A method and system for global inversion of seismic moment tensor based on reinforcement learning

Abstract

The application belongs to the technical field of seismic geophysical inversion, and discloses a seismic moment tensor global inversion method and system based on reinforcement learning. The method comprises the following steps: establishing a moment tensor parameter space, and constructing a moment tensor inversion mismatch function; training a neural network model by using candidate moment tensor parameters and corresponding mismatch values, and dynamically learning the mapping relationship between the moment tensor parameters and the mismatch function; predicting the global distribution of the mismatch function by using the trained neural network model, guiding a neighborhood algorithm to perform resampling, and realizing iterative optimization of the moment tensor parameters; outputting the moment tensor inversion result after iteration until the convergence condition is met, and completing uncertainty evaluation of the inversion result by using the finally trained neural network model. The application can realize dynamic modeling of the global distribution of the mismatch function in the moment tensor inversion process, improve the global inversion efficiency of the high-dimensional parameter space, and realize quantitative analysis of the uncertainty of the inversion result.

Description

Technical Field

[0001] This invention belongs to the field of earthquake geophysical inversion technology, specifically relating to a global inversion method and system for earthquake moment tensors based on reinforcement learning. Background Technology

[0002] Seismic moment tensor inversion is a crucial aspect of seismic source parameter inversion. It can be used to obtain information on source mechanisms, moment magnitude, and source composition such as dual-couple (DC), compensated linear vector dipole (CLVD), and isotropic (ISO). It has significant application value in areas such as source physics analysis and earthquake hazard assessment. Currently, moment tensor inversion typically uses the mismatch function between observed and theoretical waveforms as the optimization objective. The theoretical waveform is calculated based on the velocity model, and optimization algorithms are used to search for moment tensor parameters that achieve the optimal mismatch function.

[0003] For the moment tensor inversion problem, existing techniques employ nonlinear global optimization methods such as the Neighborhood Algorithm (NA). These methods iteratively optimize the moment tensor parameters by continuously generating new candidate solutions near already sampled optimal solutions, achieving good results in improving inversion efficiency and enhancing global search capabilities. In recent years, reinforcement learning, with its autonomous learning and continuous decision-making capabilities, has also been increasingly applied to the field of geophysical inversion. It optimizes the inversion process by learning sampling or search strategies, thereby improving the solution efficiency of complex nonlinear inversion problems.

[0004] However, with the increasing dimension of moment tensor inversion parameters and the ever-increasing requirements for inversion accuracy, existing methods still have certain limitations. On the one hand, the resampling of neighborhood algorithms mainly relies on resampling of the neighborhood based on the already sampled candidate solutions, and has not fully utilized the global distribution information of the target mismatch function in the parameter space. There is still room for further improvement in the global optimization efficiency in high-dimensional parameter spaces. On the other hand, existing reinforcement learning methods are mainly used to optimize the search process to guide the next search behavior, and have not yet established a global mapping relationship between moment tensor parameters and mismatch functions during the inversion process. Therefore, it is difficult to directly obtain and utilize the global distribution of the mismatch function. In addition, for high-dimensional moment tensor parameter spaces, obtaining the global distribution of the mismatch function or conducting uncertainty analysis of the inversion results usually requires a large number of forward simulation calculations, which results in high computational costs.

[0005] Therefore, how to improve the global inversion efficiency of high-dimensional moment tensor parameter space while maintaining the accuracy of moment tensor inversion, and at the same time reduce the computational cost required for global uncertainty analysis of inversion results, has become a technical problem that urgently needs to be solved in this field.

[0006] The information disclosed in this background section is only intended to enhance the understanding of the background technology of this application and should not be construed as an admission or in any way implying that the information constitutes prior art known to those skilled in the art. Summary of the Invention

[0007] The purpose of this invention is to provide a global inversion method and system for seismic moment tensor based on reinforcement learning, so as to solve the problems of low global inversion efficiency, difficulty in making full use of the global distribution of mismatch function, and high computational cost of uncertainty analysis of inversion results in existing seismic moment tensor inversion methods.

[0008] In a first aspect, the present invention provides a global inversion method for seismic moment tensor based on reinforcement learning, comprising the following steps: S1. Establish the moment tensor parameter space: Obtain the observed waveform data, station information and subsurface velocity model of the seismic event to be inverted, and construct the moment tensor parameter space; S2. Constructing the moment tensor inversion mismatch function: Establish a mismatch function to evaluate the degree of matching between the synthetic waveform corresponding to the candidate moment tensor parameters and the observed waveform data; S3. Construct a neural network model and dynamically learn the mapping relationship between moment tensor parameters and mismatch function: Construct a neural network model, train the neural network model using the sampled candidate moment tensor parameters and their corresponding mismatch values, and dynamically learn the mapping relationship between moment tensor parameters and mismatch function; S4. Predicting the global distribution of the mismatch function and adaptive resampling: Using the trained neural network model, predict the global distribution of the mismatch function in the moment tensor parameter space, determine the target region based on the global distribution of the mismatch function, use the candidate moment tensor parameters in the target region as sampling seeds, guide the neighborhood algorithm to perform resampling, and generate a new round of candidate moment tensor parameters. S5. Iterative Convergence and Uncertainty Assessment: Repeat steps S3 and S4 until the preset convergence condition is met, and output the optimal moment tensor inversion result; use the finally trained neural network model to predict the mismatch value corresponding to the candidate moment tensor parameter in the moment tensor parameter space, and perform quantitative analysis of the uncertainty of the moment tensor inversion result based on the prediction result.

[0009] The "global inversion" described in this invention refers to the process of inverting the moment tensor by dynamically learning the global distribution of the mismatch function in the parameter space through a neural network, and guiding iterative sampling based on the learned global distribution, so as to achieve the search for the global optimal solution and the quantification of the uncertainty of the inversion result.

[0010] Preferably, the moment tensor parameter space in step S1 is composed of six independent parameters of the seismic moment tensor, the six independent parameters including: The six independent parameters are normalized and then used as input to the neural network model and search parameters for the neighborhood algorithm.

[0011] Preferably, the mismatch function in step S2 is established based on the difference between the observed waveform and the synthesized waveform. The observed waveform uses three-component waveform data collected by seismic stations, and the synthesized waveform is calculated using the Green's function based on the initial location of the seismic source, the underground velocity model, and station information. The mismatch function serves as the optimization objective for neural network training and moment tensor inversion.

[0012] Furthermore, the mismatch function described in step S2 is expressed as: ; In the formula, and These represent the weights of the P-wave and S-wave, respectively. Indicates the station index; P obs Represents the observed waveform P-wave window; P syn Represents the P-wave window of the synthesized waveform; S obs Indicates the S-wave window of the observed waveform; S syn This represents the S-wave window of the synthesized waveform.

[0013] Preferably, the neural network model in step S3 takes the moment tensor parameters as input and the corresponding mismatch value as output, establishing a mapping relationship between the moment tensor parameters and the mismatch function, the expression of which is: ; In the formula, NN represents a neural network model.

[0014] Preferably, the target region in step S4 is a region with a smaller predicted mismatch value determined based on the global distribution of the predicted mismatch function.

[0015] In this invention, the "region with smaller predicted mismatch values" refers to the parameter region formed by selecting a preset number of candidate moment tensor parameters with smaller predicted mismatch values ​​after sorting the candidate moment tensor parameters according to their predicted mismatch values ​​based on the global distribution of the mismatch function predicted by the neural network. The preset number can be set according to the inversion scale and computational requirements, preferably the top 400 with smaller mismatch values.

[0016] Furthermore, in step S4, when generating a new round of candidate moment tensor parameters, both neighborhood sampling of the target region and random sampling of the moment tensor parameter space are performed simultaneously to balance local search capability and global search capability. Preferably, an ε-greedy strategy is introduced in the generation process of the candidate moment tensor parameters, wherein the ratio of neighborhood sampling to random sampling is 3~4:1.

[0017] Furthermore, in each iteration, the candidate moment tensor parameters and corresponding mismatch values ​​generated in the current iteration, together with historical sampling data, are used as training samples to update the neural network model in order to continuously optimize the mapping relationship.

[0018] Preferably, the preset convergence condition in step S5 is that the inverted mismatch function no longer decreases.

[0019] Preferably, the uncertainty assessment in step S5 includes: using the finally trained neural network model to predict the mismatch values ​​corresponding to multiple candidate moment tensor parameters in the moment tensor parameter space; selecting candidate moment tensor parameters that meet the preset mismatch conditions based on the prediction results; and statistically analyzing the variation range of the corresponding source parameters to complete the quantitative analysis of the uncertainty of the moment tensor inversion results. Further, the preset mismatch condition is that the inverted mismatch function no longer decreases. The source parameters include one or more of the following: Kagan angle, DC component, CLVD component, and ISO component.

[0020] Secondly, the present invention also provides a global inversion system for seismic moment tensors based on reinforcement learning, the system being used to implement the above method, comprising: The parameter space construction module is used to acquire the observed waveform data, station information and subsurface velocity model of the seismic event to be inverted, and to construct the moment tensor parameter space. The mismatch function construction module is used to establish a mismatch function to evaluate the degree of matching between the synthesized waveform corresponding to the candidate moment tensor parameters and the observed waveform data; The neural network training module is used to construct a neural network model and train the neural network model using the sampled candidate moment tensor parameters and their corresponding mismatch values ​​to dynamically learn the mapping relationship between the moment tensor parameters and the mismatch function. The global distribution prediction and resampling module is used to predict the global distribution of the mismatch function in the moment tensor parameter space using the trained neural network model, determine the target region based on the global distribution of the mismatch function, use the candidate moment tensor parameters in the target region as sampling seeds, guide the neighborhood algorithm to perform resampling, and generate a new round of candidate moment tensor parameters. The iterative control and result analysis module is used to control the neural network training module and the global distribution prediction and resampling module to run iteratively until the convergence condition is met, output the optimal moment tensor inversion result, and use the finally trained neural network model to complete the uncertainty assessment of the moment tensor inversion result.

[0021] Compared with the prior art, the present invention has the following beneficial effects: (1) This invention improves the global inversion efficiency of the moment tensor by dynamically learning the global distribution of the mismatch function during the iterative inversion process of the moment tensor and using the predicted global distribution of the mismatch function to guide the resampling of the neighborhood algorithm. Synthetic test results show that, under the same experimental conditions, the inversion convergence speed of this invention is 30% to 40% higher than that of the traditional neighborhood algorithm; (2) In this invention, the neural network is trained synchronously during the iterative inversion process, enabling it to directly predict the corresponding mismatch value based on the moment tensor parameters. After the inversion is completed, there is no need to perform a large number of waveform forward simulations again. The trained neural network can be used to quickly predict millions of candidate moment tensors and perform uncertainty statistical analysis on parameters such as Kagan angle, DC / CLVD / ISO ratio, etc. This avoids the problem of traditional methods requiring a large number of additional forward calculations and significantly reduces the computational cost of uncertainty analysis. (3) This invention has high inversion accuracy and good global optimization capability, and can accurately learn the high-dimensional mismatch function distribution and stably obtain the moment tensor inversion results. Experimental results show that the mismatch function distribution learned by this invention is highly consistent with the true mismatch function distribution. For example, in the moment tensor inversion experiment, the mean and standard deviation of the difference between the predicted mismatch distribution and the true mismatch distribution are only 0.0015 and 0.011, respectively. Attached Figure Description

[0022] To more clearly illustrate the technical solution of the present invention, the accompanying drawings used in the description of the specific embodiments will be briefly introduced below. Obviously, the following description is only a part of the embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0023] Figure 1 This is a schematic diagram of the method flow of the present invention.

[0024] Figure 2 This is a schematic diagram of the neural network architecture design in the method of the present invention.

[0025] Figure 3 The source location (red star), station (black triangle), and true moment tensor (beach ball diagram) are used in the synthetic test to simulate the "observation" waveform.

[0026] Figure 4 The velocity model used in the synthetic test is shown, where the blue and red lines represent the actual Vp and Vs velocities used to simulate the “observed” waveform, respectively, and the gray lines represent the 20 perturbation velocities with a maximum random perturbation of ±10%.

[0027] Figure 5 The three-component waveform is simulated using a model of the actual source location and velocity, where the red and blue dots represent the first arrivals of the P-wave and S-wave, respectively.

[0028] Figure 6 The curves show the inversion mismatch as the number of iterations increases, with the blue and red lines representing the NA and RNA methods, respectively.

[0029] Figure 7 This is a comparison between the actual mismatch distribution and the predicted mismatch distribution.

[0030] Figure 8 The distribution of the predicted mismatch function relative to the Frobenius distance (a) and Kagan angle (b) is shown in the figure. The red lines in the figure represent the 10% and 20% quantiles defined for the range of mismatch values ​​from minimum to maximum.

[0031] Figure 9 Uncertainty analysis using the predicted global distribution of the mismatch function is presented, including decomposed nodal lines (a1, a2), P / T axes (b1, b2), and diamond plots (c1, c2). The gray lines and dots in a1, a2, and c1, c2 represent the changes in the proportions of the decomposed nodal lines and the DC, CLVD, and ISO components, respectively. The red lines and dots in a1, a2, and c1, c2 represent the optimal inversion moment tensor given by the RNA method. The red circles and blue plus signs in b1 and b2 represent the changes in the P-axis and T-axis, respectively.

[0032] Figure 10 Data and application results of the M7.1 mainshock in Tibet in 2025 are presented, where (a) shows the curves of mismatch inversion using the NA and RNA methods as a function of iteration number; and (b) shows the inverted moment tensor and the proportions of DC, CLVD, and ISO components.

[0033] Figure 11 Uncertainty analysis for the 2025 Tibet M7.1 mainshock includes the variation of the predicted mismatch function with Frobenius distance (a) and Kagan angle (b), and the variation of the decomposed nodal lines, P / T axis, and the proportions of DC, CLVD, and ISO components at the 5th quantile of the mismatch function (c). In (c), the red lines and red dots in the left and right columns represent the optimal inversion moment tensor given by the RNA method, and the red circles and blue plus signs in the middle column represent the variations of the P-axis and T-axis, respectively. Detailed Implementation

[0034] This invention proposes a global inversion method, system, and storage medium for seismic moment tensor based on reinforcement learning. To facilitate understanding of this invention by those skilled in the art, specific embodiments of this invention are described below with reference to the accompanying drawings.

[0035] In this invention, unless otherwise specified, the equipment and raw materials used are commercially available or commonly used in the art. The methods in the following embodiments, unless otherwise specified, are conventional methods in the art. Unless otherwise defined, all technical and scientific terms used in this specification have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0036] Example 1: A global inversion method for seismic moment tensor based on reinforcement learning (RNA method) This embodiment provides a global inversion method for seismic moment tensors based on reinforcement learning, the overall process of which is as follows: Figure 1 As shown, the steps include the following.

[0037] S1. Establish the parameter space of the moment tensor. The observation waveform data, station information, initial location of the epicenter, and underground velocity model corresponding to the seismic event to be inverted are obtained. The observation waveform data includes three-component seismic waveform data collected by multiple seismic stations.

[0038] Earthquake sources are described using a full-moment tensor, which is represented by a second-order symmetric tensor, and its expression is as follows: ; Since the seismic moment tensor is a symmetric matrix, it contains six independent parameters: ; The above six independent parameters together constitute the six-dimensional parameter space of moment tensor inversion.

[0039] To eliminate the influence of scalar seismic moment on the moment tensor parameter search process, the six independent parameters of the moment tensor are normalized to a preset range. The six normalized independent parameters are used as input parameters for the subsequent neural network model and search parameters for the neighborhood algorithm. In this embodiment, the preset range is [-0.1, 1.0].

[0040] S2. Constructing the moment tensor inversion mismatch function Based on the initial location of the seismic source, the underground velocity model, and the station information, forward modeling is performed using Green's function to obtain the synthetic waveforms corresponding to each station.

[0041] According to the theory, time windows are extracted from the observed waveform and the synthesized waveform to obtain P-wave and S-wave waveforms respectively. In this embodiment, bandpass filtering of 0.05 Hz to 0.1 Hz is applied to the P-wave and S-wave, and the time extraction windows for the P-wave and S-wave are 30 seconds and 80 seconds respectively.

[0042] Cross-correlation alignment of the observed and synthesized waveforms is performed, followed by normalization to reduce the impact of source location errors and scalar seismic moments on the inversion results. An overall mismatch function is constructed, using the mismatch between the observed and synthesized waveforms as the optimization objective. ; In the formula, and These represent the weights of the P-wave and S-wave, respectively. Indicates the station index; P obs Represents the observed waveform P-wave window; P syn Represents the P-wave window of the synthesized waveform; S obs Indicates the S-wave window of the observed waveform; S syn This represents the S-wave window of the synthesized waveform.

[0043] The mismatch function is used to evaluate the degree of matching between the synthesized waveform and the observed waveform corresponding to the current moment tensor parameters. The smaller the mismatch value, the closer the current moment tensor parameters are to the true source parameters. The mismatch function serves as the optimization target for subsequent neural network learning and neighborhood algorithm iterative search.

[0044] S3. Construct a neural network model and dynamically learn the mapping relationship between the moment tensor parameters and the mismatch function. In the six-dimensional moment tensor parameter space, a preset number (512 in this embodiment) of initial candidate moment tensor parameters are randomly generated. The mismatch value corresponding to each candidate moment tensor parameter is calculated according to the mismatch function established in step S2. The moment tensor parameters and their corresponding mismatch values ​​are stored as sample data in the experience pool.

[0045] Building neural network models, such as Figure 2 As shown, the network structure includes one input layer (6-dimensional), three one-dimensional convolutional layers, two fully connected hidden layers, and one output layer (1-dimensional, using the sigmoid activation function). The network takes six independent parameters of the moment tensor as input and the corresponding mismatch values ​​as outputs to construct the moment tensor. The mapping relationship between the function and the mismatch function is expressed as follows: ; In the formula, NN represents a neural network model.

[0046] In each iteration, the new samples generated in the current iteration and the historical samples in the experience pool are used together as training data. The neural network model is trained through an experience replay mechanism, and the network parameters are continuously updated so that the neural network dynamically learns the mapping relationship between the moment tensor parameter space and the mismatch function. Specifically, the samples in the experience pool are sorted according to the mismatch value, and a subset of the best historical solutions obtained from previous iterations is selected. The newly sampled samples in the current iteration and the subset of the best solutions are used together as the training data for the neural network. In this embodiment, the preset proportion is the top 20%. The neural network is trained for a preset number of rounds in each iteration (64 times in this embodiment), and the updated network model parameters are saved for continued training in the next iteration.

[0047] S4. Predicting the global distribution of the mismatch function and adaptive resampling Using the neural network model trained in step S3, the mismatch values ​​corresponding to a preset number (512 in this embodiment) of candidate moment tensor parameters in the moment tensor parameter space are predicted according to the established mapping relationship between moment tensor parameters and mismatch functions. The global distribution of the mismatch function in the moment tensor parameter space is obtained. This global distribution of the mismatch function is used to characterize the distribution of predicted mismatch values ​​corresponding to each candidate moment tensor parameter in the moment tensor parameter space, and the next round of sampling area is determined accordingly.

[0048] Based on the predicted global distribution of the mismatch function, a target region with a small predicted mismatch value is determined (in this embodiment, the top 400 regions with small mismatch values), and the moment tensor parameters within this target region are selected as sampling seeds. Centered on the sampling seed, a neighborhood algorithm is used to perturb its neighborhood, generating a new round of candidate moment tensor parameters. To balance local optimization and global search capabilities, an ε-greedy strategy is introduced during the candidate moment tensor parameter generation process: neighborhood sampling (400 regions in this embodiment) is performed within the target region with a first preset probability (78% in this embodiment), and candidate moment tensor parameters (112 regions in this embodiment) are randomly generated within the entire moment tensor parameter space with a second preset probability (22% in this embodiment), wherein the first preset probability is greater than the second preset probability.

[0049] For the newly generated candidate moment tensor parameters, calculate the corresponding mismatch value according to the mismatch function established in step S2, and add the newly obtained moment tensor parameters and corresponding mismatch values ​​to the experience pool.

[0050] S5. Iterative Convergence and Uncertainty Assessment Steps S3 and S4 are repeated to continuously train the neural network model using the updated experience pool and re-predict the global distribution of the mismatch function to guide the neighborhood algorithm to complete the next round of resampling until the preset convergence condition is met, that is, the inverted mismatch function no longer decreases, reaching the preset number of iterations (64 times in this embodiment). When the preset convergence condition is met, the moment tensor parameter corresponding to the minimum mismatch value in the experience pool is extracted as the final inversion result.

[0051] Using the finally trained neural network model, the mismatch values ​​corresponding to a large number of randomly generated candidate moment tensor parameters (in the millions) in the moment tensor parameter space are predicted to obtain the global distribution of the mismatch function in the moment tensor parameter space. Candidate moment tensor parameters that meet the conditions are selected according to the preset mismatch value range (in this embodiment, the top 400 with smaller mismatch values ​​are selected), and the variation range of their Kagan angle, dual couple (DC) component, compensated linear vector dipole (CLVD) component, and isotropic (ISO) component is statistically analyzed to realize the quantitative analysis of the uncertainty of the seismic moment tensor inversion results.

[0052] Since the above uncertainty analysis directly uses the trained neural network model to predict the mismatch value corresponding to the candidate moment tensor parameter, it does not require any additional waveform forward modeling calculation, thus achieving quantitative assessment of the uncertainty of high-dimensional nonlinear inversion at a low computational cost.

[0053] Example 2: Comparative Experiment of RNA Method and NA Method 2.1 Synthesis Test Setup In this embodiment, 40 stations are set up, with epicentral distances ranging from 200 km to 500 km. Figure 3 The epicenter was located at a depth of 8 kilometers. The synthesized waveform was generated using the FK elastic forward modeling package and a one-dimensional velocity model (…). Figure 4 The calculations are based on the red and blue lines in the diagram. The total duration of the moment magnitude and the triangular source time function are Mw 6.0 and 5 seconds, respectively. The true moment tensor is randomly generated. The values ​​are (-0.556, 0.742, -0.587, 0.837, -0.023, 0.224). After moment tensor decomposition, the proportions of the DC, CLVD, and ISO components are 60.4%, 27.8%, and 11.8%, respectively. The observed waveform is a three-component (3C) waveform calculated using real source parameters and a velocity model. Figure 5 These waveforms are used as “observation” data in the synthetic test.

[0054] The RNA method follows the steps described in Example 1. To ensure fairness in the comparison, the NA method in this example is rewritten to maintain consistency with the RNA method. The only difference between the two methods lies in the resampling step; the RNA method adds neural network learning and global distribution prediction of the mismatch function. In each iteration, the NA method regenerates new candidate points around the already sampled best solution. The RNA method, on the other hand, regenerates new candidate points based on the already sampled best solution and the predicted best solution. Both the NA and RNA methods apply an ε-greedy strategy. Each iteration resamples 512 new candidate points, of which 400 are generated around the best solution and 112 are randomly generated according to the ε-greedy strategy (approximately 20%). All data processing and inversion parameters remain unchanged. A total of 64 iterations are performed for both methods.

[0055] 2.2 Comparison and Analysis of Test Results 2.2.1 Comparison of Convergence Efficiency Moment tensor inversion was performed using both RNA and NA methods. The proportions of the DC, CLVD, and ISO components inverted by the two methods were highly consistent with the true moment tensor (Table 1). The changes in the minimum mismatch value corresponding to different iteration numbers were also recorded. Figure 6 ).

[0056] Table 1. Moment tensors and the proportions of DC, CLVD, and ISO components retrieved by RNA and NA methods. True value -0.556 0.742 -0.587 0.837 -0.023 0.224 60.4% 27.8% 11.8% NA method -0.606 0.805 -0.642 0.914 -0.026 0.235 60.9% 27.5% 11.6% RNA method -0.663 0.885 -0.702 1.000 -0.028 0.266 60.5% 27.8% 11.8%

[0057] Depend on Figure 6 As can be seen, both methods gradually reduce the mismatch value and tend to converge with the increase of the number of iterations; however, the convergence speed of the RNA method is significantly faster than that of the NA method, which is one of the outstanding advantages of the RNA method. Specifically, the NA method tends to stabilize after about 50 to 60 iterations, while the RNA method reaches a stable state after about 30 to 40 iterations, improving the convergence speed by about 30% to 40%. The reason for this is that this invention utilizes a neural network to dynamically learn the mapping relationship between the moment tensor parameters and the mismatch function, and predicts the global distribution of the mismatch function in the parameter space. Based on this, it determines the region with a smaller predicted mismatch value, guides the neighborhood algorithm to perform adaptive resampling, and makes the sampling resources more concentrated in the globally optimal region, thereby reducing invalid sampling and improving the efficiency of the global inversion of the moment tensor.

[0058] 2.2.2 Global Distribution Prediction Results of Mismatch Function Using a trained neural network model, mismatch values ​​are predicted for a large number of randomly generated candidate moment tensor parameters in the moment tensor parameter space. This yields the global distribution of the mismatch function. Two dimensions of the moment tensor are varied, while the other four dimensions are fixed using the optimal inversion value, resulting in a set of two-dimensional graphs for comparison, such as... Figure 7 As shown.

[0059] Depend on Figure 7 It can be seen that the mismatch distribution learned by the neural network is highly consistent with the true mismatch distribution. Specifically, in Within the plane, the mean and standard deviation of the differences are 0.0015 and 0.011, respectively. These results demonstrate the feasibility and effectiveness of the proposed RNA method in dynamically learning and representing the global distribution of the mismatch function during moment tensor inversion. Based on the predicted global distribution of the mismatch function, regions with smaller predicted mismatch values ​​can be accurately identified, and this can be used as the basis for the next round of neighborhood algorithm resampling, thus achieving adaptive search of the moment tensor parameter space.

[0060] Compared to traditional NA methods that only perform local perturbations based on the optimal solution in historical sampling points, this invention can dynamically adjust the sampling area based on the global distribution of the predicted mismatch function, thereby improving global search capabilities.

[0061] 2.2.3 Comparison of Uncertainty Analysis Capabilities Another significant advantage of the RNA method lies in the simultaneous training of a neural network model during the inversion process. This model can directly compute the mismatch value corresponding to any moment tensor. Essentially, it is a global proxy for the mismatch function in the six-dimensional parameter space. This global distribution construction makes uncertainty analysis a low-cost post-processing step: after inversion convergence, without any additional forward simulations, the neural network can be used to randomly generate millions of candidate solutions in the parameter space and predict their mismatch values ​​in batches. This allows for backtracking of the corresponding moment tensors and statistical analysis of the variation range of parameters such as the Kagan angle, DC / CLVD / ISO component ratios. However, traditional methods require 10... 6 The additional forward modeling computations are on the order of magnitude (practically infeasible) or rely on linearized approximations (inaccurate in nonlinear problems). The RNA method, by constructing a global distribution, transforms this originally inoperable task into neural network inference that can be completed in seconds, achieving rigorous quantitative assessment of uncertainty with "zero additional cost".

[0062] After the inversion is completed, the trained neural network model is used to perform global prediction on the moment tensor parameter space to obtain the global distribution of the mismatch function in the entire moment tensor parameter space. In this embodiment, one million candidate moment tensor parameters are randomly generated in the six dimensions of the moment tensor parameter space, and the trained neural network model is used to predict the mismatch value corresponding to each candidate moment tensor parameter, thereby obtaining the global distribution of the mismatch function in the entire moment tensor parameter space. The candidate moment tensor parameters can also be generated using a uniform grid method; this embodiment uses a random generation method.

[0063] Based on the predicted global distribution of the mismatch function, candidate moment tensor parameters that meet the conditions are selected according to the preset mismatch value range, and the corresponding Kagan angle, double couple (DC) component, compensated linear vector dipole (CLVD) component and isotropic (ISO) component are statistically analyzed to achieve quantitative analysis of the uncertainty of the moment tensor inversion results.

[0064] Depend on Figure 8 It can be seen that as the allowable mismatch range gradually increases, the number of moment tensor parameters satisfying the conditions gradually increases, and the corresponding Kagan angle distribution range gradually expands; while within a smaller mismatch range, the Kagan angle is mainly concentrated in a smaller angle range, indicating that the inversion results have high consistency and stability. Based on the range of mismatch values ​​from minimum to maximum, 10% and 20% quantiles are defined (…). Figure 8 (The red line in the diagram) For each quantile, select the subset with the smallest mismatch value and backtrack it to the corresponding moment tensor to analyze the inversion uncertainty. Figure 9 ).

[0065] Figure 9 Statistical results for the DC, CLVD, and ISO components are presented across different mismatch ranges. For the 10th quantile, the mean and standard deviation of the Kagan angle relative to the optimal solution are 4.2° and 1.9°, respectively, while the standard deviations of the DC, CLVD, and ISO proportions relative to the optimal solution are 7.4%, 7.2%, and 4.2%, respectively. For the 20th quantile, the mean and standard deviation of the Kagan angle relative to the optimal solution are 7.6° and 3.1°, respectively, while the standard deviations of the DC, CLVD, and ISO proportions relative to the optimal solution are 15.8%, 16.9%, and 9.0%, respectively. It can be seen that the variation in the Kagan angle is relatively small, while the variations in the DC, CLVD, and ISO proportions are relatively large, indicating that the constraints of the nodal plane and P / T axis are superior to the DC, CLVD, and ISO proportions, especially for the 20th quantile; the uncertainty of the analytical DC component reaches approximately 15%. Uncertainty analysis is indicative for interpreting non-DC events (such as volcanoes, explosions, and hydraulic fracturing).

[0066] The method of this invention learns the mapping relationship between moment tensor parameters and mismatch function simultaneously during the inversion process, so that the same neural network model can be used to guide the adaptive resampling of the neighborhood algorithm and to predict the global distribution of the mismatch function and perform quantitative analysis of uncertainty after the inversion is completed. This realizes that the inversion optimization and uncertainty analysis share the same neural network model, avoiding the large amount of additional forward modeling calculations required by traditional methods to carry out uncertainty analysis.

[0067] Example 3: Moment Tensor Inversion Verification Based on Actual Seismic Events To further verify the applicability of the method of the present invention in actual earthquake events, the global inversion method of earthquake moment tensor based on reinforcement learning described in Example 1 was used to perform moment tensor inversion on actual earthquake events, and the inversion results were compared and analyzed with the global authoritative source mechanism catalog.

[0068] This embodiment selects a typical earthquake event: the 2025 Tibet M7.1 earthquake. The moment tensor inversion is performed using the method described in Embodiment 1, with the difference that the window lengths for P-waves and S-waves are 100 seconds each, and the frequency bands for P-waves and S-waves are 0.01~0.03 Hz and 0.01~0.03 Hz respectively, yielding the corresponding focal mechanism solution and moment magnitude.

[0069] like Figure 10 As shown, during the simulation of the M7.1 mainshock in Tibet in 2025, the RNA method stabilized after approximately 10 iterations, while the NA method stabilized after approximately 25 iterations, indicating that the RNA method converged earlier than the NA method. The DC components of the NA and RNA methods were 97.1% and 98.8%, respectively. The moment magnitudes retrieved by the NA and RNA methods were 7.12 and 7.14, respectively. The results of the two methods are highly consistent, supporting the reliability of the inversion results.

[0070] Inversion uncertainty is quantitatively assessed by using a well-trained neural network to predict the global distribution of the mismatch function. For example... Figure 11 a and Figure 11 As shown in b, the mismatch values ​​near the global minimum exhibit considerable ambiguity. Using the minimum and maximum values ​​of the mismatch function, the 5th percentile of the mismatch function is defined. Figure 11 a and Figure 11 (The red line in b) was used, and the changes in the corresponding moment tensor were evaluated. Smaller quantiles were used in this embodiment because real-world data applications involve more uncertainty than synthetic tests. Figure 11 c shows the variations in the decomposed nodal lines, P / T axes, and rhombus plots at the 5th quantile of the mismatch function. The mean and standard deviation of the Kagan angle relative to the optimal solution are 17.2° and 6.6°, respectively; the standard deviations of the DC, CLVD, and ISO proportions relative to the optimal solution are 15.9%, 26.8%, and 5.5%, respectively. The Kagan angle exhibits moderate variation. However, the proportion of the CLVD component varies significantly. This indicates that the resolved CLVD component may contain substantial uncertainty. Therefore, particular caution should be exercised when interpreting the CLVD component. In summary, application to real data from the 2025 Tibet M7.1 mainshock demonstrates that the proposed RNA method not only converges faster but also provides a feasible method for quantitatively assessing the uncertainty of the inversion moment tensor.

[0071] Subsequently, the moment tensor inversion results obtained by the method of this invention were compared with those published by the Global Centroid Moment Tensor (GCMT) and the German Research Centre for Geosciences (GFZ). Experimental results show that the moment tensor solutions and moment magnitudes obtained by the method of this invention maintain a high degree of consistency with the results published in the GCMT and GFZ catalogs, and can accurately reconstruct earthquake focal mechanisms and moment magnitude information.

[0072] The embodiments of the present invention described above do not constitute a limitation on the scope of protection of the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the claims of the present invention.

Claims

1. A global inversion method for seismic moment tensor based on reinforcement learning, characterized in that, Includes the following steps: S1. Establish the moment tensor parameter space: Obtain the observed waveform data, station information and subsurface velocity model of the seismic event to be inverted, and construct the moment tensor parameter space; S2. Constructing the moment tensor inversion mismatch function: Establish a mismatch function to evaluate the degree of matching between the synthetic waveform corresponding to the candidate moment tensor parameters and the observed waveform data; S3. Construct a neural network model and dynamically learn the mapping relationship between moment tensor parameters and mismatch function: Construct a neural network model, train the neural network model using the sampled candidate moment tensor parameters and their corresponding mismatch values, and dynamically learn the mapping relationship between moment tensor parameters and mismatch function; S4. Predicting the global distribution of the mismatch function and adaptive resampling: Using the trained neural network model, predict the global distribution of the mismatch function in the moment tensor parameter space, determine the target region based on the global distribution of the mismatch function, use the candidate moment tensor parameters in the target region as sampling seeds, guide the neighborhood algorithm to perform resampling, and generate a new round of candidate moment tensor parameters. S5. Iterative Convergence and Uncertainty Assessment: Repeat steps S3 and S4 until the preset convergence condition is met, and output the optimal moment tensor inversion result; use the finally trained neural network model to predict the mismatch value corresponding to the candidate moment tensor parameter in the moment tensor parameter space, and perform quantitative analysis of the uncertainty of the moment tensor inversion result based on the prediction result.

2. The global inversion method for seismic moment tensor based on reinforcement learning according to claim 1, characterized in that, The moment tensor parameter space mentioned in step S1 consists of six independent parameters of the seismic moment tensor, which include: The six independent parameters are normalized and then used as input to the neural network model and search parameters for the neighborhood algorithm.

3. The global inversion method for seismic moment tensor based on reinforcement learning according to claim 1, characterized in that, The mismatch function mentioned in step S2 is established based on the difference between the observed waveform and the synthesized waveform. The observed waveform uses three-component waveform data collected by seismic stations. The synthesized waveform is calculated using the Green's function based on the initial location of the seismic source, the underground velocity model, and station information. The mismatch function serves as the optimization objective for neural network training and moment tensor inversion.

4. The global inversion method for seismic moment tensor based on reinforcement learning according to claim 3, characterized in that, The mismatch function mentioned in step S2 is expressed as: ； In the formula, and These represent the weights of the P-wave and S-wave, respectively. Indicates the station index; P obs This represents the P-wave window representing the observed waveform; P syn Represents the P-wave window of the synthesized waveform; S obs Indicates the S-wave window of the observed waveform; S syn This represents the S-wave window of the synthesized waveform.

5. The global inversion method for seismic moment tensor based on reinforcement learning according to claim 1, characterized in that, The neural network model described in step S3 takes the moment tensor parameters as input and the corresponding mismatch value as output, establishing a mapping relationship between the moment tensor parameters and the mismatch function. Its expression is: ； In the formula, NN This represents a neural network model.

6. The global inversion method for seismic moment tensor based on reinforcement learning according to claim 1, characterized in that: The target region mentioned in step S4 is the region with a smaller predicted mismatch value, determined based on the global distribution of the predicted mismatch function.

7. The global inversion method for seismic moment tensor based on reinforcement learning according to claim 1, characterized in that: In step S4, when generating a new round of candidate moment tensor parameters, neighborhood sampling of the target region and random sampling of the moment tensor parameter space are performed simultaneously.

8. The global inversion method for seismic moment tensor based on reinforcement learning according to claim 7, characterized in that: The ratio of neighborhood sampling to random sampling in step S4 is 3~4:

1.

9. The global inversion method for seismic moment tensor based on reinforcement learning according to claim 1, characterized in that: The preset convergence condition in step S5 is that the inverted mismatch function no longer decreases.

10. A global inversion system for seismic moment tensor based on reinforcement learning, characterized in that, The system is used to implement the method according to any one of claims 1 to 8, comprising: The parameter space construction module is used to acquire the observed waveform data, station information and subsurface velocity model of the seismic event to be inverted, and to construct the moment tensor parameter space. The mismatch function construction module is used to establish a mismatch function to evaluate the degree of matching between the synthesized waveform corresponding to the candidate moment tensor parameters and the observed waveform data; The neural network training module is used to construct a neural network model and train the neural network model using the sampled candidate moment tensor parameters and their corresponding mismatch values ​​to dynamically learn the mapping relationship between the moment tensor parameters and the mismatch function. The global distribution prediction and resampling module is used to predict the global distribution of the mismatch function in the moment tensor parameter space using the trained neural network model, determine the target region based on the global distribution of the mismatch function, use the candidate moment tensor parameters in the target region as sampling seeds, guide the neighborhood algorithm to perform resampling, and generate a new round of candidate moment tensor parameters. The iterative control and result analysis module is used to control the neural network training module and the global distribution prediction and resampling module to run iteratively until the convergence condition is met, output the optimal moment tensor inversion result, and use the finally trained neural network model to complete the uncertainty assessment of the moment tensor inversion result.

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