A physical-data driven sequential seismic generation method

Abstract

The application relates to a physical-data-driven sequence-type earthquake generation method, which comprises the following steps: obtaining a historical earthquake record; constructing a main earthquake ground motion random field model based on a physical mechanism of the ground motion field; the physical mechanism comprises a focus, a propagation path and a local site model; obtaining main earthquake parameters according to the main earthquake ground motion random field model based on the historical earthquake record; the main earthquake parameters are used for predicting unknown main earthquake records according to the main earthquake ground motion random field model to obtain a main earthquake ground motion time history; and a main earthquake generation model is constructed based on a conditional adversarial generation network model according to the main earthquake ground motion time history to realize prediction of the ground motion field. The application generates various parameters of the main earthquake based on the physical mechanism of the ground motion field, obtains a main earthquake time history, constructs a main earthquake prediction model according to the conditional adversarial generation network, combines the physical mechanism model with artificial intelligence, improves model prediction fitness and accuracy, predicts aftershocks, improves prediction effect, avoids complex calculation and improves model construction efficiency.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of dynamic analysis, in particular to a physical-data-driven sequence type earthquake generation method. BACKGROUND

[0002] As a natural disaster with great destructive power, earthquake can cause casualties and have a significant impact on the ecological environment, regional economy and social stability. Therefore, predicting the time history of ground motion is crucial to reducing the loss of earthquake disaster.

[0003] Existing ground motion field models can be divided into empirical models for statistical regression of station data and semi-empirical and semi-theoretical models obtained from ground motion propagation mechanism and wave theory expression and regression of model parameters according to station data. Empirical models propose a series of delay coherence models according to the ground motion field data recorded by the array. Empirical coherence function models under different conditions have been proposed by many scholars. Empirical models perform well in sites similar to the array site. However, when applied to different sources and different types of local earthquakes, different empirical coherence function models show large differences. Compared with empirical models, semi-empirical and semi-theoretical models are more scientific and reasonable methods for estimating ground motion field. Semi-empirical and semi-theoretical models often start from physical mechanisms and consider shear wave propagation, traveling wave effect, site effect, etc. Models such as those based on random vibration theory and those established according to Fourier spectrum are proposed. In the construction of semi-empirical and semi-theoretical models, although the traveling wave effect, site effect, and frequency dispersion effect are considered, the construction process is usually based on single ground motion record data and related physical mechanisms for analysis and parameter determination, without considering aftershocks in the core consideration range. In actual earthquakes, aftershocks can cause additional damage to building structures that cannot be ignored, so the influence of aftershocks under earthquake action cannot be ignored.

[0004] In recent years, various ground motion field models have been proposed by domestic and foreign scholars. By establishing large and small scale site seismic analysis models, selecting a variety of source slip models, calculating local site ground motion field combining with boundary coordination relationship, and establishing average time-frequency domain correlation relationship, the local site ground motion field under any source slip model can be quickly constructed; the spectral characteristics and spatial distribution of ground motion are studied in depth using deep learning algorithm, and an intelligent ground motion field simulation method is proposed by learning and analyzing a large amount of historical ground motion data, which can quickly and accurately predict the ground motion field distribution under different site conditions.

[0005] In summary, some achievements have been made for the prediction of ground motion time history, but there are still deficiencies, mainly manifested in the following aspects: (1) the function model is quite different in different types of fields, and is not accurate enough; (2) the influence of aftershocks in earthquakes is ignored, and aftershocks are not included in the core consideration range of the model; (3) the existing sequence type ground motion field parameters are too many, and the parameter identification process is too complex.

[0006] Therefore, it is urgent to provide a physical-data-driven sequence type earthquake generation method to solve the above technical problems. SUMMARY

[0007] The present application provides a physical-data-driven sequence type earthquake generation method, which combines physical mechanism model with artificial intelligence innovation, improves model prediction fitness and accuracy, has high prediction accuracy in different types of fields, includes aftershocks in the core consideration range of the model, further improves prediction effect, and avoids too complex formula calculation, and improves model construction efficiency.

[0008] In a first aspect, the present application provides a physical-data-driven sequence type earthquake generation method, comprising the following steps: obtaining historical earthquake records; constructing a main shock ground motion random field model based on the physical mechanism of the ground motion field; wherein the physical mechanism includes a seismic source, a propagation path, and a local site model; obtaining main shock parameters according to the main shock ground motion random field model based on the historical earthquake records; wherein the main shock parameters are used to predict unknown main shock earthquake records according to the main shock ground motion random field model to obtain main shock ground motion time history; or, obtaining measured earthquake records to obtain main shock ground motion time history; constructing an aftershock generation model based on the conditional adversarial generation network model according to the main shock ground motion time history to realize the prediction of the ground motion field.

[0009] Optionally, the main shock ground motion random field model is constructed based on the physical mechanism, comprising: based on a one-dimensional wave equation, representing the generation and propagation process of main shock ground motion at a ground surface acceleration time history at a distance R from the seismic source and a distance r from the local site center, described by formula (1):

[0010]

[0011] Based on the ground surface acceleration time history, the generation and propagation process of ground motion is decomposed according to the seismic source, the propagation path, and the local site, and the amplitude spectrum and the phase spectrum of the seismic source, the propagation path, and the local site are constructed respectively, described by formula (2) and (3):

[0012]

[0013]

[0014] wherein, is the amplitude spectrum of the source, , and are the amplitude spectrum transfer functions of the propagation path, the local site soil layer and the local site plane wave field respectively, , , and are the random vectors in the models of the source, the propagation path, the local site soil layer and the plane wave field respectively, is the phase spectrum of the source, , and are the phase spectrum transfer functions of the propagation path, the local site soil layer and the local site plane wave field respectively; based on the amplitude spectrum and the phase spectrum of the source, the propagation path and the local site, the model parameters respectively describing the characteristics of the source, the propagation path and the local site are obtained by constructing the source model, the propagation path model and the local site model, so as to construct the main shock ground motion random field model.

[0015] Optionally, based on the amplitude spectrum and the phase spectrum of the source, the propagation path and the local site, the model parameters respectively describing the characteristics of the source, the propagation path and the local site are obtained by constructing the source model, the propagation path model and the local site model, so as to construct the main shock ground motion random field model, comprising: based on the amplitude spectrum and the phase spectrum of the source, the propagation path and the local site, the random variables of the source, the propagation path and the local site are obtained, which are used to describe the characteristics of the source, the propagation path and the local site to construct the source model, the propagation path model and the local site model; wherein the random variables, i.e. the model parameters, are described by formula (13):

[0016]

[0017] In the formula, represents the amplitude coefficient of the source, represents the source coefficient, and the random vector of the source model is , , , and are the random variables describing the variability of the propagation path, and the random vector of the propagation path model is , is the equivalent damping ratio of the site, is the equivalent predominant circular frequency of the site, and the random vector of the local soil layer is , is the amplitude variation coefficient of the site seismic wave, is the average apparent wave velocity of the site, and the local wave field can be represented by the random vector ; based on the source model, the propagation path model and the local site model, the main shock ground motion random field model is constructed.

[0018] Optionally, obtaining the mainshock parameters based on the mainshock ground motion random field model using the historical earthquake records includes: selecting identification earthquake records based on the historical earthquake records according to preset requirements; wherein, the preset requirements include selecting identification earthquake records with an earthquake matrix level not less than a specific order of magnitude and a peak ground acceleration not less than a specific acceleration; obtaining the amplitude spectrum model and phase spectrum model of the mainshock ground motion random field model based on the Fourier transform; and identifying the model parameters based on the identification earthquake records according to the amplitude spectrum model and the phase spectrum model, respectively. , , , , , , , as well as , Based on the identified model parameters, the corresponding optimal probability model is obtained according to the Bayesian information criterion, and the marginal probability density function of each model parameter is determined to obtain the probability distribution of the model parameters and generate the main shock parameters.

[0019] Optionally, based on the seismic records used for identification, the model parameters are identified according to the amplitude spectrum model and the phase spectrum model, respectively. , , , , , , , as well as , Specifically, this includes: fitting the amplitude spectrum model using the least squares criterion to identify the model parameters in the amplitude spectrum model. , , and The true ground motion phase spectrum is obtained based on the identified seismic records; the source coefficient is obtained based on the model parameters. Based on the phase spectrum model, the phase difference spectrum of the phase spectrum model is fitted to the true phase difference spectrum distribution using the least squares criterion, and the parameters in the phase spectrum model are identified using a genetic algorithm. , , and Based on the model parameters obtained from the identification , , and , 、 、 and identifying the model parameters in the plane wave field transfer function by least square method ; identifying apparent wave velocity in the model parameters based on time alignment and lag determination method wherein the obtained apparent wave velocity is the mean value in frequency, described by formula (16):

[0020]

[0021] wherein, is the total number of groups of two stations, is the distance of the i-th group of stations along the wave propagation direction, is the time lag between the i-th group of samples.

[0022] Optionally, the apparent wave velocity identified based on the time alignment and lag determination method further comprises: filtering the target seismic group at different frequencies using a band-pass filter, and calculating the cross-correlation function of the filtered narrow-band signals to obtain the time lag corresponding to the maximum value of the cross-correlation function , which is the apparent wave velocity corresponding to ; based on the station distance and the obtained time lag , the apparent wave velocity corresponding to is obtained; repeating the above process to obtain the apparent wave velocities corresponding to different frequencies .

[0023] Optionally, the aftershock generation model is constructed based on the conditional adversarial generative network model to realize the prediction of the seismic field, including: obtaining the main shock seismic time history based on the historical earthquake record and selecting the training set and the test set; taking the training set as the input data to perform data training according to the conditional adversarial generative network model, and constructing the aftershock generation model; taking the test set as the input data to predict the prediction accuracy of the aftershock generation model on new data according to the aftershock generation model; comparing the predicted value and the actual value of the aftershock generation model to test the prediction accuracy of the aftershock generation model.

[0024] Optionally, according to the comparison between the predicted value of the aftershock generation model and the actual value, the prediction accuracy of the aftershock generation model is verified, and the method further comprises: after the predicted value is amplitude-modulated according to PGA, the intensity parameter of the predicted value is compared with the intensity parameter of the actual value; according to needs, a specific number of predicted aftershock time histories are randomly selected, and the response spectrum thereof is compared with the real recorded response spectrum; the mean response spectrum of the predicted time history obtained by taking the training set and the test set as input data is compared with the mean response spectrum of the real record.

[0025] In a second aspect, the application provides a physics-data-driven sequence-type earthquake generation system, comprising: an acquisition module configured to acquire historical earthquake records; a main shock model module configured to construct a main shock ground motion random field model based on a physical mechanism of ground motion field; wherein the physical mechanism comprises a seismic source, a propagation path, and a local site model; a main shock time history generation module configured to obtain main shock parameters based on the historical earthquake records and the main shock ground motion random field model; wherein the main shock parameters are used to predict unknown main shock records based on the main shock ground motion random field model to obtain a main shock ground motion time history; or, to obtain a main shock ground motion time history by acquiring a measured earthquake record; and an aftershock model prediction module configured to construct an aftershock generation model based on a conditional generative adversarial network model to realize prediction of the ground motion field according to the main shock ground motion time history.

[0026] In a third aspect, the application further provides a computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the above method when executing the computer program.

[0027] In a fourth aspect, a computer readable storage medium is provided, which stores a computer program, and the computer program is executable on a processor to implement the steps of the above method.

[0028] The application has at least the following advantages:

[0029] The above steps are mainly to build a main shock ground motion random field model through a physical mechanism-based ground motion field, generate various parameters of the main shock, and comprehensively reflect various factors affecting the earthquake to provide accurate data basis for subsequent prediction of aftershocks. Then, the main shock time history is obtained according to the obtained main shock parameters, and the aftershock time history is predicted according to the generated model of the main shock based on the conditional adversarial generation network taking the main shock time history as input data. The physical mechanism model is combined with artificial intelligence innovation, and the model can be used for high-precision prediction under different types of fields. The model prediction adaptability is improved, and the aftershock is included in the core consideration range of the model. The conditional adversarial generation network is used to build the earthquake generation model, and the complex formula calculation is avoided, the model construction efficiency is improved, and the prediction effect is further improved. BRIEF DESCRIPTION OF DRAWINGS

[0030] Figure 1 An application environment diagram of a physical-data-driven sequence type earthquake generation method is shown in an embodiment;

[0031] Figure 2 A step flowchart of a physical-data-driven sequence type earthquake generation method is shown in an embodiment;

[0032] Figure 3 A structure diagram of a physical-data-driven sequence type earthquake generation method is shown in an embodiment;

[0033] Figure 4 A structure diagram of a physical mechanism of ground motion is shown in an embodiment;

[0034] Figure 5 A flowchart of identifying main shock parameters is shown in an embodiment;

[0035] Figure 6 A structure diagram of identifying main shock parameters is shown in an embodiment;

[0036] Figure 7 A Hilbert curve diagram with a side length of 8 is shown in an embodiment;

[0037] Figure 8 A CGAN network structure diagram of two-dimensional convolution is shown in an embodiment;

[0038] Figure 9 A comparison diagram of predicted aftershock time history and real aftershock according to a training set is shown in an embodiment;

[0039] Figure 10 A comparison diagram of predicted aftershock time history and real aftershock according to a test set is shown in an embodiment;

[0040] Figure 11A comparative diagram for showing the intensity parameter of the predicted aftershock time history in one embodiment;

[0041] Figure 12 A comparative diagram for showing the response spectrum of the predicted aftershock time history in one embodiment;

[0042] Figure 13 A comparative diagram for showing the predicted time history mean response spectrum according to the training set and the test set and the true one in one embodiment;

[0043] Figure 14 A schematic diagram for showing the generated ground motion field at the time of 13.5s in one embodiment;

[0044] Figure 15 A schematic diagram for showing five ground motion samples with an interval of 1000m in the generated ground motion field in one embodiment;

[0045] Figure 16 A comparative diagram for showing the building group response in one embodiment;

[0046] Figure 17 A structural block diagram of a physics-data driven sequential earthquake generation system in one embodiment;

[0047] Figure 18 A schematic structural diagram of a computer device in one embodiment. DETAILED DESCRIPTION

[0048] The present application will be further described below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely intended to explain the present application and not to limit the present application.

[0049] For the convenience of understanding, the system to which the present application is applied is described first. The ground motion field prediction method provided by the present application can be applied to the system architecture as shown in the figure. Figure 1 The system includes a user space file server 103 and a terminal device 101, and the terminal device 101 communicates with the user space file server 103 through the network. The user space file server 103 can be a file server based on the NFSv3\v4 protocol, running in the Linux environment, and the NFS (Network File System) is a network abstraction on the file system, which allows remote clients running on the terminal device 101 to access through the network in a similar way to the local file system. The terminal device 101 can be, but is not limited to, various personal computers, notebook computers, smart phones, tablet computers, etc., and the user space file server 103 can be implemented by an independent server or a server cluster composed of multiple servers.

[0050] Figure 2A physical-data-driven sequence-type earthquake generation method provided in the embodiment of the present application has a flowchart as shown in the figure. The method can include the following steps.

[0051] S201, obtaining a historical earthquake record;

[0052] S202, constructing a main shock ground motion random field model based on a physical mechanism of the ground motion field; wherein,

[0053] The physical mechanism includes a source, a propagation path, and a local site model.

[0054] S203, obtaining main shock parameters based on the historical earthquake record and the main shock ground motion random field model; wherein, the main shock parameters are used to predict unknown main shock records based on the main shock ground motion random field model to obtain a main shock time history; or, obtaining a measured earthquake record to obtain a main shock time history.

[0055] S204, constructing an aftershock generation model based on the main shock time history and a conditional generative adversarial network model to realize prediction of the ground motion field.

[0056] In the embodiment of the present application, a main shock ground motion random field model is constructed based on a physical mechanism of the ground motion field, and each parameter of the main shock is generated, so as to comprehensively reflect each factor affecting the earthquake and provide an accurate data basis for subsequent prediction of aftershocks. Then, a main shock time history is obtained based on the obtained main shock parameters, the main shock time history is taken as input data, an aftershock generation model is constructed based on a conditional generative adversarial network to predict an aftershock time history, the physical mechanism model is combined with artificial intelligence, the model can be used for high-precision prediction under different types of fields, the adaptability of the model prediction is improved, the aftershock is included in the core consideration range of the model, the conditional generative adversarial network is used to construct the aftershock generation model, and complex formula calculation is avoided, the model construction efficiency is improved, and the prediction effect is further improved.

[0057] Each step will be described in detail as follows:

[0058] Please refer to Figure 2 , Figure 3 S201, obtaining a historical earthquake record.

[0059] In the embodiment, it should be noted that a large number of sequence-type ground motion records can be collected from a database PEER and KiK–net & K–NET, and the historical earthquake record can provide a data basis for subsequent modeling analysis. The sequence-type ground motion record refers to a ground motion time history record generated by multiple continuous sub-events, such as a main shock, a foreshock, an aftershock, or different rupture stages during an earthquake process. Such a record can more truly reflect the complex characteristics of an actual earthquake, especially in strong earthquakes.

[0060] Please continue to refer toFigure 2 , Figure 3 As shown, step S202 involves constructing a random field model of the main shock ground motion based on the physical mechanism of the ground motion field; wherein, the physical mechanism includes the source, propagation path, and local site model.

[0061] In this embodiment, it should be noted that, as Figure 4 As shown, the physical mechanism is the core framework for understanding the characteristics of earthquake ground motion. The hypocenter mainly describes the dynamic process of earthquake rupture, the propagation path describes the attenuation of seismic waves from the hypocenter to the site, and the local site characterizes the modulation of the ground motion by the surface sedimentary layer. By analyzing the hypocenter, propagation path, and local site, the three subsystems are coupled through wave equations to construct a random field model of the mainshock ground motion, thereby analyzing the characteristics of the mainshock and providing a data foundation for subsequent predictive analysis.

[0062] Specifically, based on the one-dimensional wave equation, the generation and propagation process of the main shock is represented by the time history of the ground acceleration at a distance of R from the epicenter and r from the local site center, and described by formula (1):

[0063]

[0064] Based on the surface acceleration time history, the generation and propagation process of earthquake motion is decomposed according to the source, propagation path, and local site, and the amplitude spectrum and phase spectrum of the source, propagation path, and local site are constructed respectively, which are described by formulas (2) and (3):

[0065]

[0066]

[0067] In the formula, The amplitude spectrum of the earthquake source. , and These represent the amplitude spectral transfer functions for the propagation path, the local soil layer, and the local plane wavefield, respectively. , , and These are random vectors in the model representing the earthquake source, propagation path, local soil layers, and plane wave field, respectively. This represents the phase spectrum of the earthquake source. , and The phase spectrum transfer functions are obtained for the propagation path, the local soil layer, and the local plane wave field, respectively. Based on the amplitude and phase spectra of the source, propagation path, and local site, models of the source, propagation path, and local site are constructed to obtain model parameters describing the characteristics of the source, propagation path, and local site, respectively, so as to construct the random field model of the main shock ground motion.

[0068] In one example, firstly, for the source model, the dynamic process of the earthquake rupture is described, the Brune circular disk dislocation model is adopted, the dislocation is uniformly distributed and the rupture occurs instantaneously, and the shear wave propagates in the direction perpendicular to the fault plane. By assuming that the shear stress drop during the fault rupture process is a constant value, the rock displacement expression on the fault plane is obtained, which is described by formula (4):

[0069]

[0070] In the formula, is the shear stress drop of the source, and are the shear wave velocity and shear modulus of the rock near the fault, respectively, is the Brune source coefficient. Then the amplitude spectrum and phase spectrum of the displacement are obtained by Fourier transform, so that the model can be identified, as follows formula (5) and (6), which provides basic parameters for subsequent calculation.

[0071]

[0072] In the formula, the source amplitude coefficient , then the random vector of the source model .

[0073] For the propagation path model, the main description is to control the attenuation of the seismic wave from the source to the site, considering the damping energy dissipation effect of linear elastic medium, using the wave number frequency curve to reflect the frequency dispersion effect, and the amplitude spectrum transfer function is described by formula (7):

[0074]

[0075] In the formula, is the quality factor of the bedrock, is the group velocity of the seismic wave, for the purpose of simplifying the model form, the constant K is used to reflect the attenuation effect of the medium, and the empirical value is 10-5s / km. The effect of the propagation path on the phase is quite complex, and the empirical formula of the phase spectrum transfer function is adopted, which is described by formula (8):

[0076]

[0077] In the formula, , and d are random variables for describing the variability of the propagation path. The amplitude spectrum parameter K is set as a constant, then the random vector of the propagation path ;

[0078] For local site model, the surface sediment layer is simplified as an equivalent single degree of freedom system, and the amplitude spectrum transfer function is obtained from the motion equation, which is described by equation (9):

[0079]

[0080] where, is the equivalent damping ratio of the site, is the equivalent predominant circular frequency of the site. Since the distance from the bedrock to the surface is short, the influence of the distance on the phase of the seismic wave is ignored, which is described by equation (10) and can be expressed as

[0081]

[0082] and the random vector of the local soil layer is determined ;

[0083] For the wave field model on the local site, considering that the size of the local site is much smaller than the epicentral distance, it is simplified as a plane wave field, and the amplitude spectrum transfer function on the local site is obtained, which is described by equation (11):

[0084]

[0085] where, is the amplitude variation coefficient of the seismic wave of the site, which reflects the attenuation effect of the amplitude of the seismic wave along the propagation direction of the seismic wave. When calculating the phase spectrum transfer function, only the traveling wave effect is considered and the frequency dispersion effect is not considered, and the phase spectrum transfer function is:

[0086]

[0087] where, is the average apparent wave velocity of the site, and the local wave field can be described by the random vector .

[0088] According to the calculation of the random vectors , , and in the models of the seismic source, the propagation path, the local site soil layer and the plane wave field, the vector composed of the random variables in the single seismic motion random field model, i.e. the main earthquake seismic motion random field model, is described by equation (13):

[0089]

[0090] where, represents the amplitude coefficient of the seismic source, represents the seismic source coefficient, and the random vector of the seismic source model is , , , , The random vector of the propagation path model is a random variable describing the variability of the propagation path. , The equivalent damping ratio of the site is given. For the site equivalent superior circular frequency, the random vector of the local soil layer , This is the site seismic wave amplitude variation coefficient. The local wavefield can be represented by the average apparent wave velocity over the field using random vectors. express.

[0091] Based on the above analysis and calculation of the amplitude and phase spectra of the earthquake source, propagation path, and local site, random variables of the earthquake source, propagation path, and local site are obtained, which describe the characteristics of the earthquake source, propagation path, and local site respectively, comprehensively reflect the various factors affecting the earthquake, and have relatively clear physical meaning. Based on the earthquake source, propagation path, and local site model, a random field model of the main shock ground motion is constructed. This model comprehensively reflects the dispersion effect, traveling wave effect, and attenuation effect of the ground motion on the local site.

[0092] Please refer to Figure 3 , Figure 5 As shown, step S203 involves obtaining the mainshock parameters based on the mainshock ground motion random field model according to historical earthquake records, including:

[0093] Step S2031: Based on historical earthquake records, select earthquake records for identification according to preset requirements; wherein, the preset requirements include selecting earthquake records for identification with an earthquake matrix level not less than a specific order of magnitude and a peak ground acceleration not less than a specific acceleration.

[0094] In this embodiment, it should be noted that a large number of sequential ground motion records, i.e., historical earthquake records, were collected based on the PEER and KiK-net & K-NET datasets. These historical earthquake records were then filtered and processed. Since the modeling object is a strong ground motion time history, the original ground motion data were filtered based on the earthquake moment magnitude and peak ground acceleration (PGA) according to preset requirements. The final ground motion acceleration time history used meets the requirements of an earthquake moment magnitude of not less than 5 and a peak ground acceleration of not less than 0.2g.

[0095] In one example, 1014 groups of sequence-type ground motions meeting the conditions are screened out, of which the sequence-type ground motions of the I, II, III and IV type sites are 130, 636, 226 and 22 groups respectively. In addition, five groups of ground motion field time histories recorded by the SMART-1 array are selected, and the five groups of ground motion only contain main shocks. The basic information of the selected ground motion is shown in Table 1. Here, the E-W component and the N-S component in the record of each station are selected and regarded as independent ground motions for the study of the horizontal component of the ground motion. In this part, only the main shock in the identified sequence-type ground motion is analyzed, and the aftershock part is reserved for subsequent prediction analysis.

[0096] Table 1: Real sequence-type ground motion data screened out

[0097]

[0098] In addition, as shown in Figure 6 , in one example, the real ground motion time histories recorded by each station have differences in sampling frequency. In order to facilitate analysis, the sampling frequency is unified, the ground motion is uniformly amplitude-modulated according to PGA, and amplitude normalization processing is performed. Specifically, here the time history is resampled at an interval of 0.02s, and the upper limit of the corresponding frequency is 25Hz. The difference between the resampled time history and the original time history in the time domain and the frequency domain is small, and the influence on the identification result can be basically ignored. In addition, the ground motion is uniformly amplitude-modulated to 0.1g according to PGA, and amplitude normalization processing is performed, so as to provide a data basis for subsequent analysis and processing.

[0099] As shown in Figure 5 , Figure 6 , step S2032, based on the main shock ground motion random field model, the amplitude spectrum model and the phase spectrum model of the main shock ground motion random field model are obtained according to Fourier transform;

[0100] In this embodiment, it should be noted that the amplitude spectrum and the phase spectrum based on the source, the propagation path and the local site are used to obtain the random variables of the source, the propagation path and the local site:

[0101]

[0102] Combined with the generation and propagation process of the main shock ground motion represented by the acceleration time history, the Fourier amplitude spectrum and the phase spectrum in the main shock ground motion random field model are described by formulas (14) and (15):

[0103]

[0104] Step S2033, based on the identification ground record, the model parameters , 、 、 , 、 、 、 and 、 , comprising: according to the identified seismic record meeting the condition after screening, identifying the model parameters according to the amplitude spectrum model and the phase spectrum model, wherein the model parameters in the amplitude spectrum model are identified based on the amplitude spectrum model using the least square criterion fitting 、 、 and ; obtaining the real seismic phase spectrum based on the identified seismic record; based on the model parameters , according to the phase spectrum model, the phase difference spectrum of the phase spectrum model is fitted with the real phase difference spectrum distribution using the least square criterion, and the parameters in the phase spectrum model are identified using the genetic algorithm 、 、 、 ; based on the identified model parameters 、 、 and 、 、 、 and , the model parameters in the plane wave field transfer function are identified by the least square method ; the apparent wave velocity in the model parameters is identified based on the time alignment and the lag determination method , wherein the obtained apparent wave velocity is the average value in frequency, which is described by formula (16):

[0105]

[0106] In the formula, is the total number of groups of two stations, is the distance of the i-th group of stations along the wave propagation direction, is the time lag between the i-th group of samples. According to the above parameter identification, the probability distribution of the model parameters is obtained, which can be used to generate the main shock record according to the probability distribution if there is no real main shock record, so as to facilitate the subsequent prediction of aftershocks.

[0107] In this embodiment, it should be noted that, specifically, among the parameters, in order to make the model approximate the real seismic amplitude spectrum, the parameter 、 、 and The identification is performed using the least square method, and the objective function can be described by equation (17):

[0108]

[0109] wherein, is the amplitude spectrum of the model, is the amplitude spectrum of the target ground motion.

[0110] In addition, for the parameters , , and , the identification is performed based on the phase spectrum of the real ground motion, which is quite difficult. The phase difference spectrum has a more obvious feature, and the phase difference generally obeys a normal distribution or an approximate normal distribution. Based on this, the identification of the parameters 、 、 and corresponding to the phase spectrum is performed using the genetic algorithm to make the phase difference distribution of the model close to the phase difference distribution of the real ground motion, and to improve the identification efficiency. The objective function can be described by equation (18):

[0111]

[0112] wherein, is the phase difference distribution of the model phase spectrum, is the phase difference distribution of the target ground motion phase spectrum; = is the difference between two adjacent phase angles in the frequency domain. The parameter settings of the genetic algorithm are shown in Table 2:

[0113] Table 2 Parameter settings of the genetic algorithm

[0114]

[0115] For the identification of the parameters and , the physical parameters of the site center point C00 are first identified, including , , and , , , and . According to the identified parameters , , and , , , and Parameters in the plane wave field transfer function can be identified using the least squares method. The equivalent wave velocity of the site The apparent velocity can be identified based on time alignment and hysteresis determination methods. The mean value over frequency can be described by formula (19):

[0116]

[0117] In the formula, N is the total number of pairs of stations. Let be the distance of the i-th station along the wave propagation direction. The time lag between the i-th sample groups. Based on the obtained average apparent velocity in terms of frequency. A bandpass filter is used to filter the target ground motion sequence at different frequencies. Specifically, a Butterworth filter can be used, with the center frequency set to 1. bandwidth is rad / s. Calculate the cross-correlation function of the filtered narrowband signal. This leads to the time lag corresponding to the maximum value of the cross-correlation function. That is, with corresponding Substitute the station distance and time lag into equation (19), based on the station distance and the obtained time lag... ,get Corresponding apparent velocity By repeating the above process, the apparent wave velocity corresponding to different frequencies can be obtained. By fitting the sample points with equation (18) as the objective function, the equivalent quality factor on the local target site can be obtained. .

[0118] Step S2034: Based on the identified model parameters, obtain the corresponding optimal probability model according to the Bayesian information criterion, determine the marginal probability density function of each model parameter, and obtain the model parameter probability distribution to generate the main shock parameters.

[0119] In this embodiment, it should be noted that the Bayesian information criterion is used to estimate the subjective probability of the partially unknown state under incomplete information, and then the Bayesian formula is used to correct the probability of occurrence. Finally, the expected value and the corrected probability are used to make the optimal decision. The Bayesian decision theory method is a basic method in statistical pattern recognition. The Bayesian decision criterion considers not only the probability of the occurrence of each reference population, but also the loss caused by misjudgment, and has strong discrimination ability. Specifically, here the seismic records for identification are identified one by one, that is, each group of sequence type ground motion is identified, the statistical distribution is investigated, the Bayesian information criterion (BIC) is used to obtain the corresponding optimal probability model, and then the marginal probability density function of each parameter is determined, which is described by formula (20):

[0120]

[0121] In the formula, is the probability density function, is the number of sample points, , , is the parameter of the probability density function, is the number of distribution parameters. As shown in Table 3, the PDF of the source and propagation path random variable and the corresponding parameters are obtained, and the meanings of the parameters and in the table are as follows: when the probability density function is Normal, they are the mean and standard deviation, respectively; when the probability density function is Lognormal, they are the mean and standard deviation of the logarithm, respectively; and when the probability density function is Weibull, they are the shape parameter and scale parameter, respectively.

[0122] Table 3 PDF of source and propagation path random variable and corresponding parameters

[0123]

[0124] According to the marginal probability density function of the model parameters, the probability distribution of the model parameters is obtained, and the main shock parameters are finally generated, so that the main shock time history can be obtained according to the main shock parameters when the main shock time history cannot be obtained. According to the actual main shock record, the main shock time history can be obtained, which provides a data basis for subsequent prediction of aftershock data.

[0125] Referring to Figure 2 , Figure 3As shown, in step S204, a post-earthquake generation model is constructed based on the main shock ground motion time history according to the conditional adversarial generation network model to realize the prediction of the ground motion field, including: obtaining the main shock ground motion time history based on the historical earthquake record and selecting the training set and the test set; taking the training set as the input data to perform data training according to the conditional adversarial generation network model, and constructing the post-earthquake generation model; taking the test set as the input data to predict the prediction accuracy of the model on new data that has not been seen according to the post-earthquake generation model; comparing the predicted value of the post-earthquake generation model with the actual value to test the prediction accuracy of the post-earthquake generation model.

[0126] In this embodiment, it should be noted that the weight sharing and local connection features of the convolution layer can greatly reduce the parameter amount of the model, so the convolution network is mainly used here. The operation of convolution is "cyclic multiplication and sum". The "roll" of convolution refers to the flip translation operation, and the "product" refers to the integral operation. Two-dimensional convolution is mostly used in the image field and is widely used in the field of computer vision at present. Specifically, the application first selects a reasonable way to convert the time sequence into a two-dimensional matrix, and then extracts features through two-dimensional convolution to achieve the purpose of converting the main shock time history into a picture and predicting the post-earthquake time history.

[0127] As shown in Figure 7 , the Hilbert curve is a fractal curve (or called space-filling curve) that can fill a square plane. The curve can uniquely convert the time sequence into a two-dimensional matrix without corresponding calculation, maximally retains the original size and spatial position information, and can be reversibly converted back to a one-dimensional sequence, which is a more suitable conversion method in the application. Because of the special requirement for the side length of the square, the main and post-earthquake time histories are uniformly converted into square matrices of in the application, and the insufficient part is processed by zero filling. Referring to Figure 7 , it is a Hilbert curve of a square with a side length of 8.

[0128] In addition, GAN is an adversarial generation model. GAN mainly completes two tasks: manifold learning and probability distribution conversion. This is a strong support for the mathematical principle of GAN. The GAN adversarial generation network is an unsupervised model, that is, a generation model without conditional constraints, and cannot control the generated samples. Conditional adversarial network (Conditional generative adversarial nets, CGAN) is a structure that adds additional information condition y to the generator and discriminator, thereby adjusting the model, so as to guide the data generation process. Such condition y can be any type of auxiliary information: it can be a class label, or any data from different distributions.

[0129] Referring to Figure 8As shown, the CGAN establishes the correlation between the conditional information and the real data, and the discriminator in the CGAN network structure exists, which will improve the efficiency of each training. Since the purpose of the aftershock earthquake generation model is to generate the time sequence of aftershocks, the structure of the model adopts the CGAN generation model, in which the generator adopts the U-net network. The specific network structure of the generator and the discriminator is as shown in Figure 8 . In the figure, the left side of the generator is a convolution operation, and the right side is an inverse convolution operation. The input graph and the output graph are . With the convolution, the width and height of the input graph become smaller and smaller, but the number of corresponding convolution kernels increases correspondingly, which can be regarded as feature extraction. The inverse convolution on the right side makes the width and height of the graph become larger and larger, but it is still a convolution operation in essence. The matrix after the Hilbert curve change of the seismic acceleration time sequence is used as an additional condition of the model. In the model, except that the step length of the last convolution layer of the discriminator is 4, the step lengths of the remaining convolution layers are all 2. The size of all convolution kernels in the model is . In addition, for the training process of the CGAN, in order to stabilize the model training and theoretically avoid the problems existing in the training of the original GAN, the gradient penalty WGANs-G algorithm is adopted, which can improve the training stability and the quality of the training.

[0130] Specifically, in one example, as shown in Figure 9 , Figure 10 , the main shock ground motion time sequence is used to construct an aftershock earthquake generation model based on a conditional generative adversarial network model. First, according to the historical earthquake records, 6 main shock time sequences in the sequence type ground motion are randomly selected as the training set and the test set. According to the CGAN generation model, the training set is input into the conditional generative adversarial network model, a two-dimensional convolution model is trained, and then the predicted two-dimensional matrix is converted into a one-dimensional time sequence through the inverse Hilbert curve to obtain the final predicted aftershock time sequence. Then, the test set is input into the aftershock earthquake generation model, a two-dimensional convolution model is trained, and then the predicted two-dimensional matrix is converted into a one-dimensional time sequence through the inverse Hilbert curve to obtain the final predicted aftershock time sequence, and the prediction accuracy of the prediction model on new data not seen before. Finally, the predicted values obtained by taking the training set and the test set as input data are compared with the real time sequence, that is, the actual value, and it is found that the prediction effect of the aftershock earthquake generation model is good.

[0131] In addition, in one example, as shown in Figure 11 , 12As shown, the accuracy of the aftershock ground motion generation model is verified by comparing the predicted values ​​with the actual values. This includes: adjusting the predicted values ​​according to the PGA (Programme Forward Gain) and then comparing the predicted intensity parameters with the actual intensity parameters; and, as needed, randomly selecting a specific number of predicted aftershock time histories and comparing their response spectra with the actual recorded response spectra. Specifically, three randomly selected predicted aftershock time histories are compared with their response spectra. Figure 13 As shown, the predicted time-history mean response spectrum obtained by using the training set and test set as input data can also be compared with the mean response spectrum of the actual records.

[0132] A specific application simulation was conducted based on the aforementioned earthquake prediction method, selecting Putuo District of Shanghai as the epicenter. The area measured 11.83 km east-west and 9.27 km north-south, with a total area of ​​55.53 km². 2 It comprises 29,461 individual buildings. Specifically, a 6×6km area within this administrative district will be selected. 2 The area's building complex, comprising 8219 individual buildings, underwent seismic disaster simulation, demonstrating the preliminary application of the proposed sequential random field model for seismic motion in building complex seismic disaster simulation. Based on historical earthquake records and seismic hazard analysis results from the Shanghai Earthquake Bureau, the intensity values ​​for 50-year exceedance probabilities of 10% and 5% in downtown Shanghai are 7.0 and 7.3 degrees, respectively. The horizontal PGA of bedrock with 50-year exceedance probabilities of 10%, 5%, and 2-3% are 0.86 m / s². 2 1.05m / s 2 and 1.17m / s 2 Here, a sequence-type seismic field simulation was conducted in the Shanghai-Nantong potential source area. The hypocenter of this potential source area is 105 km away from the epicenter and has a focal depth of 12 km. Considering the large number of newly built residential buildings in the past 20 years, all of which have some degree of seismic fortification measures, the PGA of the main shock was specifically selected as 3.0 m / s². The site type of Putuo District is Class IV, which can be considered as the equivalent quality factor for this area. Quality factors less than SMART-1, specifically assumed The value is 15, and the other model parameters are determined by Table 3.

[0133] Reference Figure 14 The wave field of the sequential ground motion field at 13.5s was generated according to the method proposed above. Unlike uniform excitation, due to the influence of traveling wave effect and dispersion effect, the wave field at a given time has both regions at wave crest and wave trough. Moreover, due to the influence of traveling wave effect and dispersion effect, the amplitude of acceleration at each point is different, showing a significant spatial variation effect.

[0134] Five ground motion acceleration time history samples were taken from the wavefield at 1000m intervals, as follows: Figure 15 As shown, although their waveforms are quite similar, the ground motion time histories of each time period in the five samples are different due to the effects of dispersion and traveling wave. Furthermore, there is a certain time lag, which cannot be achieved by models considering only a single effect. In addition, the aftershock time histories in the sequence-type ground motions are slightly smaller in amplitude and shorter in duration than the main shock time histories, which is consistent with the statistical patterns in the measured ground motion samples.

[0135] like Figure 16 As shown, it compares the building complex response at 13.5 s under different actions of uniform excitation and sequential ground motion fields. The uniform excitation method uses ground motion at the site center with a PGA of 3 m / s². 2 .exist Figure 16 As shown in (a), in the response of a building complex under uniform excitation, the entire complex is simultaneously subjected to the same amplitude of excitation, and the differences in the responses of individual buildings are solely due to variations in structural height and restoring force parameters. For buildings of the same height and plan dimensions, their responses are identical regardless of their location within the area. This clearly contradicts the laws governing seismic motion and actual earthquake damage. However... Figure 16 (b) shows the response of the building complex under the action of the seismic field. It can be clearly observed that there are significant differences in the response of buildings at different locations. The propagation process and spatial variation effect of the seismic ground motion are clearly reflected in the figure. At this time, the response of the building is not only related to the parameters of the building itself, but also closely related to the location of the building. The seismic excitation at different locations is different, which makes the response of the same building still different.

[0136] The implementation principle of this embodiment is as follows: The above steps mainly involve constructing a mainshock random field model based on a physical mechanism ground motion field. Based on the acquired historical earthquake records, various parameters of the mainshock are generated based on the mainshock random field model, thereby comprehensively reflecting various factors affecting earthquakes and providing an accurate data foundation for subsequent aftershock prediction. Then, based on the obtained mainshock parameters, a ground motion generation model is constructed using a conditional adversarial generative network to predict aftershock time histories. This innovative combination of physical mechanism model and artificial intelligence allows the model to make high-precision predictions under different types of sites, improving the model's predictive adaptability. Furthermore, aftershocks are included in the core considerations of the model. The ground motion generation model is constructed using a conditional adversarial generative network, avoiding overly complex formula calculations, improving model construction efficiency, and further enhancing prediction results.

[0137] Reference Figure 17As shown, the application implements a physical-data-driven sequence type earthquake generation system, which can include: an acquisition module 301, a main shock model module 302, a main shock ground motion time history generation module 303, and a aftershock model prediction module 304. The main functions of each component module are as follows:

[0138] The acquisition module 301 is used to acquire historical earthquake records.

[0139] The main shock model module 302 is used to construct a main shock ground motion random field model based on the physical mechanism of ground motion field; wherein the physical mechanism includes a source, a propagation path, and a local site model.

[0140] The main shock time history generation module 303 is used to obtain main shock parameters based on the main shock ground motion random field model according to the historical earthquake records; wherein the main shock parameters are used to predict unknown main shock earthquake records according to the main shock ground motion random field model to obtain the main shock ground motion time history; or, to obtain the main shock ground motion time history by acquiring the measured earthquake records.

[0141] The aftershock model prediction module 304 is used to construct an aftershock earthquake generation model based on the conditional adversarial generation network model according to the main shock ground motion time history to realize the prediction of the ground motion field.

[0142] As shown in Figure 18 is a block diagram of a computer device according to an embodiment of the application. The computer device is intended to represent various forms of digital computers or mobile devices. The digital computer can include a desktop computer, a portable computer, a workstation, a personal digital assistant, a server, a mainframe computer, and other suitable computers. The mobile device can include a tablet computer, a smart phone, a wearable device, and the like.

[0143] As shown in Figure 18 , the device 600 includes a computing unit 601, a ROM 602, a RAM 603, a bus 604, and an input / output (I / O) interface 605, the computing unit 601, the ROM 602, and the RAM 603 are connected to each other through the bus 604. The input / output (I / O) interface 605 is also connected to the bus 604.

[0144] The computing unit 601 can perform various processes in the embodiments of the method of the present application according to computer instructions stored in the read-only memory (ROM) 602 or loaded from the storage unit 608 into the random access memory (RAM) 603. The computing unit 601 can be various general-purpose and / or special-purpose processing components with processing and computing capabilities. The computing unit 601 can include, but is not limited to, a central processing unit (CPU), a graphics processing unit (GPU), various special-purpose artificial intelligence (AI) computing chips, various computing units running machine learning model algorithms, a digital signal processor (DSP), and any appropriate processor, controller, microcontroller, etc. In some embodiments, the method provided by the embodiments of the present application can be implemented as a computer software program, which is tangibly contained in a computer readable storage medium, such as the storage unit 608.

[0145] The RAM 603 can also store various programs and data required for the operation of the device 600. Part or all of the computer program can be loaded and / or installed on the device 600 via the ROM 602 and / or the communication unit 609.

[0146] The input unit 606, the output unit 607, the storage unit 608, and the communication unit 609 in the device 600 can be connected to the I / O interface 605. Among them, the input unit 606 can be, for example, a keyboard, a mouse, a touch screen, a microphone, etc.; the output unit 607 can be, for example, a display, a speaker, an indicator light, etc. The device 600 can exchange information, data, etc. with other devices through the communication unit 609.

[0147] Various embodiments of the systems and techniques described herein can be implemented in digital electronic circuitry, integrated circuitry, a field programmable gate array (FPGA), an application specific integrated circuit (ASIC), a system on a chip (SOC), a load programmable logic device (CPLD), computer hardware, firmware, software, and / or combinations thereof.

[0148] The computer instructions for implementing the method of the present application can be written in any combination of one or more programming languages. These computer instructions can be provided to the computing unit 601, so that when the computer instructions are executed by the computing unit 601, such as a processor, each step involved in the embodiments of the method of the present application is performed.

[0149] The computer readable storage medium provided by the present application can be a tangible medium, which can contain or store computer instructions for performing each step involved in the embodiments of the method of the present application. The computer readable storage medium can include, but is not limited to, storage media in electronic, magnetic, optical, electromagnetic, etc. forms.

[0150] The above detailed description does not limit the scope of the application. Various modifications, combinations, sub-combinations and alternatives can be made to the detailed embodiment disclosed herein without departing from the spirit and the principles of the application. Any modification, equivalent replacement or improvement made within the spirit and principles of the application shall fall within the scope of the application.

Claims

1. A physics-data driven method for generating sequence-type seismic ground motions, characterized in that, Includes the following steps: Obtain historical earthquake records; A random field model of the mainshock's ground motion is constructed based on the physical mechanism of the ground motion field; among which, The physical mechanisms include the earthquake source, propagation path, and local site model; The mainshock parameters are obtained based on the historical earthquake records and the mainshock ground motion random field model; wherein... The mainshock parameters are used to predict unknown mainshock earthquake records based on the mainshock ground motion random field model to obtain the mainshock ground motion time history; or, to obtain measured earthquake records to obtain the mainshock ground motion time history. Based on the main shock ground motion time history, an aftershock ground motion generation model is constructed using a two-dimensional convolutional conditional adversarial generative network model to predict the ground motion field. The main shock ground motion time history was obtained based on the historical earthquake records, and training and test sets were selected. The training set is used as input data to train a two-dimensional convolutional conditional generative network model to construct an aftershock ground motion generation model. Using the test set as input data, the prediction accuracy of the model on new, unseen data is predicted based on the aftershock ground motion generation model. The prediction accuracy of the aftershock ground motion generation model is verified by comparing the predicted values ​​with the actual values. The measured main shock ground motion time history, or the main shock ground motion time history obtained from the main shock parameters when the main shock time history is not available, is uniformly transformed into a two-dimensional image of the main shock ground motion through Hilbert transform. Then, the two-dimensional image of the main shock ground motion is input into the aftershock ground motion generation model to obtain a two-dimensional image of the aftershock ground motion. The two-dimensional image of the aftershock ground motion is then transformed into the aftershock ground motion time history through inverse Hilbert transform. Finally, the synthetic sequence type ground motion is obtained using the aftershock ground motion time history.

2. The method according to claim 1, characterized in that, The step of using the training set as input data to train a two-dimensional convolutional conditional adversarial generative network model to construct an aftershock ground motion generation model includes: The training set is used as input data into a two-dimensional convolutional conditional adversarial generative network model to train the two-dimensional convolutional model. The two-dimensional matrix predicted by the two-dimensional convolutional model is then transformed into a one-dimensional time sequence through an inverse Hilbert curve to obtain the predicted aftershock time history. Subsequently, the aftershock ground motion generation model is trained and constructed.

3. The method according to claim 1, characterized in that, The physical mechanism based on the seismic field is used to construct the main shock random field model, including: Based on the one-dimensional wave equation, the generation and propagation process of the main shock is represented by the time history of the ground acceleration at a distance of R from the epicenter and r from the local site center, and described by formula (1): Based on the aforementioned surface acceleration time history, the generation and propagation process of earthquake motion is decomposed according to the source, propagation path, and local site, and the amplitude spectrum and phase spectrum of the source, propagation path, and local site are constructed respectively, and described by formulas (2) and (3): A(λ,ω,R,r)=A s (a,ω)·H Ap (β,ω,R)·H As (γ,ω)·H Af (n, ω, r) (2) Φ(λ,ω,R,r)=Φ s (a,w)+H Φp (β,ω,R)+H Φs (c,w)+H Φf (h,w,r) (3) In the formula, A s (α, ω) represents the amplitude spectrum of the earthquake source, H Ap (β, ω, R), H As (γ, ω) and H Af (η, ω, r) represent the amplitude spectrum transfer functions of the propagation path, the local soil layer, and the local plane wavefield, respectively; α, β, γ, and η are random vectors in the models of the source, propagation path, local soil layer, and local plane wavefield, respectively; Φ s (α, ω) is the phase spectrum of the earthquake source, H Φp (β, ω, R), H Φs (γ, ω) and H Φf (η, ω, r) are the phase spectral transfer functions of the propagation path, the local soil layer, and the local plane wave field, respectively. Based on the amplitude and phase spectra of the source, propagation path, and local site, models of the source, propagation path, and local site are constructed respectively to obtain model parameters describing the characteristics of the source, propagation path, and local site, so as to construct a random field model of the main shock ground motion.

4. The method according to claim 3, characterized in that, The source, propagation path, and local site models are constructed based on the amplitude and phase spectra of the source, propagation path, and local site, respectively, to obtain model parameters describing the characteristics of the source, propagation path, and local site, and a random field model of the mainshock ground motion is constructed, including: Based on the amplitude and phase spectra of the earthquake source, propagation path, and local site, random variables for the earthquake source, propagation path, and local site are obtained and used to describe the characteristics of the earthquake source, propagation path, and local site to construct a model of the earthquake source, propagation path, and local site; wherein, The random variables, i.e. the model parameters, are described by formula (13): λ=[A0,τ,a,b,c,d,ξ g Oh, oh g ,α0,c g ] (13) In the formula, A0=σβ / μ represents the source amplitude coefficient, τ represents the source coefficient, the random vector of the source model is α=[A0,τ], a, b, c, d are random variables describing the variability of the propagation path, and the random vector of the propagation path model is β=[α,b, c, d], ξ g ω is the equivalent damping ratio of the site. g The site equivalent superior circular frequency is a random vector of local site soil layers. γ=[ξ g ω g ], α0 is the site seismic wave amplitude variation coefficient, c g For the average apparent wave velocity of the field, the local field plane wave field can be represented by a random vector η = [α0, c g ]express; Based on the aforementioned source model, propagation path model, and local site model, a random field model of the main shock ground motion is constructed.

5. The method according to claim 4, characterized in that, Based on the historical earthquake records, the mainshock parameters are obtained according to the mainshock ground motion random field model, including: Based on the historical earthquake records, earthquake records for identification are selected according to preset requirements; wherein... The preset requirements include selecting earthquake records for identification based on the needs, with an earthquake matrix level not less than a specific order of magnitude and a peak ground acceleration not less than a specific acceleration. Based on the main shock ground motion random field model, the amplitude spectrum model and phase spectrum model of the main shock ground motion random field model are obtained according to the Fourier transform. Based on the seismic records used for identification, the model parameters A0, τ, and ξ are identified according to the amplitude spectrum model and the phase spectrum model, respectively. g ω g a, b, c, d and α0, c g ; Based on the identified model parameters, the corresponding optimal probability model is obtained according to the Bayesian information criterion, and the marginal probability density function of each model parameter is determined to obtain the probability distribution of the model parameters and generate the main shock parameters.

6. The method according to claim 5, characterized in that, The step of selecting identification earthquake records based on the historical earthquake records according to preset requirements also includes: The seismic motions recorded for identification were uniformly modulated to 0.1g using the PGA standard and then normalized.

7. The method according to claim 5 or 6, characterized in that, Based on the seismic records used for identification, the model parameters A0, τ, and ξ are identified according to the amplitude spectrum model and the phase spectrum model, respectively. g ω g a, b, c, d and α0, c g Specifically, it includes: Based on the least squares fitting of the amplitude spectrum model, the model parameters A0, τ, and ξ in the amplitude spectrum model are identified. g and ω g ; Based on the identification, the true seismic motion phase spectrum is obtained from the seismic records; Based on the source coefficient τ of the model parameter, according to the phase spectrum model, the phase difference spectrum of the phase spectrum model is fitted to the actual phase difference spectrum distribution using the least squares criterion, and the parameters a, b, c and d in the phase spectrum model are identified using a genetic algorithm. Based on the identified model parameters A0, τ, ξ g and ω g a, b, c, and d are identified by the least squares method as the model parameter α0 in the plane wave field transfer function; The apparent velocity Cg in the model parameters is identified based on the time alignment and hysteresis determination method, where the obtained apparent velocity Cg is the mean value over frequency and is described by the formula: In the formula, N is the total number of pairs of stations, and Δr i Let Δt be the distance along the wave propagation direction of the i-th group of stations. i This represents the time lag between the i-th group of samples.

8. The method according to claim 7, characterized in that, The apparent velocity Cg is identified by the time alignment and hysteresis determination method, and Cg further includes: Based on the obtained average apparent wave velocity Cg, a bandpass filter is used to filter the target ground motion group at different frequencies. The cross-correlation function R(τ) of the filtered narrowband signal is then calculated, and the time lag τ corresponding to the maximum value of the cross-correlation function is obtained. j That is, with ω j The corresponding Δt j ; Based on the station distance and the obtained time lag Δt j , to obtain ω j The corresponding apparent velocity c gi ; Repeat the above process to obtain the apparent wave velocity Cg corresponding to different frequencies.

9. The method according to claim 1, characterized in that, The step of comparing the predicted values ​​of the aftershock ground motion generation model with the actual values ​​to verify the prediction accuracy of the aftershock ground motion generation model further includes: After adjusting the predicted value according to PGA, the intensity parameter of the predicted value is calculated and compared with the intensity parameter of the actual value; As needed, a specific number of predicted aftershock time histories are randomly selected, and their response spectra are compared with the actual recorded response spectra. The predicted time-history mean response spectra obtained by using the training set and the test set as input data are compared with the actual recorded mean response spectra.

Images