the root mean square error is the specific form of the second-order two-norm: (11); Among them is the number of measurement points in the transient electromagnetic observation data, and the number of interpolated time channels included after preprocessing is the weight matrix related to the data error, which is used to measure the influence of the transient electromagnetic observation data on the inversion result under perturbation, and is represented by the standard deviation The greater the influence of noise, the smaller the weight ratio, that is It is expressed as: (12); The second term of the equation in formula (10) is order The data loss term under the norm Taking 1, the model parameter includes layer resistivity and layer depth is the initial geoelectric model parameter. At the same time, to prevent violent and unreasonable jumps in the adjacent results of the longitudinal model, use to impose a smoothness constraint matrix on the model: (13); For the Lagrange constant .

[0023] Figure 2 is the cross-sectional view of the transient electromagnetic observation data provided by the embodiment of the present invention, where the abscissa is the distance of the observation data measuring line is 520m, and the ordinate is the normalized voltage value; Figure 3 is the resistivity imaging corresponding to the inversion result provided by the embodiment of the present invention, where the abscissa is the total length of the transient electromagnetic observation data measuring line is 520m (including 52 measurement points), and the ordinate is the depth information 80m corresponding to the inversion resistivity result. Different colors in the figure represent different resistivity values; Figure 4 is the response curve diagram of the transient electromagnetic observation data of a random measurement point and the inversion model after using the method of the present invention in the example of the present invention, where the abscissa is the sampling duration and the ordinate is the normalized voltage value; the red curve is the transient electromagnetic data, and the black dashed line is the response fitting curve of the inversion result; Figure 5 is the comparison diagram of the resistivity inversion results based on the transient electromagnetic observation data, where the abscissa is the resistivity Resistivity value and the ordinate is the corresponding depth (Depth) value; the green curve is the inversion results corresponding to 50 groups of initial geoelectric models, and the red line is the average value; Figure 6 is the curve diagram of the inversion time of the transient electromagnetic observation data by the method of the present invention changing with the number of iterations in the example of the present invention, where the abscissa is the number of iterations and the ordinate is the inversion time.

[0024] For this example, the schematic cross-sectional view of the transient electromagnetic observation data is as shown in Figure 2As shown, the measuring point interval is 10m, and each data contains 21 time channels within the sampling time of 1.04μs to 0.461ms. The inversion result of the two-dimensional image using the method of the present invention is as follows: Figure 3 As shown. A random measurement point is selected from the 52 measurement points to verify the data fitting effect, as shown Figure 4 As shown, the data fitting effect is good. Figure 5 The corresponding model inversion results shown in the figure also conform to the geological structure of the test site, and the problem of falling into the local optimum is effectively avoided by inverting 50 sets of initial geoelectric models at the same time. Figure 6 As shown, the overall time taken by the present invention for this example is 75 seconds, which has extremely high efficiency and accurate inversion results.

[0025] In summary, the present invention aims at the problem that the existing transient electromagnetic observation data cannot balance the rate and accuracy due to the influence of gradient calculation in the inversion, and proposes an efficient transient electromagnetic inversion method using error-free gradient calculation automatic differentiation. The present invention uses the calculation graph implemented in the automatic differentiation framework to express the forward modeling of the transient electromagnetic equation and the inversion objective function, and uses the chain rule to accurately and efficiently calculate the model gradient for updating the model parameters. At the same time, thanks to the improvement in efficiency, the inversion algorithm has the ability to quickly invert multiple sets of initial geoelectric models, thereby reducing the multi-solution of geological model interpretation and avoiding the inversion results of iterative optimization from falling into the local optimal solution. The present invention innovatively applies an efficient gradient calculation method automatic differentiation in the field of transient electromagnetics, and uses an adaptive moment estimation method that is very compatible with automatic differentiation as an optimization algorithm method to iteratively update the model, solving the problem that the existing traditional transient electromagnetic inversion rate and accuracy cannot be balanced. This has important application prospects in actual engineering transient electromagnetic exploration.

[0026] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A transient electromagnetic fast inversion method based on automatic differentiation, characterized in that Including: Step S1: Based on the automatic differentiation mechanism of the deep learning framework, establish a forward computational graph for the transient electromagnetic forward equation; Step S2: Set initial geoelectric models according to the prior geological information of the target geological body to be inverted. The initial geoelectric models include resistivity parameters, formation thickness parameters, and the number of formation layers; Step S3: Input initial geoelectric models into the forward calculation graph, and output the corresponding sets of forward response data; Step S4: Based on the group of forward response data and the transient electromagnetic observation data of the exploration area, construct a transient electromagnetic inversion objective function based on automatic differentiation; Step S5: Use the adaptive moment estimation optimizer to iteratively optimize the inversion objective function, calculate the gradient through automatic differentiation and update the model parameters, and loop through Step S3 and Step S4 until the convergence condition is met; Step S6: Perform weighted average processing on the resistivity values of the optimized geoelectric model parameters, and output the final inverted geoelectric model.

2. The transient electromagnetic rapid inversion method based on automatic differentiation according to claim 1, characterized in that In Step S1, automatic differentiation includes two steps: forward computational graph construction and backward gradient calculation; The forward computational graph includes the following forward formulas: The relationship between the apparent conductivity and the actual conductivity of the equivalent layered geological body is constructed as: ； wherein is the observation time corresponding apparent conductivity is the comprehensive conductivity of each formation, where is the current formation number is the total number of formations is the Fréchet kernel, expressed as: ； wherein is the current depth of inversion; is the diffusion depth, which is determined by the following formula: ； where the scaling factor is 1.04; is the magnetic permeability of free space, with a value of ; is the observation time; since the apparent conductivity serves as both a parameter of the Fréchet kernel and an unknown in the calculation result, it is necessary to solve it by an iterative method, and fixed-point iteration is selected for update iteration: ； The initial value of the iteration is the average value of the layer conductivity set initially. , the number of iterations is set to 20; substituting into the secondary field equation of the homogeneous half-space model, the transient electromagnetic secondary field response can be obtained: ； wherein is the magnitude of the emission current; is the radius of the emission coil; is the magnetic field strength.

3. The transient electromagnetic rapid inversion method based on automatic differentiation according to claim 1, characterized in that, The method for generating the initial geoelectric model in Step S2 includes: Obtain prior information, determine the resistivity range data of each layer and the stratification structure of the formation; Adopt the Monte Carlo sampling method to randomly generate the resistivity values of each layer within the resistivity range according to a uniform distribution, and randomly generate the thickness of each layer to form a combination of resistivity and formation thickness as the initial geoelectric model.

4. The transient electromagnetic rapid inversion method based on automatic differentiation according to claim 1, wherein, In Step S4, constructing the inversion objective function based on automatic differentiation includes: Define the inversion objective function : ； Among them, the data fitting term representing the forward response of the initial geoelectric model and the transient electromagnetic observation data in the exploration area the error between is the data loss term under the -norm; is the forward response of the initial geoelectric model, is the model parameter of the current iteration; the root mean square error is the specific form of the second-order two-norm: ； wherein is the number of interpolation time channels included after preprocessing in the number of measurement points of transient electromagnetic observation data, is a weight matrix related to data error, used to measure the influence of transient electromagnetic observation data on the inversion result under perturbation, and is represented by the standard deviation The greater the influence of noise, the smaller the weight ratio, that is is expressed as: ； Among them represents a diagonal matrix operator; Among them represents the model constraint term under the action of the Lagrange factor, is order the data loss term under the norm; takes 1, is the initial geoelectric model parameter, and uses to impose a smoothness constraint matrix on the model: ； where the Lagrange constant .

5. The transient electromagnetic fast inversion method based on automatic differentiation according to claim 4, characterized in that, The process of calculating the gradient through automatic differentiation and updating the model parameters: By inverting the objective function Combined with the forward computational graph constructed in step S1, the automatic differential chain rule is used to update the model parameters. The calculation formula is as follows: 。 6. The transient electromagnetic rapid inversion method based on automatic differentiation according to claim 1, wherein Parameter settings of the adaptive moment estimation optimizer described in step S5: first-order moment decay factor is set to 0.9; second-order moment decay factor is set to 0.8.

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