CN112069569A - Multipoint earthquake motion synthesis method and system - Google Patents
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Abstract
The invention belongs to the technical field related to earthquake motion detection, and discloses a multipoint earthquake motion synthesis method, which comprises the following steps: s1, acquiring a power spectral density function of the bedrock; s2, simplifying the soil layer on the bedrock into a horizontal stratified homogeneous soil layer to obtain a transfer function from the bedrock to the homogeneous soil layer; s3, obtaining transfer functions from each point of the bedrock to the homogeneous soil layer in the X, Y and Z directions according to the power density function of the bedrock and the transfer function of the homogeneous soil layer, and further obtaining a self-power spectral density function and a cross-power spectral density function of the homogeneous soil layer; and S4, synthesizing the seismic dynamic acceleration of the homogeneous soil layer according to the self-power spectral density function and the cross-power spectral density function of the homogeneous soil layer. The application also provides a multipoint earthquake motion synthesis system. By the method and the system, the seismic oscillation can be accurately represented, the system has low requirement on the professional level of a user, and the research and design efficiency is effectively improved.
Description
Technical Field
The invention belongs to the technical field related to earthquake motion detection, and particularly relates to a multipoint earthquake motion synthesis method and system.
Background
The earthquake motion has the characteristics of randomness and spatial variation, and a random multi-point earthquake motion time range with the spatial variation characteristic is generally used for earthquake-proof research of longer and larger structures such as bridges and subway tunnels. However, at present, no relevant computer-aided system capable of directly obtaining multipoint earthquake motion or multipoint earthquake motion response of a field is published at home and abroad, and at present, only computer software SHAKE91 and DEEPSOIL for calculating field response and a computer system SEISMOARTIF for directly synthesizing single-point earthquake motion exist. The SHAKE91 and DEEPSOIL assume the field as a one-dimensional horizontal stratified model, and after the soil information of the field is input, the single-point acceleration response at the interface of the earth surface and each underground soil layer can be obtained through calculation according to the specified bedrock incident seismic oscillation. However, the shift 91 is a DOS interface, is cumbersome to operate, and cannot adapt to the use habits of modern researchers or engineers, the deepoil is a GUI man-machine interaction interface, and considers the influence of field nonlinearity on the acceleration response obtained by simulation, however, both the system and the shift 91 depend on given existing acceleration records, and cannot calculate random acceleration responses by themselves, so that the requirements of structural reliability analysis, parameter sensitivity analysis and the like cannot be met. The SEISMOARTIF system is irrelevant to site conditions, can only calculate a single-point random acceleration time course matched with a site response spectrum given by a user, and is separated from engineering practice to a certain extent. In addition, the three systems do not consider the spatial variability of earthquake motion, only can obtain single-point earthquake motion time history, and cannot meet the requirement of longer and larger structural earthquake-resistant research; the three structures assume the vertical incidence of seismic oscillation, do not consider the incidence angle of the bedrock seismic oscillation, only consider a single component of the seismic oscillation, and do not simultaneously consider three components of the seismic oscillation, namely the out-of-plane horizontal component, the in-plane horizontal component and the in-plane vertical component. Therefore, it is desirable to design a method and a system for synthesizing multi-point seismic motion, which can consider randomness, spatial variability and instability of seismic motion, so as to facilitate seismic research of longer and larger structures.
Disclosure of Invention
In response to the above-identified deficiencies in the art or needs for improvement, the present invention provides a method and system for multi-point seismic motion synthesis. And then, a cross-power spectrum density function between multiple points is researched by researching a transfer function at multiple points of the bedrock and transfer functions in the X, Y and Z directions of the multiple points of the bedrock to the homogeneous soil layer, and the earthquake dynamic acceleration of the homogeneous soil layer is synthesized according to the self-power spectrum density function at each point and the cross-power spectrum density function between the two points. Therefore, the method considers the incident angle and the space variability of the earthquake motion of the bedrock and is suitable for the earthquake-resistant research of the buildings with the large and large structures.
To achieve the above object, according to one aspect of the present invention, there is provided a multipoint seismic synthesis method, comprising: s1, acquiring a power spectral density function of the bedrock; s2, simplifying the soil layer on the bedrock into a horizontal stratified homogeneous soil layer, and obtaining a transfer function of the bedrock to the homogeneous soil layer; s3, obtaining transfer functions of the bedrock in the X, Y and Z directions of each point of the bedrock to the homogeneous soil layer according to the power density function of the bedrock and the transfer functions of the homogeneous soil layer, and obtaining a self-power spectral density function and a cross-power spectral density function of the homogeneous soil layer according to the transfer functions of the homogeneous soil layer in the X, Y and Z directions; and S4, synthesizing the seismic dynamic acceleration of the homogeneous soil layer according to the self-power spectral density function and the cross-power spectral density function of the homogeneous soil layer.
Preferably, the synthesis method further comprises: and S5, multiplying the seismic acceleration of the homogeneous soil layer by a Jennings window function to obtain the seismic acceleration of the homogeneous soil layer in a time domain non-stationary state.
Preferably, in step S3, a coherence loss between two points of the bedrock is obtained, and a cross-power spectral density function of the homogeneous soil layer is obtained according to the coherence loss.
Preferably, in step S1, a power spectral density function at the bedrock is obtained according to a Tajimi-Kanai power spectral density model, and the power spectral density function is calculated by the following formula:
wherein, ω isgAnd
is the center frequency and damping ratio, omega, of the function in the Tajimi-Kanai power spectral density modelfAnd
is the center frequency and damping ratio of the high-pass filter, omega is the frequency, Sg(ω) is the power spectral density function, S0Is the spectral intensity.
Preferably, step S2 includes obtaining a transfer function of the bedrock to the homogeneous soil layer according to the homogeneous soil layer characteristic parameter and a one-dimensional fluctuation theory, where the transfer function of the homogeneous soil layer is calculated by:
where H (i ω) is the transfer function, i is the imaginary unit, tLAs a soil layer angle parameter, vtIs displacement of the top of the soil layer, v0Is the outcrop displacement of the bedrock, k is the wave number, d is the thickness of the soil layer,
G*Lfor complex stiffness of the soil layer, G*RIs the complex stiffness of the bedrock.
Preferably, the calculation formula of the self-power spectral density function and the cross-power spectral density function of the homogeneous soil layer is as follows:
Sjj(ω)＝|Hj(iω)|2Sg(ω) j＝1，2，...，n
j，k＝1，2，...，n
wherein S isjj(ω) is the self-power spectral density, Hj(i ω) is the transfer function, Sjk(i ω) is a number of,
being complex conjugates of transfer functions, gammajKAs a coherence function, djkIs the distance between the two points j and k.
Preferably, in step S4, a coherence loss between two points of the bedrock is calculated by using a Sobczyk model, and the calculation formula of the coherence loss is as follows:
preferably, the calculation formula of the seismic dynamic acceleration of the homogeneous soil layer is as follows:
wherein the content of the first and second substances,
S(ω)＝L(ω)LT(ω)
t is a conjugate transpose, L (omega) is a lower triangular matrix,
is at [0, 2 π]Random phase angles that are lognormally distributed; Δ ω is the frequency interval, ωNFor the upper cut-off frequency, lm and Re are the imaginary and real parts of the complex number, Ljm(i ω) is an element corresponding to L (ω), ωnM and N are iteration parameters between 0 and N for the cut-off frequency.
According to another aspect of the present invention, there is provided a multipoint seismic synthesis system, the system comprising: the device comprises a first acquisition module, a second acquisition module and a third acquisition module, wherein the first acquisition module is used for acquiring a power spectral density function at a bedrock; the second acquisition module is used for simplifying the soil layer on the bedrock into a horizontal stratified homogeneous soil layer to obtain a transfer function from the bedrock to the homogeneous soil layer; the third obtaining module is used for obtaining transfer functions of all points of the bedrock in the X direction, the Y direction and the Z direction of the homogeneous soil layer according to the power density function of the bedrock and the transfer functions of the homogeneous soil layer, and obtaining a self-power spectrum density function and a cross-power spectrum density function of the homogeneous soil layer according to the transfer functions of the homogeneous soil layer in the X direction, the Y direction and the Z direction; and the synthesis module is used for synthesizing the seismic dynamic acceleration of the homogeneous soil layer according to the self-power spectral density function and the cross-power spectral density function of the homogeneous soil layer.
Preferably, the synthesis system further comprises: and the product module is used for multiplying the seismic dynamic acceleration of the homogeneous soil layer by a Jennings window function so as to realize the seismic dynamic acceleration of the homogeneous soil layer in a time domain non-stationary state.
Generally speaking, compared with the prior art, the multipoint earthquake motion synthesis method and system provided by the invention have the following beneficial effects:
1. the transfer function from the bedrock to the homogeneous soil layer is divided into the transfer functions in the X direction, the Y direction and the Z direction, so that the components in multiple directions of earthquake motion are realized, the study of earthquake motion with multiple incident angles can be realized, the study of earthquake motion spatial variability is also realized, and the actual situation of earthquake motion is better met;
2. by considering coherence among multiple points, seismic dynamic acceleration synthesized by the multiple points is obtained, and seismic research of a long and large structure can be realized;
3. optimizing the seismic oscillation acceleration through a window function to obtain the seismic oscillation acceleration of the homogeneous soil layer in a non-stationary state, and more conforming to the randomness of the actual seismic oscillation;
4. the multi-point earthquake motion synthesis system provided by the application modularizes the research method, and the user inputs the earthquake motion basic parameters to obtain the corresponding earthquake motion acceleration, so that the system is simple and convenient, has low requirement on the professional level of the user, and effectively improves the research and design efficiency.
Drawings
FIG. 1 schematically illustrates a step diagram of a method of multipoint seismic synthesis, according to an embodiment of the present disclosure;
FIG. 2 schematically illustrates a block diagram of a multipoint seismic synthesis system, according to an embodiment of the present disclosure;
FIG. 3 schematically illustrates a schematic view of a bridge construction according to an embodiment of the present disclosure;
fig. 4 schematically shows a structural schematic diagram of a soil-subway tunnel according to an embodiment of the present disclosure.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
Referring to FIG. 1, the present invention provides a method for multi-point seismic synthesis, which includes the following steps S1-S4, which will be described in detail below.
And S1, acquiring a power spectral density function at the bedrock.
In the embodiment of the disclosure, a filtered Tajimi-Kanai power spectrum density model is selected to obtain a power spectrum density function at a bedrock, and the seismic intensity and the frequency component of a bedrock surface are assumed to be consistent. The calculation formula of the power spectral density function at the bedrock is as follows:
wherein, | HP(ω) | denotes the high-pass filter function (first half of the formula), ωgAnd
is the center frequency and damping ratio, omega, of the function in the Tajimi-Kanai power spectral density modelfAnd
is the center frequency and damping ratio of the high-pass filter, omega is the frequency, Sg(ω) is the power spectral density function, S0Is the spectral intensity.
S2, simplifying the soil layer on the bedrock into a horizontal stratified homogeneous soil layer, and obtaining a transfer function of the bedrock to the homogeneous soil layer.
In the embodiment of the disclosure, the soil layer above the bedrock is simplified into a horizontal stratified homogeneous soil layer, and the characteristic parameters of the homogeneous soil layer are subjected to digital processing. The characteristic parameters of the homogeneous soil layer mainly comprise shear modulus, density, thickness, Poisson ratio and the like of the soil, and can also be field parameters. According to the one-dimensional fluctuation theory, the propagation process of the earthquake motion from the bedrock to the homogeneous soil layer is expressed by using a transfer function on the assumption that the earthquake motion of the bedrock is propagated to the earth surface from SH waves outside the plane or P waves and SV waves inside the plane at a certain incidence angle, and the specific calculation process is shown as follows.
[SSH][uSH]＝{PSH}
[SP-SV][uP-SV]＝{PP-SV}
Wherein, Delta2The laplacian operator is a function of,
{ omega } is the rotational strain vector, cpIs the velocity of the longitudinal shear wave, csShear wave velocity of shear wave, ω is frequency, SSHIs a stiffness matrix, P, of the soil bed rock during propagation of the out-of-plane wavesSHFor loading the array uSHIs a displacement vector of SH wave propagation, SP-SVIs a rigidity matrix u of the soil bed rock during the propagation of the in-plane wavesP-SVIs a displacement vector, PP-SVIs the load vector.
Taking SH wave as an example, the total rigidity matrix after the homogeneous soil layer and the bedrock are combined is
uSH＝[vt，vb]T
PSH＝[0，iktRG*R]T
Wherein k is the wave number, tLIs the soil layer angle parameter, d is the soil layer thickness, G*LIs complex soil layer stiffness, i is imaginary number unit, tRAs angle parameter of bedrock, G*RIs complex stiffness of the bedrock, p is the impedance ratio, vtIs displacement of the top of the soil layer, vbDisplacement of the bottom of the soil layer.
And further obtaining a transfer function from the bedrock to the homogeneous soil layer as follows:
where H (i ω) is the transfer function, i is the imaginary unit, tLAs a parameter of the angle of incidence of the soil layer, v0Is the outcrop displacement of the bedrock, k is the wave number, d is the thickness of the soil layer,
is an impedance ratio, G*LFor complex stiffness of the soil layer, G*RIs the complex stiffness of the bedrock.
And S3, obtaining transfer functions of the bedrock in the X, Y and Z directions of the homogeneous soil layer (namely transfer functions in the SH, SV and P wave directions, the specific implementation process is as above) at each point of the bedrock according to the power density function of the bedrock and the transfer functions of the homogeneous soil layer, and obtaining a self-power spectral density function and a cross-power spectral density function of the homogeneous soil layer according to the transfer functions in the X, Y and Z directions of the homogeneous soil layer.
According to the power density function and the transfer function of the homogeneous soil layer obtained in the steps S1 and S2, the transfer functions of the matrix rock in the X direction, the Y direction and the Z direction of the homogeneous soil layer at each point can be obtained, and therefore the study of seismic oscillation multiple incidence angles can be achieved, namely the study of seismic oscillation space variability is achieved, and the seismic oscillation space variability is more in line with the actual situation of seismic oscillation. Obtaining a self-power spectral density function of the homogeneous soil layer according to the transfer functions in the X direction, the Y direction and the Z direction, wherein the calculation formula of the self-power spectral density function is
Sjj(ω)＝|Hj(iω)|2Sg(ω) j＝1，2，…，n
Wherein S isjj(ω) is the self-power spectral density, Hj(i ω) is the transfer function at point j.
The cross-power spectral density function of the homogeneous soil layer can be obtained according to the transfer functions in the X direction, the Y direction and the Z direction, the coherence loss between two points of the bedrock is needed to be obtained when the cross-power spectral density function is calculated, and the cross-power spectral density function of the homogeneous soil layer is obtained according to the coherence loss. In the embodiment of the disclosure, in order to simulate the coherence of seismic motion of each point, a Sobczyk model may be selected to calculate the coherence loss between two points j and k of the bedrock, and the calculation formula of the coherence loss is as follows:
wherein, γj′k′(i ω) is the coherence function, dj′k′J, k the horizontal distance between the two points,α is an incident angle, vappBeta is a constant, depending on the wave velocity.
Further, the calculation formula of the cross-power spectral density function is as follows:
wherein S isjk(i ω) is the cross-power spectral density,
being complex conjugates of the transfer function, gammajk(djkIw) is a coherence function, djkJ, k is the horizontal distance between two points.
And S4, synthesizing the seismic dynamic acceleration of the homogeneous soil layer according to the self-power spectral density function and the cross-power spectral density function of the homogeneous soil layer.
According to the structural seismic input requirement, the peak acceleration (PGA) and the duration of seismic oscillation in the formula can be set by self. The seismic dynamic acceleration can be obtained by the following formula by using the self-power spectral density function and the cross-power spectral density function obtained above.
Wherein S isii(i ω) and Sij(i ω) are the self-power spectral density matrix and cross-power spectral density matrix, respectively. S (i ω) is a Hermitian positive definite matrix that can be decomposed into a complex lower triangular matrix L (i ω) and its Hermitian positive definite matrix LH(iω)：
S(iω)＝L(iω)LH(iω)
The decomposition of the power spectral density matrix may use Cholesky method, and the lower triangular matrix L (i ω) may be expressed as:
further, the seismic dynamic acceleration of a stationary homogeneous soil layer can be obtained by the following formula:
wherein the content of the first and second substances,
S(ω)＝L(ω)LT(ω)
t is conjugate transpose, L (omega) is lower triangular matrix, which can be obtained by Cholesky decomposition of S (omega),
is at [0, 2 π]Random phase angles that are lognormally distributed; Δ ω is the frequency interval, ωNFor the upper cut-off frequency, lm and Re are the imaginary and real parts of the complex number, Ljm(i ω) is an element corresponding to L (ω), ωnIs the cut-off frequency.
Actual seismic recordings often exhibit non-stationary properties that should be taken into account during manual simulation of seismic motion. In the embodiment of the disclosure, a Jennings window function is multiplied by the seismic dynamic acceleration of the homogeneous soil layer to obtain the seismic dynamic acceleration of the homogeneous soil layer in a time domain non-stationary state, and the Jennings window function f (t) has the following expression:
wherein, t1For seismic acceleration rise time, t2The earthquake motion stationary section end time, c is an attenuation factor, and T is earthquake duration.
Therefore, seismic acceleration of non-stationary homogeneous earth layers
Can be expressed as:
in another aspect, the present disclosure further provides a multipoint seismic motion synthesis system 200, as shown in fig. 2, where the system 200 includes:
the first obtaining module 210, for example, may execute step S1 shown in fig. 1 for obtaining a power spectral density function at a bedrock;
the second obtaining module 220, for example, may execute step S2 shown in fig. 1, configured to simplify the soil layer on the bedrock into a horizontally layered homogeneous soil layer, and obtain a transfer function of the bedrock to the homogeneous soil layer;
the third obtaining module 230, for example, may execute step S3 shown in fig. 1, configured to obtain transfer functions in three directions of X, Y and Z at each point of the bedrock to the homogeneous soil layer according to the power density function at the bedrock and the transfer functions of the homogeneous soil layer, and obtain a self-power spectral density function and a cross-power spectral density function of the homogeneous soil layer according to the transfer functions in three directions of X, Y and Z of the homogeneous soil layer;
the synthesis module 240, for example, may execute step S4 shown in fig. 1, for synthesizing the seismic dynamic acceleration of the homogeneous soil layer according to the self-power spectral density function and the cross-power spectral density function of the homogeneous soil layer.
The synthesis system further comprises a product module, wherein the product module is used for multiplying the seismic dynamic acceleration of the homogeneous soil layer by a Jennings window function so as to realize the seismic dynamic acceleration of the homogeneous soil layer in a time domain non-stationary state.
When the system in the embodiment is applied to a bridge structure, as shown in fig. 3, the ground surface multi-point seismic acceleration corresponding to each support can be obtained by calculation according to input information such as the number of bridge supports, and the obtained multi-point seismic acceleration is sequentially input to the bottom surface of each pier, so that the response of the bridge structure under the seismic acceleration multi-point input can be calculated.
When the system in the embodiment is applied to the soil-subway tunnel interaction structure, the basement rock multi-point earthquake dynamic acceleration corresponding to each row of input points can be obtained through calculation according to the row number (the row is vertical to the longitudinal direction of the tunnel, and a group of nodes highlighted in fig. 4 is a row), the longitudinal size of the grid and other input information of the soil model along the longitudinal direction of the tunnel, and the obtained multi-point earthquake dynamic acceleration is sequentially input at each row of grid nodes along the longitudinal direction of the tunnel, namely the same earthquake dynamic acceleration is input at the same row of nodes, so that the response of the tunnel structure in the soil under the basement rock earthquake multi-point input is calculated.
In summary, the present invention provides a method and a system for multi-point seismic motion synthesis. The method can realize the research on the spatial variability, randomness and non-stationarity of the earthquake motion, and better accords with the actual situation of the earthquake motion.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (10)
1. A method of multi-point seismic synthesis, the method comprising:
s1, acquiring a power spectral density function of the bedrock;
s2, simplifying the soil layer on the bedrock into a horizontal stratified homogeneous soil layer, and obtaining a transfer function of the bedrock to the homogeneous soil layer;
s3, obtaining transfer functions of the bedrock in the X, Y and Z directions of each point of the bedrock to the homogeneous soil layer according to the power density function of the bedrock and the transfer functions of the homogeneous soil layer, and obtaining a self-power spectral density function and a cross-power spectral density function of the homogeneous soil layer according to the transfer functions of the homogeneous soil layer in the X, Y and Z directions;
and S4, synthesizing the seismic dynamic acceleration of the homogeneous soil layer according to the self-power spectral density function and the cross-power spectral density function of the homogeneous soil layer.
2. The method of multipoint seismic synthesis according to claim 1, further comprising:
and S5, multiplying the seismic acceleration of the homogeneous soil layer by a Jennings window function to obtain the seismic acceleration of the homogeneous soil layer in a time domain non-stationary state.
3. The method of multi-point seismic synthesis according to claim 1, wherein in step S3, coherence loss between two points of the bedrock is obtained, and cross-power spectral density function of the homogeneous soil layer is obtained according to the coherence loss.
4. The method of multi-point seismic synthesis according to claim 1, wherein in step S1, a power spectral density function at the bedrock is obtained according to a Tajimi-Kanai power spectral density model, and the calculation formula of the power spectral density function is:
wherein, ω isgAnd
is the center frequency and damping ratio, omega, of the function in the Tajimi-Kanai power spectral density modelfAnd
is the center frequency and damping ratio of the high-pass filter, omega is the frequency, Sg(ω) is the power spectral density function, S0Is the spectral intensity.
5. The method of multipoint seismic synthesis according to claim 1, wherein step S2 includes obtaining a transfer function of the bedrock to the homogeneous soil layer according to homogeneous soil layer characteristic parameters and a one-dimensional fluctuation theory, where the calculation formula of the transfer function of the homogeneous soil layer is:
wherein H (i ω) is a transfer function and i is
tLAs a soil layer angle parameter, vtIs displacement of the top of the soil layer, v0Is the outcrop displacement of the bedrock, k is the wave number, d is the thickness of the soil layer,
is impedance, G*LFor complex stiffness of the soil layer, G*RIs the complex stiffness of the bedrock.
6. The method of multi-point seismic synthesis according to claim 3, wherein the computation formula of the self-power spectral density function and the cross-power spectral density function of the homogeneous soil layer is:
Sjj(ω)＝|Hj(iω)|2Sg(ω) j＝1，2，...，n
j，k＝1，2，...，n
wherein Hj(i ω) is the transfer function, Sjk(i ω) is a cross-power spectral density function,
being complex conjugates of transfer functions, gammajKAs a coherence function, djkIs the distance between the two points j and k.
7. The method of multi-point seismic synthesis according to claim 6, wherein in step S4, a Sobczyk model is used to calculate the coherence loss between two points of the bedrock, and the formula of the coherence loss is as follows:
wherein, γj′k′(i ω) is the coherence function, dj′k′J, k, alpha is the angle of incidence, upsilonappBeta is a constant, depending on the wave velocity.
8. The multipoint seismic synthesis method according to claim 1, wherein the seismic acceleration of the homogeneous soil layer is calculated according to the formula:
wherein the content of the first and second substances,
S(ω)＝L(ω)LT(ω)
t is a conjugate transpose, L (omega) is a lower triangular matrix,
is at [0, 2 π]Random phase angles that are lognormally distributed; Δ ω is the frequency interval, ωNFor the upper cut-off frequency, lm and Re are the imaginary and real parts of the complex number, Ljm(i ω) is an element corresponding to L (ω), ωnIs the cut-off frequency.
9. A multipoint seismic synthesis system, the system comprising:
the device comprises a first acquisition module, a second acquisition module and a third acquisition module, wherein the first acquisition module is used for acquiring a power spectral density function at a bedrock;
the second acquisition module is used for simplifying the soil layer on the bedrock into a horizontal stratified homogeneous soil layer to obtain a transfer function from the bedrock to the homogeneous soil layer;
the third obtaining module is used for obtaining transfer functions of all points of the bedrock in the X direction, the Y direction and the Z direction of the homogeneous soil layer according to the power density function of the bedrock and the transfer functions of the homogeneous soil layer, and obtaining a self-power spectrum density function and a cross-power spectrum density function of the homogeneous soil layer according to the transfer functions of the homogeneous soil layer in the X direction, the Y direction and the Z direction;
and the synthesis module is used for synthesizing the seismic dynamic acceleration of the homogeneous soil layer according to the self-power spectral density function and the cross-power spectral density function of the homogeneous soil layer.
10. The multipoint seismic synthesis system of claim 9, wherein the synthesis system further comprises:
and the product module is used for multiplying the seismic dynamic acceleration of the homogeneous soil layer by a Jennings window function so as to realize the seismic dynamic acceleration of the homogeneous soil layer in a time domain non-stationary state.
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