Potential field data inversion regularization parameter selection method based on deep learning

Abstract

The invention relates to the field of data inversion, in particular to a potential field data inversion regularization parameter selection method based on deep learning, and the method comprises the following steps: 1, building a nonlinear mapping relation among data, a model and an optimal regularization parameter based on a double-layer optimization problem, and generating a training set; 2, establishing a convolution-attention mechanism neural network by using the training set, a convolution module and a self-attention mechanism, and completing network training by using the training set; and step 3, substituting potential field abnormal data into the convolution-attention mechanism neural network to obtain an optimal regularization parameter. According to the method, the regularization parameters can be calculated more quickly and accurately in practical application, so that the result precision of the regularization inversion of the potential field data is improved. According to the method, the defects of an existing method are improved, and through simulation experiment verification, compared with a traditional method, a more accurate result can be obtained through regularization parameters obtained through the method.

Description

Technical Field

[0001] The present invention relates to the field of data inversion, and specifically to a method for selecting regularization parameters for potential field data inversion based on deep learning. Background Art

[0002] Scientists Tikhonov and Arsenin (1977) proposed the regularization inversion technique, which improved the ill-posed problem of inversion, enhanced the stability of inversion. At the same time, by introducing constraint conditions through the regularization term, the non-uniqueness problem of inversion was also improved. To a certain extent, the instability and non-uniqueness of the inversion problem were solved simultaneously. According to different geological information, different model fitting conditions (i.e., stability functions) are selected as the regularization term, which is equivalent to screening out the solutions that meet the model fitting conditions among numerous solutions. Therefore, the inversion results obtained by introducing different model fitting conditions will have different characteristics.

[0003] The key to inversion using the regularization method lies in the selection of the regularization parameter. To match the regularization parameter with the error level, quantitative or qualitative information is usually added to the problem to be solved. If the selected regularization parameter is too small, the magnetization intensity obtained by inversion will be unstable. If the selected regularization parameter is too large, an overly smooth inversion result will occur. For Tikhonov regularization, a variety of regularization parameter selection methods have been developed to select the optimal regularization parameter. Classic regularization parameter selection methods are mostly based on error analysis or heuristic criteria. The Morozov discrepancy principle requires the residual norm to match the data noise level and is applicable to scenarios where the noise statistical characteristics are known. However, it is extremely sensitive to noise estimation errors. The L-curve method selects the parameter value corresponding to the point with the maximum curvature by plotting the logarithmic curve of the residual norm and the solution norm of the regularized solution. This method does not require prior noise information and has intuitive interpretability, and is widely used in geophysical inversion software. However, the L-curve method may fail when the noise statistical characteristics are complex or the problem is highly non-linear, and the computational cost increases significantly with the increase in the number of parameter searches. Generalized cross-validation (GCV) determines the parameter by minimizing the statistical estimate of the prediction error. Its advantage is that it avoids the explicit estimation of the noise level, but the approximation of the matrix inverse involved in the calculation process may introduce numerical instability.

[0004] As the scale of inverse problems expands and the degree of non-linearity increases, traditional parameter selection methods face dual challenges of efficiency and robustness. For large-scale problems, algorithms based on Krylov subspace iteration (such as LSQR) are improved to synchronously construct the approximate paths of regularization parameters and solutions, thereby reducing the computational overhead of repeated solutions. For non-linear inversion, adaptive regularization strategies update parameters iteratively to reflect the dynamic balance between data fitting and prior constraints during the model update process. For example, the trust region method is used to control the parameter adjustment step size in electromagnetic inversion. In addition, the Bayesian inversion framework treats the regularization parameter as a random variable and performs posterior sampling through Markov chain Monte Carlo (MCMC) or variational inference. It can not only provide uncertainty quantification of parameters but also fuse multi-source prior information. However, its high computational cost limits its application in real-time inversion. Summary of the Invention

[0005] The existing methods for selecting the regularization term coefficient have a large amount of calculation and are vulnerable to noise interference. In addition, the selection of the depth weight coefficient is more based on experience. Only retain the depth weight in the model fitting regularization term, establish the mapping relationship between the regularization term coefficient, the anomaly, and the model, and accurately obtain the regularization term parameters through deep learning means to obtain accurate results.

[0006] The present invention combines the depth weight and the model fitting term into a regularization term, develops a calculation method for the regularization coefficient based on deep learning, establishes the relationship between magnetic anomalies, models, and regularization parameters, establishes a training set, and builds a deep learning network in a data-driven manner to realize the acquisition of the regularization term coefficient of actual data, solve the problems of difficult selection, complex calculation steps, and low efficiency of previous numerical calculation methods, and effectively improve the accuracy of the inversion result and the stability of the inversion of noisy anomalies. The present invention provides the following technical solutions: A method for selecting regularization parameters for potential field data inversion based on deep learning, comprising the following steps: In the first step, based on a two-layer optimization problem, establish a non-linear mapping relationship between data, model, and optimal regularization parameters to generate a training set; In the second step, use the training set, convolution module, and self-attention mechanism to establish a convolution-attention mechanism neural network, and complete the training of the network with the training set; In the third step, substitute the potential field anomaly data into the convolution-attention mechanism neural network to obtain the optimal regularization parameters.

[0007] As a further solution of the present invention: establishing a non-linear mapping relationship between data, model, and optimal regularization parameters based on a two-layer optimization problem to generate a training set includes the following steps: Establish a typical geological model, perform forward simulation on the geological model to obtain potential field anomaly data; The depth weight is placed in the model fitting term of the regularization inversion to obtain the inversion objective function: , m is the physical property parameter, d is the observed data, is the data fitting term, is the model fitting term, W d is the depth weighting function; Solve the double-layer optimization problem to obtain the optimal regularization parameter: , , A is the kernel function matrix, m is the physical property parameter, d is the observed data, is the estimated model, is the true model, is the regularization parameter; Construct a training set based on the potential field anomaly data and the optimal regularization parameter.

[0008] As a further solution of the present invention: The typical geological models include magma intrusion models, fault structure models, density anomaly models, etc.

[0009] As a further solution of the present invention: The depth weighting function W d has the specific form of: ， diag ( ) takes the diagonal elements of the matrix in the parentheses, A is the kernel function matrix, is generally taken as 1.

[0010] As a further solution of the present invention: Establishing a convolutional-attention mechanism neural network using the training set, convolutional module, and self-attention mechanism includes the following steps: Use a convolutional module that alternates between dilated convolution and ordinary convolution to extract multi-scale features and obtain a feature map; Take the magnetic anomaly amplitude as the prior weight, perform the Hadamard product of the attention mechanism and the feature map, and construct independent fully connected branches for each regularization parameter to obtain the convolutional-attention mechanism neural network. The prior weight satisfies: , , where is the processed gradient map, reflecting the changes in the significant regions in the feature map, is the attention parameter matrix for spatial weighting, is the activation function, used to normalize the weighted result to [0, 1], Ais the finally generated attention weight map, is the l feature map extracted from the layer. GlobalWeightedPooling is a weighted global pooling method that assigns weights to each channel according to the attention mechanism to achieve compression and weighted fusion of the feature map. w and b are the weights and biases of the fully connected layer respectively,

[0011] The size is determined by the feature representation after pooling. The introduction of GlobalWeightedPooling enables the model to automatically adjust the channel weights according to the importance of the features, thereby enhancing the discriminative ability of feature expression. , is 2x downsampling, is the dilation rate of the dilated convolutional kernel.

[0012] Compared with the prior art, the beneficial effects of the present invention are: The present invention can calculate the regularization parameter more quickly and accurately in practical applications, thereby improving the result accuracy of the regularization inversion of potential field data. The present invention improves the shortcomings of the existing methods. Through simulation experiments, it is verified that compared with the traditional methods, the regularization parameters obtained by the present invention can obtain more accurate results. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 is a flowchart of the method for selecting regularization parameters for potential field data inversion based on deep learning in an embodiment of the present invention.

[0014] Figure 2 is a network structure diagram of the method for selecting regularization parameters for potential field data inversion based on deep learning in an embodiment of the present invention.

[0015] Figure 3 is a comparison diagram of the selection result and the theoretical result of the method for selecting regularization parameters for potential field data inversion based on deep learning in an embodiment of the present invention.

[0016] Figure 4 is a model test setting and inversion result diagram in an embodiment of the present invention. Among them, (a) is the model diagram; (b) is the inversion result; (c) is the inversion fitting error curve; (d) is the slice of the deep learning inversion result; (e) is the slice of the L-curve inversion result.

[0017] Figure 5This is the setup and inversion result diagram of the dual geological body model experiment in the embodiments of the present invention. Among them, (a) is the diagram of the dual geological body model; (b) is the forward gravity anomaly result; (c) is the inversion fitting error curves of the deep learning method and the L-curve method under different regularization parameters; (d) is the slice of the inversion result of the deep learning method; (e) is the slice of the inversion result of the L-curve method. Specific implementation manners

[0018] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0019] The inversion of potential field data mainly depends on the linear mapping relationship between the dissection units and the observation points. The relationship between the potential field data anomaly and the subsurface physical properties is mainly as follows: (1).

[0020] Among them, A is the kernel function matrix, which is composed of the forward anomalies of the unit physical property dissection units at the observation points, m is the physical property parameter, d is the observation data. Since the subsurface physical properties to be solved in practice are much larger than the number of observation points, the formula (1) is an underdetermined equation and cannot be directly solved. The Tikhonov regularization least squares method can effectively solve this problem. After introducing the regularization term of the minimum model constraint, the problem of solving the underdetermined equation system can be obtained by minimizing the objective function. The specific objective function can be written as: (2).

[0021] is the data fitting term, is the model fitting term. The skin effect of potential field data inversion is serious. The data depth weighting function W d is introduced to improve this problem. The specific form of this weighting function is (Li and Oldenburg, 2000): (3).

[0022] Among them diag ( ) is to take the diagonal elements of the matrix in the brackets, A is the kernel function matrix, Generally, it is taken as 1. However, some researchers believe through model experiment analysis that the inversion result is more accurate when it is taken as 2 (Li and Oldenburg, 1996; Utsugi, 2019). In practical applications, it often depends on experience and inversion tests to select within this range. 。

[0023] The implementation process of the algorithm proposed in this invention is as follows: Based on the double - layer optimization problem, establish the non - linear mapping relationship between data, model and the optimal regularization parameter, generate the training set. Based on the deep - learning method, construct the intelligent framework for obtaining the regularization parameter of potential - field data inversion, and use the observed anomalies of potential - field data to realize the adaptive selection of the regularization parameter for potential - field data inversion.

[0024] 1. Generation of training - set data based on the double - layer optimization problem.

[0025] Establish typical geological models (such as magma intrusions, fault structures, density anomaly bodies, etc.), forward - simulate potential - field anomaly data, and add different intensities of noise to construct diverse training samples.

[0026] Put the depth weight ( W d ) into the model - fitting term of the regularization inversion, and the objective function of the inversion is as follows: (4).

[0027] Since the observed data is synthesized by the true model , an accurate optimal regularization parameter (ORP) can be found, such that the model residual error (MRE) between the estimated model and the true model (5).

[0028] (6).

[0029] Among them, MRE first decreases with and reaches the minimum value at , and then rises with the increase of . Solve efficiently and accurately through the binary - search algorithm.

[0030] Construct the training - label data set from the theoretical anomalies obtained by model forward - simulation and the optimal regularization parameter obtained.

[0031] 2. Hybrid deep learning network of convolutional neural network (CNN) and attention mechanism.

[0032] Refer to Figure 2 , in order to ensure that the network can efficiently learn the mapping relationship of regularization parameters, the present invention designs a convolutional-attention mechanism neural network architecture for predicting regularization parameters.

[0033] First, a convolutional module is introduced to complete the extraction of multi-scale features, and an encoder that alternates dilated convolution and ordinary convolution is adopted: (7).

[0034] Where is 2 times downsampling, is the dilation rate of the dilated convolution kernel, which is used to capture abnormal body features at different scales.

[0035] In the attention mechanism part, the magnetic anomaly amplitude is introduced as a prior weight: (8).

[0036] The attention map A and the feature map F are subjected to Hadamard product, forcing the network to focus on the regions with drastic magnetic field changes (corresponding to geological body regions).

[0037] In the network output part, for each regularization parameter , an independent fully connected branch is constructed to ensure the accuracy of the output parameters: (9).

[0038] Among them, GlobalWeightedPooling is global pooling weighted by feature importance.

[0039] During the neural network training process, the mean square error (MSE) is used as the loss function to measure the deviation between the predicted regularization parameter and the true value. Among them, the true value takes the logarithm of the optimal regularization parameter to ensure stable learning effect. The optimization algorithm uses the Adam optimizer for gradient update and combines the learning rate decay strategy to improve the training stability and convergence speed.

[0040] In actual inversion calculation, the anomaly of the potential field data is input into the trained neural network, and the optimal regularization parameter can be quickly predicted, avoiding the traversal calculation of traditional methods, improving the calculation efficiency, optimizing the regularization weight, and realizing stable inversion under different scenarios.

[0041] The following describes the specific implementation of the present invention in detail with specific embodiments.

[0042] Refer to Figure 1, Figure 3 and Figure 4 , to demonstrate the effect of selecting regularization parameters based on deep learning, a scatter plot of the results of selecting regularization parameters for deep learning and the L-curve method under the validation set of the network as shown in Figure 3 is drawn. Comparing it with the optimal regularization parameter, it can be seen from Figure 3 that the result obtained by the L-curve has a large error, while the result predicted by the deep learning method is in good agreement with the theoretical result, verifying the accuracy of the method of the present invention.

[0043] A model as shown in Figure 4 (a) is established. The underground inversion area is 3200m×3200m×1200m, divided into 32*32*12 regular grids. The residual density of the geological body is 1 g / cm 3 , and its positions in the X, Y, and Z directions are 1300m~1900m, 1300m~1900m, and 300m~600m. The gravity anomaly forward modeling of the above model is carried out and 5% random noise is added, and the result is as shown in Figure 4 (b). The regularization parameters are selected by the deep learning and L-curve methods, and the regularization inversion is carried out, and the results are as shown in Figure 4 (d) and Figure 4 (e).

[0044] Figure 4 (c) shows the inversion fitting error curves obtained by regularization inversion using different regularization parameters calculated by deep learning (blue line) and L-curve (orange line). It can be seen from Figure 4 that the fitting error of deep learning is lower and the inversion result converges faster. Figures 4(d) and Figure 4 (e) respectively show the slices of the inversion results of deep learning and the L-curve. Comparing Figures 4(d) and Figure 4 (e), it can be seen that the density distribution of the inversion result based on deep learning is more in line with the model setting. The model test results show that the deep learning method is significantly superior to the L-curve method in terms of robustness, accuracy, and efficiency.

[0045] A two-geological-body model as shown in Figure 5 (a) is established. The model consists of two cubes with different depths, simulating geological bodies at different depths underground. The entire inversion area is 3200m × 3200m × 1200m. The residual densities of the two cubes are both 1g / cm³, and the positions and volumes are set to different sizes respectively to simulate abnormal bodies with different depths. The gravity anomaly forward modeling of this model is carried out, and 5% random noise is added to the observed data, and the result is as shown in Figure 5 (b).

[0046] The regularization parameter is selected by using the deep learning method (DNN) and the L-curve method respectively, and the regularization inversion is carried out. Figure 5 (c) shows the inversion fitting error curves under different regularization parameters, where the blue line is the result of the deep learning method and the orange line is the result of the L-curve method. From Figure 5 it can be seen that the deep learning method shows a faster convergence rate in the initial stage of iteration and maintains a lower fitting error after more than 20 iterations, while the fitting error of the L-curve method decreases slowly, indicating that the selected regularization parameter fails to maintain the inversion stability.

[0047] Figure 5 (d) and Figure 5 (e) are the sliced diagrams of the inversion results obtained by the deep learning method and the L-curve method respectively. It can be clearly seen from the results that Figure 5 in (d), the spatial distribution of the density anomaly body is more consistent with the original model, with clear boundaries and accurate burial depths; while Figure 5 (e) shows that the position of the anomaly body is shifted. The experimental results show that the regularization method based on deep learning is superior to the traditional L-curve method in terms of inversion accuracy, stability and computational efficiency.

[0048] In addition, it should be understood that although this specification is described according to the embodiments, not every embodiment only contains an independent technical solution. This narrative way of the specification is only for clarity. Those skilled in the art should regard the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A method for selecting regularization parameters in inversion of potential field data based on deep learning, characterized in that, It includes the following steps: In the first step, a nonlinear mapping relationship between data, model, and optimal regularization parameter is established based on a double-layer optimization problem to generate a training set; In the second step, a convolutional-attention mechanism neural network is established using the training set, convolutional module, and self-attention mechanism, and the network is trained with the training set; In the third step, the potential field anomaly data is substituted into the convolutional-attention mechanism neural network to obtain the optimal regularization parameter.

2. The method for selecting regularization parameters for inversion of potential field data based on deep learning according to claim 1, wherein The step of establishing a nonlinear mapping relationship between data, model, and optimal regularization parameter based on a double-layer optimization problem to generate a training set includes the following steps: A typical geological model is established, and forward simulation is performed on the geological model to obtain potential field anomaly data; The depth weight is placed in the model fitting term of the regularization inversion to obtain the inversion objective function: , m is a physical property parameter, d is the observed data, is the data fitting term, is the model fitting term, W d is the depth weighting function; Solve the double-layer optimization problem to obtain the optimal regularization parameter: , , A is the kernel function matrix, m is the physical property parameter, d is the observed data, is the estimated model, is the true model, is the regularization parameter; A training set is constructed based on the potential field anomaly data and the optimal regularization parameter.

3. The method for selecting regularization parameters for inversion of potential field data based on deep learning according to claim 2, wherein The typical geological model includes a magma intrusion body model, a fault structure model, and a density anomaly body model.

4. The method for selecting regularization parameters for inversion of potential field data based on deep learning according to claim 2 or 3, characterized in that, The depth weighting function W d has the following specific form: , diag ( ) takes the diagonal elements of the matrix inside the parentheses, A is the kernel function matrix, takes 1.

5. The method for selecting regularization parameters in inversion of potential field data based on deep learning according to claim 1 or 2, characterized in that, The step of establishing a convolutional-attention mechanism neural network using the training set, convolutional module, and self-attention mechanism includes the following steps: Multi-scale feature extraction is performed using a convolutional module that alternates between dilated convolution and ordinary convolution to obtain a feature map; Taking the magnetic anomaly amplitude as the prior weight, performing the Hadamard product of the attention mechanism and the feature map, and constructing independent fully connected branches for each regularization parameter to obtain a convolutional-attention mechanism neural network, the prior weight satisfies: , , where is the processed gradient map, is the attention parameter matrix for spatial weighting, is the activation function, A is the finally generated attention weight map, is the feature map extracted by the l th layer, GlobalWeightedPooling is the weighted global pooling method, w and b are the weights and biases of the fully connected layer respectively, The size is determined by the pooled features.

6. The method for selecting regularization parameters in inversion of potential field data based on deep learning according to claim 5, wherein The convolutional module with alternating dilated convolution and ordinary convolution is , is a 2x downsampling, is the dilation rate of the dilated convolutional kernel.

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