CN115437008B - A method and system for inversion of Rayleigh wave dispersion curve based on geostatistics - Google Patents
A method and system for inversion of Rayleigh wave dispersion curve based on geostatistics Download PDFInfo
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Abstract
本发明涉及一种基于地质统计学的瑞雷波频散曲线反演方法及系统，属于地震横波速度反演技术领域。先基于频散方程构建反演方程，利用反演方程进行迭代优化，得到每一台站的第一地震横波速度结构。然后根据所有台站的第一地震横波速度结构和位置确定每一台间待估点的多个第二初始地震横波速度结构，并利用频散方程计算得到第二瑞雷波频散曲线，最后以台间待估点对应的所有第二瑞雷波频散曲线为输入，利用第二目标函数确定最优的第二瑞雷波频散曲线，以确定每一台间待估点的第二地震横波速度结构。本发明能够同时获得台站和台间的地震横波速度结构，可以大大提高横向分辨率。
The present invention relates to a Rayleigh wave dispersion curve inversion method and system based on geological statistics, and belongs to the technical field of seismic shear wave velocity inversion. First, an inversion equation is constructed based on a dispersion equation, and iterative optimization is performed using the inversion equation to obtain the first seismic shear wave velocity structure of each station. Then, multiple second initial seismic shear wave velocity structures of each inter-station point to be estimated are determined based on the first seismic shear wave velocity structure and position of all stations, and the second Rayleigh wave dispersion curve is calculated using the dispersion equation. Finally, all the second Rayleigh wave dispersion curves corresponding to the inter-station point to be estimated are used as input, and the optimal second Rayleigh wave dispersion curve is determined using the second objective function to determine the second seismic shear wave velocity structure of each inter-station point to be estimated. The present invention can simultaneously obtain the seismic shear wave velocity structure of stations and stations, and can greatly improve the lateral resolution.
Description
Technical Field
The invention relates to the technical field of seismic transverse wave velocity inversion, in particular to a Rayleigh wave dispersion curve inversion method and system based on geostatistics.
Background
At present, the seismic transverse wave velocity structure is mostly obtained through Rayleigh wave dispersion curve inversion, but the method only can obtain the seismic transverse wave velocity structure of the station, but can not obtain the seismic transverse wave velocity structure among stations, and in engineering application, the problem of low transverse resolution of inversion results exists.
Based on this, an inversion technique capable of improving the lateral resolution is demanded.
Disclosure of Invention
The invention aims to provide a Rayleigh wave dispersion curve inversion method and system based on geostatistics, which can simultaneously obtain a transverse velocity structure of an earthquake between a station and can greatly improve transverse resolution.
In order to achieve the above object, the present invention provides the following solutions:
A method of inversion of a rayleigh wave dispersion curve based on geostatistics, the inversion method comprising:
For each station, acquiring a first initial seismic transverse wave velocity structure and a first Rayleigh wave dispersion curve of the station, constructing an inversion equation based on a dispersion equation, and carrying out iterative optimization by using the inversion equation with the first initial seismic transverse wave velocity structure and the first Rayleigh wave dispersion curve as inputs to obtain the first seismic transverse wave velocity structure of the station, wherein the Rayleigh wave dispersion curve is a change curve of Rayleigh wave phase velocity along with frequency change;
determining a plurality of second initial seismic transverse wave velocity structures of points to be estimated among all stations according to the first seismic transverse wave velocity structures and positions of all the stations, wherein the points to be estimated among the stations are grid nodes between two adjacent stations;
For each second initial seismic transverse wave velocity structure of each point to be estimated among the stations, taking the second initial seismic transverse wave velocity structure as input, and calculating to obtain a second Rayleigh wave dispersion curve by using the dispersion equation;
And for each inter-station point to be estimated, taking all second Rayleigh wave dispersion curves corresponding to the inter-station point to be estimated as input, and determining an optimal second Rayleigh wave dispersion curve by using a second objective function, wherein a second initial seismic transverse wave velocity structure corresponding to the optimal second Rayleigh wave dispersion curve is the second seismic transverse wave velocity structure of the inter-station point to be estimated.
A geostatistical-based rayleigh wave dispersion curve inversion system, the inversion system comprising:
The system comprises a station speed inversion module, a frequency inversion equation, a first Rayleigh wave speed inversion module, a first frequency inversion module and a second frequency inversion module, wherein the station speed inversion module is used for acquiring a first initial seismic transverse wave speed structure and a first Rayleigh wave dispersion curve of each station;
The inter-station velocity initial determining module is used for determining a plurality of second initial seismic transverse wave velocity structures of points to be estimated among all stations according to the first seismic transverse wave velocity structures and the positions of all the stations;
The forward modeling module is used for calculating a second Rayleigh wave dispersion curve by using the dispersion equation by taking the second initial seismic transverse wave velocity structure as input for each second initial seismic transverse wave velocity structure of each point to be estimated among the stations;
and the inter-station velocity estimation module is used for taking all second Rayleigh wave dispersion curves corresponding to the inter-station points to be estimated as input for each inter-station point to be estimated, determining an optimal second Rayleigh wave dispersion curve by using a second objective function, wherein a second initial seismic transverse wave velocity structure corresponding to the optimal second Rayleigh wave dispersion curve is the second seismic transverse wave velocity structure of the inter-station points to be estimated.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
the invention is used for providing a Rayleigh wave dispersion curve inversion method and a system based on geostatistics, wherein for each station, an inversion equation is constructed based on a dispersion equation, and taking the first initial seismic transverse wave velocity structure and the first Rayleigh wave dispersion curve of the station as inputs, and performing iterative optimization by using an inversion equation to obtain the first seismic transverse wave velocity structure of the station. And then determining a plurality of second initial seismic transverse wave velocity structures of points to be estimated among all stations according to the first seismic transverse wave velocity structures and the positions of all stations, taking the second initial seismic transverse wave velocity structures as input, calculating by using a dispersion equation to obtain second Rayleigh wave dispersion curves, taking all the second Rayleigh wave dispersion curves corresponding to the points to be estimated among the stations as input, and determining an optimal second Rayleigh wave dispersion curve by using a second objective function, wherein the second initial seismic transverse wave velocity structures corresponding to the optimal second Rayleigh wave dispersion curves are the second seismic transverse wave velocity structures of the points to be estimated among the stations, so that the second seismic transverse wave velocity structures of the points to be estimated among the stations are obtained. The invention can obtain the earthquake transverse wave velocity structure between the stations at the same time, and can greatly improve the transverse resolution.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings that are needed in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of the inversion method according to embodiment 1 of the present invention;
fig. 2 is a system block diagram of an inversion system according to embodiment 2 of the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The invention aims to provide a Rayleigh wave dispersion curve inversion method and system based on geostatistics, which can simultaneously obtain a transverse wave velocity structure of a station and a seismic between stations, greatly improve transverse resolution and obtain a transverse wave velocity structure with higher transverse resolution.
In order that the above-recited objects, features and advantages of the present invention will become more readily apparent, a more particular description of the invention will be rendered by reference to the appended drawings and appended detailed description.
Example 1:
The embodiment is used for providing a method for inversion of a rayleigh wave dispersion curve based on geostatistics, as shown in fig. 1, the inversion method comprises the following steps:
S1, for each station, acquiring a first initial seismic transverse wave velocity structure and a first Rayleigh wave dispersion curve of the station, constructing an inversion equation based on a dispersion equation, and carrying out iterative optimization by using the inversion equation by taking the first initial seismic transverse wave velocity structure and the first Rayleigh wave dispersion curve as inputs to obtain the first seismic transverse wave velocity structure of the station, wherein the Rayleigh wave dispersion curve is a change curve of Rayleigh wave phase velocity along with frequency change;
The station in this embodiment is an earthquake station, and refers to a basic earthquake observation mechanism with at least one earthquake observation field, observation facilities and implementation management functions.
In S1, acquiring the first initial seismic shear wave velocity structure of the station may include acquiring a rock type (or lithology) of each horizon of the station, determining an initial velocity of the horizon according to the rock type of the horizon for each horizon, specifically, the rock type corresponds to a velocity range, for example, a shear wave velocity range of 30-4500 m/S for sinking basalt, randomly selecting a velocity from the velocity range as the initial velocity of the horizon, and forming the first initial seismic shear wave velocity structure by the initial velocities of all the horizons, thereby roughly estimating the first initial seismic shear wave velocity structure of the station according to the rock type of each horizon of the station, wherein the first initial seismic shear wave velocity structure includes the initial velocity of each horizon. Since the rock type corresponds only roughly to the seismic shear wave velocity structure, there is still a need to determine the exact first seismic shear wave velocity structure of the station by subsequent inversion, which will be used as an initial model for subsequent inversion.
In S1, acquiring a first Rayleigh wave dispersion curve of a station can comprise collecting time domain seismic waveform data of the station, extracting Rayleigh wave components of the time domain seismic waveform data, wherein signals except obvious reflection signals at two sides of a common seismic channel are regarded as Rayleigh waves, so that the Rayleigh wave components can be obtained by directly cutting out the signals, the Rayleigh wave components can be understood as a change curve of the Rayleigh wave phase velocity along with the change of the time, and the Rayleigh wave components are processed by a cross-correlation method to estimate to obtain the first Rayleigh wave dispersion curve, wherein the Rayleigh wave dispersion curve is the change curve of the Rayleigh wave phase velocity along with the change of the frequency.
Before constructing an inversion equation based on a dispersion equation, the present embodiment first determines the form of a rayleigh wave dispersion curve inversion solution.
The dispersion equation generally comprises frequency f j, rayleigh wave phase velocity C Rj, seismic shear wave velocity V s, seismic longitudinal wave velocity V p, density ρ and thickness d in the form:
F(fj,CRj,Vs,Vp,ρ,d)=0 (j=1,2,...,m);
Wherein m represents the number of frequencies, C Rj is a real number, V s,Vp and ρ are N-dimensional vectors, d is an N-1-dimensional vector, and N is the number of horizons. In the subsequent inversion process, when the Rayleigh wave dispersion curve is known, the parameters V s,Vp, ρ and d in the dispersion equation can be solved. In general, the rayleigh wave phase velocity is only sensitive to the seismic transverse wave velocity and insensitive to the seismic longitudinal wave velocity, density and thickness, so the seismic longitudinal wave velocity, density and thickness can be known quantities. Furthermore, the dispersion equation can be regarded as a hidden function describing the rayleigh wave phase velocity and the seismic transverse wave velocity V s at a certain frequency f j, and the m dispersion equations are solved to obtain the rayleigh wave dispersion curve corresponding to a certain seismic transverse wave velocity structure, so that the solution of the rayleigh wave dispersion curve inversion is the seismic transverse wave velocity structure. Based on the above, in this embodiment, the first initial seismic transverse wave velocity structure obtained by rough estimation is used as an initial model for inversion, and inversion processing is performed on the initial model, so as to finally obtain a more accurate first seismic transverse wave velocity structure.
The embodiment can collect the relevant geological data of the working area to determine the speed, density and thickness of the earthquake longitudinal wave, so that the prior geological information is collected in advance. Wherein, the thickness d= (d 1,d2,…,dN-1) of each layer is determined, N represents the number of layers, the last layer is assumed to be a uniform half space, and the thickness is infinite.
In this embodiment, constructing the inversion equation based on the dispersion equation may include:
(1) Performing taylor expansion on the dispersion equation to obtain a first function;
Let the seismic transverse wave velocity structure of the underground medium at the position of the seismic station be V s＝(vs1,vs2,…,vsN)T, the Rayleigh wave phase velocity be C R＝(CR1,CR2,…,CRm)T, and carry out Taylor expansion on the dispersion equation, and the obtained first function is:
JΔVs＝ΔCR;
the method comprises the steps of setting a first seismic transverse wave velocity structure, setting a second seismic transverse wave velocity structure, setting a delta V s as a Jacobian matrix, setting a delta C R as a delta C R, wherein the delta V s represents a small disturbance of the first seismic transverse wave velocity structure, the small disturbance represents a difference value of the first seismic transverse wave velocity structure in two adjacent iterations in the iterative optimization process of the subsequent inversion, and the small disturbance represents a difference value of the Rayleigh wave phase velocity in the two adjacent iterations in the iterative optimization process of the subsequent inversion.
(2) Constructing a first objective function based on the first function;
In this embodiment, the first objective function is as follows:
Wherein Φ is a first objective function, J is a Jacobian matrix, deltaV s is the difference of the velocity structures of the first seismic transverse wave in two adjacent iterations, deltaC R is the difference of the phase velocities of the Rayleigh waves in two adjacent iterations, W is a weight matrix of positive definite diagonal for balancing the residual influence of different frequencies, W can be a known matrix given by people or a covariance matrix of data errors, W=L T L, wherein L is a diagonal matrix, and lambda is a regularization parameter.
(3) And carrying out minimization treatment on the first objective function to obtain an inversion equation.
The first objective function is used for evaluating inversion results and solving the descent quantity, and the first seismic transverse wave velocity structure obtained through inversion is enabled to be as small as possible. And (3) performing minimization treatment on phi to obtain an inversion equation, wherein the minimization treatment is a process of instructing the first objective function to calculate the partial derivative of DeltaV s, and setting the partial derivative value to be 0 so as to calculate the minimum value of the function. The inversion equation is used to describe the amount of descent obtained by solving the descent direction of the objective function as follows:
ΔVs＝V(Λ2+λI)-1ΛUTd;
singular value decomposition is performed on a=lj to obtain a=uΛv T, where U, Λ, and V are respectively a left eigenvector matrix, a diagonal matrix, and a right eigenvector matrix, I is a unit matrix, and d=lΔc R represents a weighted phase velocity vector.
Based on the inversion equation, the following iterative format can be constructed:
(ΔVs)n+1＝V(Λ2+λI)-1ΛUT(d)n;
(Vs)n+1＝(Vs)n+(ΔVs)n+1;
Wherein (DeltaV s)n+1 represents the increment of the velocity structure of the seismic transverse wave in the n+1th iteration, (d) n represents the weighted phase velocity vector in the n-th iteration, (V s)n+1 and (V s)n represent the velocity structures of the seismic transverse wave in the n+1 and n-th iterations, respectively).
In this embodiment, the first initial seismic transverse velocity structure and the first rayleigh wave dispersion curve are used as inputs, and the inversion equation is used to perform continuous iterative optimization until (when the modulus of Δv s)n+1 is smaller than a certain threshold, such as 0.001, the loop is exited, so as to obtain the first seismic transverse velocity structure of the seismic station
Because the first objective function contains the regularization parameter lambda, the embodiment can quantize the relation between the regularization parameter lambda and the first objective function by using an L-curve method, determine the value of the regularization parameter lambda by setting the value range of the regularization parameter lambda as [100,0.01] and output an inversion result. The method comprises the steps of selecting a plurality of values randomly in a value range of a regularization parameter lambda, executing an inversion process for each value to obtain a seismic transverse wave velocity structure, carrying the seismic transverse wave velocity structure into a first objective function to obtain a first function value (namely a fitting difference value in front of an addition number) and a second function value (namely a roughness value in back of the addition number) of the first objective function, obtaining a fitting difference value and a roughness value corresponding to each value, taking the fitting difference value as an ordinate, taking the roughness value as an abscissa, taking fitting difference values and the roughness value corresponding to all values as data points, performing L curve fitting, and taking the regularization parameter at an inflection point as an optimal regularization parameter, wherein the seismic transverse wave velocity structure corresponding to the optimal regularization parameter is the first seismic transverse wave velocity structure of a station output by S1.
And S1, completing the inversion process of the station position underground medium seismic transverse wave velocity structure, and obtaining a first seismic transverse wave velocity structure of each station.
According to the embodiment, the earthquake transverse wave velocity structure between the stations is estimated by using a geostatistical method, the geostatistical method is used for estimating the earthquake transverse wave velocity structure of the underground medium between two earthquake stations, samples with spatial correlation and diversity are obtained, and inversion results with higher transverse resolution can be obtained through sample optimization, and the subsequent S2-S4 can be seen.
S2, determining a plurality of second initial seismic transverse wave velocity structures of points to be estimated among all stations according to the first seismic transverse wave velocity structures and positions of all the stations, wherein the points to be estimated among the stations are grid nodes between two adjacent stations;
in this embodiment, the underground medium of the working area is discretized to obtain a plurality of grid nodes. The working area comprises each station in the S1, the earthquake transverse wave speed structure of the grid node corresponding to the station is calculated by the S1, the grid nodes among the stations are points to be estimated among the stations, and the earthquake transverse wave speed structure is calculated by the S2-S4.
And (3) placing the obtained first seismic transverse wave velocity structures of all the underground mediums of the seismic stations at the grid nodes corresponding to the first seismic transverse wave velocity structures, and randomly simulating the second initial seismic transverse wave velocity structures of the points to be estimated among the stations by taking velocity values on the grid nodes as known conditions to obtain a plurality of second initial seismic transverse wave velocity structures of the points to be estimated among each station. Specifically, the stochastic simulation process may include:
(1) Randomly defining the estimation sequence of points to be estimated among a plurality of groups of all stations to obtain a plurality of random simulation sequences;
(2) For each random simulation sequence, fitting according to the first seismic transverse wave velocity structures and positions of all stations to obtain a variation function, and determining a second initial seismic transverse wave velocity structure of a point to be estimated among the first stations by using the variation function;
(3) Fitting a new variation function according to the first seismic transverse wave speed structures and positions of all stations and the second initial seismic transverse wave speed structures and positions of the points to be estimated among all stations with known speeds, and determining the second initial seismic transverse wave speed structure of the points to be estimated among the next stations by using the new variation function;
before interpolation, a variation function needs to be established for describing the statistical characteristics of the seismic transverse wave velocity structure along with the spatial variation. The value of the variation function in geostatistics is obtained by the following formula:
Where h is a range, M represents the total number of all the nodes with known speed, the nodes include stations and points to be estimated between stations, Z (x i) is the value of the seismic transverse wave speed structure of the ith node x i with known speed, Z (x i +h) is the value of the seismic transverse wave speed structure of the node with a distance h from x i, and the above function v describes a quantitative relationship and needs to be fitted to obtain a continuous form thereof.
And carrying out nonlinear fitting on the distance (calculated according to the position of the node) of the node with known speed and the speed by utilizing the quantitative relation, wherein the fitting is carried out to obtain a variation function which can be valued for any distance, specifically, firstly, obtaining the value of v (h) according to the node with known speed, and fitting parameters such as a base station value, a variation range, a hysteresis distance and the like by using the values of a plurality of h to obtain a function v (h) corresponding to any h, wherein the type of the variation function in the embodiment is a spherical model, an exponential function model or a power function model. Taking the spherical model as an example, the variogram can be expressed as:
wherein c represents a base station value, h represents a hysteresis distance, i.e., a distance, and a represents a variation.
The method for determining the second initial seismic shear wave velocity structure of the point to be estimated among the stations by using the new variation function can comprise the steps of estimating the mean value and the variance of the point to be estimated among the stations by using the seismic shear wave velocity structure of the node with known velocity and the variation function, wherein the mean value and the variance are actually kriging Jin Junzhi and kriging variance, namely, a kriging equation set is established through constraints such as variance minimization in the kriging interpolation process, and the weight coefficient required by interpolation is solved, so that the kriging interpolation of the position to be estimated is further obtained, the weight coefficient is used as kriging Jin Junzhi, and the kriging variance is obtained through kriging mean value calculation. The local probability distribution of the point to be estimated among the stations can be determined according to the mean value and the variance, and the local probability distribution can be determined after the mean value and the variance are determined by assuming that the seismic transverse wave velocity structure of the point to be estimated among the stations meets normal distribution. And extracting a random sample from the local probability distribution, wherein the value of the random sample is the second initial seismic transverse wave velocity structure of the point to be estimated among the stations. And (3) recording the estimated point between stations as a node with known speed, re-estimating the variation function, after the estimation of the estimated point between stations is completed, the sample is added, the variation function can be re-estimated, the calculation of the estimated point between the next stations is carried out, and the above processes are repeated until the calculation of the estimated point between all stations is completed.
(4) Judging whether second initial seismic transverse wave velocity structures of points to be estimated among all stations are obtained or not;
(5) If yes, ending iteration, wherein all second initial seismic transverse wave velocity structures of points to be estimated among all the stations in random simulation sequence form a plurality of second initial seismic transverse wave velocity structures of the points to be estimated among the stations;
(6) If not, returning to the step of obtaining a new variation function by fitting the first seismic transverse wave speed structure and position of all the stations and the second initial seismic transverse wave speed structure and position of the to-be-estimated point among all the stations with known speeds.
Based on the above process, the embodiment can generate multiple groups of second initial seismic transverse wave velocity structures of points to be estimated among stations under the same grid, combine the first seismic transverse wave velocity structures of the stations to form multiple groups of random implementation models, and the multiple groups of random implementation models can be understood as multiple seismic transverse wave velocity structure samples obtained from the same working area. In S3, the samples are subjected to forward solving, and in S4, a random realization model with optimal matching is selected by utilizing the correlation between forward results of the samples and known forward results to be used as a final seismic transverse wave velocity structure.
S3, for each second initial seismic transverse wave velocity structure of each point to be estimated among the stations, taking the second initial seismic transverse wave velocity structure as input, and calculating to obtain a second Rayleigh wave dispersion curve by using the dispersion equation;
This step is the forward process of multiple sets of randomly implemented models. For each point to be estimated among stations, a plurality of groups of random realization models are provided, and for the plurality of groups of random realization models, a plurality of groups of Rayleigh wave dispersion curves corresponding to the random realization models are generated by using a dispersion equation, and the Rayleigh wave dispersion curves can be determined according to the plurality of groups of Rayleigh wave dispersion curves I.e. phase velocity, where j represents the j-th set of stochastic realization models and i represents the i-th inter-station point to be estimated.
And S4, for each inter-platform point to be estimated, taking all second Rayleigh wave dispersion curves corresponding to the inter-platform point to be estimated as input, and determining an optimal second Rayleigh wave dispersion curve by using a second objective function, wherein a second initial seismic transverse wave velocity structure corresponding to the optimal second Rayleigh wave dispersion curve is the second seismic transverse wave velocity structure of the inter-platform point to be estimated.
The second objective function of this embodiment is:
wherein, phi i is the second objective function, PV i is the estimated value of Rayleigh wave phase velocity of the point to be estimated between the ith stations; and the Rayleigh wave phase velocity of a j second Rayleigh wave dispersion curve which is the point to be estimated among the ith stations.
The calculation formula of the estimated value of the Rayleigh wave phase velocity of the point to be estimated between the ith stations is as follows:
wherein s=1, 2,..n 1,N1 is N 1 nodes nearest to the point to be estimated between the ith stations, the size of N 1 can be set by itself, ω s is the reciprocal of the distance from the ith node to the point to be estimated between the ith stations, PV s is the rayleigh wave phase velocity of the ith node, and the nodes include the station and the point to be estimated between the stations.
And through a second objective function, the Rayleigh wave phase velocity of the i-th inter-station point to be estimated with the largest correlation coefficient with the PV i can be selected as the optimal phase velocity, and the second initial seismic transverse wave velocity structure corresponding to the optimal phase velocity is the optimal matching result of the inter-station point to be estimated, namely the second seismic transverse wave velocity structure of the inter-station point to be estimated.
In this embodiment, unlike the conventional technique of determining the transverse wave velocity between seismic stations by using a linear interpolation method, the random simulation method adopted in S2 can increase the randomness and diversity of data on the premise of fully considering the spatial statistical correlation, and S3 and S4 provide a preferable basis for a large number of random implementation models, so as to ensure that a more reliable result is selected from the random implementation models in S2, and thus a seismic transverse wave velocity structure with higher transverse resolution can be obtained.
Example 2:
The embodiment is used for providing a rayleigh wave dispersion curve inversion system based on geostatistics, as shown in fig. 2, the inversion system includes:
The system comprises a station speed inversion module M1, a frequency inversion equation, a first Rayleigh wave frequency dispersion curve and a second Rayleigh wave frequency dispersion module, wherein the station speed inversion module M1 is used for acquiring a first initial seismic transverse wave speed structure and a first Rayleigh wave frequency dispersion curve of each station;
the inter-station velocity initial determining module M2 is used for determining a plurality of second initial seismic transverse wave velocity structures of points to be estimated among all stations according to the first seismic transverse wave velocity structures and positions of all stations;
The forward modeling module M3 is configured to calculate, for each of the second initial seismic transverse wave velocity structures of the points to be estimated between the stations, a second rayleigh wave dispersion curve by using the dispersion equation with the second initial seismic transverse wave velocity structure as an input;
The inter-platform velocity estimation module M4 is configured to determine, for each point to be estimated between the platforms, an optimal second rayleigh wave dispersion curve by using a second objective function with all second rayleigh wave dispersion curves corresponding to the point to be estimated between the platforms as input, where a second initial seismic transverse wave velocity structure corresponding to the optimal second rayleigh wave dispersion curve is a second seismic transverse wave velocity structure of the point to be estimated between the platforms.
In this specification, each embodiment is mainly described in the specification as a difference from other embodiments, and the same similar parts between the embodiments are referred to each other. For the system disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant points refer to the description of the method section.
The principles and embodiments of the present invention have been described herein with reference to specific examples, which are intended to facilitate an understanding of the principles and concepts of the invention and are to be varied in scope and detail by persons of ordinary skill in the art based on the teachings herein. In view of the foregoing, this description should not be construed as limiting the invention.
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