Seismic oscillation intensity parameter prediction method considering complex terrain effect

Abstract

The invention provides a seismic oscillation intensity parameter prediction method considering a complex terrain effect, and belongs to the technical field of seismic engineering. According to the method, terrain data such as elevation, gradient and curvature are introduced, a comprehensive terrain effect coefficient formula is constructed, an existing seismic oscillation prediction equation is corrected, the amplification effect of the terrain on seismic oscillation is comprehensively considered, and seismic oscillation intensity parameters of a complex terrain area can be predicted more accurately.

Description

Technical Field

[0001] The invention belongs to the technical field of earthquake engineering, and in particular relates to a method for predicting earthquake motion intensity parameters taking into account complex terrain effects. Background Art

[0002] Earthquake intensity parameters are mainly used to evaluate the impact of earthquakes on buildings, structures and infrastructure. The prediction of earthquake intensity parameters can provide a basis for structural design to ensure that buildings have sufficient earthquake resistance during earthquakes.

[0003] In related technologies, the seismic motion intensity parameter prediction method continuously improves the prediction accuracy of seismic motion intensity parameters by studying fixed influencing factors such as magnitude-related terms, fault-related terms, and site effect terms. There are few methods to consider the influence of complex terrain effects, resulting in the amplification, refraction, and reflection effects of complex terrain on seismic waves often not being fully considered in existing models, affecting the prediction accuracy of seismic motion intensity parameters in complex terrain areas.

[0004] Therefore, it is necessary to provide a method for predicting earthquake intensity parameters taking into account the complex terrain effect to solve the above problems. Summary of the invention

[0005] The present invention provides a method for predicting earthquake intensity parameters taking into account the effects of complex terrain. By introducing terrain data such as elevation, slope, and curvature, a comprehensive terrain effect coefficient formula is constructed, the existing earthquake prediction equation is corrected, and the amplification effect of terrain on earthquake motion is fully considered, thereby more accurately predicting the earthquake intensity in complex terrain areas, which can effectively solve at least one technical problem in the background technology.

[0006] In order to solve the above-mentioned technical problems, the present invention is achieved as follows:

[0007] A method for predicting earthquake intensity parameters considering complex terrain effects comprises the following steps:

[0008] Step S1, collecting data on site condition parameters, earthquake source parameters and ground motion intensity parameters under historical earthquakes in the target area;

[0009] Step S2, collecting original terrain data of the target area, selecting a target site in the target area, evenly distributing multiple sampling points in the circumferential range of different distances from the target site, calculating the relative elevation, slope and curvature of each sampling point and the target site, and taking the relative elevation, slope and curvature of all sampling points as simplified terrain data of the target area;

[0010] Step S3, considering the influence of complex terrain effects, introducing terrain effect coefficients into the traditional earthquake prediction equation to correct the earthquake prediction equation;

[0011] Step S4, based on the revised earthquake prediction equation, a prediction model is constructed by using the maximum likelihood estimation method, and the data of the site condition parameters, earthquake source parameters and earthquake intensity parameters obtained in step S1 and the simplified terrain data obtained in step S2 are input into the prediction model for iterative training until the prediction model converges or reaches the maximum number of iterations;

[0012] Step S5, for the prediction of earthquake intensity parameters of any target area, the simplified terrain data of all sampling points are input into the trained prediction model, and the predicted values ​​of the earthquake parameters of the target area are output.

[0013] As a preferred improvement, the earthquake source parameters include moment magnitude, fault dip, fault slip angle, focal depth, depth of the upper edge of the fault rupture surface from the surface, width of the fault rupture surface, the shortest distance from the fault rupture surface projected to the surface from the station, the shortest distance from the surface station to the fault rupture surface, and the shortest distance from the upper edge of the fault rupture surface projected to the surface from the station; the site condition parameters include the average shear wave velocity of the soil layer within the first 30 meters depth.

[0014] As a preferred improvement, the earthquake intensity parameters include response spectrum acceleration, peak ground acceleration and peak ground velocity at corresponding periods.

[0015] As a preferred improvement, the terrain data of the target area includes the elevation, curvature and slope at any position in the target area, which are extracted by downloading a 30-meter spatial resolution elevation data model from the Global Digital Elevation Model Version 3 database using ArcMap software.

[0016] As a preferred improvement, the revised earthquake motion prediction equation is expressed as:

[0017] lnY=f mag +f dis +f flt +f hng +f site +f sed +f hyp +f dip +f atn +f topo ;

[0018] Where, Y represents the ground motion parameter; f mag 、f dis 、f flt 、f hng 、f site 、f sed 、f hyp 、f dip 、f atnThe terms represent magnitude-related term, geometric attenuation term, fault type term, hanging wall effect term, site response term, basin response term, focal depth term, fault dip term and inelastic attenuation term respectively; f topo represents the comprehensive terrain effect coefficient, expressed as:

[0019]

[0020] In the formula, c 1 、c 2 、c 3 、c 4 、c 5 、c 6 All represent coefficients; A topo represents the terrain response coefficient; λ avg represents the weighted average slope of all sampling points; C avg represents the weighted mean curvature of all sampling points; tanh(·) represents the hyperbolic tangent function;

[0021] in:

[0022]

[0023] In the formula, c 7 、c 8 、c 9 、c 10 、c 11 、c 12 Both represent coefficients; Δh i represents the elevation difference between the i-th sampling point and the target site; n represents the total number of all sampling points; w i represents the weight of the i-th sampling point, which is determined by the distance between the sampling point and the target site. The closer the distance, the greater the weight. i The larger the value of i represents the slope of the i-th sampling point; C i represents the curvature of the i-th sampling point; ΔH avg represents the weighted average elevation difference of all sampling points; σ ΔH Represents the standard deviation of the elevation differences of all sampling points; where:

[0024]

[0025] As a preferred improvement, in step S2, "evenly distributing multiple sampling points within the circumferential range of different distances from the target site" specifically includes the following process:

[0026] Eight sampling points are evenly distributed in the circumferential range of 400 meters and 800 meters from the target site. The eight sampling points are distributed in eight directions of due north, northeast, due east, southeast, due south, southwest, due west and northwest of the target site.

[0027] As a preferred improvement, the weight w of the i-th sampling point is i The value of is determined by the following rules:

[0028] When the distance between the i-th sampling point and the target site is 400 meters, the value is 1.2;

[0029] When the distance between the i-th sampling point and the target site is 800 meters, the value is 0.8.

[0030] As a preferred improvement, step S4 specifically includes the following steps:

[0031] Step S41: construct the earthquake intensity parameter Y of the i-th sampling point i The prediction equation is expressed as:

[0032] LqCy i =f mag +f dis +f flt +f hng +f site +f sed +f hyp +f dip +f atn +f topo ;

[0033] Step S42, using the probability density function of the lognormal distribution to establish a log-likelihood function to estimate the unknown parameter c in the prediction equation 1 ,c 2 ,c 3 ...c 11 ,c 12 , the log-likelihood function L(c 1 ,c 2 ,c 3 ...c 11 ,c 12 ) is expressed as:

[0034]

[0035] In the formula, represents the logarithmic predicted median of the i-th sampling point; ln(σ i ) represents the logarithmic prediction standard deviation of the i-th sampling point;

[0036] Step S43, by maximizing the log-likelihood function, the unknown parameter c can be obtained. 1 ,c 2 ,c 3 ...c 11 ,c 12 The best estimate of The optimization problem to be solved is expressed as:

[0037]

[0038] As a preferred improvement, the unknown parameter c 1 ,c 2 ,c 3 ...c 11 ,c 12 The optimal estimate is obtained by gradient descent method.

[0039] The beneficial effects of the present invention are:

[0040] By introducing complex terrain effects and an improved parameter fitting method based on maximum likelihood estimation, the accuracy of earthquake intensity prediction is significantly improved, especially in areas with complex terrain, showing better adaptability. This method can not only effectively capture the nonlinear impact of terrain on earthquake motion, but also improve the robustness and statistical efficiency of parameter estimation. By improving the prediction accuracy of the model, the present invention provides a more reliable basis for the design of engineering structures under complex terrain, thereby helping to improve the city's earthquake resistance and resilience construction. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for describing the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative work, among which:

[0042] Figure 1 A flowchart showing the steps of a method for predicting earthquake intensity parameters taking into account complex terrain effects provided by the present invention;

[0043] Figure 2 A schematic diagram showing the distribution of sampling points in and around the target site;

[0044] Figure 3 A simplified topographic diagram showing the target site surrounded by a mountain top.

[0045] Figure 4 A simplified topographic diagram showing the flat terrain surrounding the target site;

[0046] Figure 5 A simplified topographic diagram showing the target site surrounded by a valley terrain;

[0047] Figure 6 A comparison diagram showing the prediction model proposed by the present invention and the CB2014 empirical model prediction in the prior art under mountain top terrain;

[0048] Figure 7 A comparison chart showing the prediction model proposed in the present invention and the CB2014 empirical model prediction in the prior art under valley terrain. DETAILED DESCRIPTION

[0049] The following will be combined with the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0050] like Figure 1-Figure 5 As shown, this embodiment provides a method for predicting earthquake intensity parameters taking into account complex terrain effects, comprising the following steps:

[0051] Step S1, collecting data on site condition parameters, earthquake source parameters and ground motion intensity parameters under historical earthquakes in the target area.

[0052] The earthquake source parameters include moment magnitude, fault dip, fault slip angle, focal depth, depth of the upper edge of the fault rupture surface from the ground surface, width of the fault rupture surface, the shortest distance from the fault rupture surface projected to the ground surface to the station, the shortest distance from the ground station to the fault rupture surface, and the shortest distance from the upper edge of the fault rupture surface projected to the ground surface to the station; site condition parameters include the average shear wave velocity of the soil layer within the first 30 meters depth.

[0053] The earthquake intensity parameters include the response spectrum acceleration, peak ground acceleration and peak ground velocity under the corresponding period.

[0054] Step S2, collecting the original terrain data of the target area, selecting a target site in the target area, evenly distributing multiple sampling points within the circumferential range of different distances from the target site, calculating the relative elevation, slope and curvature of each sampling point and the target site, and taking the relative elevation, slope and curvature of all sampling points as the simplified terrain data of the target area.

[0055] The topographic data of the target area include the elevation, curvature and slope at any location in the target area, which are extracted by downloading the 30-meter spatial resolution elevation data model from the third edition of the Global Digital Elevation Model database using ArcMap software.

[0056] In actual terrain, the terrain data of points at different directions and distances from the target site are different. If the complete terrain data of the target area is used as the object of research, it will bring about the problem of excessive calculation, affecting the efficiency of prediction or even failing to complete the prediction smoothly. Therefore, this application uses multi-point sampling to use the relative elevation, slope and curvature of multiple sampling points and the target site as simplified terrain data of the target area, which can greatly reduce the amount of calculation.

[0057] Specifically, in this embodiment, "evenly distributing multiple sampling points within the circumferential range at different distances from the target site" specifically includes the following process: evenly distributing 8 sampling points within the circumferential range of 400 meters and 800 meters from the target site, and the 8 sampling points are distributed in eight directions of due north, northeast, due east, southeast, due south, southwest, due west and northwest of the target site.

[0058] For a target area of ​​a certain size, the same type of topography usually has a certain distance of continuity. The distance value intervals of 400 meters and 800 meters are relatively small, which can ensure that the topography within the value interval presents a single feature as much as possible, and the two distance intervals can also be used to reflect the topography of the target area at different distances; 8 sampling points are distributed in the eight directions of the target site: due north, northeast, due east, southeast, due south, southwest, due west and northwest, which are used to reflect the topography of the study area at different directions. The combination of the two methods enables the terrain data obtained by sampling to better restore the actual terrain of the target site, thereby more accurately and comprehensively revealing the impact of complex terrain on seismic parameters. The terrain data formed comprehensively considers elevation, slope and curvature, and has a wider applicability than the traditional method of single terrain features.

[0059] Step S3, considering the influence of complex terrain effects, introducing terrain effect coefficients into the traditional earthquake prediction equation to correct the earthquake prediction equation.

[0060] The revised earthquake motion prediction equation is expressed as:

[0061] lnY=f mag +f dis +f flt +f hng +f site +f sed +f hyp +f dip +f atn +f topo ;

[0062] Where, Y represents the ground motion parameter; f mag 、f dis 、f flt 、f hng 、fsite 、f sed 、f hyp 、f dip 、f atn The terms represent magnitude-related term, geometric attenuation term, fault type term, hanging wall effect term, site response term, basin response term, focal depth term, fault dip term and inelastic attenuation term respectively; f topo represents the comprehensive terrain effect coefficient, expressed as:

[0063]

[0064] In the formula, c 1 、c 2 、c 3 、c 4 、c 5 、c 6 All represent coefficients; A topo represents the terrain response coefficient; λ avg represents the weighted average slope of all sampling points; C avg represents the weighted mean curvature of all sampling points; tanh(·) represents the hyperbolic tangent function;

[0065] in:

[0066]

[0067] In the formula, c 7 、c 8 、c 9 、c 10 、c 11 、c 12 Both represent coefficients; Δh i represents the elevation difference between the i-th sampling point and the target site; n represents the total number of all sampling points; w i represents the weight of the i-th sampling point, which is determined by the distance between the sampling point and the target site. The closer the distance, the greater the weight. i The larger the value of i represents the slope of the i-th sampling point; C i represents the curvature of the i-th sampling point; ΔH avg represents the weighted average elevation difference of all sampling points; σ ΔH Represents the standard deviation of the elevation differences of all sampling points; where:

[0068]

[0069] The weight w of the i-th sampling point i The value of is determined by the following rules:

[0070] When the distance between the i-th sampling point and the target site is 400 meters, the value is 1.2;

[0071] When the distance between the i-th sampling point and the target site is 800 meters, the value is 0.8.

[0072] Step S4, based on the revised seismic motion prediction equation, a prediction model is constructed using the maximum likelihood estimation method, and the data of the site condition parameters, earthquake source parameters and seismic motion intensity parameters obtained in step S1 and the simplified terrain data obtained in step S2 are input into the prediction model for iterative training until the prediction model converges or the maximum number of iterations is reached.

[0073] Step S4 specifically includes the following steps:

[0074] Step S41: construct the earthquake intensity parameter Y of the i-th sampling point i The prediction equation is expressed as:

[0075] LqCy i =f mag +f dis +f flt +f hng +f site +f sed +f hyp +f dip +f atn +f topo ;

[0076] Step S42, using the probability density function of the lognormal distribution to establish a log-likelihood function to estimate the unknown parameter c in the prediction equation 1 ,c 2 ,c 3 ...c 11 ,c 12 , the log-likelihood function L(c 1 ,c 2 ,c 3 ...c 11 ,c 12 ) is expressed as:

[0077]

[0078] In the formula, represents the logarithmic predicted median of the i-th sampling point; ln(σ i ) represents the logarithmic prediction standard deviation of the i-th sampling point;

[0079] Step S43, by maximizing the log-likelihood function, the unknown parameter c can be obtained. 1 ,c 2 ,c 3 ...c 11 ,c 12 The best estimate of The optimization problem to be solved is expressed as:

[0080]

[0081] Unknown parameter c 1 ,c 2 ,c 3 ...c 11 ,c 12 The optimal estimate is obtained by the gradient descent method. The gradient descent method is an iterative optimization algorithm. The principle is to calculate the gradient of the objective function with respect to the unknown parameters, and then gradually adjust the unknown parameters along the direction of gradient descent so that the value of the objective function gradually decreases, thereby approaching the optimal solution. This algorithm is applicable to most optimization problems of log-likelihood functions, has good convergence and computational efficiency, and can quickly obtain the optimal estimate of the parameters, ensuring that the seismic parameter prediction model of the present invention under complex terrain effects can obtain accurate and stable parameter fitting results.

[0082] In order to verify the effectiveness of the prediction model of the present invention, a comparative test was set up with the prediction model of the present invention and the CB2014 empirical model in the prior art. The seismic parameters were predicted in target areas with different terrains. The performance indicators used in the test included RMSE, MAE and R 2 The indicators,prediction performance comparison data are shown in Table 1:

[0083] Table 1 Comparison of the prediction performance of the prediction model of the present invention and the CB2014 empirical model in the prior art

[0084]

[0085]

[0086] Figure 6 A comparison diagram showing the prediction model proposed by the present invention and the CB2014 empirical model prediction in the prior art under mountain top terrain; Figure 7 A comparison chart showing the prediction model proposed in the present invention and the CB2014 empirical model prediction in the prior art under valley terrain.

[0087] Combined with Table 1 and Figure 6-Figure 7It can be seen that: under the conditions of mountain top and valley terrain, the prediction model of the present invention has a higher degree of agreement with the actual observation value than the CB2014 empirical model, showing a fitting accuracy that is significantly better than the CB2014 empirical model. The prediction median line of the prediction model of the present invention is closer to the reference line, indicating that it has a smaller deviation in the overall prediction, showing a better prediction accuracy. The reason is that: the terrain has a significant impact on the amplification effect of seismic wave propagation and ground motion, especially under complex terrain conditions such as mountain tops and valleys. Therefore, the prediction model of the present invention adds terrain factors on the basis of the CB2014 model, and these parameters can more accurately characterize the terrain characteristics of the site, and describe the influence of these terrains on ground motion, thereby improving the prediction accuracy of the model. In the construction process of the prediction model, the model of the present invention constructs a nonlinear relationship through multiple terrain variables, so that it has a stronger fitting ability in the face of complex terrain and non-uniform site conditions, and can effectively capture the complex influence of terrain on ground motion parameters, so that the model has higher prediction accuracy and applicability under various terrain conditions.

[0088] The embodiments of the present invention are described above in conjunction with the accompanying drawings, but the present invention is not limited to the above-mentioned specific implementation modes, which are merely illustrative rather than restrictive. Under the guidance of the present invention, ordinary technicians in this field can also make many forms without departing from the scope of protection of the present invention and the claims, all of which are within the protection of the present invention.

Claims

1. A method for predicting earthquake intensity parameters considering complex terrain effects, characterized in that: The steps include: Step S1, collecting data on site condition parameters, earthquake source parameters and ground motion intensity parameters under historical earthquakes in the target area; Step S2, collecting original terrain data of the target area, selecting a target site in the target area, evenly distributing multiple sampling points in the circumferential range of different distances from the target site, calculating the relative elevation, slope and curvature of each sampling point and the target site, and taking the relative elevation, slope and curvature of all sampling points as simplified terrain data of the target area; Step S3, considering the influence of complex terrain effects, introducing terrain effect coefficients into the traditional earthquake prediction equation to correct the earthquake prediction equation; Step S4, based on the revised earthquake prediction equation, a prediction model is constructed by using the maximum likelihood estimation method, and the data of the site condition parameters, earthquake source parameters and earthquake intensity parameters obtained in step S1 and the simplified terrain data obtained in step S2 are input into the prediction model for iterative training until the prediction model converges or reaches the maximum number of iterations; Step S5, for the prediction of earthquake intensity parameters of any target area, the simplified terrain data of all sampling points are input into the trained prediction model, and the predicted values ​​of the earthquake parameters of the target area are output.

2. The method for predicting earthquake intensity parameters considering complex terrain effects according to claim 1, characterized in that: The earthquake source parameters include moment magnitude, fault dip, fault slip angle, focal depth, depth of the upper edge of the fault rupture surface from the ground surface, width of the fault rupture surface, the shortest distance from the fault rupture surface projected to the ground surface to the station, the shortest distance from the ground station to the fault rupture surface, and the shortest distance from the upper edge of the fault rupture surface projected to the ground surface to the station; site condition parameters include the average shear wave velocity of the soil layer within the first 30 meters depth.

3. The method for predicting earthquake intensity parameters considering complex terrain effects according to claim 1, characterized in that: The earthquake intensity parameters include the response spectrum acceleration, peak ground acceleration and peak ground velocity under the corresponding period.

4. The method for predicting earthquake intensity parameters considering complex terrain effects according to claim 1, characterized in that: The topographic data of the target area, including the elevation, curvature, and slope at any location within the target area, were extracted using ArcMap software by downloading the 30-m spatial resolution elevation data model from the Global Digital Elevation Model Version 3 database.

5. The method for predicting earthquake intensity parameters considering complex terrain effects according to claim 1, characterized in that: The revised earthquake motion prediction equation is expressed as: lnY=f mag +f dis +f flt +f hng +f site +f sed +f hyp +f dip +f atn +f topo ; Where, Y represents the ground motion parameter; f mag 、f dis 、f flt 、f hng 、f site 、f sed 、f hyp 、f dip 、f atn The terms represent magnitude-related term, geometric attenuation term, fault type term, hanging wall effect term, site response term, basin response term, focal depth term, fault dip term and inelastic attenuation term respectively; f topo represents the comprehensive terrain effect coefficient, expressed as: In the formula, c1, c2, c3, c4, c5, c6 are coefficients; A topo represents the terrain response coefficient; λ avg represents the weighted average slope of all sampling points; C avg represents the weighted mean curvature of all sampling points; tanh(·) represents the hyperbolic tangent function; in: In the formula, c7, c8, c9, c 10 、c 11 、c 12 Both represent coefficients; Δh i represents the elevation difference between the i-th sampling point and the target site; n represents the total number of all sampling points; w i represents the weight of the i-th sampling point, which is determined by the distance between the sampling point and the target site. The closer the distance, the greater the weight. i The larger the value of i represents the slope of the i-th sampling point; C i represents the curvature of the i-th sampling point; ΔH avg represents the weighted average elevation difference of all sampling points; σ ΔH Represents the standard deviation of the elevation differences of all sampling points; where:

6. The method for predicting earthquake intensity parameters considering complex terrain effects according to claim 5, characterized in that: In step S2, "evenly distributing multiple sampling points within the circumferential range of different distances from the target site" specifically includes the following process: Eight sampling points are evenly distributed in the circumferential range of 400 meters and 800 meters from the target site. The eight sampling points are distributed in eight directions of due north, northeast, due east, southeast, due south, southwest, due west and northwest of the target site.

7. The method for predicting earthquake intensity parameters considering complex terrain effects according to claim 6, characterized in that: The weight w of the i-th sampling point i The value of is determined by the following rules: When the distance between the i-th sampling point and the target site is 400 meters, the value is 1.2; When the distance between the i-th sampling point and the target site is 800 meters, the value is 0.

8.

8. The method for predicting earthquake intensity parameters considering complex terrain effects according to claim 5, characterized in that: Step S4 specifically includes the following steps: Step S41: construct the earthquake intensity parameter Y of the i-th sampling point i The prediction equation is expressed as: lnY i =f mag +f dis +f flt +f hng +f site +f sed +f hyp +f dip +f atn +f topo ; Step S42, using the probability density function of the log-normal distribution to establish a log-likelihood function, and estimating the unknown parameters c1, c2, c3...c in the prediction equation 11 ,c 12 , the log-likelihood function L(c1,c2,c3...c 11 ,c 12 ) is expressed as: In the formula, represents the logarithmic predicted median of the i-th sampling point; ln(σ i ) represents the logarithmic prediction standard deviation of the i-th sampling point; Step S43, by maximizing the log-likelihood function, the unknown parameters c1, c2, c3...c 11 ,c 12 The best estimate of The optimization problem to be solved is expressed as:

9. The method for predicting earthquake intensity parameters considering complex terrain effects according to claim 8, characterized in that: Unknown parameters c1, c2, c3...c 11 ,c 12 The optimal estimate is obtained by gradient descent method.

Images