A method and system for natural earthquake magnitude estimation

Abstract

The application belongs to the technical field of earthquake monitoring, and in particular to a method and system for natural earthquake magnitude estimation, wherein three-component seismic waveform data is subjected to multi-layer feature extraction and dimension compression through three cascaded convolution modules; after the extracted features are further compressed through a pooling layer, a fully connected layer and a ReLU activation function, a final magnitude estimation result is output; a DS-Mamba module is connected to each convolution module, a long-time sequence dependency of the three-component seismic waveform data is captured through state space modeling, and local detailed features are focused on by using a depth separable convolution. The application establishes a nonlinear mapping relationship between seismic data and magnitude, realizes accurate and automatic estimation of the earthquake magnitude, and effectively reduces the error of the magnitude estimation.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of earthquake monitoring, and in particular to a method and system for natural earthquake magnitude estimation. BACKGROUND

[0002] With the rapid development of society, earthquake monitoring and early warning have become an important means to protect human life and property safety. In earthquake-prone areas, accurate earthquake monitoring can effectively reduce disaster losses and provide important scientific basis for post-earthquake rescue. With the increasing demand for earthquake disaster prevention and mitigation around the world and the rapid progress of earthquake observation technology, the complexity and accuracy requirements of earthquake monitoring systems are continuously improving. Due to the significant differences in seismic wave propagation characteristics in different geological structure regions, this method based on local experience lacks universality and is difficult to be applied to earthquake monitoring in a global range.

[0003] The differences in geological structure of different tectonic regions around the world can significantly change the propagation characteristics and attenuation laws of seismic waves, which makes the traditional earthquake magnitude estimation method based on regional empirical parameters have obvious limitations. Its calculation depends on the empirical data of a specific region, which often leads to systematic deviation when applied across regions, thereby significantly reducing the accuracy and reliability of magnitude estimation.

[0004] Due to the significant differences in seismic wave propagation characteristics in different geological structure regions, this method based on local experience lacks universality and is difficult to be applied to earthquake monitoring in a global range.

[0005] In the field of magnitude estimation, the magnitude estimation method based on deep learning effectively avoids the subjectivity and limitations of manual feature extraction in traditional methods through end-to-end learning. However, due to its inherent local receptive field characteristics, traditional convolutional neural networks (CNN) may not be able to effectively capture long-distance dependencies when processing seismic signals with significant spatio-temporal correlations. This limitation to some extent restricts the performance improvement of the magnitude estimation model, resulting in large magnitude estimation errors. SUMMARY

[0006] The first aspect embodiment of the application provides a method for natural earthquake magnitude estimation, which solves the problem of large magnitude estimation error.

[0007] The second aspect embodiment of the application provides a system for natural earthquake magnitude estimation.

[0008] The method for natural earthquake magnitude estimation according to the first aspect embodiment of the application comprises:

[0009] The three-component seismic waveform data is subjected to multi-layer feature extraction and dimension compression through three cascaded convolution modules; after the extracted features are further compressed through a pooling layer, the final output of the magnitude estimation result is output through a fully connected layer and a ReLU activation function;

[0010] Each convolution module is followed by a DS-Mamba module, which captures the long-time sequence dependence of the three-component seismic waveform data through state space modeling, and focuses on local detailed features using deep separable convolution.

[0011] Further, the DS-Mamba module performs layer normalization on the input data, mapping the input data to first data with a standard normal distribution with a mean of 0 and a variance of 1;

[0012] The first data is subjected to time sequence modeling to roughly extract key seismic phase features in the first data to form second data by dynamically adjusting parameters;

[0013] The second data is layer normalized to third data;

[0014] Local features within a single channel of the third data are extracted through deep convolution to form fourth data, and cross-channel information fusion of the third data and the fourth data is realized through point-by-point convolution to output estimated magnitude data.

[0015] Further, the first data is subjected to time sequence modeling to roughly extract key seismic phase features in the first data to form second data, including:

[0016] The first data is mapped to a high-dimensional feature space through a fully connected layer;

[0017] The first data in the high-dimensional feature space is quickly scanned through a one-dimensional convolution layer to capture key seismic phase features;

[0018] The key seismic phase features are strengthened through a smooth nonlinear transformation;

[0019] The strengthened key seismic phase features are extracted from the first data through a state space model;

[0020] The key seismic phase features are reduced in dimension and output.

[0021] Further, the state space model includes a state equation and an output equation, and the continuous time form of the state equation and the output equation is represented as:

[0022] wherein is a state matrix, is an input matrix, is an output matrix, is a time-continuous input signal, For a time-continuous hidden state, For time-continuous output signals, Hidden state with continuous time The derivative;

[0023] Discretizing the state equation and output equation yields: ,in, The state matrix is ​​the discretized state matrix. The input matrix is ​​discretized. It is the identity matrix. For the discretized sampling interval, For the discretized time... The hidden state, For the discretized time... The hidden state, For the discretized time... The input signal, For the discretized time... The output signal;

[0024] The discretized state matrix and the discretized sampling interval are dynamically adjusted according to the input signal.

[0025] Furthermore, the discretized state matrix and the discretized sampling interval are dynamically adjusted according to the input signal, including:

[0026] In the initial stage, the sampling interval of the discretization is adjusted to a maximum value and the input matrix after discretization is adjusted to a minimum value to skip noise and early P-waves;

[0027] When the P-wave arrives, decrease the discretization sampling interval and increase the discretized input matrix;

[0028] Between the arrival times of the P-wave and the S-wave, the discretized sampling interval and the discretized input matrix are dynamically adjusted.

[0029] When the S-wave arrives, the discretized sampling interval is adjusted to a minimum value, and the discretized input matrix is ​​set to a maximum value.

[0030] After the S-wave passes, the discretized sampling interval is gradually increased and the discretized input matrix is ​​gradually decreased.

[0031] A system for estimating the magnitude of a natural earthquake according to a second aspect of this application includes:

[0032] Three cascaded convolutional modules perform multi-layer feature extraction and dimensionality compression on the three-component seismic waveform data;

[0033] DS-Mamba module, connected after each convolutional module, captures long temporal dependencies of three-component seismic waveform data through state space modeling, and utilizes deep separable convolution to focus on local detailed features;

[0034] pooling layer, further compresses the extracted features;

[0035] first fully connected layer and ReLU activation function, outputs magnitude estimation results according to the further compressed features.

[0036] Further, the DS-Mamba module comprises:

[0037] The first layer normalization module performs layer normalization processing on the input data, and maps the input data to the first data with a mean of 0 and a variance of 1, which is a standard normal distribution;

[0038] The Mamba module performs temporal modeling on the first data, and roughly extracts key seismic phase features in the first data to form second data by dynamically adjusting parameters;

[0039] The second layer normalization module normalizes the second data to the third data;

[0040] The deep separable convolution module extracts local features in a single channel of the third data to form fourth data through deep convolution, and realizes cross-channel information fusion of the third data and the fourth data through point-by-point convolution, and outputs estimated magnitude data.

[0041] Further, the Mamba module comprises:

[0042] The second fully connected layer maps the first data to a high-dimensional feature space;

[0043] The one-dimensional convolution layer quickly scans the first data in the high-dimensional feature space to capture key seismic phase features;

[0044] The first SiLU activation function strengthens the key seismic phase features through smooth nonlinear transformation;

[0045] The state space model extracts the strengthened key seismic phase features from the first data;

[0046] The third fully connected layer reduces and outputs the key seismic phase features.

[0047] Further, the state space model comprises a state equation and an output equation, and the continuous time form of the state equation and the output equation is represented as:

[0048] wherein is a state matrix, is an input matrix, is an output matrix, is a time-continuous input signal, is a hidden state, is a time-continuous output signal, is a time-continuous hidden state derivative;

[0049] Discretizing the state equation and the output equation results in: wherein, is a discretized state matrix, is a discretized input matrix, is an identity matrix, is a discretized sampling interval, is a hidden state at time after discretization, is a hidden state at time after discretization, is an input signal at time after discretization, is an output signal at time after discretization;

[0050] The discretized state matrix and the discretized sampling interval are dynamically adjusted with the input signal.

[0051] Further, the discretized state matrix and the discretized sampling interval are dynamically adjusted with the input signal, comprising:

[0052] In an initial phase, the discretized sampling interval and the discretized input matrix are adjusted, skipping noise and early P-waves;

[0053] Upon arrival of a P-wave, the discretized sampling interval is reduced and the discretized input matrix is increased;

[0054] Between the arrival of the P-wave and the arrival of the S-wave, the discretized sampling interval and the discretized input matrix are dynamically adjusted;

[0055] Upon arrival of the S-wave, the discretized sampling interval is adjusted to a minimum value and the discretized input matrix is adjusted to a maximum value;

[0056] After the S-wave, the discretized sampling interval is gradually increased and the discretized input matrix is gradually reduced.

[0057] Compared with the prior art, the application has the beneficial effects that the application establishes a nonlinear mapping relationship between seismic data and magnitude, realizes accurate and automatic estimation of the earthquake magnitude, and effectively reduces the error of the magnitude estimation. By using a dynamic selection mechanism, the key seismic phase features in the seismic waveform are adaptively focused, the calculation amount is effectively reduced while maintaining long sequence modeling, and the response speed is improved. BRIEF DESCRIPTION OF DRAWINGS

[0058] Figure 1 A network structure block diagram of a system for natural earthquake magnitude estimation is provided for the embodiments of the application.

[0059] Figure 2 A network structure block diagram of a DS-Mamba module is provided for the embodiments of the application. DETAILED DESCRIPTION

[0060] In order to make the purpose, technical scheme and advantages of the application more clear, the application is further described in detail below in combination with embodiments. It should be understood that the specific embodiments described herein are only used to explain the application and not to limit the application.

[0061] In the application, three-component seismic waveform data is based on the spatial distribution characteristics of the research area and the preset magnitude range to screen the qualified earthquake events; according to the P-wave first arrival time, the three-component seismic waveform data is intercepted by using a fixed length time window.

[0062] A system for natural earthquake magnitude estimation is constructed, and a DS-Mamba module is proposed, which simultaneously focuses on the global features and local features of the data. A nonlinear mapping relationship between seismic data and magnitude is established, accurate and automatic estimation of the earthquake magnitude is realized, and the error of the magnitude estimation is effectively reduced. The key seismic phase features in the waveform are adaptively focused, the calculation amount is effectively reduced while maintaining long sequence modeling, and the response speed is improved.

[0063] Referring to Figure 1 The system for natural earthquake magnitude estimation provided by the embodiments of the application includes:

[0064] Three cascaded convolution modules perform multi-layer feature extraction and dimension compression on the three-component seismic waveform data;

[0065] The DS-Mamba module is connected after each convolution module, captures the long time sequence dependence of the three-component seismic waveform data by state space modeling, and focuses on local detailed features by using depth separable convolution;

[0066] The pooling layer further compresses the extracted features;

[0067] The first fully connected layer and the ReLU activation function output the magnitude estimation result according to the further compressed features.

[0068] Three cascaded convolution modules are used for multi-layer feature extraction and dimension compression, each of which includes a convolution layer, a dropout layer and a down-sampling layer. A DS-Mamba module is connected to each convolution module to capture the long-term temporal dependence of the seismic waveform through state space modeling and focus on local detailed features by using a depth separable convolution.

[0069] In an embodiment, referring to the network structure of the DS-Mamba module shown in Figure 2 The network structure of the DS-Mamba module includes:

[0070] The first layer normalization module performs layer normalization processing on the input data, and maps the input data to the first data with a standard normal distribution with a mean of 0 and a variance of 1.

[0071] The Mamba module performs temporal modeling on the first data, dynamically adjusts the parameters, and roughly extracts the key seismic phase features in the first data to form the second data.

[0072] The second layer normalization module normalizes the second data to the third data.

[0073] The depth separable convolution module extracts local features within a single channel of the third data to form the fourth data by using a depth convolution, and realizes cross-channel information fusion between the third data and the fourth data by using a point-by-point convolution to output the estimated magnitude data.

[0074] The DS-Mamba module processes seismic data from two levels of rough and fine through a multi-level information extraction mechanism. Due to the large amplitude difference in seismic data, in order to alleviate the problem of gradient disappearance, the input data is first normalized to a standard normal distribution with a mean of 0 and a variance of 1, thereby significantly improving the stability of the system training stage. Subsequently, the Mamba module performs time series modeling, which can effectively capture the global information in the seismic sequence in the three-component seismic waveform data by virtue of its global perception ability. By introducing a selective mechanism, the parameters can be dynamically adjusted to roughly extract key seismic phase features in the three-component seismic waveform data, such as the first arrival time, amplitude mutation, and phase inversion of P and S waves. Finally, the data is processed through layer normalization and depth separable convolution: the depth separable convolution is composed of depth convolution and pointwise convolution, the depth convolution is responsible for extracting local features within a single channel, and then through the GELU activation function, the pointwise convolution realizes cross-channel information fusion through 1x1 convolution, which significantly reduces the number of parameters while maintaining the expression ability. In addition, the local perception advantage of convolution operation is fully utilized to efficiently extract local detailed features of seismic waveforms, effectively enhancing the sensitivity to subtle changes in seismic waveforms.

[0075] Due to the weak energy of microseismic events in natural seismic signals, the hidden travel time difference information of seismic phases, and the significant differences in regional velocity structure, the effective signal features are easily covered by background noise. Therefore, in an embodiment, the Mamba module includes:

[0076] The second fully connected layer maps the first data to a high-dimensional feature space;

[0077] The one-dimensional convolution layer quickly scans the first data in the high-dimensional feature space to capture key seismic phase features;

[0078] The first SiLU activation function strengthens the key seismic phase features through a smooth nonlinear transformation;

[0079] The state space model extracts the strengthened key seismic phase features from the first data;

[0080] The third fully connected layer reduces the key seismic phase features to a dimension and outputs them.

[0081] Firstly, the second fully connected layer maps the first data to a high-dimensional feature space, enhancing the feature expression ability, realizing the decoupling and enhancement of signal features, thus highlighting the effective components and suppressing noise interference, providing high-quality input for the subsequent selective mechanism. Subsequently, the one-dimensional convolutional layer quickly scans the seismic waveform, sensitively capturing key local features and mutations (such as P-wave and S-wave arrival); the first SiLU activation function further strengthens these features through smooth nonlinear transformation, suppressing irrelevant background noise while retaining and enhancing weak but important signals that may represent seismic phases. The data output by the second fully connected layer is also directly subjected to a second SiLU activation function for nonlinear transformation of the first data in the high-dimensional feature space, and then enters the state space model together with the data processed by the one-dimensional convolutional layer and the first SiLU activation function. The state space model extracts key seismic phase features from the seismic waveform and realizes adaptive selective filtering and enhancement of seismic signals through a gating mechanism. Finally, the third fully connected layer completes the dimension reduction output.

[0082] In an embodiment, the state space model includes a state equation and an output equation, and its continuous time form can be represented as:

[0083] wherein is a state matrix, is an input matrix, is an output matrix, is a time-continuous input signal, is a time-continuous hidden state, is a time-continuous output signal, is a derivative of the time-continuous hidden state .

[0084] Discretization of the above equation gives: ,

[0085] wherein is a discretized state matrix, is a discretized input matrix, is an identity matrix, is a discretized sampling interval. is a discretized hidden state at time , which compresses all historical information from the beginning of the sequence to time , is a discretized hidden state at time , is a discretized input signal at time , is a discretized output signal at time .

[0086] Adjusting the discretized state matrix and the discretized sampling interval dynamically according to the input signal, comprising:

[0087] Adjusting the discretized sampling interval to a maximum value and the discretized input matrix to a minimum value in an initial stage to skip noise and early P waves;

[0088] When the P wave arrives, reducing the discretized sampling interval and increasing the discretized input matrix to enhance the extraction of P wave characteristics;

[0089] Between the arrival of the P wave and the arrival of the S wave, dynamically adjusting the discretized sampling interval and the discretized input matrix to monitor useful information;

[0090] When the S wave arrives, adjusting the discretized sampling interval to a minimum value and the discretized input matrix to a maximum value;

[0091] After the S wave, gradually increasing the discretized sampling interval and reducing the discretized input matrix, and combining with the hidden state at the discretization time to quickly ignore the decaying tail wave.

[0092] Unlike the fixed , and in the traditional state space model, the application introduces a selective mechanism to establish a nonlinear mapping relationship between , and and the input signal at the discretization time , which can be dynamically adjusted according to the input signal at the discretization time . In seismic signals, the P wave arrives first, with small amplitude but containing key information such as source location and occurrence time; the subsequently arriving S wave has large amplitude and carries main energy, which is the core basis for estimating magnitude. By dynamically adjusting and , adaptive focusing of key information is achieved.

[0093] Specifically, in the initial stage, the maximum and the minimum are used to skip noise and early P waves; when the P wave arrives, is sharply reduced, is increased to enhance the extraction of P wave characteristics; between the P wave and the S wave, and will be dynamically adjusted to continuously monitor useful information; when the S wave arrives, adjusting to a minimum value, to a maximum value to fully capture key features related to magnitude; after the S wave, gradually increasing, decreasing, and combining with the historical state, i.e., the discretized moment of the hidden state , quickly ignoring the decay tail, thereby efficiently completing the magnitude estimation task.

[0094] A system for natural earthquake magnitude estimation established by the present application needs to be trained before use. The data set used is derived from the STEAD (Stanford) earthquake data set and the TXED (Texas) earthquake data set. The STEAD data set is recorded by 2613 receivers (seismographs) around the world and contains earthquake event signals and noise data. The TXED data set includes seismic waveform and noise records in the Texas region of the United States. The present application focuses on the analysis of seismic phenomena, so only the part of the data set related to seismic signals is selected. In these two data sets, each waveform has three channels, representing east-west, north-south, and vertical direction recordings, with a duration of 60 seconds and a sampling frequency of 100 Hz.

[0095] For each three-component seismic waveform data, the 30-second time window data from 1 second before to 29 seconds after the P-wave first arrival time is extracted. The selected magnitude unit is ML, and the selected magnitude data covers from slight shaking to moderate intensity earthquakes, with a specific numerical range of 0 to 5.5. In the STEAD earthquake data set, a total of 517216 seismic waveforms are obtained, and in the TXED earthquake data set, a total of 197553 seismic waveforms are obtained.

[0096] To further ensure the stability and generalization ability of model training, the labeled data set is randomly divided into three parts: training set (85% of the total), validation set (5% of the total), and test set (10% of the total). The training set is mainly used for preliminary learning and parameter adjustment of the model; the validation set is used for stage evaluation during model training to timely discover and correct possible overfitting or underfitting problems; and the test set is used as the final test standard to comprehensively evaluate the performance and accuracy of the model.

[0097] The loss function used by the system for natural earthquake magnitude estimation in the embodiment of the present application is the square loss function, which can be represented as: wherein, N represents the number of samples, y represents the true value of the i-th sample, x represents the predicted value of the i-th sample.

[0098] ​​The application uses the determinate coefficient (R2), mean, root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE) as evaluation criteria for the prediction results. The R2 coefficient is used to measure the degree of fitting of the regression model to the data, with a maximum value of 1 and a minimum value of 0. The closer the value is to 1, the better the model, and the closer the value is to 0, the worse the model. It can be represented as: , represents the mean of the true values.

[0099] The mean is represented as the average of the difference between the true value and the predicted value, which can be represented as: ;

[0100] The root mean square error is used to measure the deviation between the predicted value and the true value, and is sensitive to outliers in the data. It can be represented as: ;

[0101] The mean absolute error measures the average absolute difference between the predicted value and the true value, which can be represented as: .

[0102] The mean absolute percentage error calculates the percentage deviation between the predicted value and the true value to provide a clear measure, which can be represented as: .

[0103] Referring to Table 1, the performance comparison results of the MagNet model (Magnitude Estimation Network), CNN model (Convolutional Neural Network), ViT model (Vision Transformer), and the system of the application in the earthquake magnitude estimation task on the STEAD dataset. From the five key evaluation indicators of R2, Mean, RMSE, MAE, and MAPE, the system of the application shows significant advantages: the R2 coefficient reaches 0.9331, indicating that the model has strong explanatory power; the Mean value is -0.0022, which is closest to the ideal zero value; and it also leads in other indicators (RMSE=0.1874, MAE=0.1300, MAPE=19.27%). In contrast, the ViT model performs secondly, while the MagNet model and the CNN model have obvious gaps in each indicator. This comparison result fully proves the superior performance of the application in the earthquake magnitude estimation task.

[0104] Table 1 is a comparison of the performance of the MagNet model, the CNN model, the ViT model and the system of the present application in estimating the earthquake magnitude on the STEAD dataset.

[0105]

[0106] Table 2 shows the performance comparison results of the MagNe model, the CNN model, the ViT model and the present application on the TXED dataset. From the five key evaluation indicators of R2, Mean, RMSE, MAE and MAPE, the present application shows overall advantages: the R2 coefficient reaches 0.9175, the Mean value is 0.0044, which is closest to the ideal zero value; at the same time, it also leads in other indicators (RMSE = 0.1667, MAE = 0.1193, MAPE = 10.00%). The ViT model ranks second with an R2 coefficient of 0.9062 and an MAPE of 10.66%, while the MagNet model and the CNN model have relatively weak indicators, and the MAPE of the MagNet model is as high as 24.12%. This comparison result fully proves the excellent performance of the present application on the TXED dataset.

[0107] Table 2 Comparison results of different models on TXED dataset

[0108]

[0109] On the other hand, the embodiment of the present application provides a method for natural earthquake magnitude estimation, comprising:

[0110] The three-component seismic waveform data is subjected to multi-layer feature extraction and dimension compression through three cascaded convolution modules; after the extracted features are further compressed through the pooling layer, the earthquake magnitude estimation result is finally output through the full connection layer and the ReLU activation function;

[0111] Each convolution module is followed by a DS-Mamba module, which captures the long-time sequence dependence of the three-component seismic waveform data through state space modeling, and focuses on local detailed features using deep separable convolution.

[0112] In an embodiment, the DS-Mamba module performs layer normalization processing on the input data, mapping the input data to first data with a standard normal distribution with a mean of 0 and a variance of 1;

[0113] The first data is subjected to time sequence modeling, and by dynamically adjusting the parameters, the key seismic phase features in the first data are roughly extracted to form second data;

[0114] The second data is layer normalized to third data;

[0115] The local features in the third data single channel are extracted by deep convolution to form fourth data, and the third data and the fourth data are fused by point-by-point convolution to output the estimated magnitude data.

[0116] In an embodiment, the first data is time-series modeled, and key seismic phase features in the first data are roughly extracted by dynamically adjusting parameters to form second data, including:

[0117] The first data is mapped to a high-dimensional feature space by a fully connected layer;

[0118] The first data in the high-dimensional feature space is quickly scanned by a one-dimensional convolution layer to capture key seismic phase features;

[0119] The key seismic phase features are strengthened by a smooth nonlinear transformation;

[0120] The strengthened key seismic phase features are extracted from the first data by a state space model;

[0121] The key seismic phase features are dimensionally reduced and output.

[0122] In an embodiment, the state space model includes a state equation and an output equation, and the continuous time form of the state equation and the output equation is represented as:

[0123] , wherein is a state matrix, is an input matrix, is an output matrix, is a time-continuous input signal, is a hidden state, is a time-continuous output signal, is a derivative of the time-continuous hidden state ;

[0124] The state equation and the output equation are discretized to obtain: , wherein is a discretized state matrix, is a discretized input matrix, is an identity matrix, is a discretized sampling interval, is a hidden state at a time after discretization, is a hidden state at a time after discretization, is an input signal at a time after discretization, is an output signal at a time after discretization;

[0125] The discretized state matrix and the discretized sampling interval are dynamically adjusted according to the input signal.

[0126] In an embodiment, the discretized state matrix and the discretized sampling interval are dynamically adjusted according to the input signal, comprising:

[0127] The discretized sampling interval and the discretized input matrix are adjusted in an initial stage, and noise and early P waves are skipped.

[0128] When the P wave arrives, the discretized sampling interval is reduced, the discretized input matrix is increased, and the extraction of P wave characteristics is enhanced.

[0129] Between the time when the P wave arrives and the time when the S wave arrives, the discretized sampling interval and the discretized input matrix are dynamically adjusted, and useful information is monitored.

[0130] When the S wave arrives, the discretized sampling interval is adjusted to a minimum value, and the discretized input matrix is adjusted to a maximum value.

[0131] After the S wave, the discretized sampling interval is gradually increased and the discretized input matrix is gradually reduced, and in combination with the hidden state at time , the decay tail wave is quickly ignored.

[0132] The method of the present application effectively captures long-distance dependencies. With the help of a dynamic selective mechanism, the key features in the waveform are adaptively focused. While effectively reducing the network parameter amount, higher evaluation indicators are obtained, and more accurate estimation of the magnitude is achieved.

[0133] The above only describes the preferred embodiments of the present application and is not intended to limit the present application. Any modifications, equivalent replacements and improvements made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A method for estimating the magnitude of natural earthquakes, characterized in that, include: The three-component seismic waveform data is processed through three cascaded convolutional modules for multi-layer feature extraction and dimensionality compression. After further compression of the extracted features by pooling layers, the magnitude estimation result is finally output through fully connected layers and the ReLU activation function. Each convolutional module is followed by a DS-Mamba module, which captures long-term temporal dependencies of three-component seismic waveform data through state-space modeling and focuses on local detailed features using depthwise separable convolution.

2. The method for estimating the magnitude of a natural earthquake according to claim 1, characterized in that, The DS-Mamba module performs layer normalization on the input data, mapping the input data to the first data of a standard normal distribution with a mean of 0 and a variance of 1. Time series modeling is performed on the first data, and key seismic phase features in the first data are roughly extracted by dynamically adjusting parameters to form the second data; The second data layer is normalized to the third data layer; The third data is extracted by deep convolution to form the fourth data, and the third data and the fourth data are fused by pointwise convolution to output the estimated magnitude data.

3. The method for estimating the magnitude of a natural earthquake according to claim 1, characterized in that, Time-series modeling is performed on the first data. By dynamically adjusting parameters, key seismic phase features in the first data are roughly extracted to form the second data, including: The first data is mapped to a high-dimensional feature space through a fully connected layer; The first data in the high-dimensional feature space is quickly scanned by a one-dimensional convolutional layer to capture key seismic phase features. Key seismic phase characteristics are enhanced through smooth nonlinear transformations; Enhanced key seismic phase features were extracted from the first data using a state-space model. The key seismic phase features are reduced in dimension and output.

4. The method for estimating the magnitude of a natural earthquake according to claim 3, characterized in that, The state-space model includes state equations and output equations, which are expressed in continuous-time form as follows: ,in The state matrix, For the input matrix, For the output matrix, For a time-continuous input signal, For a time-continuous hidden state, For time-continuous output signals, Hidden state with continuous time The derivative; Discretizing the state equation and output equation yields: ,in, The state matrix is ​​the discretized state matrix. The input matrix is ​​discretized. It is the identity matrix. For the discretized sampling interval, For the discretized time... The hidden state, For the discretized time... The hidden state, For the discretized time... The input signal, For the discretized time... The output signal; The discretized state matrix and the discretized sampling interval are dynamically adjusted according to the input signal.

5. The method for estimating the magnitude of a natural earthquake according to claim 4, characterized in that, The discretized state matrix and the discretized sampling interval are dynamically adjusted according to the input signal, including: In the initial stage, the sampling interval of the discretization is adjusted to a maximum value and the input matrix after discretization is adjusted to a minimum value to skip noise and early P-waves; When the P-wave arrives, decrease the discretization sampling interval and increase the discretized input matrix; Between the arrival times of the P-wave and the S-wave, the discretized sampling interval and the discretized input matrix are dynamically adjusted. When the S-wave arrives, the discretized sampling interval is adjusted to a minimum value, and the discretized input matrix is ​​set to a maximum value. After the S-wave passes, the discretized sampling interval is gradually increased and the discretized input matrix is ​​gradually decreased.

6. A system for estimating the magnitude of natural earthquakes, characterized in that, include: Three cascaded convolutional modules perform multi-layer feature extraction and dimensionality compression on the three-component seismic waveform data; The DS-Mamba module, which is attached after each convolutional module, captures the long temporal dependencies of the three-component seismic waveform data through state space modeling and focuses on local detailed features using depthwise separable convolution. Pooling layers further compress the extracted features; The first fully connected layer and ReLU activation function output magnitude estimates based on the characteristics of further compression.

7. The system for estimating the magnitude of natural earthquakes according to claim 6, characterized in that, The DS-Mamba module includes: The first-level normalization module performs layer normalization processing on the input data, mapping the input data to the first data of a standard normal distribution with a mean of 0 and a variance of 1; The Mamba module performs time-series modeling on the first data and, by dynamically adjusting parameters, roughly extracts key seismic phase features from the first data to form the second data. The second-level normalization module normalizes the second data layer into the third data; The depthwise separable convolution module extracts local features within a single channel of the third data through depthwise convolution to form the fourth data. The fourth data is then fused with the third data and the fourth data through pointwise convolution to output the estimated magnitude data.

8. The system for estimating the magnitude of natural earthquakes according to claim 7, characterized in that, The Mamba module includes: The second fully connected layer maps the first data to a high-dimensional feature space; One-dimensional convolutional layers rapidly scan the first data in the high-dimensional feature space to capture key seismic phase features; The first SiLU activation function enhances key seismic phase characteristics through smooth nonlinear transformation; State-space model, extracting enhanced key seismic phase features from the first data; The third fully connected layer reduces the dimensionality of key seismic phase features for output.

9. The system for estimating the magnitude of natural earthquakes according to claim 8, characterized in that, The state-space model includes state equations and output equations, which are expressed in continuous-time form as follows: ,in The state matrix, For the input matrix, For the output matrix, For time-continuous input signals, In hidden state, For time-continuous output signals, Hidden state with continuous time The derivative; Discretizing the state equation and output equation yields: ,in, The state matrix is ​​the discretized state matrix. The input matrix is ​​discretized. It is the identity matrix. For the discretized sampling interval, For the discretized time... The hidden state, For the discretized time... The hidden state, For the discretized time... The input signal, For the discretized time... The output signal; The discretized state matrix and the discretized sampling interval are dynamically adjusted according to the input signal.

10. The system for estimating the magnitude of natural earthquakes according to claim 9, characterized in that, The discretized state matrix and the discretized sampling interval are dynamically adjusted according to the input signal, including: In the initial stage, the discretized sampling interval and the discretized input matrix are adjusted to skip noise and early P-waves; When the P-wave arrives, decrease the discretization sampling interval and increase the discretized input matrix; Between the arrival times of the P-wave and the S-wave, the discretized sampling interval and the discretized input matrix are dynamically adjusted. When the S-wave arrives, the discretized sampling interval is adjusted to a minimum value, and the discretized input matrix is ​​set to a maximum value. After the S-wave passes, the discretized sampling interval is gradually increased and the discretized input matrix is ​​gradually decreased.

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