A method for synthesizing multi-dimensional non-stationary ground motions near faults considering the characteristics of finite-fault sources

Abstract

The present invention relates to the technical field of seismology, and provides a method for synthesizing near-fault multi-dimensional non-stationary ground motions considering finite-fault source characteristics, including: (1) using a near-fault spatial coherence function model that can consider different specified magnitudes, source mechanism parameters, and source depth conditions to obtain the coherence coefficients of the horizontal components of ground motions between each site within the target site; (2) constructing a power spectrum matrix between each site within the target site according to the power spectrum and the coherence function model; (3) decomposing the power spectrum matrix, calculating the amplitudes and phase angles corresponding to different frequency components between sites, and using the trigonometric series method to synthesize the stationary ground motion time histories of each point within the site; (4) modulating the stationary ground motion using the time history envelope function to form a spatially correlated non-stationary ground motion field of the target site considering finite-fault source characteristics. The present invention can preferably synthesize a non-stationary ground motion field.

Description

Technical Field

[0001] The present invention relates to the technical field of seismology, and in particular, to a method for synthesizing multi-dimensional non-stationary ground motions near a fault considering the characteristics of a finite-fault earthquake source. Background Art

[0002] In recent years, large earthquake disasters have shown that the damage to many structures in the near field of large earthquakes often exceeds the current expectations of engineering seismic fortification, which is related to the complexity of near-fault ground motions. In the near field of large earthquakes, significantly affected by the earthquake source rupture process, the ground motions not only have strong amplitudes but also show strong spatial differences. With the development of China's infrastructure network towards complex mountainous areas and geological tectonic regions, it is often inevitable for structures near or crossing active fault zones. The seismic fortification basis for engineering structures in the near-fault area has become an urgent need. At present, when designing the seismic resistance of structures in the near and across-fault areas, seismic excitations often adopt measured records, or further adopt multiple different measured records to consider the influence of ground motion uncertainty. However, due to the unpredictability of large earthquakes and the sparse distribution of stations near the earthquake source, the near-field records of the main shocks of large earthquakes are particularly scarce, especially the measured records at the across-fault parts are even rarer, and the spatial differences of the ground motion field in the near-fault area cannot be fully described. Therefore, it is of great practical significance to provide a seismic load basis for structures in the near and across-fault areas.

[0003] The ground motion at a site is the result of the combined influence of the earthquake source rupture process, propagation attenuation effect, and local site soil layer, which also causes differences in the duration, amplitude, and spectral characteristics of the ground motion. To avoid serious damage to bridge structures under near and across-fault seismic actions, the "Code for Seismic Design of Highway Bridges" (JTG / T 2231-01—2020) clearly states that: "When there are geological discontinuities or topographic features in the site within a bridge span that may cause significant differences in the ground motion parameters of each pier, or the total length of a bridge span exceeds 600 m, multi-point non-uniform excitation should be adopted to consider the spatial variation of the ground motion, including wave propagation effect, coherence effect, and site differences of different tower and pier foundations". The common practice is to synthesize multi-point non-uniform excitation based on the random vibration theory, and the reasonable selection of the power spectrum model and coherence function model is the key to random ground motion synthesis. However, for the coherence effect, currently, most empirical coherence function models focus on describing the influence of coherence on frequency and station spacing. In the development process in recent years, it has gradually evolved from initially only considering the traveling wave effect to being able to simultaneously consider the traveling wave effect, incoherent effect, and local site effect, while the research on the influence of earthquake source characteristics on the coherence effect is still less. In addition, the established coherence function models are mostly for the coherence of one ground motion component, or assume that the coherence of the two horizontal orthogonal components is the same, which is significantly inconsistent with the actual situation where the coherence of different components of the ground motion is significantly different.

[0004] Due to insufficient consideration of the characteristics of finite-fault earthquake sources and the differences in the coherence of ground motion components, the synthesized ground motion field is not reasonable enough to describe the spatial difference characteristics of multi-dimensional ground motion in the near-source area, which may lead to the risk of insufficient seismic fortification levels for structures in the near- and cross-fault areas. Therefore, aiming at the deficiencies in the description of near-fault effects by existing spatially correlated ground motion synthesis methods, a near-fault multi-dimensional non-stationary ground motion synthesis method that can consider the characteristics of finite-fault earthquake sources is invented, which can provide a reference for the seismic loads in the seismic design of structures in the near- and cross-fault areas. Summary of the Invention

[0005] The content of the present invention is to provide a near-fault multi-dimensional non-stationary ground motion synthesis method that considers the characteristics of finite-fault earthquake sources, which can solve the problem of insufficient consideration of the influence of the characteristics of finite-fault earthquake sources in the near-field area on the coherence function in the spatially correlated ground motion field synthesis method.

[0006] A near-fault multi-dimensional non-stationary ground motion synthesis method that considers the characteristics of finite-fault earthquake sources according to the present invention includes the following steps:

[0007] (1) Using a near-fault spatial coherence function model that can consider different specified magnitudes, earthquake source mechanism parameters, and earthquake source depths, obtain the coherence coefficients of the horizontal components of ground motion between each field point within the target site;

[0008] (2) According to the power spectrum and the coherence function model, construct the power spectrum matrix between each field point within the target site;

[0009] (3) Decompose the power spectrum matrix, calculate the amplitudes and phase angles corresponding to different frequency components between field points, and use the trigonometric series method to synthesize the stationary ground motion time history of each point within the site;

[0010] (4) Modulate the stationary ground motion using the time history envelope function to form a spatially correlated non-stationary ground motion field of the target site that considers the characteristics of finite-fault earthquake sources.

[0011] Preferably, in step (1), the coherence function model uses a spatial coherence function model that considers the characteristics of finite-fault earthquake sources.

[0012] Preferably, in step (1), the specific calculation order of the coherence coefficient is: first, according to the actual earthquake source mechanism parameters, earthquake source depth, epicentral distance, and point-to-point spacing, calculate the regression coefficient in the statistical relationship between the characteristic parameters of the coherence function model and the magnitude; then, according to the specified magnitude and the regression coefficient, calculate the characteristic parameters of the coherence function model for different horizontal component ground motion time histories, and substitute them into the coherence function model to obtain the ground motion coherence coefficient curves between field points with different magnitudes and different horizontal components.

[0013] Preferably, in step (2), the power spectrum is the Du Xiuli-Chen Houqun power spectrum, which can take into account different site types and is specifically characterized by three parameters: spectral intensity factor, site dominant frequency, and site soil damping ratio.

[0014] Preferably, in step (2), the power spectrum matrix is extended based on the power spectra of all field points within the site and the different coherence functions corresponding to the parallel fault components and perpendicular fault components between any two points.

[0015] Preferably, in step (3), the Cholesky decomposition is used for the decomposition of the power spectrum matrix. The directions of the stationary ground motions synthesized by the trigonometric series method correspond to the components of the coherence function in step (1), namely, the time histories of the stationary ground motions of the parallel fault components and the perpendicular fault components.

[0016] Preferably, in step (4), the time history envelope function is a piecewise function, including three segments: rising, stationary, and decaying, thereby forming the non-stationary ground motion time histories of the parallel fault components and the perpendicular fault components.

[0017] The beneficial effects of the present invention are as follows:

[0018] (1) In the present invention, the synthesis of non-stationary ground motions in the near-fault region can take into account the differences in spatial coherence between different horizontal components. Most of the currently established coherence function models are for the coherence of one ground motion component, or assume that the coherence of the two orthogonal horizontal components is the same, which is significantly inconsistent with the actual situation where there are significant differences in the coherence of different components of ground motions. Different from the existing random ground motion synthesis methods, the present invention uses corresponding coherence function models for the parallel fault components and the perpendicular fault components respectively, thereby constructing a multi-point multi-dimensional power spectrum matrix that can consider the differences in coherence between different horizontal components, and then synthesizing the corresponding ground motion time histories of different horizontal components.

[0019] (2) In the present invention, the synthesis of non-stationary ground motions in the near-fault region can take into account different future specified magnitudes and seismogenic fault characteristic scenarios. At present, most of the empirical coherence function models focus on describing the influence of coherence on frequency and station spacing, and have gradually developed from only considering the traveling wave effect at the beginning to being able to consider the traveling wave effect, incoherent effect, and local site effect simultaneously in recent years. However, there is still little research on the influence of source characteristics on the coherence effect. Different from the existing random ground motion synthesis methods, in the coherence function model adopted by the present invention, the coherence coefficient is related to the magnitude, source characteristics, source depth, etc. through the statistical relationship parameters of the coherence coefficient and magnitude, and can quantitatively give the coherence coefficients of different horizontal components of ground motions under different specified earthquake source characteristic conditions, which is more suitable for predicting future earthquake scenarios.

[0020] (3) In the present invention, the synthesis of non-stationary ground motions in the near-fault region can consider the influence of fault type, source mechanism parameters, and source depth factors. In the near-field region of large earthquakes, the ground motion field is controlled by the earthquake source, and source mechanism parameters, source depth, etc. will all have a significant impact on the spatial distribution characteristics of the ground motion field in the near-fault region. However, the coherence function models adopted in current spatial-correlated multi-point ground motion synthesis methods often consider less the differences in future earthquake source characteristics. Different from existing synthesis methods, the present invention considers the mechanism parameters, source depth, etc. of the future earthquake occurrence fault in the coherence function model, and thus the synthesized ground motion field can better reflect the significant impact of the source rupture process in the near-fault region on the ground motion field. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 is a flow chart of a near-fault multi-dimensional non-stationary ground motion synthesis method considering finite-fault source characteristics;

[0022] FIG. 2(a) is an example diagram of the coherence coefficient curves of the parallel-fault components corresponding to different magnitudes in the case of a strike-slip fault;

[0023] FIG. 2(b) is an example diagram of the coherence coefficient curves of the vertical-fault components corresponding to different magnitudes in the case of a strike-slip fault;

[0024] FIG. 3(a) is an example diagram of the coherence coefficient curves of the parallel-fault components corresponding to different magnitudes in the case of a dip-slip fault;

[0025] FIG. 3(b) is an example diagram of the coherence coefficient curves of the vertical-fault components corresponding to different magnitudes in the case of a dip-slip fault;

[0026] Figure 4 is a schematic diagram of the acceleration time history of a field point in the near-fault region synthesized under strike-slip fault conditions;

[0027] Figure 5 is a schematic diagram for comparing the differences in the acceleration, velocity, and displacement time histories of ground motions at different field points synthesized under strike-slip fault conditions;

[0028] Figure 6 is a schematic diagram for comparing the differences in the displacement time histories corresponding to selected field points under strike-slip fault conditions;

[0029] FIG. 7(a) is a schematic diagram of the acceleration Fourier spectrum of the parallel-fault component corresponding to a selected field point under strike-slip fault conditions;

[0030] FIG. 7(b) is a schematic diagram of the acceleration Fourier spectrum of the vertical-fault component corresponding to a selected field point under strike-slip fault conditions. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0031] To further understand the content of the present invention, the present invention will be described in detail in combination with the accompanying drawings and embodiments. It should be understood that the embodiments are only for explaining the present invention rather than limiting it.

[0032] Embodiment

[0033] As Figure 1 shown, this embodiment provides a method for synthesizing near-fault multi-dimensional non-stationary ground motions considering the characteristics of finite-fault earthquake sources, which includes the following steps:

[0034] (1) Using a near-fault spatial coherence function model that can consider different set magnitudes, earthquake source mechanism parameters, and earthquake source depths, obtain the coherence coefficients of the horizontal components of ground motions between each site in the target site.

[0035] The coherence function model adopts a spatial coherence function model considering the characteristics of finite-fault earthquake sources.

[0036] The specific calculation sequence of the coherence coefficient is as follows: First, according to the actual earthquake source mechanism parameters, earthquake source depth, epicentral distance, and point pair spacing, calculate the regression coefficients in the statistical relationship between the characteristic parameters of the coherence function model and the magnitude; then, according to the set magnitude and the regression coefficients, calculate the characteristic parameters of the coherence function model for different horizontal component ground motion time histories, and substitute them into the coherence function model to obtain the coherence coefficient curves of ground motions between sites with different magnitudes and different horizontal components.

[0037] Coherence function γ kl (iw n ,d kl ) can be described as:

[0038] γ kl (iw n ,d kl ) = γ kl (iw n ,d kl )|exp(-iw n d kl / v app )

[0039] In the formula, wn is the nth frequency point; dkl is the projection of the horizontal distance between two points along the direction of seismic wave propagation; vapp is the apparent wave velocity of the seismic wave; γ kl (iw n )| is the hysteretic coherence function, and i is the imaginary unit. The hysteretic coherence coefficient adopts the Loh hysteretic coherence function model, and the calculation formula is:

[0040] γ kl (iw n ,d kl )| = exp[-(a + bw n 2)d kl

[0041] In the formula, a and b are the characteristic parameters of the Loh coherence function model, and the corresponding relationship with the magnitude is:

[0042] log(a) = β0 + β1M w

[0043] log(b) = β2 + β3M w

[0044] In the formula, β0, β1, β2, and β3 are regression coefficients, and M w is the magnitude. Among them, the regression coefficient β is related to the fault dip the focal depth H and the epicentral distance R epi and the corresponding relationship between the station spacing d is:

[0045]

[0046] In the formula, λ0, λ1, λ2, λ3, and λ4 are the parameters corresponding to the variables in the above formula. The parameter values corresponding to the parallel fault component and the vertical fault component in the strike-slip and dip-slip cases are shown in Tables 1 to 4.

[0047] Table 1 Parameter values of the parallel fault component in the strike-slip case

[0048] Parameter <![CDATA[λ0]]> <![CDATA[λ1]]> <![CDATA[λ2]]> <![CDATA[λ3]]> <![CDATA[λ4]]> <![CDATA[β0]]> -3.5220 0.0186 -0.0200 -0.0350 0.8764 <![CDATA[β1]]> 0.4290 -0.0022 -0.0010 -0.0038 -0.1525 <![CDATA[β2]]> -7.3111 0.0045 0.0711 0.0749 0.5428 <![CDATA[β3]]> 0.6844 -0.0010 -0.0122 -0.0193 -0.1231

[0049] Table 2 Parameter values of the vertical fault component in the strike-slip case

[0050] Parameter <![CDATA[λ0]]> <![CDATA[λ1]]> <![CDATA[λ2]]> <![CDATA[λ3]]> <![CDATA[λ4]]> <![CDATA[β0]]> -1.4901 -0.0199 -0.0124 -0.1784 1.6367 <![CDATA[β1]]> 0.1756 0.0024 -0.0015 0.0354 -0.2435 <![CDATA[β2]]> -7.1080 0.0004 0.0654 0.0125 0.6570 <![CDATA[β3]]> 0.5729 -0.0009 -0.0077 0.0078 -0.0881

[0051] Table 3 Parameter values of the parallel fault component in the dip-slip case

[0052] Parameter <![CDATA[λ0]]> <![CDATA[λ1]]> <![CDATA[λ2]]> <![CDATA[λ3]]> <![CDATA[λ4]]> <![CDATA[β0]]> -3.3001 0.0189 -0.0147 -0.0857 1.0589 <![CDATA[β1]]> 0.4472 -0.0026 -0.0015 -0.0009 -0.1818 <![CDATA[β2]]> -7.1989 0.0107 0.0611 0.0722 0.4220 <![CDATA[β3]]> 0.6682 -0.0019 -0.0107 -0.0133 -0.1161

[0053] Table 4 Parameter values of the vertical fault component in the dip-slip case

[0054]

[0055]

[0056] Taking the strike-slip fault as an example, with a fault dip of 30°, a focal depth of 10 km, an epicentral distance of 0 km, and a point-to-point spacing of 200 m, the variation of the coherence coefficients of the parallel fault component and the vertical fault component corresponding to different magnitudes with frequency is shown in Figs. 2(a) and 2(b). With the same working conditions, the variation of the coherence coefficients of the parallel fault component and the vertical fault component corresponding to different magnitudes in the dip-slip fault case is shown in Figs. 3(a) and 3(b).​

[0057] (2) Construct the power spectral matrix between each field point within the target site according to the power spectrum and coherence function model.

[0058] The Du-Xiuli-Chen Houqun power spectrum is adopted for the power spectrum, and the Du-Xiuli-Chen Houqun power spectrum can consider different site types, and is specifically characterized by three parameters: spectral intensity factor, site dominant frequency, and site soil damping ratio.

[0059] The Du-Xiuli-Chen Houqun power spectrum model can be described as:

[0060]

[0061] In the formula, wn is the nth frequency point, ξg and wg respectively represent the damping ratio and dominant frequency of the surface covering layer, S0 is the spectral intensity factor, D is a parameter related to the seismic source, and w0 is the low-frequency corner frequency.

[0062] The power spectral matrix is extended based on the power spectra of all field points within the site and the different coherence functions corresponding to the parallel fault components and vertical fault components between any two points.

[0063] In this embodiment, when the frequency is wn, the one-dimensional power spectral matrix S(iwn) corresponding to r spatial points within the simulation area is:

[0064]

[0065] In the formula, S kl (iw n ) is the cross-power spectral density function between any two points, and its calculation formula is:

[0066]

[0067] In the formula, S kk (iw n ), S ll (iw n ) respectively represent the auto-power spectral density functions of field point k and field point l. γ kl (iw n ,d kl ) is the coherence function between point k and point l.

[0068] Then, the above power spectral matrix is extended according to the following formula to obtain the multi-point multi-dimensional power spectral function matrix:

[0069]

[0070] In the formula, x and y respectively correspond to the parallel fault component and the vertical fault component. Among them, S klxx (w n) and Sklyy(wn) correspond to the power spectral density functions of the parallel fault component and the vertical fault component respectively; the hysteretic coherence coefficients corresponding to Sklxy(wn) and Sklyx(wn) are both taken as 0.3.

[0071] (3) Decompose the power spectral matrix, calculate the amplitudes and phase angles corresponding to different frequency components between field points, and synthesize the stationary ground motion time histories of each point in the site using the trigonometric series method.

[0072] The decomposition of the power spectral matrix uses Cholesky decomposition. The direction of the stationary ground motion synthesized using the trigonometric series method corresponds to the components of the coherence function in step (1), that is, the stationary ground motion time histories of the parallel fault component and the vertical fault component.

[0073] The synthesis formula for the stationary ground motion time history Uj(t) of a certain horizontal component at field point j is:

[0074]

[0075] In the formula, a jm (w n ) and θ jm (w n ) are the amplitude and phase angle of the nth frequency component considering the coherence between the jth point and the mth point; N is the number of trigonometric series; φ mn is a random phase angle, satisfying a uniform distribution on (0, 2π).

[0076] The amplitude ajm(w n ) and phase angle θ jm (w n ) of the nth frequency component considering the coherence between the jth point and the mth point are:

[0077]

[0078] In the formula, Im represents the imaginary part of a complex number, Re represents the real part of a complex number, and ljm(iwn) is obtained by performing Cholesky decomposition on the power spectral function matrix S(iwn). The S(iwn) is a Hermite matrix and a positive definite matrix, and thus can be decomposed by Cholesky as:

[0079] S(iw n ) = L(iw n )L H (iw n )

[0080] L(iwn) is the corresponding lower triangular matrix after Cholesky decomposition, and the expression is:

[0081]

[0082] (4) Modulate the stationary ground motion using the time history envelope function to form a spatially correlated non-stationary ground motion field at the target site considering the characteristics of the finite-fault source.

[0083] To obtain non-stationary seismic waves, the generated stationary seismic waves need to be multiplied by a non-stationary modulation function. Finally, the non-stationary ground motion time histories corresponding to the horizontal parallel fault component and the vertical fault component at the j-th point can be synthesized. An example of the synthesized ground motion in the strike-slip case is shown in Figure 4 . Among them, the time history envelope function is a piecewise function, including three segments: rising, stationary, and decaying. The expression is:

[0084]

[0085] In the formula, t1 and t2 are the start and end times of the strong earthquake segment respectively, and c is a parameter controlling the decay rate, with a value of 0.55.

[0086] According to the corresponding angle transformation formula, the generated horizontal component can be rotated to the specified direction as:

[0087]

[0088] In the formula, θ is the rotation angle; A x and Ay represent the synthesized non-stationary ground motions corresponding to the parallel fault component and the vertical fault component respectively; A L and A T represent the non-stationary ground motions of the two horizontal components after rotating the angle θ respectively.

[0089] Integrate the synthesized horizontal component acceleration time history to obtain the velocity time history and displacement time history. Among them, the acceleration, velocity, and displacement time histories between any two field points in the case of a strike-slip fault are shown in Figure 5 , and the displacement time history differences corresponding to the selected field points are shown in Figure 6 . Fourier transform the synthesized horizontal component acceleration time history, and the acceleration Fourier spectra of the selected field points can be obtained as shown in Figures 7(a) and 7(b).

[0090] This embodiment provides multi-dimensional non-stationary ground motion time history loads for the seismic fortification of structures in the near-fault area under the set seismic source characteristic scenarios. The involved coherence function model considers the characteristics of the finite-fault source, and the synthesized seismic energy can reflect the control effect of the near-fault source on the ground motion field.

[0091] This embodiment reflects future multiple set seismic scenarios by establishing the relationship between the characteristic parameters of the coherence function model and the characteristics of the finite-fault source. By establishing the statistical relationship between the magnitude-coherence function characteristic parameters and factors such as dip angle and source depth, the synthesized ground motion time history can better reflect the complexity of the spatially correlated ground motion in the near-fault area.

[0092] In this embodiment, a coherence function model is established for two different horizontal components of parallel faults and vertical faults, and different fault slip types are considered, so that the constructed power spectral matrix can take into account the spatial differences between different components under a given fault motion type, and finally synthesize the non-stationary ground motion time history of the specified horizontal component.

[0093] The above is a schematic description of the present invention and its implementation manners. This description is not restrictive. What is shown in the drawings is only one of the implementation manners of the present invention, and the actual structure is not limited thereto. Therefore, if those of ordinary skill in the art are inspired by it and, without departing from the purpose of the present invention, design similar structural manners and embodiments to this technical solution without creative efforts, they shall fall within the protection scope of the present invention.

Claims

1. A method for synthesizing near-fault multi-dimensional non-stationary ground motions considering finite-fault source characteristics, characterized in that: It includes the following steps: (1) Using a near-fault spatial coherence function model that can consider different specified magnitudes, source mechanism parameters, and source depths, obtain the seismic ground motion horizontal component coherence coefficients between each site within the target site; (2) According to the power spectrum and the coherence function model, construct the power spectrum matrix between each site within the target site; (3) Decompose the power spectrum matrix, calculate the amplitudes and phase angles corresponding to different frequency components between sites, and synthesize the stationary seismic ground motion time histories of each point within the site using the trigonometric series method; (4) Modulate the stationary seismic ground motion using the time history envelope function to form the spatially correlated non-stationary seismic ground motion field of the target site considering the characteristics of the finite-fault source; 2. The near-fault multi-dimensional non-stationary ground motion synthesis method considering the characteristics of finite-fault seismic sources according to claim 1, characterized in that: In step (1), the coherence function model uses a spatial coherence function model considering the characteristics of the finite-fault source.

3. The near-fault multi-dimensional non-stationary ground motion synthesis method considering the characteristics of finite-fault seismic sources according to claim 2, wherein: In step (1), the specific calculation sequence of the coherence coefficient is as follows: First, according to the actual source mechanism parameters, source depth, epicentral distance, and point pair spacing, calculate the regression coefficients in the statistical relationship between the characteristic parameters of the coherence function model and the magnitude; then, according to the specified magnitude and the regression coefficients, calculate the characteristic parameters of the coherence function model for different horizontal component seismic ground motion time histories, and substitute them into the coherence function model to obtain the seismic ground motion coherence coefficient curves between sites with different magnitudes and different horizontal components.

4. The near-fault multi-dimensional non-stationary ground motion synthesis method considering the characteristics of finite-fault seismic sources according to claim 3, characterized in that: In step (2), the power spectrum uses the Du-Xiuli-Chen Houqun power spectrum, and the Du-Xiuli-Chen Houqun power spectrum can consider different site types and is specifically characterized by three parameters: spectral intensity factor, site dominant frequency, and site soil damping ratio.

5. The near-fault multi-dimensional non-stationary ground motion synthesis method considering the characteristics of a finite fault source according to claim 4, wherein: In step (2), the power spectrum matrix is extended based on the power spectra of all sites within the site and the different coherence functions corresponding to the parallel fault components and vertical fault components between any two points.

6. The near-fault multi-dimensional non-stationary ground motion synthesis method considering the characteristics of a finite fault source according to claim 5, characterized in that: In step (3), the decomposition of the power spectrum matrix uses the Cholesky decomposition, and the direction of the stationary seismic ground motion synthesized using the trigonometric series method corresponds to the components of the coherence function in step (1), that is, the stationary seismic ground motion time histories of the parallel fault component and the vertical fault component.

7. The near-fault multi-dimensional non-stationary ground motion synthesis method considering the characteristics of finite-fault earthquake sources according to claim 6, characterized in that: In step (4), the time history envelope function is a piecewise function, including three segments: rising, stationary, and decaying, thereby forming the non-stationary seismic ground motion time histories of the parallel fault component and the vertical fault component.

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