A fast inversion method for transient electromagnetics based on automatic differentiation

Abstract

The present invention discloses a method for rapid transient electromagnetic inversion based on automatic differentiation, which belongs to the research field of geophysical electromagnetic data processing and analysis technology. The present invention uses a forward calculation graph implemented in an automatic differentiation framework to express the forward modeling of the transient electromagnetic forward equation and the inversion objective function, and uses an adaptive moment estimation optimizer and the chain rule to accurately and efficiently calculate the model gradient for updating the model parameters. The present invention innovatively applies an efficient gradient calculation method, automatic differentiation, to the field of transient electromagnetics, and uses an adaptive moment estimation method that is very compatible with automatic differentiation as an optimization algorithm to iteratively update the model, solving the problem of the existing traditional transient electromagnetic inversion that is caused by gradient calculation and the incompatibility between speed and accuracy. This has important application prospects in actual engineering transient electromagnetic exploration.

Description

Technical Field

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

[0002] Transient electromagnetic (TEM) is a geophysical exploration method that utilizes artificial field sources. It uses an ungrounded ring source or grounded wire source to emit a pulsed excitation field into the ground. A coil or grounded electrode is used to capture the secondary induced eddy current field in the subsurface medium, thereby measuring the resistivity of the medium during the pauses in the pulsed magnetic field. By analyzing the time-varying characteristics of the secondary induced eddy current field, the distribution of formation resistivity can be studied, thereby solving related geological problems. Inversion of the subsurface resistivity based on the secondary induced eddy current field is a key step in TEM exploration.

[0003] The core of transient electromagnetic inversion lies in processing and analyzing collected transient electromagnetic observation data to continuously update and construct a model of the physical properties of the subsurface medium from a given initial geoelectrical model, thereby obtaining formation characteristic parameters (such as resistivity and rock thickness) that cannot be directly measured. Iterative optimization and global optimization are both commonly used model updating strategies in inversion. Global optimization methods offer advantages in searching for the global optimal solution, but their computational efficiency is relatively low compared to iterative optimization, and inversion parameter adjustment is more complex. Therefore, iterative optimization remains the preferred method for field data processing. Among common iterative optimization algorithms, gradient calculation is a core issue. Finite difference methods and adjoint state methods are currently the main gradient calculation methods. However, the numerical stability of traditional finite difference-based gradient calculation methods decreases when the model is complex, the electrical interface varies drastically, or the number of models is large. Furthermore, the adjoint state equation in complex media is difficult to derive, and the calculation of the gradient requires both forward and backward propagation of the field, which is computationally expensive. Furthermore, to alleviate the problem of iterative optimization methods easily falling into local minima, performing multiple inversions from multiple initial geoelectrical models is an effective strategy, but this also increases the computational complexity. Therefore, there is an urgent need for a new method that can perform gradient calculations quickly and with high precision, thereby efficiently carrying out transient electromagnetic inversion, in order to enhance the application value of transient electromagnetic methods 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 backtracking 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 completed automatically, making the inversion very efficient. In the field of transient electromagnetic inversion, the automatic differentiation method has not yet been well applied.

[0005] Therefore, there is an urgent need to develop an efficient and accurate inversion method that can minimize time costs while meeting precision requirements, accurately calculate gradient information, and rapidly perform iterative optimization. This method should be able to invert multiple initial geoelectrical models in a short period of time, accurately estimate geoelectrical model parameters, and ensure the reliability of the results. This would provide a new technical means for the rapid processing and reliable interpretation of transient electromagnetic observation data, significantly enhancing 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 cannot be taken into account at the same time during the inversion of existing transient electromagnetic observation data due to the influence of gradient calculation. A transient electromagnetic fast inversion method based on automatic differentiation is proposed. This method provides an efficient gradient calculation means, 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:

[0008] 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;

[0009] 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 the number of formation layers;

[0010] Step S3: The initial geoelectric model inputs the forward calculation graph and outputs the corresponding Group forward response data;

[0011] Step S4: Based on the Combine forward response data with transient electromagnetic observation data of the exploration area to construct a transient electromagnetic inversion objective function based on automatic differentiation;

[0012] Step S5: Adopting the adaptive moment estimation optimizer to iteratively optimize the inversion objective function, calculating the gradient through automatic differentiation and updating the model parameters, and cyclically executing steps S3 and S4 until the convergence condition is met;

[0013] Step S6: After optimization The resistivity values ​​of the geoelectric model parameters are weighted averaged to output the final inversion geoelectric model.

[0014] Furthermore, in step S1, automatic differentiation includes two steps: forward computation graph construction and backward gradient calculation;

[0015] The forward computation graph includes the following forward equations:

[0016] The relationship between the apparent conductivity and actual conductivity of the equivalent layered geological body is:

[0017] ;

[0018] in Observation time The corresponding apparent conductivity is: is the comprehensive conductivity of each formation, where is the current stratum number, is the total number of strata; is the Fréchet kernel, which is expressed as:

[0019] ;

[0020] in is the current depth of the inversion; is the diffusion depth, which is determined by the following formula:

[0021] ;

[0022] The scaling factor is 1.04; is the magnetic permeability of free space, which is ; is the observation time; due to the apparent conductivity As a Fréchet nucleus The unknown quantities of the parameters and calculation results need to be solved through iterative methods, and fixed point iteration is selected for update iteration:

[0023] ;

[0024] The initial value of the iteration is the average value of the initial layer conductivity. , set the number of iterations to 20; Substituting the quadratic field equation of the uniform half-space model into the transient electromagnetic quadratic field response can be obtained:

[0025] ;

[0026] in is the emission current; is the radius of the transmitting coil; is the magnetic field strength.

[0027] Furthermore, the method for generating the initial geoelectric model in step S2 includes:

[0028] Obtain prior information to determine the resistivity range data and stratigraphic structure of each stratum;

[0029] The Monte Carlo sampling method is used to randomly generate the resistivity value of each stratum according to a uniform distribution within the resistivity range, and the thickness of each stratum is randomly generated to form a combination of resistivity and stratum thickness as the initial geoelectric model.

[0030] Furthermore, in step S4, constructing the inversion objective function based on automatic differentiation includes:

[0031] Define the inversion objective function :

[0032] ;

[0033] in, Data fitting term representing the forward response of the initial geoelectric model and transient electromagnetic observation data of the exploration area The error between for Step Data loss term under the norm; 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 is the specific expression of the second-order second norm:

[0034] ;

[0035] in is the number of interpolated time channels included in the number of measurement points of transient electromagnetic observation data after preprocessing, is a weight matrix related to data error, which is used to measure the impact of disturbance on inversion results of transient electromagnetic observation data. Indicates that the greater the impact of noise, the smaller the weight ratio, that is, Expressed as:

[0036] ;

[0037] in represents a diagonal matrix operator;

[0038] in represents the model constraint term under the Lagrangian factor, for Step Data loss term under the norm; Take 1, are the initial geoelectric model parameters, using Apply a smoothness constraint matrix to the model:

[0039] ;

[0040] The Lagrange constant .

[0041] Furthermore, the gradient is calculated and the model parameters are updated through automatic differentiation:

[0042] By inverting the objective function Combined with the forward computation graph constructed in step S1, the automatic differentiation chain derivation rule is used to update the model parameters. The calculation formula is:

[0043] .

[0044] Furthermore, 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 Set the value of 0.8.

[0045] Through the above design scheme, the present invention has the following beneficial effects compared with the prior art:

[0046] The present invention addresses the problem of the inability to strike a balance between rate and accuracy in the inversion of transient electromagnetic observation data due to the influence of gradient calculation during inversion, and proposes an efficient transient electromagnetic inversion method using error-free gradient calculation and automatic differentiation. The present invention uses a computational 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 for backpropagation calculation, the model gradient can be calculated very accurately and efficiently for updating the model parameters. In addition, thanks to the improved efficiency, the inversion algorithm has the ability to quickly invert multiple sets of initial geoelectric models, thereby reducing the multi-solution nature of the geoelectric model interpretation and preventing the inversion results of iterative optimization from falling into local optimal solutions. The present invention innovatively applies an efficient gradient calculation method, automatic differentiation, to the field of transient electromagnetics, using adaptive moment estimation adapted to automatic differentiation as an optimization algorithm for iterative model updates, solving the problem of the inability to strike a balance between rate and accuracy in traditional transient electromagnetic inversion. This has important application prospects in actual engineering transient electromagnetic exploration. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] 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:

[0048] Figure 1 This is a flow chart of the transient electromagnetic fast inversion method based on automatic differentiation;

[0049] Figure 2 A cross-sectional view of transient electromagnetic observation data provided by an embodiment of the present invention;

[0050] Figure 3 A resistivity image corresponding to the inversion result provided by an embodiment of the present invention;

[0051] 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;

[0052] Figure 5 A comparison chart of resistivity inversion results based on transient electromagnetic observation data;

[0053] Figure 6 The graph is a graph showing how the inversion time of transient electromagnetic observation data using the method of the present invention changes with the number of iterations in an example of the present invention. DETAILED DESCRIPTION

[0054] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, 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 intended to limit the present invention.

[0055] Figure 1 The flow chart of the transient electromagnetic fast inversion method based on automatic differentiation is shown. Figure 1 As shown, the transient electromagnetic fast inversion method based on automatic differentiation proposed by the present invention includes the following steps:

[0056] Step S1: Based on the automatic differentiation mechanism of the deep learning framework, a forward calculation graph of the transient electromagnetic forward equation under the automatic differentiation framework is constructed;

[0057] Step S2: Setting An initial geoelectrical model within a reasonable range estimated from the inversion target geological body, including different resistivity values, formation thicknesses, and number of formation layers;

[0058] Step S3: Combine the forward computation graph in step S1 above and convert the The initial geoelectric model is input into the forward calculation graph, and we get Forward response data corresponding to the initial geoelectric model;

[0059] Step S4: The above step S3 obtained A set of initial geoelectric model forward responses and transient electromagnetic observation data of the exploration area Combined with, the transient electromagnetic inversion objective function is established under the automatic differentiation framework;

[0060] 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, the objective function value drops to the final value or the set maximum number of iterations is not reached, the gradient information of each model parameter is calculated by automatic differentiation, the model is updated by backpropagation, and the corresponding response is generated. The process of steps S3 and S4 is repeated until the convergence condition is met;

[0061] Step S6: The output of the adaptive moment estimation optimizer (Adam) The resistivity values ​​of the optimized geoelectric model parameters are weighted averaged to obtain the final inversion geoelectric model.

[0062] In step S1, automatic differentiation consists of two steps: forward computation graph construction and backward gradient calculation. Forward graph construction is a forward modeling approach within the automatic differentiation framework. The forward mode also involves constructing the computation graph and performing the actual computation. During the inverse process, when constructing the forward computation graph for the forward calculation, for each computational operation (such as addition, multiplication, or exponentialization) performed on an input variable, the automatic differentiation framework records all involved computational operations, input variables, and output variables, organizing them into a computational graph. In this computational graph, each computational operation is considered a "node," and input and output variables are connected to these nodes via "edges." Therefore, computational graph construction and the actual computation process proceed synchronously: with each forward operation, a node is added to the computational graph, along with the operation and its gradient calculation rules. Backward gradient calculation begins with the output variable and uses the chain rule to calculate the gradients of each parameter in reverse along the computational graph. Ultimately, backpropagation accumulates gradients 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 the node. These gradients are obtained by multiplying the gradients passed by the upstream nodes with the local derivatives of the node operation step by step.

[0063] The specific forward calculation graph includes the following forward equations:

[0064] The relationship between the apparent conductivity and actual conductivity of the equivalent layered geological body is:

[0065] (1);

[0066] in Observation time The corresponding apparent conductivity is: is the comprehensive conductivity of each formation, where is the current stratum number, is the total number of strata; is the Frechet kernel, which means:

[0067] (2);

[0068] in is the current depth of the inversion; is the diffusion depth, which is determined by the following formula:

[0069] (3);

[0070] The scaling factor is 1.04; is the magnetic permeability of free space, which is ; is the observation time, due to the apparent conductivity As a Fréchet nucleus The unknown quantities of the parameters and calculation results need to be solved through iterative methods, and fixed point iteration is selected for update iteration:

[0071] (4);

[0072] The initial value of the iteration is the average value of the initial layer conductivity. , set the number of iterations to 20; Substituting the quadratic field equation of the uniform half-space model into the transient electromagnetic quadratic field response can be obtained:

[0073] (5);

[0074] in is the emission current; is the radius of the transmitting coil; is the magnetic field strength.

[0075] For step S2, in this example There are 50 groups, that is, 50 groups of initial geoelectric models are input as input variables to the inversion geoelectric model obtained by the present invention. The resistivity of the initial geoelectric model is selected by obtaining the prior information resistivity range data, and the 50 groups of geoelectric models are randomly generated according to the uniform distribution by the Monte Carlo sampling method (Monte Carlo Simulation). At the same time, dynamic variables are introduced to accelerate the exploration of parameter space with reference to the existing technology, and gradient information is used to guide the random walk to further improve the efficiency of the algorithm.

[0076] After obtaining 50 sets of initial geoelectric models, the corresponding 50 sets of 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. According to formula (1), 50 sets of inversion objective functions are constructed and the algorithm is updated and iterated based on the obtained gradient information. Adaptive moment estimation is selected as the parameter update optimization algorithm. The specific theoretical basis is:

[0077] 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 (gradient square mean) to adapt to the gradient changes of different parameters, such as in the In the iterations, the gradient calculated by automatic differentiation is set to :

[0078] (6);

[0079] in, is the first-order moment estimate (momentum term) at the current moment, which represents the exponentially weighted average of the gradient and is used to smooth the gradient direction. is the first-order moment estimate of the previous moment (historical momentum); Is the first-order moment attenuation factor, which represents the attenuation rate of the historical gradient weight. Based on experience, its value is set to 0.9 in this example. For the second-order moment estimation:

[0080] (7);

[0081] in, is the second-order moment estimate (adaptive learning rate term) at the current moment, which represents the exponentially weighted average of the square of the gradient and reflects the magnitude of the gradient change. is the second-order moment estimate of the previous moment (the mean of the squared historical gradient). is the second-order moment attenuation factor, which also represents the attenuation rate of the historical gradient weight. Based on experience, its value is set to 0.8 in this example. and Initialized to 0, the initial deviation needs to be eliminated by correction:

[0082] (8);

[0083] and Represents the weight decay rate of the control history gradient direction of the first-order moment and the second-order moment power respectively.

[0084] The corrected first-order and second-order moment estimates are closer to the true gradient distribution. Finally, the parameters are updated based on the corrected moment estimates:

[0085] (9);

[0086] in For the Model parameters after iterations; For the Model parameters after iterations; is the global learning rate; To prevent the denominator from being zero, a small constant The adaptive moment estimation method independently adjusts the learning rate for each parameter based on the first- and second-order moment estimates of the gradient: the learning rate decreases when the gradient is large (stabilizing updates) and increases when the gradient is small (accelerating convergence). This method also uses early stopping to stop training when the inversion objective function value converges, saving time and cost. The tolerance for early stopping is set to 100.

[0087] In this example, transient electromagnetic observation data Input, and apply the above adaptive moment estimation algorithm to update the target inversion objective function , specifically expressed as:

[0088] (10);

[0089] The first term of formula (10) is Step Data loss term under the norm. are the model parameters of the current iteration. is the forward response of the current model; Take 2 and set the root mean square error is the specific expression of the second-order second norm:

[0090] (11);

[0091] in is the number of measurement points in the transient electromagnetic observation data, and the number of interpolation time channels included after preprocessing, is a weight matrix related to data error, which is used to measure the impact of disturbance on inversion results of transient electromagnetic observation data. Indicates that the greater the impact of noise, the smaller the weight ratio, that is, Expressed as:

[0092] (12);

[0093] The second term of formula (10) is Step Data loss term under the norm. Take 1, model parameter Contains layer resistivity and layer depth, is the initial geoelectric model parameter. In order to prevent the adjacent results of the longitudinal model from producing drastic and unreasonable jumps, Apply a smoothness constraint matrix to the model:

[0094] (13);

[0095] For the Lagrange constant, .

[0096] Figure 2 A cross-sectional view of transient electromagnetic observation data provided by an embodiment of the present invention, wherein the horizontal axis is the observation data measurement line distance of 520m, and the vertical axis is the normalized voltage value; Figure 3 This is the resistivity imaging corresponding to the inversion result provided by an embodiment of the present invention. The horizontal axis is the total length of the transient electromagnetic observation data line, which is 520 meters (including 52 measurement points), and the vertical axis is the depth information corresponding to the inversion resistivity result, which is 80 meters. Different colors in the figure represent different resistivity values. Figure 4 Figure 1 is a graph showing transient electromagnetic observation data from a random measurement point and the response curve of the inversion model after using the method of the present invention, where the horizontal axis is the sampling time and the vertical axis is the normalized voltage value; the red curve is the transient electromagnetic data, and the black dotted line is the response fitting curve of the inversion result; Figure 5 This is a comparison chart of resistivity inversion results based on transient electromagnetic observation data, where the horizontal axis is the resistivity value and the vertical axis is the corresponding depth value; the green curve is the inversion result corresponding to 50 sets of initial geoelectric models, and the red line is the average value; Figure 6 The figure is a graph showing the variation of the inversion time of the transient electromagnetic observation data using the method of the present invention versus the number of iterations in an example of the present invention, wherein the horizontal axis is the number of iterations and the vertical axis is the inversion time.

[0097] For this example, the cross-sectional diagram of transient electromagnetic observation data is as follows: Figure 2 As shown, the measurement point interval is 10m, and each data contains 21 time channels within the sampling time of 1.04μs to 0.461ms. The inversion two-dimensional image results using the method of the present invention are as follows: Figure 3 As shown. Randomly select one measurement point 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 are also consistent with the geological structure of the test site, and the simultaneous inversion of 50 sets of initial geoelectric models effectively avoids the problem of falling into local optimality. 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.

[0098] In summary, the present invention addresses the problem that the speed and accuracy of existing transient electromagnetic observation data cannot be balanced due to the influence of gradient calculation during inversion, and proposes an efficient transient electromagnetic inversion method using error-free gradient calculation automatic differentiation. The present invention uses a 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 improved efficiency, the inversion algorithm has the ability to quickly invert multiple sets of initial geoelectric models, thereby reducing the multi-solution nature of geological model interpretation and avoiding the inversion results of iterative optimization from falling into local optimal solutions. The present invention innovatively applies an efficient gradient calculation method, automatic differentiation, to the field of transient electromagnetics, and uses an adaptive moment estimation method that is very compatible with automatic differentiation as an optimization algorithm to iteratively update the model, solving the problem of the existing traditional transient electromagnetic inversion rate and accuracy being unbalanced. This has important application prospects in actual engineering transient electromagnetic exploration.

[0099] 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 scope of protection of the present invention.

Claims

1. A fast transient electromagnetic inversion method based on automatic differentiation, characterized in that: include: 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 the number of formation layers; Step S3: The initial geoelectric model inputs the forward calculation graph and outputs the corresponding Group forward response data; Step S4: Based on the Combine forward 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: Adopting the adaptive moment estimation optimizer to iteratively optimize the inversion objective function, calculating the gradient through automatic differentiation and updating the model parameters, and cyclically executing steps S3 and S4 until the convergence condition is met; Step S6: After optimization Perform weighted average processing of resistivity values ​​on the geoelectric model parameters and output the final inversion geoelectric model; In step S4, constructing the inversion objective function based on automatic differentiation includes: Define the inversion objective function : ； in, Data fitting term representing the forward response of the initial geoelectric model and transient electromagnetic observation data of the exploration area The error between for Step Data loss term under the norm; 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 is the specific expression of the second-order second norm: ； in is the number of interpolated time channels included in the number of measurement points of transient electromagnetic observation data after preprocessing, is a weight matrix related to data error, which is used to measure the impact of disturbance on inversion results of transient electromagnetic observation data. Indicates that the greater the impact of noise, the smaller the weight ratio, that is, Expressed as: ； in represents a diagonal matrix operator; in represents the model constraint term under the Lagrangian factor, for Step Data loss term under the norm; Take 1, are the initial geoelectric model parameters, using Apply a smoothness constraint matrix to the model: ； The Lagrange constant .

2. The method for rapid transient electromagnetic inversion based on automatic differentiation according to claim 1, characterized in that: In step S1, automatic differentiation includes two steps: forward computation graph construction and reverse gradient calculation; The forward computation graph includes the following forward equations: The relationship between the apparent conductivity and actual conductivity of the equivalent layered geological body is: ； in Observation time The corresponding apparent conductivity is: is the comprehensive conductivity of each formation, where is the current stratum number, is the total number of strata; is the Fréchet kernel, which is expressed as: ； in is the current depth of the inversion; is the diffusion depth, which is determined by the following formula: ； The scaling factor is 1.04; is the magnetic permeability of free space, which is ; is the observation time; due to the apparent conductivity As a Fréchet nucleus The unknown quantities of the parameters and calculation results need to be solved through iterative methods, and fixed point iteration is selected for update iteration: ； The initial value of the iteration is the average value of the initial layer conductivity. , set the number of iterations to 20; Substituting the quadratic field equation of the uniform half-space model into the transient electromagnetic quadratic field response can be obtained: ； in is the emission current; is the radius of the transmitting coil; is the magnetic field strength.

3. The method for rapid transient electromagnetic inversion 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 to determine the resistivity range data and stratigraphic structure of each stratum; The Monte Carlo sampling method is used to randomly generate the resistivity value of each stratum according to a uniform distribution within the resistivity range, and the thickness of each stratum is randomly generated to form a combination of resistivity and stratum thickness as the initial geoelectric model.

4. The method for rapid transient electromagnetic inversion based on automatic differentiation according to claim 1, characterized in that: The process of calculating gradients and updating model parameters through automatic differentiation: By inverting the objective function Combined with the forward computation graph constructed in step S1, the automatic differentiation chain derivation rule is used to update the model parameters. The calculation formula is: 。 5. The method for rapid transient electromagnetic inversion based on automatic differentiation according to claim 1, characterized in that: Parameter settings of the adaptive moment estimation optimizer in step S5: first-order moment attenuation factor The value of is set to 0.9; the second-order moment attenuation factor Set the value of 0.8.

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