A method, device, equipment and medium for predicting seismic ground motion response of a mountain

Abstract

The application discloses a method, device, equipment and medium for predicting seismic response of a mountain, obtains the equivalent shear wave velocity of the ground surface of at least one position and the elevation of the position; takes any position as a to-be-predicted position, and determines the topographic slope, topographic curvature and average elevation within a preset mountain range around the to-be-predicted position based on the elevation of the at least one position; determines the topographic relative elevation of the to-be-predicted position based on the elevation and the average elevation, and determines the ridge index of the to-be-predicted position based on the topographic relative elevation and the topographic slope of the to-be-predicted position; determines the topographic correction parameter of the to-be-predicted position by using the topographic slope, the topographic curvature, the topographic relative elevation and the ridge index; determines the source distance between the source position of a current time earthquake and the to-be-predicted position, and predicts the first seismic response information by using the magnitude, the source distance, the equivalent shear wave velocity of the to-be-predicted position and the topographic correction parameter, thereby improving the prediction accuracy of the seismic response of the mountain.

Description

Technical Field

[0001] This application relates to the field of earthquake engineering technology, and in particular to a method, apparatus, equipment and medium for predicting the seismic response of a mountain. Background Technology

[0002] Among related technologies, it is possible to predict the seismic response of mountains, that is, the dynamic response of mountains under earthquake action. However, due to the special topography (such as ridges, valleys, steep slopes, faults, etc.) and complex geological conditions (such as rock and soil stratification, differences in weathering, etc.) of mountains in complex mountainous areas, the mountains will have a significant impact on the propagation of seismic waves, resulting in a large deviation in the prediction of the seismic response of mountains in complex mountainous areas. Summary of the Invention

[0003] This application provides a method, apparatus, equipment, and medium for predicting the seismic response of mountains, in order to solve the problem of large prediction deviations in the seismic response of complex mountainous areas in related technologies.

[0004] To address the aforementioned technical problems, embodiments of this application provide a method for predicting the seismic response of a mountain, comprising: Obtain the elevation of at least one location on the mountain and the equivalent shear wave velocity within a preset depth range below the surface at said location; Take any of the locations mentioned above as the location to be predicted, and determine the terrain slope, terrain curvature, and average elevation of the location to be predicted within a preset mountainous area around the location to be predicted based on the elevation of the at least one location. Based on the elevation and average elevation of the location to be predicted, the relative elevation of the terrain at the location to be predicted is determined, and based on the relative elevation and slope of the terrain at the location to be predicted, the ridge index of the location to be predicted is determined. The terrain correction parameters for the location to be predicted are determined using the terrain slope, terrain curvature, terrain relative elevation, and ridge index. The source location of the earthquake at the current time and the source distance of the location to be predicted are determined. Then, the moment magnitude of the earthquake, the source distance, the equivalent shear wave velocity corresponding to the location to be predicted, and the terrain correction parameters are used to predict the first ground motion response information of the location to be predicted.

[0005] In this embodiment, by obtaining the elevation and equivalent shear wave velocity of the mountain location, topographic parameters such as terrain slope, terrain curvature, terrain relative elevation, and ridge index are calculated, and terrain correction parameters are determined accordingly. Finally, the first ground motion response information is predicted by combining the moment magnitude, source distance, and equivalent shear wave velocity. This fully considers the influence of complex mountain terrain on seismic wave propagation and can effectively improve the prediction accuracy of mountain ground motion response.

[0006] Optionally, the method for predicting the seismic response of the mountain includes: Based on at least one of the elevation, terrain slope, terrain curvature, terrain relative elevation, and ridge index of the location to be predicted, a terrain feature vector of the location to be predicted is constructed. Acquire the initial P-wave characteristics acquired by the preset earthquake detection equipment for the earthquake and the ground motion observation information of the earthquake by the earthquake detection equipment at the current time; The terrain feature vector, the initial P-wave feature quantity, and the current time ground motion observation information are input into a preset ground motion response prediction model to obtain the second ground motion response information of the location to be predicted.

[0007] In this embodiment, by constructing a terrain feature vector and combining the initial P-wave feature quantity collected by the seismic detection equipment with real-time ground motion observation information, the second ground motion response information is obtained by inputting a preset ground motion response prediction model. This method integrates static terrain features, rapid source estimation information and real-time dynamic observation data, and solves the problem that purely data-driven models learn the statistical correlation between data and lack physical mechanism constraints.

[0008] Optionally, the seismic response prediction model stores a memory vector of input information for at least one historical time and a hidden state of the input information for the at least one historical time; the input information for the historical time includes the topographic feature vector, the initial P-wave feature quantity, and the seismic motion observation information for the historical time. The step of inputting the terrain feature vector, the initial P-wave feature quantity, and the current time seismic motion observation information into a preset seismic motion response prediction model to obtain the second seismic motion response information of the location to be predicted includes: Using the aforementioned seismic response prediction model, based on the memory vector, the terrain feature vector, the initial P-wave feature quantity, and the seismic observation information at the current time, the memory vector is updated to obtain the target memory vector of the input information at the current time. Using the earthquake ground motion response prediction model, based on the target memory vector and the hidden state of the input information at the at least one historical time, the hidden state of the input information at the current time is determined; Using the seismic response prediction model, determine the first weight of the hidden state of the input information at the current time and the second weight of the hidden state of the input information at at least one historical time. Using the earthquake ground motion response prediction model, the second earthquake ground motion response information is determined based on the first weight, the second weight, the hidden state of the input information at the current time, and the hidden state of the input information at at least one historical time.

[0009] In this embodiment, by storing the memory vector and hidden states of historical input information in the seismic ground motion response prediction model, and using an attention mechanism to determine the weights of the hidden states at the current and historical moments, the second seismic ground motion response information is finally obtained through weighted summation. This method fully utilizes the memory capacity of Long Short-Term Memory networks for temporal information and the focusing ability of attention mechanisms on key moments, enabling automatic identification of key features such as strong pulses and peak values ​​in seismic waveforms, thereby improving the accuracy and robustness of prediction.

[0010] Optionally, the method for predicting the seismic response of the mountain includes: Acquire training data and the label information of the training data; the training data includes training terrain feature vectors of training locations in a preset training mountain, initial P-wave feature quantities of the training earthquakes in the training mountain by the seismic detection equipment, and training ground motion observation information of the training earthquakes by the seismic detection equipment at the current time; the label information is the standard ground motion response information of the training data; Using the training data and its label information, a preset neural network model is trained to obtain the seismic response prediction model.

[0011] In this embodiment, by acquiring training data and label information, the neural network model is trained using the training terrain feature vector of the training mountain, the initial training P-wave feature quantity, and the training ground motion observation information to obtain a ground motion response prediction model. This method establishes an end-to-end mapping model from terrain features, P-wave features, and real-time observations of ground motion response, enabling the model to learn the nonlinear laws of ground motion response in complex mountainous areas and providing a usable model for subsequent real-time prediction.

[0012] Optionally, the step of using the training data and the label information of the training data to train a preset neural network model to obtain the seismic response prediction model includes: The training data is input into the neural network model to obtain the inferred ground motion response information of the training data; the inferred ground motion response information includes the particle acceleration of the seismic wave of the training earthquake at the training location and the Cauchy stress tensor at the training location; The data loss parameters of the inferred ground motion response information are determined using the inferred ground motion response information and the standard ground motion response information. Using the density of the soil and rock medium at the training location, the particle acceleration, the Cauchy stress tensor, and a preset body force term, the residual of the elastic wave equation for the training earthquake at the training location and within a preset range around the training location is determined. Using the preset number of physical constraint sampling points at the training location and within a preset range around the training location, as well as the residual of the elastic wave equation, the physical constraint parameters for the inferred ground motion response information are determined. Based on the preset training parameters in the neural network model, the regularization parameters for the inferred seismic response information are determined. The target loss parameter for the inferred seismic response information is determined based on the data loss parameter, the physical constraint parameter, and the regularization parameter. Based on the target loss parameters, the neural network model is adjusted to obtain the seismic response prediction model.

[0013] In this embodiment, a composite loss function is used to simultaneously optimize data loss, physical constraint loss, and regularization loss when training the neural network model. The physical constraint loss is constructed based on the residuals of the elastic wave equation, forcing the neural network predictions to satisfy this fundamental physical law. This method overcomes the shortcomings of purely data-driven models, such as lack of physical constraints and poor generalization ability in sparse data regions, significantly improving the reliability and interpretability of the model in complex mountainous areas.

[0014] Optionally, the first seismic response information is predicted using a preset physical model; the method for predicting the seismic response of the mountain includes: Using the first prediction variance preset by the physical model and the second prediction variance preset by the seismic response prediction model, the third weight of the first seismic response information and the fourth weight of the second seismic response information are determined. The initial ground motion response information of the location to be predicted is determined by using the third weight, the fourth weight, the first ground motion response information, and the second ground motion response information.

[0015] In this embodiment, the first ground motion response information predicted by the physical model and the second ground motion response information predicted by the ground motion response prediction model are fused by Bayesian weighting according to their respective prediction variances to obtain the initial ground motion response information. This achieves complementary fusion of physical mechanisms and data characteristics, resulting in a more accurate and stable initial prediction result than any single model.

[0016] Optionally, the method for predicting the seismic response of the mountain includes: Obtain the seismic motion observation information of the earthquake at any future time from the earthquake detection equipment; The initial covariance of the initial ground motion response information is determined using the third weight, the fourth weight, the first prediction variance, and the second prediction variance. Based on the ground motion observation information at any of the future times, the initial ground motion response information and the initial covariance are predicted to obtain the predicted ground motion response information and predicted covariance at any of the future times. Based on the predicted covariance, the preset observation matrix, and the preset observation noise covariance, the Kalman gain of the predicted covariance is determined, and based on the Kalman gain and the predicted ground motion response information, the target ground motion response information for any future time is determined.

[0017] In this embodiment, an extended Kalman filter is used to update the initial ground motion response information in real time. By utilizing the ground motion observation information acquired in real time in the future, the estimation of the ground motion response at the predicted location is continuously corrected through steps such as state prediction, Kalman gain calculation and state update, thereby improving the timeliness and reliability of the prediction results of the mountain ground motion response.

[0018] This application also discloses a device for predicting the seismic response of a mountain, comprising: An elevation acquisition module is used to acquire the elevation of at least one location on the mountain and the equivalent shear wave velocity within a preset depth range below the surface at the location. The terrain slope determination module is used to take any of the locations as locations to be predicted, and based on the elevation of the at least one location, determine the terrain slope, terrain curvature, and average elevation of the location to be predicted within a preset mountainous area surrounding the location to be predicted. The ridge index determination module is used to determine the relative elevation of the terrain at the location to be predicted based on the elevation and average elevation of the location to be predicted, and to determine the ridge index of the location to be predicted based on the relative elevation and slope of the terrain at the location to be predicted. The terrain correction parameter determination module is used to determine the terrain correction parameters for the location to be predicted by using the terrain slope, the terrain curvature, the terrain relative elevation and the ridge index. The first ground motion response information prediction module is used to determine the source location of the earthquake at the current time and the source distance of the location to be predicted, and to predict the first ground motion response information of the location to be predicted using the moment magnitude of the earthquake, the source distance, the equivalent shear wave velocity corresponding to the location to be predicted, and the terrain correction parameters.

[0019] Optionally, the device for predicting the seismic response of the mountain includes: The terrain feature vector construction module is used to construct a terrain feature vector of the location to be predicted based on at least one of the elevation, terrain slope, terrain curvature, terrain relative elevation and ridge index of the location to be predicted. The initial P-wave characteristic acquisition module is used to acquire the initial P-wave characteristic of the earthquake collected by the preset seismic detection equipment and the ground motion observation information of the earthquake by the seismic detection equipment at the current time. The second ground motion response information acquisition module is used to input the terrain feature vector, the initial P-wave feature quantity and the ground motion observation information at the current time into a preset ground motion response prediction model to obtain the second ground motion response information of the location to be predicted.

[0020] Optionally, the seismic response prediction model stores a memory vector of input information for at least one historical time and a hidden state of the input information for the at least one historical time; the input information for the historical time includes the topographic feature vector, the initial P-wave feature quantity, and the seismic motion observation information for the historical time. The second seismic response information acquisition module includes: The target memory vector acquisition submodule is used to update the memory vector based on the memory vector, the terrain feature vector, the initial P-wave feature quantity, and the current time ground motion observation information using the seismic response prediction model, so as to obtain the target memory vector of the input information at the current time. The hidden state determination module is used to determine the hidden state of the input information at the current time based on the target memory vector and the hidden state of the input information at least one historical time using the seismic response prediction model. The first weight determination module is used to determine the first weight of the hidden state of the input information at the current time and the second weight of the hidden state of the input information at at least one historical time using the seismic response prediction model. The second ground motion response information determination submodule is used to determine the second ground motion response information using the ground motion response prediction model, based on the first weight, the second weight, the hidden state of the input information at the current time, and the hidden state of the input information at at least one historical time.

[0021] Optionally, the device for predicting the seismic response of the mountain includes: The training data acquisition module is used to acquire training data and the label information of the training data; the training data includes training terrain feature vectors of training locations in a preset training hill, initial P-wave feature quantities of the training earthquakes in the training hills obtained by the seismic detection equipment, and training ground motion observation information of the training earthquakes obtained by the seismic detection equipment at the current time; the label information is the standard ground motion response information of the training data. The model training module is used to train a preset neural network model using the training data and the label information of the training data to obtain the seismic response prediction model.

[0022] Optionally, the model training module includes: The data input submodule is used to input the training data into the neural network model to obtain the inferred ground motion response information of the training data; the inferred ground motion response information includes the particle acceleration of the seismic wave of the training earthquake at the training location and the Cauchy stress tensor at the training location; The data loss parameter determination submodule is used to determine the data loss parameters of the inferred ground motion response information using the inferred ground motion response information and the standard ground motion response information; The physical constraint parameter determination submodule is used to determine the elastic wave equation residual of the training earthquake at the training location and within a preset range around the training location by using the density of the soil and rock medium at the training location, the particle acceleration, the Cauchy stress tensor, and a preset body force term. It also uses a preset number of physical constraint sampling points at the training location and within a preset range around the training location, as well as the elastic wave equation residual, to determine the physical constraint parameters of the inferred ground motion response information. The regularization parameter determination submodule is used to determine the regularization parameters of the inferred seismic response information based on the preset training parameters in the neural network model. The target loss parameter determination submodule is used to determine the target loss parameter of the inferred seismic response information based on the data loss parameter, the physical constraint parameter, and the regularization parameter. The model obtains a sub-module, which is used to adjust the neural network model based on the target loss parameters to obtain the seismic response prediction model.

[0023] Optionally, the first seismic response information is predicted using a preset physical model; the device for predicting the seismic response of the mountain includes: The second weight determination module is used to determine the third weight of the first ground motion response information and the fourth weight of the second ground motion response information by using the first prediction variance preset by the physical model and the second prediction variance preset by the ground motion response prediction model. The initial ground motion response information determination module is used to determine the initial ground motion response information of the location to be predicted by using the third weight, the fourth weight, the first ground motion response information, and the second ground motion response information.

[0024] Optionally, the device for predicting the seismic response of the mountain includes: The seismic motion observation information acquisition module is used to acquire the seismic motion observation information of the earthquake by the earthquake detection equipment at any future time; The initial covariance determination module is used to determine the initial covariance of the initial ground motion response information by using the third weight, the fourth weight, the first prediction variance, and the second prediction variance. The prediction covariance module is used to predict the initial ground motion response information and the initial covariance based on the ground motion observation information at any of the future times, so as to obtain the predicted ground motion response information and the predicted covariance at any of the future times. The target ground motion response information determination module is used to determine the Kalman gain of the predicted covariance based on the predicted covariance, the preset observation matrix, and the preset observation noise covariance, and to determine the target ground motion response information for any future time based on the Kalman gain and the predicted ground motion response information.

[0025] This application also discloses an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the method described in this application.

[0026] This application also discloses a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the method described in this application. Attached Figure Description

[0027] Figure 1 This is a flowchart illustrating the steps of a method for predicting the seismic response of a mountain, as provided in an embodiment of this application. Figure 2 This is a structural block diagram of a device for predicting the seismic response of a mountain, as provided in an embodiment of this application. Detailed Implementation

[0028] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.

[0029] It should be understood that the step numbers used in the text are for ease of description only and are not intended to limit the order in which the steps are performed.

[0030] To facilitate understanding of the technical solutions and effects of the embodiments of this application, the relevant technologies of this application will be briefly described below.

[0031] In related technologies, the mountains in complex mountainous areas have a significant impact on the propagation of seismic waves. The seismic ground response in different regions of the mountain may be unevenly distributed, leading to a large deviation in the prediction of the seismic ground response in complex mountainous areas. The influence of mountains in complex mountainous areas on seismic waves is mainly manifested in topographic amplification effect, focusing reflection effect, and resonance effect.

[0032] When predicting the seismic response of mountains, related technologies can be mainly divided into two categories: methods based on physical numerical simulation (such as finite difference and spectral element method) and methods based on pure data-driven methods (such as convolutional neural networks and long short-term memory networks).

[0033] However, while physical numerical simulation methods can accurately depict the propagation of seismic waves in mountains, they require the establishment of complex mathematical-physical models, resulting in a huge amount of computation. Completing a single seismic wave propagation calculation in a mountainous area typically takes several hours or even days, making it difficult to meet the real-time requirements of second-level early warning and minute-level response after an earthquake.

[0034] While purely data-driven methods offer fast inference speeds, these models learn statistical correlations between data points, lacking physical constraints. In complex mountainous regions with sparse samples, the limited number of training samples leads to poor generalization ability and unreliable predictions of extreme earthquake events. Furthermore, the outputs of purely data-driven models suffer from weak interpretability.

[0035] Furthermore, related technologies typically use seismic parameters at a single moment to statically predict mountain ground motion responses. This makes it impossible to update the prediction results and correct errors based on real-time seismic observation information during the earthquake, resulting in insufficient timeliness and reliability of the predicted mountain ground motion responses.

[0036] Reference Figure 1The flowchart illustrates the steps of a method for predicting the seismic response of a mountain, as provided in an embodiment of this application. Specifically, it may include the following steps: Step 101: Obtain the elevation of at least one location on the mountain and the equivalent shear wave velocity within a preset depth range below the surface at the location; In the embodiments of this application, the mountain may have special topography and complex geological conditions, which will have a huge impact on the propagation of seismic waves.

[0037] In this embodiment, multi-source data acquisition and preprocessing of the mountain can be performed. Specifically, the following multi-source data of the mountain can be acquired and integrated: high-resolution DEM (Digital Elevation Model) data of the mountain, engineering geological data of the mountain, historical ground motion records of the mountain, real-time strong earthquake observation data, and regional GNSS (Global Navigation Satellite System) displacement data. The spatial resolution of the DEM data is not less than 30m, preferably 10m. Spatial resolution refers to the actual ground size corresponding to each grid cell in the DEM. A spatial resolution of 10m means that one pixel represents a 10m × 10m ground area. Engineering geological data includes: soil and rock stratification of the mountain, shear wave velocity measurement data, overburden thickness, etc. The sampling rate of the real-time strong earthquake observation data is not less than 100Hz.

[0038] The data preprocessing process for multi-source data includes: time synchronization, coordinate unification, bandpass filtering (0.1-25Hz) to remove high-frequency and low-frequency noise, baseline correction, data completion, and data normalization.

[0039] The preprocessed acceleration time history of a strong earthquake can be recorded as follows: in, For the preprocessed acceleration time history, This is the original acceleration record. This is the baseline drift term.

[0040] In this embodiment, the equivalent shear wave velocity at any location within a preset depth range below the surface can be determined using the formula for calculating the equivalent shear wave velocity. The preset depth range can be 30m. The equivalent shear wave velocity reflects the hardness or softness of the soil at that location. The formula for calculating the equivalent shear wave velocity is as follows: in, Let be the equivalent shear wave velocity at any location, and n be the number of soil layers within a depth of 30m below the surface at that location. Let be the thickness of the i-th layer of soil below the surface at this location. Let be the shear wave velocity of the i-th soil layer.

[0041] Step 102: Take any of the locations as the location to be predicted, and determine the terrain slope, terrain curvature, and average elevation of the location to be predicted within a preset mountainous area around the location to be predicted based on the elevation of the at least one location. In this embodiment, any location on the mountain can be used as the location to be predicted. Based on the elevation of at least one location, the terrain slope of the location to be predicted is determined using a terrain slope calculation formula. Terrain slope reflects the degree of inclination of the earth's surface. The terrain slope calculation formula is as follows: Where x is the x-coordinate of the location to be predicted, and y is the y-coordinate of the location to be predicted. is the slope of the terrain at the location to be predicted, and z is the elevation of the location to be predicted.

[0042] The topographic curvature of a location can be determined using the formula for calculating topographic curvature. Topographic curvature reflects the degree of unevenness or depression of the Earth's surface. Ridges have negative topographic curvature, while valleys have positive topographic curvature. The formula for calculating topographic curvature is: Where C(x, y) is the terrain curvature at the location to be predicted.

[0043] In this embodiment of the application, based on the elevation of at least one location of the mountain, the average elevation within a preset mountainous area surrounding the location to be predicted can also be determined.

[0044] Step 103: Based on the elevation and average elevation of the location to be predicted, determine the relative elevation of the terrain at the location to be predicted, and based on the relative elevation and slope of the terrain at the location to be predicted, determine the ridge index of the location to be predicted. In this embodiment, the average elevation within a pre-defined mountainous area surrounding the location to be predicted is determined using a formula for calculating relative elevation. Based on the average elevation and elevation of the location to be predicted, the relative elevation of the terrain at that location can be determined. The formula for calculating relative elevation is as follows: in, The relative elevation of the terrain at the location to be predicted. Let R be the elevation of the location to be predicted, R be the radius of the preset mountainous area surrounding the location to be predicted, and Ω(R) represent the neighborhood window with radius R centered at the location to be predicted. This represents the number of grid cells within the neighborhood window. Represents the x-coordinate of any position within the neighborhood window. Represents the vertical coordinate of any position within the domain window. R represents the elevation of any location within the neighborhood window, and R can be 500 meters.

[0045] In this embodiment, based on the relative elevation and slope of the terrain at the location to be predicted, the ridge index of the location can be determined using the ridge index calculation formula. The ridge index reflects the ridge or valley landform characteristics of the location to be predicted. The ridge index calculation formula is as follows: in, This is the ridge index.

[0046] In this embodiment of the application, parameters such as the elevation of the location to be predicted, the terrain slope, the terrain curvature, the terrain relative elevation, the ridge index, and the equivalent shear wave velocity can be combined into a multidimensional feature vector F.

[0047] in, This represents the distance between the location to be predicted and the known active fault.

[0048] Step 104: Using the terrain slope, terrain curvature, terrain relative elevation, and ridge index, determine the terrain correction parameters for the location to be predicted; In this embodiment, a physical model can be constructed, and this physical model can be used to determine the first ground motion response information at the location to be predicted. The physical model, also known as the GMPE (Ground Motion Prediction Equation) model, can be: Where Y represents the first ground motion response information at the location to be predicted, including: PGA (Peak Ground Acceleration), PGV (Peak Ground Velocity), or Sa(T), etc. Peak ground acceleration is the maximum ground acceleration at the location to be predicted during an earthquake. Peak ground velocity is the maximum ground velocity at the location to be predicted during an earthquake. Sa(T) is the acceleration response spectrum value, and T is the period.

[0049] M represents the moment magnitude of the earthquake at the current time, and R represents the distance between the focal location of the earthquake at the current time and the focal location to be predicted. ε is the terrain correction term. ε is the residual term, which follows a normal distribution N(0, σ²) and represents the random error that the model cannot explain.

[0050] The regression coefficients are undetermined and can be obtained by fitting them to historical ground motion records using the least squares method. Specifically: It is the source strength reference term (constant term), used to characterize the reference site conditions (i.e., The logarithmic reference strength of seismic motion under the conditions of taking the reference value, the source distance approaching 0, and the moment magnitude M taking the reference value. is the magnitude scaling factor, used to reflect the rate at which the logarithmic amplitude of the ground motion increases linearly with the moment magnitude M, and can describe the scaling effect of the source intensity on the ground motion. The geometric diffusion and inelastic attenuation coefficients characterize the logarithmic attenuation rate caused by geometric diffusion and medium damping absorption of seismic waves as the source distance R increases. <0. This is the near-field saturation distance parameter, in km (kilometers), used to physically saturate and constrain the earthquake motion amplitude when the source distance R approaches 0, thus avoiding near-field prediction divergence. This is the site magnification factor, reflecting the equivalent shear wave velocity. The linear amplification of the logarithmic amplitude of earthquake motion is usually <0 indicates amplification in soft fields and attenuation in hard fields. The least squares fitting process is as follows: By selecting historical ground motion records, the physical model is rewritten in matrix form as the following linear observation equations: Where Y is the logarithmic ground motion observation sample vector; Let be the vector of parameters to be estimated; ε be the residual vector, which follows a normal distribution. X is the design matrix, and the i-th row of the design matrix is: [1, , , ] The steps to solve the matrix form of the linear observation equation are as follows: (1) Given Initial value (e.g.) ), construct about , , , The linear regression equation is solved using OLS (Ordinary Least Squares): (2) Fixed , , , ,right Perform a one-dimensional grid search within the interval [1, 30] km with a step size of 0.5 km to minimize the sum of squared residuals. This is the optimal solution for this step: (3) Iterate alternately between (1) and (2) until the relative change of RSS between the two iterations is less than 1. This is considered convergence.

[0051] (4) After fitting, the residuals follow the order of... σ is the logarithmic standard deviation. .

[0052] In one example: , , , , ,correspond .

[0053] Terrain correction items In This is the topographic correction factor, which can be determined through regression analysis of historical seismic motion records of the mountain. Specifically, This is the slope amplification factor (dimensionless), used to quantify the amplification effect of terrain slope on the logarithmic amplitude of seismic motion. ; This is the relative elevation magnification factor, in units of... It is used to quantify the amplification effect of relative terrain elevation on the logarithmic amplitude of ground motion, typically ; It is the ridge index amplification factor (dimensionless), used to quantify the overall amplification or attenuation effect of ridge / valley landforms; This is the curvature correction factor, in meters, used to quantify the influence of topographic curvature on the logarithmic amplitude of ground motion. The regression determination steps are as follows: (1) Sample selection: Select samples from historical strong earthquake datasets located in complex mountainous areas (S≥15° or | There are approximately 3,800 records of strong earthquakes (≥50 m). (2) Residual calculation: according to the above fitting coefficients Calculate the predicted values ​​without terrain correction and obtain the terrain residuals: (3) Multiple linear regression: For independent variable, Least squares estimation for the dependent variable : (4) Significance test: t-test (significance level α=0.05) was used for each coefficient, insignificant terms were removed and F-test was performed; (5) Cross-validation: Ten-fold cross-validation was used to verify... The stability of the mean, variance, and regression coefficients; In one example, , , , .

[0054] In the embodiments of this application, the terrain slope, terrain curvature, terrain relative elevation, and ridge index of the location to be predicted are used, and the terrain correction parameters of the location to be predicted can be determined using the calculation formula of the terrain correction term.

[0055] Step 105: Determine the epicenter location of the earthquake at the current time and the epicenter distance of the location to be predicted, and use the moment magnitude of the earthquake, the epicenter distance, the equivalent shear wave velocity corresponding to the location to be predicted, and the terrain correction parameters to predict the first ground motion response information of the location to be predicted.

[0056] In the embodiments of this application, the earthquake magnitude, focal distance, equivalent shear wave velocity corresponding to the location to be predicted, and terrain correction parameters are used to determine the first ground motion response information of the location to be predicted using a physical model.

[0057] In this embodiment, by obtaining the elevation and equivalent shear wave velocity of the mountain location, topographic parameters such as terrain slope, terrain curvature, terrain relative elevation, and ridge index are calculated, and terrain correction parameters are determined accordingly. Finally, the first ground motion response information is predicted by combining the moment magnitude, source distance, and equivalent shear wave velocity. This fully considers the influence of complex mountain terrain on seismic wave propagation and can effectively improve the prediction accuracy of mountain ground motion response.

[0058] In some embodiments of this application, the method for predicting the seismic response of the mountain includes: Based on at least one of the elevation, terrain slope, terrain curvature, terrain relative elevation, and ridge index of the location to be predicted, a terrain feature vector of the location to be predicted is constructed. Acquire the initial P-wave characteristics acquired by the preset earthquake detection equipment for the earthquake and the ground motion observation information of the earthquake by the earthquake detection equipment at the current time; The terrain feature vector, the initial P-wave feature quantity, and the current time ground motion observation information are input into a preset ground motion response prediction model to obtain the second ground motion response information of the location to be predicted.

[0059] In this embodiment of the application, the seismic response prediction model is a data-driven model.

[0060] In this embodiment, the topographic feature vector of the location to be predicted, the initial P-wave feature quantity acquired by the seismic detection equipment, and the seismic motion observation information of the earthquake at the current time are input into the seismic motion response model to obtain the second seismic motion response information of the location to be predicted, output by the seismic motion response model. The seismic detection equipment can be a seismic station, and the initial P-wave feature quantity is the feature parameter extracted from the P-wave signal when the primary wave (P-wave) first arrives at the seismic detection equipment after the earthquake.

[0061] In this embodiment, by constructing a terrain feature vector and combining the initial P-wave feature quantity collected by the seismic detection equipment with real-time ground motion observation information, the second ground motion response information is obtained by inputting a preset ground motion response prediction model. This method integrates static terrain features, rapid source estimation information and real-time dynamic observation data, and solves the problem that purely data-driven models learn the statistical correlation between data and lack physical mechanism constraints.

[0062] In some embodiments of this application, the seismic response prediction model stores a memory vector of input information for at least one historical time and a hidden state of the input information for the at least one historical time; the input information for the historical time includes the topographic feature vector, the initial P-wave feature quantity, and the seismic motion observation information for the historical time. The step of inputting the terrain feature vector, the initial P-wave feature quantity, and the current time seismic motion observation information into a preset seismic motion response prediction model to obtain the second seismic motion response information of the location to be predicted includes: Using the aforementioned seismic response prediction model, based on the memory vector, the terrain feature vector, the initial P-wave feature quantity, and the seismic observation information at the current time, the memory vector is updated to obtain the target memory vector of the input information at the current time. Using the earthquake ground motion response prediction model, based on the target memory vector and the hidden state of the input information at the at least one historical time, the hidden state of the input information at the current time is determined; Using the seismic response prediction model, determine the first weight of the hidden state of the input information at the current time and the second weight of the hidden state of the input information at at least one historical time. Using the earthquake ground motion response prediction model, the second earthquake ground motion response information is determined based on the first weight, the second weight, the hidden state of the input information at the current time, and the hidden state of the input information at at least one historical time.

[0063] In this embodiment of the application, the input sequence of the seismic ground motion response prediction model can be (t=1, 2, ..., T). Where, The input information at time t includes: the terrain feature vector F of the location to be predicted, the initial P-wave feature quantity, and the ground motion observation information at the current time.

[0064] The seismic response prediction model can be obtained by training a BiLSTM-Attention (Bidirectional Long Short-Term Memory-Attention) neural network model that combines attention mechanisms.

[0065] The seismic ground motion response prediction model incorporates memory units, which store memory vectors of the input information. The core calculations of the seismic ground motion response prediction model are as follows: (1) Gate of Oblivion: Among them, f t The output vector of the forget gate determines the memory vector c of the input information from the previous time step. t−1 The degree to which each element is forgotten. σ is the Sigmoid activation function. W f The weight matrix of the forget gate. t−1 The hidden state of the input information from the previous time step represents the encoded summary of the input information from the previous time step by the seismic ground motion response prediction model. t : Input information for the current time. b f : The bias vector of the forget gate.

[0066] (2) Input gate: Among them, i t The output vector of the input gate determines the current candidate memory cell. The memory vector written into the memory unit The proportion. Let be the weight matrix of the input gate. is the bias vector of the input gate.

[0067] (3) Candidate memory units: in, : Candidate memory cell vector, representing the new memory vector to be written to the memory cell at the current time. This is the weight matrix for candidate memory units. is the bias vector for candidate memory cells.

[0068] (4) Memory cell state update: in, : The memory vector of the memory unit at the current time. : The memory vector of the memory unit in the previous time.

[0069] (5) Output gate: in, The output vector of the output gate determines how much information in the memory vector of the memory cell at the current time is output as a hidden state. .

[0070] (6) Hidden state output: The hidden state of the input information at the current time represents the encoded summary of the current and historical inputs by the seismic ground motion response prediction model.

[0071] In this embodiment, the seismic response prediction model stores a memory vector of input information for at least one historical time and a hidden state of input information for at least one historical time. The input information for historical time includes topographic feature vectors, initial P-wave features, and historical seismic observation information.

[0072] The seismic ground motion response prediction model can update the memory vector based on the input information from at least one historical time and the input information at the current time, thus obtaining the target memory vector for the input information at the current time. Based on the target memory vector and the hidden state of the input information from at least one historical time, the hidden state of the input information at the current time is determined. It should be noted that the hidden state of the input information at the current time is obtained by the seismic ground motion response prediction model running two independent LSTM networks in parallel to process the forward and reverse time series information respectively, and then concatenating the hidden states of the two networks. This ensures that the hidden state of the input information at each time simultaneously contains both past and future contextual information.

[0073] in, The hidden state output by the forward LSTM at time t is calculated in chronological order t=1→T, encoding information from the start time to the current time. The hidden state output by the inverse LSTM at time t is calculated in reverse time order t=T→1, encoding information from the termination time to the current time.

[0074] The seismic response prediction model introduces an attention mechanism to adaptively assign a first weight to the hidden state of the current input information and a second weight to the hidden state of the input information from at least one historical time.

[0075] in, The attention at time t is scored, representing the importance of the hidden state at that time; v is the projection vector of the attention layer; This is the weight matrix of the attention layer; : Bias vector of the attention layer. This is for normalized attention weights.

[0076] Using a seismic ground motion response prediction model, based on the first weight, the second weight, the hidden state of the input information at the current time, and the hidden state of the input information at at least one historical time, the second seismic ground motion response information can be determined.

[0077] in, This is the second ground motion response information.

[0078] In this embodiment, by storing the memory vector and hidden states of historical input information in the seismic ground motion response prediction model, and using an attention mechanism to determine the weights of the hidden states at the current and historical moments, the second seismic ground motion response information is finally obtained through weighted summation. This method fully utilizes the memory capacity of Long Short-Term Memory networks for temporal information and the focusing ability of attention mechanisms on key moments, enabling automatic identification of key features such as strong pulses and peak values ​​in seismic waveforms, thereby improving the accuracy and robustness of prediction.

[0079] In some embodiments of this application, the method for predicting the seismic response of the mountain includes: Acquire training data and the label information of the training data; the training data includes training terrain feature vectors of training locations in a preset training mountain, initial P-wave feature quantities of the training earthquakes in the training mountain by the seismic detection equipment, and training ground motion observation information of the training earthquakes by the seismic detection equipment at the current time; the label information is the standard ground motion response information of the training data; Using the training data and its label information, a preset neural network model is trained to obtain the seismic response prediction model.

[0080] In this embodiment of the application, the seismic response prediction model can be obtained by training a BiLSTM-Attention neural network model.

[0081] In this embodiment of the application, training data and label information of the training data can be obtained, and the BiLSTM-Attention neural network model can be trained using the training data and label information to obtain a seismic response prediction model.

[0082] In this embodiment, by acquiring training data and label information, the neural network model is trained using the training terrain feature vector of the training mountain, the initial training P-wave feature quantity, and the training ground motion observation information to obtain a ground motion response prediction model. This method establishes an end-to-end mapping model from terrain features, P-wave features, and real-time observations of ground motion response, enabling the model to learn the nonlinear laws of ground motion response in complex mountainous areas and providing a usable model for subsequent real-time prediction.

[0083] In some embodiments of this application, the step of using the training data and the label information of the training data to train a preset neural network model to obtain the seismic response prediction model includes: The training data is input into the neural network model to obtain the inferred ground motion response information of the training data; the inferred ground motion response information includes the particle acceleration of the seismic wave of the training earthquake at the training location and the Cauchy stress tensor at the training location; The data loss parameters of the inferred ground motion response information are determined using the inferred ground motion response information and the standard ground motion response information. Using the density of the soil and rock medium at the training location, the particle acceleration, the Cauchy stress tensor, and a preset body force term, the residual of the elastic wave equation for the training earthquake at the training location and within a preset range around the training location is determined. Using the preset number of physical constraint sampling points at the training location and within a preset range around the training location, as well as the residual of the elastic wave equation, the physical constraint parameters for the inferred ground motion response information are determined. Based on the preset training parameters in the neural network model, the regularization parameters for the inferred seismic response information are determined. The target loss parameter for the inferred seismic response information is determined based on the data loss parameter, the physical constraint parameter, and the regularization parameter. Based on the target loss parameters, the neural network model is adjusted to obtain the seismic response prediction model.

[0084] In this embodiment, training data can be input into a neural network model to obtain inferred ground motion response information from the training data. The inferred ground motion response information may include the particle acceleration of the seismic waves of the training earthquake at the training location and the Cauchy stress tensor at the training location.

[0085] In the embodiments of this application, inferred ground motion response information and standard ground motion response information can be used, and the data loss parameters of the inferred ground motion response information can be determined using the calculation formula of the data loss parameters.

[0086] in, Let i be the data loss parameter, and i represent the i-th training sample in the training data. For the inferred seismic response information of the i-th training sample, This represents standard ground motion response information, where N is the total number of training samples.

[0087] In the embodiments of this application, the physical constraint parameters can be determined by using the calculation formula of the physical constraint parameters to infer the seismic response information.

[0088] in, Here, M represents the number of physical constraint sampling points, and j represents the j-th physical constraint sampling point. Let be the density of the soil / rock medium, ü be the second time derivative of the particle acceleration, σ be the Cauchy stress tensor, and f be the body force term.

[0089] In this embodiment of the application, the regularization parameters for inferring seismic response information can be determined based on the preset training parameters in the neural network model.

[0090] in, Here, θ is the regularization parameter, and θ represents all trainable parameters of the neural network.

[0091] In this embodiment of the application, a composite loss function is designed to ensure that the neural network prediction results conform to the physical mechanism constraints: in, , , These are the weighting coefficients. It can be 1.0. It can be 0.1. It can be 0.001. The target loss parameter.

[0092] In this embodiment, a target loss parameter for inferring seismic response information can be determined based on data loss parameters, physical constraint parameters, and regularization parameters. Based on the target loss parameter, the neural network model can be adjusted to obtain a seismic response prediction model.

[0093] In this embodiment, a composite loss function is used to simultaneously optimize data loss, physical constraint loss, and regularization loss when training the neural network model. The physical constraint loss is constructed based on the residuals of the elastic wave equation, forcing the neural network predictions to satisfy this fundamental physical law. This method overcomes the shortcomings of purely data-driven models, such as lack of physical constraints and poor generalization ability in sparse data regions, significantly improving the reliability and interpretability of the model in complex mountainous areas.

[0094] In some embodiments of this application, the first seismic response information is predicted using a preset physical model; the method for predicting the seismic response of the mountain includes: Using the first prediction variance preset by the physical model and the second prediction variance preset by the seismic response prediction model, the third weight of the first seismic response information and the fourth weight of the second seismic response information are determined. The initial ground motion response information of the location to be predicted is determined by using the third weight, the fourth weight, the first ground motion response information, and the second ground motion response information.

[0095] In this embodiment, the third weight of the first ground motion response information and the fourth weight of the second ground motion response information are determined using the first prediction variance preset by the physical model and the second prediction variance preset by the ground motion response prediction model. The third and fourth weights are determined by Bayesian variance weighting, resulting in higher weights for the high-confidence model. in, As the third weight, It is the fourth weight. The first prediction variance of the physical model. The second prediction variance of the seismic ground motion response prediction model is estimated using k-fold cross-validation on historical datasets. Weights and Dynamically adjusts with model confidence to meet + =1 In the embodiments of this application, the initial ground motion response information of the location to be predicted can be determined by using the third weight, the fourth weight, the first ground motion response information, and the second ground motion response information.

[0096] in, This is the initial ground motion response information; This is the first ground motion response information. This is the second ground motion response information.

[0097] In this embodiment, the first ground motion response information predicted by the physical model and the second ground motion response information predicted by the ground motion response prediction model are fused by Bayesian weighting according to their respective prediction variances to obtain the initial ground motion response information. This achieves complementary fusion of physical mechanisms and data characteristics, resulting in a more accurate and stable initial prediction result than any single model.

[0098] In some embodiments of this application, the method for predicting the seismic response of the mountain includes: Obtain the seismic motion observation information of the earthquake at any future time from the earthquake detection equipment; The initial covariance of the initial ground motion response information is determined using the third weight, the fourth weight, the first prediction variance, and the second prediction variance. Based on the ground motion observation information at any of the future times, the initial ground motion response information and the initial covariance are predicted to obtain the predicted ground motion response information and predicted covariance at any of the future times. Based on the predicted covariance, the preset observation matrix, and the preset observation noise covariance, the Kalman gain of the predicted covariance is determined, and based on the Kalman gain and the predicted ground motion response information, the target ground motion response information for any future time is determined.

[0099] In this embodiment, seismic motion observation information of an earthquake at any future time can be obtained from an earthquake detection device, and the seismic response information can be updated and assimilated in real time over future periods based on this seismic motion observation information. Specifically, after an earthquake occurs, the initial seismic response information at the current time is determined, and real-time seismic motion observation information collected by the earthquake detection device can be continuously received within a preset response time window. The obtained initial seismic response information is then updated in real time using an extended Kalman filter (EKF).

[0100] In extended Kalman filtering, the seismic response information at the location to be predicted can be defined as the state variable x. k Real-time ground motion observation information is defined as the observation variable z. k k represents the discrete time step index (k=0, 1, 2…), and each time step corresponds to the arrival of real-time ground motion observation information.

[0101] Extended Kalman filtering involves the following equations: (1) State prediction equation: in, : A priori estimate of the state at time k based on real-time ground motion observation information at time k−1, i.e., ground motion response information before using ground motion observation information at the current time. : State transition matrix. : The posterior estimate at time k−1, i.e., the optimal ground motion response information estimate after fusing real-time ground motion observation information at the previous time. : Control input matrix. : Control vector.

[0102] (2) Covariance prediction equation: in, : The covariance of the prior estimate represents the uncertainty of the predicted state value. : Covariance of the posterior estimate from the previous time step. The process noise covariance matrix characterizes the uncertainty of the state transition model itself (such as model error). (3) Kalman gain: in, Kalman gain; Observation matrix; : Observation noise covariance matrix.

[0103] (4) State update equation: in, Posterior state estimation is the optimal seismic response information estimate after integrating real-time seismic ground motion observation information at the current moment, and it is also the rolling prediction result at the current moment. : The observed variable at the current moment. : Observation residuals.

[0104] (5) Covariance update equation: in, The covariance of the posterior estimate represents the uncertainty after merging the observations. : Identity matrix.

[0105] In this embodiment, the seismic motion observation information of an earthquake at any future time can be obtained from the seismic detection equipment; the initial covariance of the initial seismic motion response information is determined using the third weight, the fourth weight, the first prediction variance, and the second prediction variance; based on the seismic motion observation information at any future time, the initial seismic motion response information and the initial covariance are predicted to obtain the predicted seismic motion response information and the predicted covariance at any future time; based on the predicted covariance, the preset observation matrix, and the preset observation noise covariance, the Kalman gain of the predicted covariance is determined, and based on the Kalman gain and the predicted seismic motion response information, the target seismic motion response information at any future time is determined.

[0106] In a specific example, the steps of extended Kalman filtering can be: (1) Setting variables and initial conditions State variables For: Seismic ground motion response information at the location to be predicted. Observed variables This refers to real-time ground motion observation information of earthquakes obtained by earthquake detection equipment. The response window is 0-30 seconds, and an EKF update is triggered every 1 second.

[0107] When k=0, the initial conditions are: ① Initial state values, i.e., initial ground motion response information: .

[0108] ② The initial covariance of the initial ground motion response information is determined using the third weight, the fourth weight, the first prediction variance, and the second prediction variance. : ③State transition matrix Control input matrix Control vector .

[0109] ④ Observation matrix .

[0110] ⑤ Process noise covariance ; Observation noise covariance .

[0111] (2) The k=1th update (after t=5.2s, ) ①State prediction: ; ② Covariance prediction: ; ③ Kalman gain: ; ④ Status Update: ; ⑤ Covariance Update: .

[0112] (3) The k=2nd update (after t=6.2s, ) ①State prediction: ; ② Covariance prediction: ; ③ Kalman gain: ; ④ Status Update: ; ⑤ Covariance Update: .

[0113] (4) Convergence analysis of rolling update With the continuous injection of real-time ground motion observation information, covariance Monotonically decreasing (0.071→0.020→0.016→…), state estimation Gradually approximate the measured true value (measured PGA = 5.24 m / ). Up to k=6 (approximately 10.2 s after the earthquake), The relative error decreased from 4.0% to 0.2%; the time taken for a single EKF update was less than 5ms.

[0114] In a specific example, the target seismic response information includes: (1) Peak ground acceleration (PGA); ; (2) Peak ground velocity (PGV); ; (3) Acceleration response spectrum Sa(T); ; Where T is the natural period of the single-degree-of-freedom system, ξ is the damping ratio (usually taken as 5%), ω=2π / T is the angular frequency, and u(t) is the relative displacement response of the single-degree-of-freedom system, which is obtained by solving the following vibration equation: (4) Earthquake Intensity I Based on a combined estimate using PGA and PGV: in, , , These are preset coefficients.

[0115] In this embodiment, an extended Kalman filter is used to update the initial ground motion response information in real time. By utilizing the ground motion observation information acquired in real time in the future, the estimation of the ground motion response at the predicted location is continuously corrected through steps such as state prediction, Kalman gain calculation and state update, thereby improving the timeliness and reliability of the prediction results of the mountain ground motion response.

[0116] In this embodiment, a multi-scale feature parameterization extraction system for complex mountainous terrain and site is constructed, a physical-data dual-driven hybrid prediction model is established, and extended Kalman filtering is used to achieve real-time rolling updates. This significantly improves the accuracy, timeliness, and robustness of seismic ground motion response prediction in complex mountainous areas, providing reliable technical support for earthquake early warning, emergency rescue, and earthquake disaster reduction decision-making in mountainous areas. This application solves the problem in existing technologies that simply use magnitude, epicentral distance, and site shear wave velocity as inputs without fully considering the effects of complex mountainous terrain on seismic wave amplification, focusing, and shielding, resulting in large errors in mountainous areas and prediction deviations of more than 50% for some sites.

[0117] In this application, a multi-scale feature parameterization extraction system for terrain and site conditions suitable for complex mountainous areas is proposed. It comprehensively utilizes multi-dimensional features such as slope, curvature, relative height, ridge index, and equivalent shear wave velocity to systematically characterize the impact of mountainous terrain on seismic motion. A hybrid prediction model driven by both physics and data is constructed, organically integrating an improved GMPE model that considers terrain correction with an attention-based BiLSTM neural network. A Bayesian variance weighting strategy is used to dynamically balance the weights of the two models, ensuring both physical interpretability and leveraging the strong fitting capability of data-driven approaches. A physics-guided composite loss function is designed, incorporating the residuals of the elastic wave equation as a physical constraint term into the neural network training objective, improving the model's generalization ability in sparse sample regions and the reliability of predictions for extreme events. An extended Kalman filter algorithm is introduced to achieve real-time rolling updates, continuously refining prediction results using real-time observation data from strong-motion seismic networks, achieving, for the first time, second-level dynamic updates for mountainous ground motion prediction. A multi-scale, multi-parameter synchronous output mechanism is proposed, which can simultaneously output multiple types of engineering parameters such as PGA, PGV, response spectrum, and seismic intensity, directly serving the needs of earthquake early warning, emergency rescue, and seismic design.

[0118] In a specific example, the earthquake in a certain region originated from the Xianshuihe Fault Zone, with its epicenter located in a high mountain valley area at an altitude of approximately 1800m. The terrain in the seismic zone is highly undulating, with slopes generally exceeding 30°, and relative elevation differences exceeding 400m at some local ridges, resulting in significant spatial variations in ground motion. A total of 17 strong-motion monitoring stations were deployed in the study area, with station spacing ranging from 2 to 30km and a sampling rate of 200Hz.

[0119] The extracted terrain-site feature parameters are as follows: Slope S (MS) = 34.7°, curvature C (MS) = −0.023 (negative value indicates that the site is located on a ridge protrusion); relative height Hr (MS) = 218m (within a 500m radius neighborhood); ridge index SRI (MS) = 152.4; equivalent shear wave velocity VS30 (MS) = 412 m / s (Class II site).

[0120] The first round of output for all 214 prediction grid points in the study area was completed 4.2 seconds after the earthquake (about 3 seconds after the arrival of the P wave).

[0121] ① Improved GMPE physical model (including terrain correction term) outputs PGA prediction value: Yphy = 4.83 m / s², corresponding to prediction standard deviation σ p =0.41 m / s²; ②The BiLSTM-Attention neural network model outputs the PGA prediction value: Y NN =5.12 m / s², corresponding to the prediction standard deviation σ d =0.27 m / s²; ③ Through Bayesian variance-weighted fusion (w p =0.30, w d =0.70), final predicted value: Ŷ=0.30×4.83+0.70×5.12=5.03 m / s² ④ The measured PGA is 5.24 m / s², and the absolute relative error is: |5.03−5.24| / 5.24×100%≈4.0% In the evaluation of the measured records from 17 strong-motion stations in this earthquake, the PGA prediction error (measured by σ_lnY) of the method provided in this application embodiment and the methods in related technologies are compared as shown in Table 1 below.

[0122] Table 1: Comparison of PGA prediction error (measured by σ_lnY) between the method provided in this application and methods in related technologies. As shown in Table 1, the PGA prediction log standard deviation σ_lnY of the method provided in this application embodiment is 0.34, which is 56.4% lower than that of the GMPE model in related technologies and 34.6% lower than that of pure CNN data-driven methods in related technologies. The median relative error of the prediction is far better than that of the methods in related technologies. The time taken for a single complete prediction is about 0.8 seconds, which meets the real-time requirements of early warning and is about 14,400 times more efficient than finite difference numerical simulation.

[0123] It should be noted that, for the sake of simplicity, the method embodiments are all described as a series of actions. However, those skilled in the art should understand that the embodiments of this application are not limited to the described order of actions, because according to the embodiments of this application, some steps can be performed in other orders or simultaneously. Secondly, those skilled in the art should also understand that the embodiments described in the specification are all preferred embodiments, and the actions involved are not necessarily required by the embodiments of this application.

[0124] Reference Figure 2 This application also discloses a structural block diagram of a device for predicting the seismic response of a mountain, comprising: The elevation acquisition module 201 is used to acquire the elevation of at least one location of the mountain and the equivalent shear wave velocity within a preset depth range below the surface of the location. The terrain slope determination module 202 is used to take any of the locations as locations to be predicted, and determine the terrain slope, terrain curvature and average elevation of the location to be predicted and the area of ​​the preset mountainous region surrounding the location to be predicted based on the elevation of the at least one location. Ridge index determination module 203 is used to determine the relative elevation of the terrain at the location to be predicted based on the elevation and average elevation of the location to be predicted, and to determine the ridge index of the location to be predicted based on the relative elevation and slope of the terrain at the location to be predicted. The terrain correction parameter determination module 204 is used to determine the terrain correction parameters for the location to be predicted by using the terrain slope, the terrain curvature, the terrain relative elevation and the ridge index. The first ground motion response information prediction module 205 is used to determine the source location of the earthquake at the current time and the source distance of the location to be predicted, and to predict the first ground motion response information of the location to be predicted using the moment magnitude of the earthquake, the source distance, the equivalent shear wave velocity corresponding to the location to be predicted, and the terrain correction parameters.

[0125] In one optional embodiment of this application, the device for predicting the seismic response of the mountain includes: The terrain feature vector construction module is used to construct a terrain feature vector of the location to be predicted based on at least one of the elevation, terrain slope, terrain curvature, terrain relative elevation and ridge index of the location to be predicted. The initial P-wave characteristic acquisition module is used to acquire the initial P-wave characteristic of the earthquake collected by the preset seismic detection equipment and the ground motion observation information of the earthquake by the seismic detection equipment at the current time. The second ground motion response information acquisition module is used to input the terrain feature vector, the initial P-wave feature quantity and the ground motion observation information at the current time into a preset ground motion response prediction model to obtain the second ground motion response information of the location to be predicted.

[0126] In one optional embodiment of this application, the seismic response prediction model stores a memory vector of input information for at least one historical time and a hidden state of the input information for the at least one historical time; the input information for the historical time includes the topographic feature vector, the initial P-wave feature quantity, and the seismic motion observation information for the historical time. The second seismic response information acquisition module includes: The target memory vector acquisition submodule is used to update the memory vector based on the memory vector, the terrain feature vector, the initial P-wave feature quantity, and the current time ground motion observation information using the seismic response prediction model, so as to obtain the target memory vector of the input information at the current time. The hidden state determination module is used to determine the hidden state of the input information at the current time based on the target memory vector and the hidden state of the input information at least one historical time using the seismic response prediction model. The first weight determination module is used to determine the first weight of the hidden state of the input information at the current time and the second weight of the hidden state of the input information at at least one historical time using the seismic response prediction model. The second ground motion response information determination submodule is used to determine the second ground motion response information using the ground motion response prediction model, based on the first weight, the second weight, the hidden state of the input information at the current time, and the hidden state of the input information at at least one historical time.

[0127] In one optional embodiment of this application, the device for predicting the seismic response of the mountain includes: The training data acquisition module is used to acquire training data and the label information of the training data; the training data includes training terrain feature vectors of training locations in a preset training hill, initial P-wave feature quantities of the training earthquakes in the training hills obtained by the seismic detection equipment, and training ground motion observation information of the training earthquakes obtained by the seismic detection equipment at the current time; the label information is the standard ground motion response information of the training data. The model training module is used to train a preset neural network model using the training data and the label information of the training data to obtain the seismic response prediction model.

[0128] In one optional embodiment of this application, the model training module includes: The data input submodule is used to input the training data into the neural network model to obtain the inferred ground motion response information of the training data; the inferred ground motion response information includes the particle acceleration of the seismic wave of the training earthquake at the training location and the Cauchy stress tensor at the training location; The data loss parameter determination submodule is used to determine the data loss parameters of the inferred ground motion response information using the inferred ground motion response information and the standard ground motion response information; The physical constraint parameter determination submodule is used to determine the elastic wave equation residual of the training earthquake at the training location and within a preset range around the training location by using the density of the soil and rock medium at the training location, the particle acceleration, the Cauchy stress tensor, and a preset body force term. It also uses a preset number of physical constraint sampling points at the training location and within a preset range around the training location, as well as the elastic wave equation residual, to determine the physical constraint parameters of the inferred ground motion response information. The regularization parameter determination submodule is used to determine the regularization parameters of the inferred seismic response information based on the preset training parameters in the neural network model. The target loss parameter determination submodule is used to determine the target loss parameter of the inferred seismic response information based on the data loss parameter, the physical constraint parameter, and the regularization parameter. The model obtains a sub-module, which is used to adjust the neural network model based on the target loss parameters to obtain the seismic response prediction model.

[0129] In one optional embodiment of this application, the first seismic response information is predicted using a preset physical model; the seismic response prediction device for the mountain includes: The second weight determination module is used to determine the third weight of the first ground motion response information and the fourth weight of the second ground motion response information by using the first prediction variance preset by the physical model and the second prediction variance preset by the ground motion response prediction model. The initial ground motion response information determination module is used to determine the initial ground motion response information of the location to be predicted by using the third weight, the fourth weight, the first ground motion response information, and the second ground motion response information.

[0130] In one optional embodiment of this application, the device for predicting the seismic response of the mountain includes: The seismic motion observation information acquisition module is used to acquire the seismic motion observation information of the earthquake by the earthquake detection equipment at any future time; The initial covariance determination module is used to determine the initial covariance of the initial ground motion response information by using the third weight, the fourth weight, the first prediction variance, and the second prediction variance. The prediction covariance module is used to predict the initial ground motion response information and the initial covariance based on the ground motion observation information at any of the future times, so as to obtain the predicted ground motion response information and the predicted covariance at any of the future times. The target ground motion response information determination module is used to determine the Kalman gain of the predicted covariance based on the predicted covariance, the preset observation matrix, and the preset observation noise covariance, and to determine the target ground motion response information for any future time based on the Kalman gain and the predicted ground motion response information.

[0131] It is understood that the above-described device embodiments correspond to the method embodiments of this application, and can implement the method provided by any of the above-described method embodiments of this application.

[0132] It should be noted that the device embodiments described above are merely illustrative, and some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Furthermore, in the accompanying drawings of the device embodiments provided in this application, the connection relationships between modules indicate that they have communication connections, which can specifically be implemented as one or more communication buses or signal lines. Those skilled in the art can understand and implement this without any creative effort.

[0133] Based on the embodiments of the above methods, another embodiment of this application provides a terminal device, which includes a processor, a memory, and a computer program stored in the memory and configured to be executed by the processor. When the processor executes the computer program, it implements the method described in any embodiment of this application.

[0134] For example, in this embodiment, the computer program can be divided into one or more modules, which are stored in the memory and executed by the processor to complete this application. The one or more module units may be a series of computer program instruction segments capable of performing a specific function, which describe the execution process of the computer program in the terminal device.

[0135] The terminal device may be a desktop computer, laptop, handheld computer, or cloud server, etc. The terminal device may include, but is not limited to, a processor and a memory.

[0136] The processor can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor can be a microprocessor or any conventional processor. The processor is the control center of the terminal device, connecting all parts of the terminal device via various interfaces and lines.

[0137] Based on the above-described method embodiments, another embodiment of this application provides a computer-readable storage medium including a stored computer program, wherein, when the computer program is executed, it controls the device where the computer-readable storage medium is located to perform the method described in any of the above-described method embodiments of this application.

[0138] The modules / units integrated in the device / terminal equipment, if implemented as software functional units and sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include: any entity or device capable of carrying the computer program code, recording media, USB flash drives, portable hard drives, magnetic disks, optical disks, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc.

[0139] Based on the above-described method embodiments, another embodiment of this application provides a computer program product, including a computer program or instructions, which, when executed by a communication device, implements the method described in any of the above-described method embodiments of this application.

[0140] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of this application. It should be understood that the above descriptions are merely specific embodiments of this application and are not intended to limit the scope of protection of this application. In particular, it should be noted that any modifications, equivalent substitutions, or improvements made by those skilled in the art within the spirit and principles of this application should be included within the scope of protection of this application.

Claims

1. A method for predicting the seismic response of a mountain, characterized in that, include: Obtain the elevation of at least one location on the mountain and the equivalent shear wave velocity within a preset depth range below the surface at said location; Take any of the locations mentioned above as the location to be predicted, and determine the terrain slope, terrain curvature, and average elevation of the location to be predicted within a preset mountainous area around the location to be predicted based on the elevation of the at least one location. Based on the elevation and average elevation of the location to be predicted, the relative elevation of the terrain at the location to be predicted is determined, and based on the relative elevation and slope of the terrain at the location to be predicted, the ridge index of the location to be predicted is determined. The terrain correction parameters for the location to be predicted are determined using the terrain slope, terrain curvature, terrain relative elevation, and ridge index. The source location of the earthquake at the current time and the source distance of the location to be predicted are determined. Then, the moment magnitude of the earthquake, the source distance, the equivalent shear wave velocity corresponding to the location to be predicted, and the terrain correction parameters are used to predict the first ground motion response information of the location to be predicted.

2. The method for predicting the seismic response of a mountain according to claim 1, characterized in that, The method for predicting the seismic response of the mountain includes: Based on at least one of the elevation, terrain slope, terrain curvature, terrain relative elevation, and ridge index of the location to be predicted, a terrain feature vector of the location to be predicted is constructed. Acquire the initial P-wave characteristics acquired by the preset earthquake detection equipment for the earthquake and the ground motion observation information of the earthquake by the earthquake detection equipment at the current time; The terrain feature vector, the initial P-wave feature quantity, and the current time ground motion observation information are input into a preset ground motion response prediction model to obtain the second ground motion response information of the location to be predicted.

3. The method for predicting the seismic response of a mountain according to claim 2, characterized in that, The seismic response prediction model stores a memory vector of input information for at least one historical time and a hidden state of the input information for the at least one historical time; the input information for the historical time includes the topographic feature vector, the initial P-wave feature quantity, and the seismic observation information for the historical time. The step of inputting the terrain feature vector, the initial P-wave feature quantity, and the current time seismic motion observation information into a preset seismic motion response prediction model to obtain the second seismic motion response information of the location to be predicted includes: Using the aforementioned seismic response prediction model, based on the memory vector, the terrain feature vector, the initial P-wave feature quantity, and the seismic observation information at the current time, the memory vector is updated to obtain the target memory vector of the input information at the current time. Using the earthquake ground motion response prediction model, based on the target memory vector and the hidden state of the input information at the at least one historical time, the hidden state of the input information at the current time is determined; Using the seismic response prediction model, determine the first weight of the hidden state of the input information at the current time and the second weight of the hidden state of the input information at at least one historical time. Using the earthquake ground motion response prediction model, the second earthquake ground motion response information is determined based on the first weight, the second weight, the hidden state of the input information at the current time, and the hidden state of the input information at at least one historical time.

4. The method for predicting the seismic response of a mountain according to claim 2, characterized in that, The method for predicting the seismic response of the mountain includes: Acquire training data and the label information of the training data; the training data includes training terrain feature vectors of training locations in a preset training mountain, initial P-wave feature quantities of the training earthquakes in the training mountain by the seismic detection equipment, and training ground motion observation information of the training earthquakes by the seismic detection equipment at the current time; the label information is the standard ground motion response information of the training data; Using the training data and its label information, a preset neural network model is trained to obtain the seismic response prediction model.

5. The method for predicting the seismic response of a mountain according to claim 4, characterized in that, The step of training a preset neural network model using the training data and the label information of the training data to obtain the seismic response prediction model includes: The training data is input into the neural network model to obtain the inferred ground motion response information of the training data; the inferred ground motion response information includes the particle acceleration of the seismic wave of the training earthquake at the training location and the Cauchy stress tensor at the training location; The data loss parameters of the inferred ground motion response information are determined using the inferred ground motion response information and the standard ground motion response information. Using the density of the soil and rock medium at the training location, the particle acceleration, the Cauchy stress tensor, and a preset body force term, the residual of the elastic wave equation for the training earthquake at the training location and within a preset range around the training location is determined. Using the preset number of physical constraint sampling points at the training location and within a preset range around the training location, as well as the residual of the elastic wave equation, the physical constraint parameters for the inferred ground motion response information are determined. Based on the preset training parameters in the neural network model, the regularization parameters for the inferred seismic response information are determined. The target loss parameter for the inferred seismic response information is determined based on the data loss parameter, the physical constraint parameter, and the regularization parameter. Based on the target loss parameters, the neural network model is adjusted to obtain the seismic response prediction model.

6. The method for predicting the seismic response of a mountain according to claim 2, characterized in that, The first seismic response information is predicted using a preset physical model; the method for predicting the seismic response of the mountain includes: Using the first prediction variance preset by the physical model and the second prediction variance preset by the seismic response prediction model, the third weight of the first seismic response information and the fourth weight of the second seismic response information are determined. The initial ground motion response information of the location to be predicted is determined by using the third weight, the fourth weight, the first ground motion response information, and the second ground motion response information.

7. The method for predicting the seismic response of a mountain according to claim 6, characterized in that, The method for predicting the seismic response of the mountain includes: Obtain the seismic motion observation information of the earthquake at any future time from the earthquake detection equipment; The initial covariance of the initial ground motion response information is determined using the third weight, the fourth weight, the first prediction variance, and the second prediction variance. Based on the ground motion observation information at any of the future times, the initial ground motion response information and the initial covariance are predicted to obtain the predicted ground motion response information and predicted covariance at any of the future times. Based on the predicted covariance, the preset observation matrix, and the preset observation noise covariance, the Kalman gain of the predicted covariance is determined, and based on the Kalman gain and the predicted ground motion response information, the target ground motion response information for any future time is determined.

8. A device for predicting the seismic response of a mountain, characterized in that, include: An elevation acquisition module is used to acquire the elevation of at least one location on the mountain and the equivalent shear wave velocity within a preset depth range below the surface at the location. The terrain slope determination module is used to take any of the locations as locations to be predicted, and based on the elevation of the at least one location, determine the terrain slope, terrain curvature, and average elevation of the location to be predicted within a preset mountainous area surrounding the location to be predicted. The ridge index determination module is used to determine the relative elevation of the terrain at the location to be predicted based on the elevation and average elevation of the location to be predicted, and to determine the ridge index of the location to be predicted based on the relative elevation and slope of the terrain at the location to be predicted. The terrain correction parameter determination module is used to determine the terrain correction parameters for the location to be predicted by using the terrain slope, the terrain curvature, the terrain relative elevation and the ridge index. The first ground motion response information prediction module is used to determine the source location of the earthquake at the current time and the source distance of the location to be predicted, and to predict the first ground motion response information of the location to be predicted using the moment magnitude of the earthquake, the source distance, the equivalent shear wave velocity corresponding to the location to be predicted, and the terrain correction parameters.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the method as described in any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the method as described in any one of claims 1 to 7.

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