A Transient Electromagnetic Inversion Method for Neural Networks Based on Hybrid Meme WOA Pretraining
By introducing hybrid meme WOA pre-training and multiple optimization strategies in deep neural networks, the problem that traditional TEM inversion methods rely on initial models and dimensionality reduction methods cannot effectively deal with high dimensionality and information overlap, achieving higher inversion accuracy and imaging quality.
Patent Information
- Application Number
- CN202310044301.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2023-01-30
- Publication Date
- 2025-06-17
- Estimated Expiration
- 2043-01-30
AI Technical Summary
Traditional gradient-based iterative optimization methods are highly dependent on the initial model in TEM inversion, which is prone to extreme values, and commonly used dimensionality reduction methods cannot effectively eliminate information overlap, making it difficult to accurately process TEM data.
A deep neural network based on mixed meme WOA pre-trained is adopted to design nonlinear convergence factors, introduce adaptive inertial weights and gene mutation strategies, coordinate the relationship between global search and local search, avoid premature convergence, and use deep neural networks to quickly and accurately predict underground layered electrical structures.
The inversion accuracy of neural networks has been improved, from 10% to about 2%, the inversion ability of deep neural networks has been enhanced, and the accuracy of inversion imaging has been improved.
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Figure CN116413818B_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of geophysical transient electromagnetic method, and particularly relates to a transient electromagnetic inversion method based on a neural network pre-trained by a hybrid meme whale optimization algorithm (WOA). Background Art
[0002] TEM inversion infers the underground geoelectric structure based on the acquired time-domain induced magnetic field signal. The traditional gradient-based iterative optimization method takes the underground geoelectric structure as the optimization object and minimizes the L2 objective function of the predicted induced magnetic field signal and the acquired signal. This method highly depends on the initial model, and the iterative process is prone to fall into extreme values. To avoid this problem, non-linear inversion methods such as particle swarm optimization, genetic algorithm, simulated annealing, and artificial neural network have been proposed. Among them, with the formation of related research on machine learning and artificial intelligence, the theories and corresponding algorithms related to artificial neural networks have developed most rapidly, and they have not only been widely applied in transient electromagnetic inversion but also in other electromagnetic detection problems.
[0003] In recent years, a large number of studies have shown that neural networks can be applied to geophysical inversion calculations and are one of the effective methods to solve geophysical electromagnetic non-linear inversion problems. Foreign scholars have applied neural network inversion to controlled-source audio-frequency magnetotelluric and direct current sounding data processing, demonstrating the effectiveness of this method in solving geophysical electromagnetic inversion problems. Subsequently, domestic scholars have used neural networks to achieve non-linear inversion of electromagnetic data. Compared with traditional linearized iterative inversion, deep neural network (DNN) inversion can obtain more refined inversion results. However, the high-dimensionality and ill-posedness of TEM samples are still the main obstacles hindering the training efficiency of neural networks. Common dimensionality reduction methods include principal component analysis (PCA), kernel PCA, and dictionary learning. Assuming that there is multicollinearity among standardized original variables, that is, there is non-negligible information overlap among original variables, the above common dimensionality reduction methods cannot effectively eliminate this overlap and are difficult to accurately process TEM data.
[0004] Pre-training neural network parameters through heuristic algorithms has become a common solution to improve the training quality of neural networks. In the evolutionary process of a single heuristic algorithm, it is difficult to balance the evolutionary speed and direction of the individual itself and the social group. The corresponding optimization problem is the debate between global optimization and local optimization. It is difficult to effectively maintain the diversity of the population, which makes the optimization process prone to premature convergence and falling into local optima. In recent years, the memetic algorithm has successfully solved many complex heuristic optimization problems, and its performance is better than that obtained by using global optimization methods alone. Considering that the Whale Optimization Algorithm (WOA) can achieve the transition process from global search to local search through the "shrinking and encircling mechanism" and has been used to improve the training process of neural networks for 20 test functions, WOA can be used as a basic global optimization algorithm. Summary of the Invention
[0005] The present invention aims to provide a neural network transient electromagnetic inversion method based on hybrid memetic WOA pre-training to improve the prediction accuracy of the TEM inversion neural network.
[0006] To achieve the above object, the present invention provides the following technical solutions:
[0007] A neural network transient electromagnetic inversion method based on hybrid memetic WOA pre-training includes the steps of:
[0008] S1. Establish a layered geoelectric model sample by equally spaced sampling according to the resistivity index;
[0009] S2. Construct a deep neural network, and pre-train the weights and biases in the deep neural network by using the hybrid memetic WOA algorithm;
[0010] S3. Train the deep neural network obtained in step S2 and use it to predict the geoelectric structure of the unknown earth.
[0011] The memetic strategy in the hybrid memetic WOA algorithm includes:
[0012] Design a non-linear convergence factor α;
[0013] Introduce an adaptive inertia weight during the position update process;
[0014] Based on enriching the population diversity, introduce the gene mutation strategy in the genetic algorithm and the niche strategy in the particle swarm optimization algorithm.
[0015] Further, the layered geoelectric model sample includes M geoelectric models {m i , i = 1, 2,..., M}, and the geoelectric model contains N resistivity parameters and N - 1 layer thickness parameters;
[0016] The vertical component B of the vertical induced magnetic field generated by a step current in the frequency domain z is as follows:
[0017]
[0018] The magnetic field response in the time domain is obtained through the following Fourier transform:
[0019]
[0020] B z The derivative with respect to time is expressed as:
[0021]
[0022] The time-domain response of the above integral is obtained through the second derivative property of the function, as follows:
[0023] dB z (t)dt =
[0024]
[0025] where I is the excitation current, a is the coil radius, h is the height of the transmitting coil in the vertical direction, z is the height of the receiving coil from the ground, J1(*) is the first-order Bessel function, λ is the wavelength, μ0 is the magnetic permeability of free space, r TE is the reflection coefficient, and ω is the angular frequency.
[0026] Furthermore, the non-linear convergence factor α designed in the WOA algorithm is expressed as:
[0027]
[0028] where both ζ1 and ζ2 are non-linear adjustment coefficients.
[0029] Furthermore, in the stages of surrounding the prey and randomly searching for the prey in the WOA algorithm,
[0030] When adopting the straight-line trajectory update strategy, an adaptive weight ω1 is introduced in the step term adap :
[0031]
[0032] When using the logarithmic spiral trajectory update strategy, an adaptive weight ω2 is introduced in the assumed prey position term adap :
[0033]
[0034] The adaptive inertia weight is expressed as:
[0035]
[0036]
[0037] Among them, the parameter t max is the maximum iteration period, t is the current iteration period, γ is the adjustment coefficient, γ is selected as 0.5, and x is the optimal state of the optimization parameter at t.
[0038] The beneficial effects of the present invention are as follows:
[0039] The present invention uses the WOA algorithm as the basic global optimization algorithm, and uses the memetic strategy to optimize the WOA global optimization algorithm to coordinate the relationship between global search and local search, avoiding the premature convergence problem of WOA; uses the deep neural network and TEM observation data to quickly and accurately predict the complex underground layered electrical structure. The hybrid memetic WOA method enhances the inversion ability of the deep neural network, improves the accuracy of inversion imaging, and improves the inversion accuracy of the neural network from 10% to about 2%; the method of the present invention can be widely applied to the field of transient electromagnetic rapid imaging, and has good practical value and application prospects for quickly and accurately predicting the underground electrical structure. Description of the Drawings
[0040] Figure 1 is a flowchart of a neural network transient electromagnetic inversion method based on hybrid memetic WOA pre-training provided by an embodiment of the present invention;
[0041] Figure 2 is a flowchart of a deep neural network;
[0042] Figure 3 is a flowchart of a hybrid memetic WOA algorithm;
[0043] Figure 4 is a schematic diagram of a five-layer geoelectric model and its TEM response. Specific Embodiments
[0044] The present invention will be further described in detail below with reference to the drawings and embodiments:
[0045] As Figure 1 shown, a neural network transient electromagnetic inversion method based on hybrid memetic WOA pre-training includes:
[0046] (1) Sample establishment
[0047] Establish a layered geoelectric model sample. Determine the number of layers N of the geoelectric model. Then the geoelectric model contains N resistivity parameters and N - 1 layer thickness parameters, a total of 2N - 1 parameters, and construct M geoelectric models {m i , i = 1, 2,..., M}.
[0048] In the layered geoelectric model, the initial field excited by a horizontal coil is incident vertically from the surface into the subsurface. Through propagation in the medium, transmission and reflection at the electrical interfaces, a secondary field signal is generated at the surface. To reduce the influence of lateral inhomogeneity, we often measure the vertical component of the magnetic field at the center of the coil. The vertical magnetic field signal generated by a step current can be expressed as:
[0049]
[0050] where I is the excitation current, a is the coil radius, h is the height of the transmitting coil in the vertical direction, z is the height of the receiving coil above the ground, and J1(*) is the first-order Bessel function. r TE is the reflection coefficient, which can be calculated from the mutual impedance ^γ and the self-impedance γ:
[0051]
[0052] For the i-th layer, the self-impedance can be expressed as:
[0053] γ i = u i / iωμ0(3)
[0054] The mutual impedance can be expressed as:
[0055]
[0056] where the conductivity of the i-th layer is σ i , the layer thickness is h i , the electrical coefficient u i =(λ 2 +iωμ0σ i ) 1 / 2 , under the quasi-static condition, the wavelength λ = u0, μ0 is the magnetic permeability of free space, and ω is the angular frequency. i = 0 represents the air medium.
[0057] Equation (1) can obtain the vertical component of the vertical induced magnetic field in the frequency domain, and the magnetic field response in the time domain can be obtained through the following Fourier transform:
[0058]
[0059] where the real part of the magnetic field and the cosine function are even functions, and the imaginary part and the sine function are odd functions. Therefore, in the above expression of the time-domain field, the real part is an even function, the imaginary part is an odd function, and the integral of the imaginary part is zero. After simplification, when t > 0, using the symmetry of the even function, the derivative of the magnetic field with respect to time can be obtained:
[0060]
[0061] The discrete calculation of the above integral can be performed by the broken line approximation method, and the time-domain response can be obtained through the second derivative property of the function, as follows:
[0062]
[0063] Example:
[0064] Construct a resistivity data set D based on an exponentially equidistant sequence rh o = {10 0:0.2:4}, and a layer thickness data set D h = {10 0:0.2:3}. For a five-layer geoelectric model, N = 5 can be set. Each electrical model has 5 resistivity parameters and 4 layer thickness parameters, for a total of 9 parameters.
[0065] Traverse all the parameters in the resistivity data set D rho and the layer thickness data set D h . Then the total number of layered model samples M = 20 5 × 15 4 .
[0066] Calculate the frequency-domain response corresponding to each geoelectric model according to formula (1), which can be simplified to:
[0067]
[0068] Among them, the discrete calculation of the first-order Bessel function J1(*) is calculated through the Hankel transform. The above form can be changed to:
[0069]
[0070] Among them, λ i is the sampling point, W i is the weight, with i = 1, 2,..., n, and a total of n = 140 discrete sampling points. The weight coefficients are shown in Table 1
[0071] Table 1 Hankel transform coefficients
[0072] -6.76671159511E-14 3.39808396836E-13 -7.43411889153E-13 8.93613024469E-13 -5.47341591896E-13 -5.84920181906E-14 5.20780672883E-13 -6.92656254606E-13 6.88908045074E-13 -6.39910528298E-13 5.82098912530E-13 -4.84912700478E-13 3.54684337858E-13 -2.10855291368E-13 1.00452749275E-13 5.58449957721E-15 -5.67206735175E-14 1.09107856853E-13 -6.04067500756E-14 8.84512134731E-14 2.22321981827E-14 8.38072239207E-14 1.23647835900E-13 1.44351787234E-13 2.94276480713E-13 3.39965995918E-13 6.17024672340E-13 8.25310217692E-13 1.32560792613E-12 1.90949961267E-12 2.93458179767E-12 4.33454210095E-12 6.55863288798E-12 9.78324910827E-12 1.47126365223E-11 2.20240108708E-11 3.30577485691E-11 4.95377381480E-11 7.43047574433E-11 1.11400535181E-10 1.67052734516E-10 2.50470107577E-10 3.75597211630E-10 5.63165204681E-10 8.44458166896E-10 1.26621795331E-09 1.89866561359E-09 2.84693620927E-09 4.26886170263E-09 6.40104325574E-09 9.59798498616E-09 1.43918931885E-08 2.15798696769E-08 3.23584600810E-08 4.85195105813E-08 7.27538583183E-08 1.09090191748E-07 1.63577866557E-07 2.45275193920E-07 3.67784458730E-07 5.51470341585E-07 8.26916206192E-07 1.23991037294E-06 1.85921554669E-06 2.78777669034E-06 4.18019870272E-06 6.26794044911E-06 9.39858833064E-06 1.40925408889E-05 2.11312291505E-05 3.16846342900E-05 4.75093313246E-05 7.12354794719E-05 1.06810848460E-04 1.60146590551E-04 2.40110903628E-04 3.59981158972E-04 5.39658308918E-04 8.08925141201E-04 1.21234066243E-03 1.81650387595E-03 2.72068483151E-03 4.07274689463E-03 6.09135552241E-03 9.09940027636E-03 1.35660714813E-02 2.01692550906E-02 2.98534800308E-02 4.39060697220E-02 6.39211368217E-02 9.16763946228E-02 1.28368795114E-01 1.73241920046E-01 2.19830379079E-01 2.51193131178E-01 2.32380049895E-01 1.17121080205E-01 -1.17252913088E-01 -3.52148528535E-01 -2.71162871370E-01 2.91134747110E-01 3.17192840623E-01 -4.93075681595E-01 3.11223091821E-01 -1.36044122543E-01 5.12141261934E-02 -1.90806300761E-02 7.57044398633E-03 -3.25432753751E-03 1.49774676371E-03 -7.24569558272E-04 3.62792644965E-04 -1.85907973641E-04 9.67201396593E-05 -5.07744171678E-05 2.67510121456E-05 -1.40667136728E-05 7.33363699547E-06 -3.75638767050E-06 1.86344211280E-06 -8.71623576811E-07 3.61028200288E-07 -1.05847108097E-07 -1.51569361490E-08 6.67633241420E-08 -8.33741579804E-08 8.31065906136E-08 -7.53457009758E-08 6.48057680299E-08 -5.37558016587E-08 4.32436265303E-08 -3.37262648712E-08 2.53558687098E-08 -1.81287021528E-08 1.20228328586E-08 -7.10898040664E-09 3.53667004588E-09 -1.36030600198E-09 3.52544249042E-10 -4.53719284366E-11
[0073] The sampling points are calculated by the following formula:
[0074]
[0075] Among them, a = -7.91001919, s = 8.79671439570e-02
[0076] The magnetic field response in the time domain can be obtained through Fourier transform. In the discrete form of formula (6), the discrete frequency sequence is ω = 10 -5:5.E-04:15 .
[0077] (2) Construct a deep neural network
[0078] The neural network can be used to predict the corresponding geoelectric model based on the observed apparent resistivity response. This model can be obtained from the constitutive relations learned and approximated by the neural network. The constitutive relations represent the inversion process and are fitted by adjusting the weights and biases of the neurons, as Figure 2 shown. The neurons in the hidden layer are fully connected. The observed apparent resistivity is fed into the neural network through the input layer, and the geoelectric model is obtained from the output layer. The hidden layer between these two layers is used to fit the non - linear constitutive relations.
[0079] To make the hidden layer conform to the non - linear constitutive relations, an activation function is added to the neurons. This activation function maps the features represented by the neurons into another dimensional space, in which a linear method can be used to fit the non - linear relations to solve the problem. For such fitting problems, the most commonly used activation function is the rectified linear unit (ReLU) function, which usually allows the deep neural network to be trained faster without unsupervised pre - training.
[0080] (3) Establish a hybrid meme WOA algorithm
[0081] In the WOA algorithm, let the size of the whale population be N and the dimension of the search space be M. The position of a whale can be represented as X i ={X i 1 ,X i 2 ,…,X i M}, i = 1, 2, …, N. Each whale does not know its exact position. The optimal position at the current moment can be represented as X * ={X i * ,X i * ,…,X i *}, i = 1, 2, …, N. Let the maximum number of iterations be t max , at the t(i = 1, 2, ..., t max ) moment, the position update of the whale can be expressed as:
[0082] X(t + 1)=X*(t)-A·D(8)
[0083] D is the distance between two sets of population positions and can be expressed as:
[0084] D = C·X*(t)-X(t)(9)
[0085] A and C are respectively expressed as:
[0086] A = 2α·r - α(10)
[0087] C = 2r(11)
[0088] The coefficient C is generated by a random vector, and the coefficient A is generated by a random vector and a convergence factor. The traditional convergence factor is α = 2 - 2t / t max 。
[0089] The meme strategy in the hybrid meme WOA algorithm includes:
[0090] 1) Nonlinear convergence factor α
[0091] WOA uses the meme information of coefficient A in its search mechanism to prevent the optimization process from falling into local optima. The value of parameter A mainly depends on the change of the convergence factor α. When the convergence factor α is large, |A| is more likely to be greater than 1, and the global optimization process dominates, which is more suitable for the early stage of the optimization process. When the convergence factor α is small, |A| is difficult to be greater than or equal to 1, which is necessary to force the whales to move away from the currently assumed prey. The whale group performs better by using the bubble net attack to capture prey and is more suitable for the later convergence stage of the optimization process.
[0092] The convergence factor α in traditional WOA changes linearly, resulting in a fixed conversion speed when switching from global optimal search to local optimal. Ideally, the global optimal search process in the early stage will be slower and more detailed, while the local optimal convergence trend in the later stage will be faster. This requires the convergence factor α to change slowly in the early stage of optimization and faster in the later stage. The nonlinear convergence factor α is designed as follows:
[0093]
[0094] 2) Adaptive inertia weight
[0095] An adaptive inertia weight is introduced in the position update process of WOA to better balance the local optimization and global optimization processes, thereby improving the optimization accuracy of the algorithm. The specific improvement formula is as follows:
[0096]
[0097] In the stage of surrounding the prey and randomly searching for the prey, when using the straight-line trajectory update strategy, an adaptive weight ω1 is introduced in the step term adap :
[0098]
[0099] When using the logarithmic spiral trajectory update strategy, an adaptive weight ω2 is introduced in the assumed prey position term adap :
[0100]
[0101] The adaptive weight is expressed as:
[0102]
[0103]
[0104] Among them, the parameter t max is the maximum iteration period, t is the current iteration period, γ is the adjustment coefficient, γ is selected as 0.5, and x is the optimal state of the optimization parameter at t.
[0105] The weight of the current optimal position (assuming the prey position) increases with the increase of the number of iterations, indicating that the prey selected after each iteration is closer to the theoretical optimal value; that is to say, the optimal solution of the current population is more and more attractive to the whales in the population, enabling them to find the prey more accurately, and improving the convergence speed and optimization accuracy of the algorithm.
[0106] 3) Population diversity
[0107] During the WOA optimization process, the population diversity gradually decreases, specifically manifested as the population individuals gathering at one or more specific positions in the search space, which means that the algorithm may converge prematurely. The smaller the population diversity, the more clustering, indicating that the optimization process is in the convergence stage; otherwise, the group is in the random search stage, and the optimization process still has strong global optimization ability.
[0108] To enrich the population diversity, we added a mutation operation during the optimization process to make the process jump out of the local optimum and enter other regions of the solution space to continue searching. Assume that the population fitness is f = {f i , i = 1, 2, …, N}, where f i is the fitness of the i-th individual whale in the population. Then, the population aggregation degree can be expressed by the fitness variance as:
[0109]
[0110] When the variance of the population fitness is less than a certain threshold or the prey has not changed significantly within the maximum number of iterations, the following mutation operation is performed on some individuals in the population with a certain probability:
[0111] X(t) = X(t)(1 + 0.2ε)(19)
[0112] In addition to the gene mutation strategy in genetic algorithms, niche formation is another effective strategy to enhance population diversity. The present invention uses a pre-selection-based niche strategy, regarding offspring individuals with low fitness as bad genes, restricting their replacement of parents, and avoiding their inheritance. It is confirmed that the fitness of individuals participating in the offspring evolution process needs to be higher than that of their parents. The flowchart of the hybrid memetic WOA algorithm is as Figure 3 shown.
[0113] Example:
[0114] The pseudo-code execution process of the hybrid memetic WOA algorithm is described as follows:
[0115]
[0116]
[0117] Among them, the non-linear adjustment coefficients ζ1 and ζ2 (Formula 12) are set to 3 and 2 respectively. ω1 adap and ω2 adap (Formulas 16, 17), the change range value of γ is set to 0.5, κ is the step size of the weight, and is set to 1. When the population mutates (Formula 15), ε is a random variable with a Gaussian distribution between [-1, 1].
[0118] (4) Training the deep neural network
[0119] The training process of DNN training is shown as follows:
[0120]
[0121]
[0122] (5) Case analysis
[0123] As Figure 4 shown in a, assume a five-layer TEM geoelectric model, and the resistivity of each layer is 500 Ω·m, 200 Ω·m, 1000 Ω·m, and 50 Ω·m respectively; the thickness of each layer is 15 m, 10 m, 20 m, and 30 m respectively. The induced magnetic response of this five-layer geoelectric model is the hypothetical response signal used to predict the hypothetical parameters of the geoelectric model.
[0124] The geoelectric models predicted by four inversion methods were compared. The four models can effectively reflect the assumed five-layer geoelectric model, but the prediction accuracies are different. The geoelectric model of DNN starts from the resistivity and thickness of the first layer, has the largest error, and the prediction deviates significantly. When predicting the thickness of the fourth layer, the deviation is the largest. After pre-optimizing the parameters in DNN using the WOA method, the prediction accuracy of WOA-DNN is slightly improved. On this basis, using a hybrid strategy to improve the optimization efficiency of WOA can further improve the prediction accuracy of DNN.
[0125] The corresponding TEM responses of the predicted geoelectric models are as Figure 4 shown in Fig. b. The predicted signal has a high degree of fit with the assumed signal. The fit is magnified and analyzed within the time window range of about 1e-5 s, and the fitting accuracy of the response signal conforms to the change in the fitting accuracy of the geoelectric models predicted by different methods. However, within the time window of about 1e-5 seconds, the signs of the reaction change. At this time, the fitting trend of the response data is different from the prediction ability of each inversion method shown by the fitting results of the geoelectric model. Although the mismatches generated by such numerical calculations do not affect the overall evaluation of the fitness level of the observed response, this indicates that a method with stronger prediction ability cannot guarantee a better fit to the response signal on each time channel. Table 2 shows the geoelectric models predicted by the four schemes.
[0126] Table 2 Five-layer geoelectric models predicted by different DNNs and their errors
[0127]
[0128] *APE is the absolute percentage of error (Absolute percent error, APE), and MAPE is the mean absolute error (mean APE, MAPE)
[0129] From the perspective of the final absolute percentage of error, the prediction accuracy of a single DNN is the worst, and the error is higher than 10%. After adding the WOA strategy, the error is reduced to about 5%. The prediction accuracy of the hybrid memetic WOA-DNN is the highest, and the error can be controlled within 2%.
[0130] The above are only embodiments of the present invention. Specific technical solutions and / or common knowledge such as characteristics well known in the art are not described in detail herein. It should be noted that for those skilled in the art, without departing from the technical solution of the present invention, several deformations and improvements can still be made, which should also be regarded as the protection scope of the present invention, and these will not affect the implementation effect of the present invention and the practicality of the patent. The protection scope required by this application should be based on the content of its claims, and the specific implementation manners described in the specification can be used to explain the content of the claims.
Claims
1. A transient electromagnetic inversion method for neural network based on hybrid meme WOA pre-training, characterized in that, Including the steps: S1. Establish a layered geoelectric model sample by equally spaced sampling according to the resistivity index; S2. Construct a deep neural network, and pre-train the weights and biases in the deep neural network using the hybrid meme WOA algorithm; S3. Train the deep neural network obtained in step S2, and use it to predict the geoelectric structure of the unknown earth; The meme strategy in the hybrid meme WOA algorithm includes: Design a non-linear convergence factor α; Introduce an adaptive inertia weight during the position update process; Based on enriching the population diversity, introduce the gene mutation strategy in the genetic algorithm and the niche strategy in the particle swarm optimization algorithm.
2. The transient electromagnetic inversion method for neural network based on hybrid meme WOA pre-training according to claim 1, characterized in that: The layered geoelectric model samples include M geoelectric models {m i , i = 1, 2, …, M}, where the geoelectric model contains N resistivity parameters and N - 1 layer thickness parameters; The vertical component B of the vertical induced magnetic field generated by a step current in the frequency domain z is as follows: Obtain the magnetic field response in the time domain through the following Fourier transform: B z The derivative with respect to time is expressed as: The time-domain response of the above integral is obtained through the second derivative property of the function, as follows: Wherein, I is the exciting current, a is the coil radius, h is the height of the transmitting coil in the vertical direction, z is the height of the receiving coil from the ground, J1(*) is the first-order Bessel function, λ is the wavelength, μ0 is the magnetic permeability of free space, r TE is the reflection coefficient, and ω is the angular frequency.
3. The transient electromagnetic inversion method for neural network based on hybrid meme WOA pre-training according to claim 1, characterized in that, The non-linear convergence factor α designed in the WOA algorithm is expressed as: Where ζ1 and ζ2 are both non-linear adjustment coefficients.
4. The transient electromagnetic inversion method for neural network based on hybrid meme WOA pre-training according to claim 1, characterized in that, During the prey encircling and random prey searching phases of the WOA algorithm, When adopting the straight-line trajectory update strategy, an adaptive weight ω1 is introduced in the step item adap : When using the logarithmic spiral trajectory update strategy, an adaptive weight ω2 is introduced into the assumed prey position term adap : The adaptive inertia weight is expressed as: Among them, the parameter t max is the maximum iteration period, t is the current iteration period, γ is the adjustment coefficient, γ is selected as 0.5, and x is the optimal state of the optimization parameter at t.
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