A multi-modal deep learning earthquake early warning epicenter distance estimation method and system

Abstract

The application discloses a multi-modal deep learning earthquake early warning epicentral distance estimation method and system, belonging to the technical field of earthquake early warning. Three-component acceleration waveforms containing P-wave first arrival are obtained, and after baseline correction, P-wave picking, real-time simulation filtering and unified instrument response, a time window segment is intercepted; a time domain waveform, a continuous time-frequency diagram and a physical parameter sequence three-mode input are constructed, features are extracted by an LSTM, a two-dimensional convolution and a one-dimensional convolution branch respectively, and after intermediate weighted fusion, the epicentral distance is output by a multilayer perception machine regression; a 1-10 second progressive network instance is configured to update rollingly. The application can independently measure and calculate by a single station, multi-dimensional information is fused to improve the epicentral distance estimation precision and stability, and supports earthquake early warning damage range evaluation.

Description

Technical Field

[0001] This invention belongs to the field of earthquake early warning and strong ground motion signal processing technology, specifically involving a multimodal deep learning method and system for estimating epicentral distance in earthquake early warning. Background Technology

[0002] Earthquake early warning systems issue alerts seconds to tens of seconds before destructive ground motion, serving as an effective means of mitigating earthquake disasters. Rapid and accurate estimation of the epicentral distance is one of the most challenging aspects, as the assessment of potential damage and the strategy for issuing early warning information largely depend on this parameter. Current technologies for epicentral distance estimation have generally developed along two lines. The first line is the traditional empirical method, represented by the B-Δ and C-Δ methods. This method involves fitting a function to the acceleration envelope within seconds of the P-wave's arrival and then estimating the epicentral distance based on the empirical relationship between the fitting coefficients and the epicentral distance. Researchers both domestically and internationally have established corresponding empirical formulas for the strong ground motion record rate in China. The second approach is data-driven machine learning methods. For example, the epicentral distance estimation device disclosed in NEC Corporation's authorized patent CN109416408B trains a learning model based on the correspondence between waveform data and epicentral distance and estimates the epicentral distance over time periods. Another example is the research on single-station epicentral distance estimation based on convolutional neural networks, which directly extracts features from the original waveform as input. Yet another example is the research on single-station estimation using dozens of artificial features extracted from P-wave signals as input to shallow models such as random forests, gradient boosting, or support vector machines. All of these have achieved accuracy superior to traditional empirical methods.

[0003] However, existing technologies still face the following objective problems at the technical level. First, traditional empirical methods rely solely on a single fitting coefficient of the initial envelope of P-waves and depend on linear assumptions. This leads to a significant decrease in estimation accuracy when seismic wave propagation paths are complex or when background noise interference is significant. Second, while existing deep learning-based epicentral distance estimation schemes have begun to attempt to integrate multimodal information such as waveforms and seismic parameters, current multimodal frameworks are primarily geared towards magnitude classification or general early warning tasks. They have not yet addressed the combined challenges of unifying responses from different instruments, parallel extraction of time-frequency and parametric modes, and second-by-second rolling updates within short time windows for epicentral distance regression tasks. Some schemes still rely solely on the original time-domain waveform or manually extracted parametric features, failing to fully utilize the multi-scale time-frequency features inherent in the waveform and limiting the model's ability to represent complex information. Third, shallow models relying on manually generated features require manual feature engineering, cannot automatically extract deep features from the original waveform, and are sensitive to the selection of features and kernel functions. Fourth, existing schemes have not established a fusion and complementarity mechanism between different modal information. Under low signal-to-noise ratio conditions, once a single modal feature fails, the model estimation performance will significantly decrease.

[0004] Therefore, how to unify the instrument response under the mixed input conditions of strong ground motion monitoring network and intensity meter network, and fully integrate multimodal information of time domain, time frequency domain and physical parameters, while supporting second-by-second rolling updates of short time windows after P waves, and improving the accuracy and stability of epicentral distance estimation under heterogeneous instruments, different noise levels and different epicentral distance ranges, has become an urgent technical problem to be solved in the field of earthquake early warning. Summary of the Invention

[0005] (a) Technical problems to be solved The technical problem to be solved by the present invention is to provide a multimodal deep learning-based method and system for estimating epicentral distance in earthquake early warning.

[0006] (II) Technical Solution To address the aforementioned technical problems, this invention provides a multimodal deep learning-based earthquake early warning epicentral distance estimation system, comprising a data acquisition module, a preprocessing module, a feature construction module, a multimodal estimation network, and an estimation output module. The data acquisition module is used to acquire the three-component acceleration waveform containing the first arrival of the P wave recorded by the target station; The preprocessing module is used to sequentially perform baseline correction, P-wave arrival time picking, real-time simulation filtering, and segment truncation on the three-component acceleration waveform. The segment truncation is based on the picked P-wave arrival time and extracts a waveform segment of a preset time window length from the P-wave arrival time to the time after the P-wave arrival time. The real-time simulation filtering unifies the three-component acceleration waveform into an instrument response waveform with a target natural period and a target damping ratio to eliminate response differences between different types of instruments. The feature construction module is used to construct input data for three modes from the waveform segment: using the three-component sampling sequence of the waveform segment as the time-domain waveform of the first mode; performing continuous wavelet transform on the waveform segment to obtain the time-frequency diagram as the second mode; and calculating three amplitude parameters, six energy parameters and one period parameter from the waveform segment to form the physical parameter sequence as the third mode. The multimodal estimation network is a trained network comprising a temporal feature branch, a time-frequency feature branch, a parameter feature branch, a fusion layer, and a regression layer. The temporal feature branch is a multi-layered stacked Long Short-Term Memory (LSTM) network, with batch normalization layers between adjacent LSM layers, used to extract the temporal features of the time-domain waveform. The time-frequency feature branch is a multi-layered stacked two-dimensional convolutional network used to extract the time-frequency features of the time-frequency graph. The parameter feature branch is a multi-layered stacked one-dimensional convolutional network used to extract the parameter features of the physical parameter sequence. The fusion layer... The inter-modal fusion method multiplies the one-dimensional feature vectors corresponding to the time-series features, the time-frequency features, and the parameter features by their respective preset weights and then concatenates them along the feature dimension to obtain the fused features; the regression layer is a multilayer perceptron, and its last layer uses a linear activation function to perform regression operations on the fused features to obtain the epicentral distance estimate; the preset time window length takes a value in the range of one to ten seconds, and the multimodal estimation network is configured with multiple network instances that progress second by second for different time window lengths, so as to continuously output the epicentral distance estimate at the corresponding time as the P-wave triggering time advances; The estimation output module is used to output the estimated epicentral distance.

[0007] Preferably, the preset weights are: 40% for the time-series features, 35% for the time-frequency features, and 25% for the parameter features.

[0008] Preferably, each convolutional layer in the two-dimensional convolutional network and the one-dimensional convolutional network is followed by a batch normalization layer, an activation layer, and a pooling layer in sequence.

[0009] Preferably, the real-time simulation filtering includes: performing a Fourier transform on the waveform to obtain a spectrum, multiplying the spectrum by the ratio of the target instrument transfer function to the original instrument transfer function, and then performing an inverse Fourier transform to obtain the simulated waveform; the target instrument transfer function is constructed based on the target natural period and the target damping ratio according to the frequency response of a second-order vibration system.

[0010] To address the aforementioned technical problems, this invention also provides a multimodal deep learning-based method for estimating epicentral distance in earthquake early warning systems, comprising the following steps: S1, acquire the three-component acceleration waveform containing the first arrival of the P wave recorded by the target station; S2, perform baseline correction, P-wave arrival time picking, real-time simulation filtering, and segment truncation sequentially on the three-component acceleration waveform. The segment truncation is based on the picked P-wave arrival time and extracts a waveform segment of a preset time window length from the P-wave arrival time to the time after the P-wave arrival time. The real-time simulation filtering unifies the three-component acceleration waveform into an instrument response waveform with a target natural period and a target damping ratio to eliminate response differences between different types of instruments. S3, construct input data for three modes from the waveform segment: use the three-component sampling sequence of the waveform segment as the time-domain waveform of the first mode; perform continuous wavelet transform on the waveform segment to obtain the time-frequency diagram as the second mode; calculate three amplitude parameters, six energy parameters and one period parameter from the waveform segment to form the physical parameter sequence as the third mode; S4, the input data of the three modalities are input into a trained multimodal estimation network, which includes a temporal feature branch, a time-frequency feature branch, a parameter feature branch, a fusion layer, and a regression layer. The temporal feature branch extracts the temporal features of the time-domain waveform using a multi-layer stacked long short-term memory network, and the activation values ​​between adjacent long short-term memory network layers are normalized by a batch normalization layer. The time-frequency feature branch extracts the time-frequency features of the time-frequency map using a multi-layer stacked two-dimensional convolutional network. The parameter feature branch extracts the parameter features of the physical parameter sequence using a multi-layer stacked one-dimensional convolutional network. The fusion layer multiplies the one-dimensional feature vectors corresponding to the temporal features, time-frequency features, and parameter features by their respective preset weights and then concatenates them along the feature dimension to obtain fused features. The regression layer performs regression operations on the fused features using a multilayer perceptron, and the last layer of the multilayer perceptron uses a linear activation function to output the estimated epicentral distance. S5, output the estimated epicentral distance; The preset time window length is taken from one to ten seconds. The multimodal estimation network is configured with multiple network instances that increase second by second for different time window lengths, so as to continuously output the epicentral distance estimate at the corresponding time as the P-wave triggering time progresses.

[0011] Preferably, the preset weights are: 40% for the time-series features, 35% for the time-frequency features, and 25% for the parameter features.

[0012] Preferably, the real-time simulation filtering in S2 includes: performing a Fourier transform on the waveform to obtain the spectrum, multiplying the spectrum by the ratio of the target instrument transfer function to the original instrument transfer function, and then performing an inverse Fourier transform to obtain the simulated waveform; the target instrument transfer function is constructed based on the target natural period and the target damping ratio according to the frequency response of a second-order vibration system.

[0013] Preferably, as the P-wave triggering time progresses, for each time step forward, the network instance with the corresponding time window length is called with the updated waveform segment to re-execute feature construction and estimation, and continuously outputs the epicentral distance estimate for the corresponding time.

[0014] Preferably, the method is deployed on the server or edge computing device at the earthquake early warning center or station to process the real-time waveform stream transmitted by the strong motion network or intensity meter network. When the target station is in a single-station trigger state, S1 to S5 are executed directly with the three-component acceleration waveform of the station. The estimated epicentral distance is output without the need for multi-station network positioning. The potential damage range is delineated based on the estimated epicentral distance and the location of the target station, and early warning information is generated and sent to the early warning information release unit.

[0015] The present invention provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the aforementioned multimodal deep learning-based earthquake early warning epicentral distance estimation method.

[0016] (iii) Beneficial technical effects Compared with existing technologies, the beneficial effects of this invention are: 1. This invention addresses the mixed input scenario of strong ground motion monitoring networks and intensity meter networks. First, it unifies instrument responses through real-time simulation filtering, eliminating response differences between different types of instruments. Then, it uses three modes as network input: time-domain waveform, time-frequency graph obtained from continuous wavelet transform, and P-wave physical parameter sequence. Features are extracted by time-series feature branch, time-frequency feature branch, and parameter feature branch respectively. Unlike existing multi-modal frameworks for multi-directional magnitude classification tasks, this invention designs a three-modal branch and intermediate weighted fusion structure specifically for epicentral distance regression tasks. The time-domain waveform preserves the temporal evolution details of the signal, the time-frequency graph provides multi-scale time-frequency local features, and the physical parameter sequence reflects prior seismological knowledge. These three types of information complement each other, significantly improving the accuracy of epicentral distance estimation.

[0017] 2. In this invention, the feature vectors of the three branches are weighted and concatenated according to preset weights in the fusion layer using an intermediate fusion method. The contribution ratios of time-series features, time-frequency features, and parameter features are determined to be 40%, 35%, and 25%, respectively, based on feature importance analysis. Even when any mode is affected by noise, the other modes can still provide effective information. Comparative examples two to four use time-domain waveforms, time-frequency graphs, and physical parameter sequences to train networks with the same structure in single modes. The results show that the estimation accuracy of any mode used alone is lower than that of the three-mode fusion scheme, indicating that there is an information complementarity effect among the three types of modal features. The estimation error of the multimodal fusion model in each signal-to-noise ratio interval is lower than that of the traditional method, and the estimation results are stable for different noise levels.

[0018] 3. This invention configures multiple network instances with progressively increasing time window lengths of one to ten seconds. As the P-wave trigger time advances, the network instances of the corresponding time window length are called sequentially to continuously output estimated values. As the time window is extended, the estimation accuracy gradually converges. When the time window is ten seconds, the standard deviation of the error drops to 20.84 kilometers and the coefficient of determination rises to 0.788, realizing rapid rough estimation in the early stage of the warning and accurate correction in the later stage.

[0019] 4. This invention can directly output the estimated epicentral distance from the three-component waveform of a single station in the triggering state, without waiting for multiple stations to trigger and network positioning calculation, thus shortening the time from P-wave triggering to obtaining the epicentral distance parameter and gaining early warning time for potential damage range assessment and early warning information dissemination. Attached Figure Description

[0020] Figure 1 This is a schematic diagram of the structure of a multimodal deep learning-based earthquake early warning epicentral distance estimation system provided in an embodiment of the present invention; Figure 2 A flowchart of a multimodal deep learning-based earthquake early warning epicentral distance estimation method provided in an embodiment of the present invention. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. This invention aims to fully integrate multimodal information from the time domain, time-frequency domain, and physical parameters of seismic waveforms to improve the accuracy and stability of epicentral distance estimation in earthquake early warning under different noise levels and different epicentral distance intervals. It should be understood that the specific embodiments described herein are only for explaining the invention and are not intended to limit the invention.

[0022] I. Detailed Implementation of the System like Figure 1 As shown, the system described in this embodiment includes a data acquisition module, a preprocessing module, a feature construction module, a multimodal estimation network, and an estimation output module. The overall working principle of the system is as follows: the data acquisition module sends the waveform recorded by the target station to the preprocessing module. The preprocessed waveform is then converted into input data for three modes by the feature construction module. These three modes are respectively fed into three feature branches of the multimodal estimation network. After fusion and regression, the branch features are fused, and the estimated epicentral distance is output by the estimation output module. In terms of hardware, each of the above modules can be deployed on a server in an earthquake early warning center or on edge computing devices at the station. Except for the data acquisition module, which has a hardware connection to the station's data acquisition equipment, all other modules are implemented in the form of computer programs.

[0023] The input data for the data acquisition module comes from the strong-motion recorder or intensity meter at the target station. It processes the three-component acceleration waveform after the first arrival of the P-wave, with a sampling rate of 100 Hz, i.e., three sampling sequences in the north-south, east-west, and vertical directions. The data acquisition module connects to the station's data acquisition equipment via wired or wireless network, and transmits the continuous waveform stream to the preprocessing module after being truncated according to trigger events.

[0024] The preprocessing module receives the waveform transmitted from the data acquisition module and sequentially performs four processing steps: baseline correction, P-wave arrival time acquisition, real-time simulation filtering, and segment truncation. Baseline correction eliminates instrument drift and prevents trend terms from contaminating subsequent integral parameter calculations. P-wave arrival time acquisition utilizes a phase acquisition network combined with manual calibration to provide a time reference for segment truncation. The real-time simulation filtering performs a Fourier transform on the original waveform to obtain the spectrum, multiplies it by the ratio of the target instrument transfer function to the original instrument transfer function, and then performs an inverse Fourier transform to obtain the simulated waveform. The transfer function is constructed based on the instrument's natural period and damping ratio according to the frequency response of a second-order vibration system. The real-time simulation filtering uniformly simulates the waveform with a period of one second and a damping ratio of 0.707. The acceleration response is optimized to eliminate differences in response between different instruments. This filtering is achieved through frequency domain multiplication. To maintain no phase shift at the arrival time of the seismic phase, a zero-phase filtering strategy is adopted, i.e., the waveform is forward-filtered and then reverse-filtered, or non-causal zero-phase processing is achieved through look-ahead buffering. The resulting processing delay does not exceed one sampling interval (ten milliseconds at 100 Hz sampling), and does not affect the earthquake early warning timeliness. Segment extraction is based on the arrival time of the picked P-wave, extracting waveform segments from the P-wave arrival time to a preset time window length, with the preset time window length ranging from one to ten seconds. The preprocessed waveform segments are then transmitted to the feature construction module.

[0025] The feature construction module transforms waveform segments into input data in three modalities. The first modality is the time-domain waveform, i.e., the three-component sampling sequence of the waveform segment itself, with its tensor organized by batch number, sampling point number, and component number. The second modality is the time-frequency plot, obtained by performing a continuous wavelet transform on the waveform segment. The mother wavelet is the Morlet wavelet, which combines the localization analysis capabilities of the time and frequency domains, and can characterize the multi-scale abrupt changes of non-stationary signals like seismic signals. Its tensor is organized by batch number, frequency number, sampling point number, and component number. The third modality is the physical parameter sequence, calculated from the waveform within a preset time window after the P-wave arrival. Ten physical parameters are calculated and arranged in a fixed order to form a one-dimensional vector, namely: peak vertical acceleration (in gal); peak vertical velocity (in cm / s); peak vertical displacement (in cm); cumulative absolute velocity (in cm / s); and integral of squared acceleration (in gal). 2 • Second; integral of the square of velocity, in centimeters 2 / second; integral of the square of displacement, in centimeters. 2• Seconds; destructive intensity, which is the instrumental seismic intensity, calculated according to the instrumental intensity calculation method specified in the Chinese Seismic Intensity Table (GB / T 17742), obtained by converting peak acceleration and peak velocity, or calculated by the Japan Meteorological Agency intensity calculation method (JMA intensity) from the acceleration time history integral; Arias intensity, in centimeters per second; characteristic period, in seconds; the ten parameters are Z-score standardized according to the mean and standard deviation of the training set statistics before being input into the network to eliminate dimensional differences. The characteristic period reflects the dominant periodic characteristics of the waveform and is calculated as follows: the autocorrelation function of the vertical velocity waveform within a preset time window after the first arrival of the P-wave is obtained, and the time interval corresponding to the first zero crossing point of the autocorrelation function is taken, or according to... The calculation is performed, where a and v are the acceleration and velocity time histories, respectively, and the integration interval is the preset time window. The input data for the three modes are transmitted to the corresponding branches of the multimodal estimation network.

[0026] The multimodal estimation network is the core of the system described in this embodiment, including a temporal feature branch, a time-frequency feature branch, a parameter feature branch, a fusion layer, and a regression layer. The temporal feature branch processes time-domain waveforms and employs a six-layer stacked Long Short-Term Memory (LSTM) network. The number of units in each layer is 32, 64, 64, 128, 128, and 256, respectively. Batch normalization layers are set between adjacent layers to stabilize the inter-layer activation value distribution and accelerate convergence. A dropout layer with a dropout rate of 0.2 is set after the final batch normalization layer. L2 regularization is applied to each layer, and the weights are initialized using a truncated normal distribution. The gating mechanism of the LSM network can capture the temporal dependencies in the waveform and extract the long-term evolution pattern of the signal. The time-frequency feature branch processes the time-frequency map using six stacked 2D convolutional layers with a kernel size of 4x4. The number of kernels is 64, 128, 128, 256, 256, and 512, respectively, with a stride of 1. Each convolutional layer is followed by a batch normalization layer, a modified linear unit activation layer, and an average pooling layer with a stride of 2. The final output is a 1D feature vector after a flattening layer. The local receptive field of the 2D convolution can extract multi-scale local time-frequency features from the time-frequency map. The parametric feature branch processes the physical parameter sequence using four stacked 1D convolutional layers with a kernel number of 64, 128, 128, and 256, respectively. The remaining configuration is the same as the time-frequency feature branch. The 1D convolution can extract combined features between parameters along the parameter sequence dimension.

[0027] The fusion layer employs an intermediate fusion approach, concatenating the feature vectors output from the three branches according to preset weights to obtain the fused features. This intermediate fusion avoids the training instability caused by mutual interference between gradient propagation of different modes in early fusion, and overcomes the weakness in cross-modal correlation capture capability of late-stage fusion. The preset weights were determined through feature importance analysis: temporal features account for 40%, time-frequency features for 35%, and parametric features for 25%. This ratio indicates that the temporal waveform is the mode with the most information in epicentral distance estimation, while time-frequency and parametric features support stable estimation results under low signal-to-noise ratio conditions. The regression layer is a multilayer perceptron, comprising three fully connected layers. The first two layers use modified linear unit activation with a dropout rate of 0.2, while the last layer uses a linear activation function to output the epicentral distance estimate. All fully connected layers are subject to L2 regularization with a decay coefficient of 0.01. The network training uses the Adam optimizer with a learning rate of 0.001, a batch size of 128, and a loss function of mean squared error. Ten percent of the training data is randomly divided into a validation set. An early stopping strategy is adopted: when the validation set loss does not decrease for ten consecutive rounds, the training is terminated and the model weights with the best validation performance are saved.

[0028] The estimation output module receives the epicentral distance estimate from the regression layer and transmits it to the earthquake early warning information release unit according to the early warning service protocol for use in potential damage range assessment and early warning information release. In scenarios where multiple network instances are deployed, the estimation output module outputs a sequence of estimated values ​​corresponding to the time window length according to the trigger time, so as to realize the continuous updating of the estimation results as the waveform arrives.

[0029] II. Detailed Implementation of the Method like Figure 2 As shown, the method described in this embodiment uses the above-mentioned system as a carrier and includes steps S1 to S5 in the order of execution time.

[0030] Step S1 is executed by the data acquisition module. Its input condition is that the target station is in the triggered state. The execution action is to acquire the three-component acceleration waveform of the station including the first arrival of the P wave. The output result is the waveform data captured according to the trigger event and transmitted to the preprocessing module.

[0031] Step S2 is executed by the preprocessing module, which takes the waveform data output from S1 as input. The actions performed are, in sequence, baseline correction, P-wave arrival time acquisition, real-time simulation filtering, and segment truncation. The output is a waveform segment with the P-wave arrival time as the reference and a length of a preset time window. In this step, the real-time simulation filtering ensures that the waveforms of the seismometer, strong-motion meter, and intensity meter have uniform response characteristics, providing a consistent data foundation for cross-instrument applications.

[0032] Step S3 is executed by the feature construction module. Its input is the waveform segment output by S2. The execution action is to construct input data for three modes: using the waveform segment itself as the time domain waveform, performing continuous wavelet transform on the waveform segment to obtain the time-frequency diagram, calculating the physical parameter sequence composed of three amplitude parameters, six energy parameters and one period parameter from the waveform segment, and outputting the input data for the three modes and transmitting them to the corresponding feature branches respectively.

[0033] Step S4 is performed by a multimodal estimation network, which takes input data from three modalities as input. The actions are as follows: the temporal feature branch extracts temporal features from the time-domain waveform layer by layer using a multi-layer long short-term memory network and performs batch normalization; the time-frequency feature branch extracts time-frequency features from the time-frequency map using a multi-layer two-dimensional convolutional network; and the parametric feature branch extracts parametric features from the physical parameter sequence using a multi-layer one-dimensional convolutional network. The outputs of each convolutional layer are sequentially processed by batch normalization, activation, and pooling. The fusion layer concatenates the feature vectors from the three branches according to preset weights to obtain the fused features. The regression layer performs regression operations on the fused features using a multi-layer perceptron and outputs the epicentral distance estimate after linear activation at the final layer. This parallel processing of the three branches and the intermediate weighted fusion in this step allow the modal features to complement each other while maintaining their individual representational integrity, which is the direct technical source of improved estimation accuracy and stability.

[0034] Step S5 is executed by the estimation output module. Its input is the estimated epicentral distance value output from S4. The execution action is to output the estimated value to the early warning information release unit according to the early warning service protocol. The output result is the epicentral distance parameter that can be used for damage range assessment and early warning release. When the preset time window length is one to ten seconds and multiple network instances are configured to advance second by second, as the P-wave trigger time advances, the feature construction and estimation are re-executed with the network instance of the corresponding time window length using the updated waveform segment at each time step, and the estimated epicentral distance value at the corresponding time is continuously output.

[0035] III. Example 1: Training and Three-Second Time Window Estimation Scenarios Based on Multi-Regional Strong Seismic Data This embodiment uses a standard scenario as the basis, with the system deployed on a server at an earthquake early warning center. Data sources include strong-motion records from the Japanese K-Net and KiK-Net strong-motion networks and the China Earthquake Networks Center, totaling 6103 earthquake events with magnitudes ranging from 3.0 to 7.7 and epicentral distances within 200 kilometers, resulting in 172,777 three-component acceleration waveforms. Randomly divided by earthquake event number, 120,957 waveforms from 4270 events were used for training, and 51,820 waveforms from 1833 events were used for testing, ensuring no overlap between the training and testing sets at the event level. In the preprocessing stage, baseline correction was performed on all records. The arrival time of the P-wave was picked up using a phase-picking network, and records with large errors were manually calibrated. Real-time simulation filtering uniformly simulated the acceleration records to a response with a period of one second and a damping ratio of 0.707. A waveform segment three seconds after the arrival time of the P-wave was extracted as the baseline. In the feature construction stage, Morlet wavelet transform is used to generate a time-frequency map, and ten physical parameters are calculated from three-second waveform segments. The network structure and training configuration are as described above, with preset weights of 40% for time-series features, 35% for time-frequency features, and 25% for parameter features. Training is conducted for sixty epochs using an early stopping strategy. Test results show a coefficient of determination of 0.56, a mean absolute error of 22.18 km, and a standard deviation of 30.16 km. Within the epicentral distance ranges of 0–50 km, 50–100 km, 100–150 km, and 150–200 km, as well as within different signal-to-noise ratio ranges, the estimation error is consistently lower than that of traditional methods, and the overall prediction bias is controlled within three standard deviations.

[0036] IV. Example 2: Continuous estimation per second and verification scenario using independent earthquake cases This embodiment presents a differentiated scenario. The system is deployed on edge computing devices at the station, designed for real-time streaming of early warning data. The preset time window length ranges from one to ten seconds, increasing sequentially each second, and ten network instances are configured. After a P-wave is triggered, the network instance corresponding to the one-second time window is called in the first second to output the first estimated epicentral distance. Subsequently, for each second increment, feature construction and estimation are re-executed with the updated waveform segment, sequentially calling network instances of the corresponding time window length to continuously output estimated values ​​for ten time points. The early warning information dissemination unit uses this to achieve rolling correction of the estimation results. To verify generalization capability, twenty independent historical earthquake events not involved in the training were selected for offline testing, ranging in magnitude from 3.0 to 6.9, with epicentral distances within 200 kilometers, resulting in 1213 three-component records. The test results show that as the time window length increases from one second to ten seconds, the estimation bias distribution exhibits a significant convergence trend. The bias distribution is relatively wide under a one-second time window, becomes symmetrical around zero bias from a three-second time window onwards, and reaches its optimal state under a ten-second time window, with the standard deviation of the error decreasing to 20.84 kilometers, the mean absolute error decreasing to 13.672 kilometers, and the coefficient of determination increasing to 0.788. This scenario differs from Example 1 in deployment environment, time window configuration, and data organization, indicating that the system described in this example is equally valid under real-time deployment at the edge and continuous estimation across multiple instances.

[0037] V. Comparative Examples Comparative Example 1 uses the traditional B-Δ method, employing the same test set and using the logarithmic formula for fitting the initial acceleration envelope of the P-wave to obtain the fitting coefficients. The epicentral distance is then estimated based on the empirical relationship between the fitting coefficients and the epicentral distance. The results are: coefficient of determination 0.12, mean absolute error 32.76 km, and standard deviation of error 41.85 km. Comparative Examples 2 to 4 use single-mode ablation models, training networks with the same structure using single branches for time-domain waveforms, time-frequency graphs, and physical parameter sequences, respectively. The results are as follows: time-domain single-mode coefficient of determination 0.54, mean absolute error 23.37 km, standard deviation of error 31.08 km; time-frequency single-mode coefficient of determination 0.52, mean absolute error 24.12 km, standard deviation of error 31.97 km; parametric single-mode coefficient of determination 0.50, mean absolute error 25.09 km, standard deviation of error 32.89 km.

[0038] The performance comparison of epicentral distance estimation between the embodiments and the comparative examples is shown in the table below. As can be seen from the data in the table, all three indicators of the present invention are superior to traditional empirical methods and any single-mode scheme, and the advantage is further amplified within a ten-second time window. This indicates that the improved accuracy and stability brought about by multimodal weighted fusion stems from the information complementarity between the features of the three modalities.

[0039] Performance comparison of epicentral distance estimation between Example 1 and the comparative example on a test set of 51,820 data points Table 1(a)

[0040] Note: The data in this table are all based on the same test set of Example 1, and the test results within a three-second window after the P-wave trigger. All indicators are statistical results from 51,820 test waveforms. The training set and test set are divided according to earthquake events and have no overlap.

[0041] Example 2: Second-by-second convergence results on 1213 independent earthquake cases Table 1(b)

[0042] Note: This table is based on offline test results of 1213 three-component records from 20 independent historical earthquake events that were not included in the training; each indicator is a statistical result output by calling the corresponding network instance under the corresponding time window length.

[0043] This invention can also be implemented as a computer-readable storage medium and an electronic device. The computer-readable storage medium stores a computer program, which, when executed by a processor, implements steps S1 to S5 of the method described in this embodiment. The storage medium can be a read-only memory, random access memory, magnetic disk, or optical disk, etc. The electronic device includes a memory and a processor. The computer program stored in the memory, when executed by the processor, implements the steps of the method described in this embodiment. The electronic device can be a server in an earthquake early warning center or an edge computing device at a station.

[0044] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A multimodal deep learning-based earthquake early warning epicentral distance estimation system, comprising a data acquisition module, a preprocessing module, a feature construction module, a multimodal estimation network, and an estimation output module, characterized in that: The data acquisition module is used to acquire the three-component acceleration waveform containing the first arrival of the P wave recorded by the target station; The preprocessing module is used to sequentially perform baseline correction, P-wave arrival time picking, real-time simulation filtering and segment truncation on the three-component acceleration waveform. The segment truncation is based on the picked P-wave arrival time and truncates waveform segments from the P-wave arrival time to a preset time window length after the P-wave arrival time. The real-time simulation filter unifies the three-component acceleration waveform into an instrument response waveform with the target natural period and the target damping ratio, thereby eliminating the response differences between different types of instruments. The feature construction module is used to construct input data for three modes from the waveform segment: using the three-component sampling sequence of the waveform segment as the time-domain waveform of the first mode; performing continuous wavelet transform on the waveform segment to obtain the time-frequency diagram as the second mode; and calculating three amplitude parameters, six energy parameters and one period parameter from the waveform segment to form the physical parameter sequence as the third mode. The multimodal estimation network is a trained network, including a temporal feature branch, a time-frequency feature branch, a parameter feature branch, a fusion layer, and a regression layer; the temporal feature branch is a multi-layer stacked long short-term memory network, with a batch normalization layer between adjacent long short-term memory network layers, used to extract the temporal features of the time-domain waveform; the time-frequency feature branch is a multi-layer stacked two-dimensional convolutional network, used to extract the time-frequency features of the time-frequency map; The parameter feature branch is a multi-layer stacked one-dimensional convolutional network used to extract parameter features from the physical parameter sequence; The fusion layer multiplies the one-dimensional feature vectors corresponding to the time-series features, time-frequency features, and parameter features by their respective preset weights and then concatenates them along the feature dimension to obtain fused features. The regression layer is a multilayer perceptron, and its last layer uses a linear activation function to perform regression operations on the fused features to obtain the epicentral distance estimate. The preset time window length is taken from one second to ten seconds. The multimodal estimation network is configured with multiple network instances that progress second by second for different time window lengths to continuously output the epicentral distance estimate at the corresponding time as the P-wave triggering time advances. The estimation output module is used to output the estimated epicentral distance.

2. The multimodal deep learning-based earthquake early warning epicentral distance estimation system according to claim 1, characterized in that, The preset weights are: 40% for the time-series features, 35% for the time-frequency features, and 25% for the parameter features.

3. The multimodal deep learning-based earthquake early warning epicentral distance estimation system according to claim 1, characterized in that, In both the two-dimensional and one-dimensional convolutional networks, each convolutional layer is followed by a batch normalization layer, an activation layer, and a pooling layer in sequence.

4. The multimodal deep learning-based earthquake early warning epicentral distance estimation system according to claim 1, characterized in that, The real-time simulation filtering includes: performing a Fourier transform on the waveform to obtain the spectrum, multiplying the spectrum by the ratio of the target instrument transfer function to the original instrument transfer function, and then performing an inverse Fourier transform to obtain the simulated waveform; the target instrument transfer function is constructed based on the target natural period and the target damping ratio according to the frequency response of a second-order vibration system.

5. A multimodal deep learning-based method for estimating epicentral distance in earthquake early warning, characterized in that, Includes the following steps: S1, acquire the three-component acceleration waveform containing the first arrival of the P wave recorded by the target station; S2, perform baseline correction, P-wave arrival time picking, real-time simulation filtering and segment truncation on the three-component acceleration waveform in sequence. The segment truncation is based on the picked P-wave arrival time and truncates a waveform segment from the P-wave arrival time to a preset time window after the P-wave arrival time. The real-time simulation filter unifies the three-component acceleration waveform into an instrument response waveform with the target natural period and the target damping ratio, thereby eliminating the response differences between different types of instruments. S3, construct input data for three modes from the waveform segment: use the three-component sampling sequence of the waveform segment as the time-domain waveform of the first mode; perform continuous wavelet transform on the waveform segment to obtain the time-frequency diagram as the second mode; calculate three amplitude parameters, six energy parameters and one period parameter from the waveform segment to form the physical parameter sequence as the third mode; S4, input the input data of the three modalities into the trained multimodal estimation network, the multimodal estimation network including a temporal feature branch, a time-frequency feature branch, a parameter feature branch, a fusion layer and a regression layer; The temporal features of the temporal waveform are extracted by the temporal feature branch using a multi-layer stacked long short-term memory network. The activation values ​​between adjacent long short-term memory network layers are normalized by a batch normalization layer. The time-frequency features of the time-frequency map are extracted from the time-frequency feature branch using a multi-layer stacked two-dimensional convolutional network; The parameter features of the physical parameter sequence are extracted from the parameter feature branches using a multi-layer stacked one-dimensional convolutional network; The fusion layer multiplies the one-dimensional feature vectors corresponding to the time-series features, the time-frequency features, and the parameter features by their respective preset weights and then concatenates them along the feature dimension to obtain fused features. The regression layer performs regression operations on the fused features using a multilayer perceptron, and the last layer of the multilayer perceptron uses a linear activation function to output the estimated epicentral distance. S5, output the estimated epicentral distance; The preset time window length is taken from one to ten seconds. The multimodal estimation network is configured with multiple network instances that increase second by second for different time window lengths, so as to continuously output the epicentral distance estimate at the corresponding time as the P-wave triggering time progresses.

6. The multimodal deep learning-based earthquake early warning epicentral distance estimation method according to claim 5, characterized in that, The preset weights are: 40% for the time-series features, 35% for the time-frequency features, and 25% for the parameter features.

7. The multimodal deep learning-based earthquake early warning epicentral distance estimation method according to claim 5, characterized in that, The real-time simulation filtering described in S2 includes: performing a Fourier transform on the waveform to obtain the spectrum, multiplying the spectrum by the ratio of the target instrument transfer function to the original instrument transfer function, and then performing an inverse Fourier transform to obtain the simulated waveform; the target instrument transfer function is constructed based on the target natural period and the target damping ratio according to the frequency response of a second-order vibration system.

8. The multimodal deep learning-based earthquake early warning epicentral distance estimation method according to claim 5, characterized in that, As the P-wave triggering time progresses, for each time step forward, the network instance with the corresponding time window length is called with the updated waveform segment to re-execute feature construction and estimation, and continuously outputs the epicentral distance estimate for the corresponding time.

9. The multimodal deep learning-based earthquake early warning epicentral distance estimation method according to any one of claims 5-8, characterized in that, The method is deployed on the server or edge computing device at the earthquake early warning center or station to process the real-time waveform stream transmitted by the strong motion network or intensity meter network. When the target station is in a single-station trigger state, S1 to S5 are executed directly with the three-component acceleration waveform of that station. The estimated epicentral distance is output without the need for multi-station network positioning. Based on the estimated epicentral distance and the location of the target station, the potential damage range is delineated, early warning information is generated, and sent to the early warning information release unit.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the multimodal deep learning earthquake early warning epicentral distance estimation method according to any one of claims 5-8.

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