A method for predicting seismic intensity parameters considering complex topographic effects

Abstract

This invention provides a method for predicting seismic intensity parameters that considers the effects of complex terrain, belonging to the field of earthquake engineering technology. By introducing terrain data such as elevation, slope, and curvature, this invention constructs a comprehensive terrain effect coefficient formula, correcting existing seismic prediction equations and comprehensively considering the amplification effect of terrain on seismic motions. This allows for more accurate prediction of seismic intensity parameters in areas with complex terrain.

Description

Technical Field

[0001] This invention belongs to the field of earthquake engineering technology, specifically relating to a method for predicting seismic motion intensity parameters that takes into account complex terrain effects. Background Technology

[0002] Seismic intensity parameters are primarily used to assess the impact of earthquakes on buildings, structures, and infrastructure. Predictions of seismic intensity parameters can provide a basis for structural design, ensuring that buildings have sufficient seismic resistance during earthquakes.

[0003] In related technologies, methods for predicting ground motion intensity parameters continuously improve the prediction accuracy of ground motion intensity parameters by studying fixed influencing factors such as magnitude correlation terms, fault correlation terms, and site effect terms. However, few methods consider the influence of complex terrain effects. As a result, the amplification, refraction, and reflection effects of complex terrain on seismic waves are often not fully considered in existing models, which affects the prediction accuracy of ground motion intensity parameters in complex terrain areas.

[0004] Therefore, it is necessary to provide a method for predicting seismic intensity parameters that takes into account the effects of complex terrain in order to solve the above problems. Summary of the Invention

[0005] This invention provides a method for predicting seismic intensity parameters that takes 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 to correct the existing seismic prediction equation. This method comprehensively considers the amplification effect of terrain on seismic motion, thereby more accurately predicting the seismic intensity in complex terrain areas. It can effectively solve at least one technical problem in the background art.

[0006] To solve the above-mentioned technical problems, the present invention is implemented as follows:

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

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

[0009] Step S2: Collect the original terrain data of the target area, select the target site in the target area, and evenly distribute multiple sampling points within the circumferential range at different distances from the target site. Calculate the relative elevation, slope and curvature of each sampling point relative to the target site, and use the relative elevation, slope and curvature of all sampling points as the simplified terrain data of the target area.

[0010] Step S3: Considering the influence of complex terrain effects, a terrain effect coefficient is introduced into the traditional seismic motion prediction equation to modify the seismic motion prediction equation.

[0011] Step S4: Based on the modified seismic motion prediction equation, a prediction model is constructed using the maximum likelihood estimation method. The site condition parameters, earthquake source parameters, and seismic motion intensity parameters obtained in Step S1, as well as the simplified topographic 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 ground motion intensity parameters of any target area, input the simplified terrain data of all sampling points into the trained prediction model and output the predicted values ​​of ground motion parameters for the target area.

[0013] As a preferred improvement, the earthquake source parameters include moment magnitude, fault dip angle, fault slip angle, source depth, depth of the upper edge of the fault rupture surface from the ground surface, width of the fault rupture surface, shortest distance from the ground surface projected to the station, shortest distance from the ground station to the fault rupture surface, and 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 of depth.

[0014] As a preferred improvement, the seismic intensity parameters include the response spectrum acceleration, peak ground acceleration, and peak ground velocity for the corresponding period.

[0015] As a preferred improvement, the terrain data of the target area includes the elevation, curvature, and slope at any location within the target area. This data is obtained by downloading a 30-meter spatial resolution elevation data model from the Global Digital Elevation Model, 3rd Edition database and extracting it using ArcMap software.

[0016] As a preferred improvement, the modified seismic 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] In the formula, Y represents the seismic motion parameter; f mag f dis f flt f hng f site f sed f hyp f dip f atnThe terms represent the magnitude correlation term, geometric attenuation term, fault type term, hanging wall effect term, site response term, basin response term, focal depth term, fault dip angle term, and inelastic attenuation term, respectively; f topo The comprehensive topographic effect coefficient is expressed as:

[0019]

[0020] In the formula, c1, c2, c3, c4, c5, and c6 all represent coefficients; A topo Represents the terrain response coefficient; λ avg C represents the weighted average slope of all sampling points; avg The tanh function represents the weighted average curvature of all sampled points; tanh(·) represents the hyperbolic tangent function.

[0021] in:

[0022]

[0023] In the formula, c7, c8, c9, c 10 c 11 c 12 All represent coefficients; Δh i The elevation difference between the i-th sampling point and the target site is represented by n; the total number of sampling points is represented by w. i The weight of the i-th sampling point is determined by its distance from the target site; the closer the distance, the higher the weight of the sampling point. i The larger the value of λ, the better. i C represents the slope of the i-th sampling point; i ΔH represents the curvature of the i-th sampling point; avg σ represents the weighted average elevation difference of all sampling points. ΔH This represents the standard deviation of the elevation differences of all sampling points; where:

[0024]

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

[0026] Eight sampling points were evenly distributed in the circumferential ranges of 400 meters and 800 meters from the target site. The eight sampling points were located in the 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 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 ground motion intensity parameter Y at the i-th sampling point. i The prediction equation is expressed as:

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

[0033] Step S42: Establish the log-likelihood function using the probability density function of the log-normal distribution, and estimate 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 represented as:

[0034]

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

[0036] Step S43: By maximizing the log-likelihood function, the unknown parameters c1, c2, c3...c can be obtained. 11 ,c 12 The optimal estimate The optimization problem to be solved is expressed as:

[0037]

[0038] As a preferred improvement, the unknown parameters c1, c2, c3...c 11 ,c 12 The optimal estimate is obtained by solving the gradient descent method.

[0039] The beneficial effects of this invention are as follows:

[0040] By incorporating complex terrain effects and an improved parameter fitting method based on maximum likelihood estimation, the accuracy of seismic intensity prediction is significantly improved, exhibiting superior adaptability, especially in areas with complex terrain. This method not only effectively captures the nonlinear influence of terrain on seismic motion but also improves the robustness and statistical efficiency of parameter estimation. By enhancing the model's prediction accuracy, this invention provides a more reliable basis for the design of engineering structures in complex terrains, thereby contributing to improving the seismic resistance and resilience of cities. Attached Figure Description

[0041] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. 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 effort, wherein:

[0042] Figure 1 This is a flowchart illustrating the steps of a method for predicting seismic intensity parameters that takes 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 topographical diagram showing that the target site is surrounded by mountain peaks.

[0045] Figure 4 A simplified topographical diagram showing the flat terrain surrounding the target site.

[0046] Figure 5 A simplified topographical diagram showing that the target site is surrounded by valley terrain.

[0047] Figure 6 This diagram shows a comparison between the prediction model proposed in this invention and the existing CB2014 empirical model for mountain top terrain.

[0048] Figure 7 This figure shows a comparison between the prediction model proposed in this invention and the CB2014 empirical model in the prior art for valley terrain. Detailed Implementation

[0049] The technical solutions of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0050] like Figures 1-5 As shown, this embodiment provides a method for predicting seismic intensity parameters considering complex terrain effects, including the following steps:

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

[0052] Earthquake source parameters include moment magnitude, fault dip angle, 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, shortest distance from the ground surface projected to the station, shortest distance from the ground station to the fault rupture surface, and 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 of depth.

[0053] Seismic intensity parameters include response spectrum acceleration, peak ground acceleration, and peak ground velocity for the corresponding period.

[0054] Step S2: Collect the original terrain data of the target area. Select the target site in the target area and evenly distribute multiple sampling points within the circumferential range at different distances from the target site. Calculate the relative elevation, slope and curvature of each sampling point relative to the target site. Use the relative elevation, slope and curvature of all sampling points as the simplified terrain data of the target area.

[0055] The terrain data for the target area includes the elevation, curvature, and slope at any location within the target area. This data was obtained by downloading a 30-meter spatial resolution elevation data model from the Global Digital Elevation Model (GEM) 3rd edition database and extracting it using ArcMap software.

[0056] In actual terrain, the terrain data varies at points at different locations and distances within the target site. Using complete terrain data of the target area as the research object would result in excessive computational load, affecting prediction efficiency and even preventing successful prediction. Therefore, this application uses a multi-point sampling method, employing the relative elevation, slope, and curvature of multiple sampling points relative to the target site as simplified terrain data for the target area, which can significantly reduce the computational load.

[0057] Specifically, in this embodiment, "evenly distributing multiple sampling points within the circumferential range at different distances from the target site" includes the following process: evenly distributing 8 sampling points within the circumferential range at 400 meters and 800 meters from the target site, with the 8 sampling points distributed in the 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 terrain usually exhibits continuity over a certain distance. The relatively small distance ranges of 400 meters and 800 meters ensure that the terrain within these ranges exhibits a single characteristic, and these two distance ranges can also reflect the terrain conditions of the target area at different distances. Eight sampling points are distributed in eight directions—north, northeast, east, southeast, south, southwest, west, and northwest—to reflect the terrain conditions of the study area in different directions. The combination of these two methods allows the sampled terrain data to better reconstruct the actual terrain of the target site, thus revealing the impact of complex terrain on seismic motion parameters more accurately and comprehensively. The resulting terrain data comprehensively considers elevation, slope, and curvature, and has wider applicability compared to traditional methods that rely on single terrain features.

[0059] Step S3: Considering the influence of complex terrain effects, a terrain effect coefficient is introduced into the traditional seismic motion prediction equation to modify the seismic motion prediction equation.

[0060] The revised seismic 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] In the formula, Y represents the seismic motion parameter; f mag f dis f flt f hng f site f sed f hyp f dip f atn The terms represent the magnitude correlation term, geometric attenuation term, fault type term, hanging wall effect term, site response term, basin response term, focal depth term, fault dip angle term, and inelastic attenuation term, respectively; f topo The comprehensive topographic effect coefficient is expressed as:

[0063]

[0064] In the formula, c1, c2, c3, c4, c5, and c6 all represent coefficients; A topo Represents the terrain response coefficient; λ avg C represents the weighted average slope of all sampling points; avgThe tanh function represents the weighted average curvature of all sampled points; tanh(·) represents the hyperbolic tangent function.

[0065] in:

[0066]

[0067] In the formula, c7, c8, c9, c 10 c 11 c 12 All represent coefficients; Δh i The elevation difference between the i-th sampling point and the target site is represented by n; the total number of sampling points is represented by w. i The weight of the i-th sampling point is determined by its distance from the target site; the closer the distance, the higher the weight of the sampling point. i The larger the value of λ, the better. i C represents the slope of the i-th sampling point; i ΔH represents the curvature of the i-th sampling point; avg σ represents the weighted average elevation difference of all sampling points. ΔH This 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 modified seismic motion prediction equation, a prediction model is constructed using the maximum likelihood estimation method. The site condition parameters, earthquake source parameters, and seismic motion intensity parameters obtained in Step S1, as well as the simplified topographic 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.

[0073] Step S4 specifically includes the following steps:

[0074] Step S41, construct the ground motion intensity parameter Y at the i-th sampling point. i The prediction equation is expressed as:

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

[0076] Step S42: Establish the log-likelihood function using the probability density function of the log-normal distribution, and estimate 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 represented as:

[0077]

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

[0079] Step S43: By maximizing the log-likelihood function, the unknown parameters c1, c2, c3...c can be obtained. 11 ,c 12 The optimal estimate The optimization problem to be solved is expressed as:

[0080]

[0081] Unknown parameters c1, c2, c3...c 11 ,c 12 The optimal estimate is obtained using the gradient descent method. Gradient descent is an iterative optimization algorithm that works by calculating the gradient of the objective function with respect to unknown parameters, and then gradually adjusting the unknown parameters along the gradient descent direction to decrease the value of the objective function, thus approaching the optimal solution. This algorithm is applicable to most log-likelihood function optimization problems, exhibits good convergence and computational efficiency, and can quickly obtain the optimal estimate of the parameters, ensuring that the seismic motion parameter prediction model of this invention under complex terrain effects can obtain accurate and stable parameter fitting results.

[0082] To verify the effectiveness of the prediction model of this invention, a comparative experiment was conducted between the prediction model of this invention and the existing CB2014 empirical model. Seismic motion parameters were predicted in target areas with different terrains. The performance indicators used in the experiment included RMSE, MAE, and R... 2 The metrics and predictive performance comparison data are shown in Table 1:

[0083] Table 1. Comparison of prediction performance between the prediction model of this invention and the existing CB2014 empirical model.

[0084]

[0085]

[0086] Figure 6 This diagram shows a comparison between the prediction model proposed in this invention and the existing CB2014 empirical model for mountain top terrain. Figure 7 This figure shows a comparison between the prediction model proposed in this invention and the CB2014 empirical model in the prior art for valley terrain.

[0087] Combined with Table 1 and Figures 6-7 It can be seen that, under mountaintop and valley terrain conditions, the prediction model of this invention has a higher degree of agreement with actual observations compared to the CB2014 empirical model, demonstrating significantly better fitting accuracy. The predicted median line of the prediction model of this invention is closer to the reference line, indicating a smaller overall prediction bias and superior prediction accuracy. This is because terrain has a significant impact on seismic wave propagation and ground motion amplification, especially under complex terrain conditions such as mountaintops and valleys. Therefore, the prediction model of this invention incorporates terrain factors based on the CB2014 model. These parameters can more accurately characterize the terrain features of the site and describe the influence of this terrain on ground motion, thereby improving the model's prediction accuracy. In the construction of the prediction model, this invention uses a nonlinear relationship constructed through the interaction of multiple terrain variables, giving it a stronger fitting ability under complex terrain and non-uniform site conditions. It can effectively capture the complex influence of terrain on ground motion parameters, making the model more accurate and applicable under various terrain conditions.

[0088] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims, and all of these forms are within the protection scope of the present invention.

Claims

1. A method for predicting seismic intensity parameters considering complex terrain effects, characterized in that, Includes the following steps: Step S1: Collect data on site condition parameters, earthquake source parameters, and ground motion intensity parameters under historical earthquakes in the target area; Step S2: Collect the original terrain data of the target area, select the target site in the target area, and evenly distribute multiple sampling points within the circumferential range at different distances from the target site. Calculate the relative elevation, slope and curvature of each sampling point relative to the target site, and use the relative elevation, slope and curvature of all sampling points as the simplified terrain data of the target area. Step S3: Considering the influence of complex terrain effects, a terrain effect coefficient is introduced into the traditional seismic motion prediction equation to modify the seismic motion prediction equation. Step S4: Based on the modified seismic motion prediction equation, a prediction model is constructed using the maximum likelihood estimation method. The site condition parameters, earthquake source parameters, and seismic motion intensity parameters obtained in Step S1, as well as the simplified topographic 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 ground motion intensity parameters of any target area, input the simplified topographic data of all sampling points into the trained prediction model and output the predicted value of ground motion parameters of the target area. In step S2, "evenly distributing multiple sampling points within a circumferential range at different distances from the target site" specifically includes the following process: Eight sampling points were evenly distributed in the circumferential ranges of 400 meters and 800 meters from the target site. The eight sampling points were distributed in the eight directions of due north, northeast, due east, southeast, due south, southwest, due west and northwest of the target site. The revised seismic motion prediction equation is expressed as: ； In the formula, Indicates seismic motion parameters; The terms represent magnitude-related terms, geometric attenuation terms, fault type terms, hanging wall effect terms, site response terms, basin response terms, focal depth terms, fault dip angle terms, and inelastic attenuation terms, respectively. The comprehensive topographic effect coefficient is expressed as: ； In the formula, All represent coefficients; Indicates the terrain response coefficient; This represents the weighted average slope of all sampling points; This represents the weighted average curvature of all sampled points; Represents the hyperbolic tangent function; in: ； In the formula, All represent coefficients; Indicates the first i The elevation difference between each sampling point and the target site; n This represents the total number of all sampling points; Indicates the first i The weight of each sampling point is determined according to its distance from the target site; the closer the distance, the higher the weight. The larger the value of ; Indicates the first i The slope of each sampling point; Indicates the first i The curvature of each sampling point; This represents the weighted average elevation difference of all sampling points; This represents the standard deviation of the elevation differences of all sampling points; where: ； ； ； 。 2. The method for predicting seismic intensity parameters considering complex terrain effects according to claim 1, characterized in that, Earthquake source parameters include moment magnitude, fault dip angle, 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, shortest distance from the ground surface projected to the station, shortest distance from the ground station to the fault rupture surface, and 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 of depth.

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

4. The method for predicting seismic intensity parameters considering complex terrain effects according to claim 1, characterized in that, The terrain data for the target area includes the elevation, curvature, and slope at any location within the target area. This data was obtained by downloading a 30-meter spatial resolution elevation data model from the Global Digital Elevation Model, 3rd Edition database and extracting it using ArcMap software.

5. The method for predicting seismic intensity parameters considering complex terrain effects according to claim 1, characterized in that, No. i Weight of each sampling point The value of is determined by the following rules: No. i When the distance between a sampling point and the target site is 400 meters, the value is 1.2; No. i When the distance between a sampling point and the target site is 800 meters, the value is 0.

8.

6. The method for predicting seismic intensity parameters considering complex terrain effects according to claim 1, characterized in that, Step S4 specifically includes the following steps: Step S41, construct the first i Seismic intensity parameters at each sampling point The prediction equation is expressed as: ； Step S42: Establish the log-likelihood function using the probability density function of the log-normal distribution, and estimate the unknown parameters in the prediction equation. Log-likelihood function Represented as: ； In the formula, Indicates the first i The logarithmic predicted median of each sampling point; Indicates the first i Logarithmic prediction standard deviation of each sampling point; Step S43: By maximizing the log-likelihood function, the unknown parameters can be obtained. The optimal estimate The optimization problem to be solved is expressed as: 。 7. The method for predicting seismic intensity parameters considering complex terrain effects according to claim 6, characterized in that, Unknown parameters The optimal estimate is obtained by solving the gradient descent method.

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