Method for dynamically monitoring underground structure change of target area by using regional earthquake
By setting up a sub-platform array in the monitoring area and fitting the spatial autocorrelation method and Bessel function, the transverse wave velocity structure of the underground medium is inverted and a three-dimensional velocity model is constructed, which solves the problem that the existing technology cannot dynamically obtain the underground three-dimensional structure under the station network, and realizes the ability to dynamically monitor the changes in the underground structure.
Patent Information
- Application Number
- CN202411943755.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-12-27
- Publication Date
- 2025-05-09
- Estimated Expiration
- 2044-12-27
AI Technical Summary
The prior art cannot dynamically obtain the underground three-dimensional structure information below the station network and cannot build a three-dimensional speed model.
By setting up a sub-platform array in the monitoring area, using the spatial autocorrelation method to calculate the spatial autocorrelation coefficient, fit these coefficients using the Bessel function, invert the transverse wave velocity structure of the underground medium, and construct a three-dimensional velocity model through spatial interpolation.
It realizes dynamic acquisition of underground three-dimensional structure changes information, can monitor underground structure changes in real time or near real time, and is suitable for rapid response to emergency situations such as geological disasters.
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Figure CN119960021A_ABST
Abstract
Description
Technical Field
[0001] The invention relates to an improvement of a technology for dynamically monitoring underground structure changes using earthquakes, belongs to the field of dynamic earthquake monitoring, and in particular to a method for dynamically monitoring underground structure changes in a target area using regional earthquakes. Background Art
[0002] Earthquakes, also known as ground motions or seismic vibrations, are natural phenomena that occur when the earth's crust releases energy rapidly, causing the ground to vibrate. When an earthquake occurs, a special type of seismic wave, called a surface wave, is generated. These surface waves can reveal the properties of the underground medium and provide us with important information about the internal structure of the earth. Obtaining the properties of the underground medium is essential for a variety of applications, including monitoring and positioning of seismic networks, monitoring of induced earthquakes, and detection of mining voids. By monitoring the dynamic changes in the properties of the underground medium, we can conduct real-time dynamic monitoring of the expansion of the mining voids in the region, changes in groundwater levels caused by water pumping and injection operations, etc. This type of monitoring is similar to the cloud maps used in weather forecasts, which can provide intuitive information about changes in the earth's interior. However, existing earthquake monitoring methods have a major limitation: they cannot dynamically obtain three-dimensional structural information of the underground below the network, that is, they cannot construct a three-dimensional velocity model.
[0003] A Chinese patent application with application number CN202410820820.9 and application date June 24, 2024 discloses a stability analysis system for a wharf structure under seismic waves, including a stability analysis system. The present invention collects seismic wave data of a target wharf through an acquisition unit, and establishes an overall three-dimensional model corresponding to the target wharf, and adapts the collected seismic wave data of the target wharf to the established overall three-dimensional model corresponding to the target wharf, thereby utilizing the propagation and reflection characteristics of seismic waves underground, and inferring underground structure and geological information such as stratigraphic distribution, lithology, cracks, faults, etc. through seismic inversion through the arrival time and amplitude information of the seismic wave data, thereby determining the stability of the wharf structure, and providing architectural information and geological information of the target wharf with the assistance of an Internet of Things unit and an artificial intelligence unit, thereby improving the accuracy of the stability analysis. However, the above scheme does not solve the problem of not being able to dynamically obtain the underground three-dimensional structure below the station network.
[0004] The information disclosed in this background technology section is only intended to increase the understanding of the overall background of this patent application, and should not be regarded as acknowledging or suggesting in any form that the information constitutes the prior art already known to ordinary technicians in this field. Summary of the invention
[0005] The purpose of the present invention is to overcome the problem in the prior art that it is impossible to dynamically obtain the three-dimensional underground structure beneath the network, and to provide a method for dynamically monitoring the underground structure changes in the target area by using regional earthquakes to dynamically obtain the changes in the three-dimensional underground structure beneath the network.
[0006] To achieve the above objectives, the technical solution of the present invention is: a method for dynamically monitoring the underground structure changes in a target area using regional earthquakes, the method for dynamically monitoring the underground structure changes in a target area using regional earthquakes comprises the following steps:
[0007] The first step is to select a station in the seismic network in the monitoring area as the central station, then set a preset radius for the central station, identify and select all stations within the preset radius, and then form all the stations into a sub-array, obtain the seismic surface wave data of each station in the corresponding sub-array, and form a data set;
[0008] The second step is to use the spatial autocorrelation method to calculate the distance relationship between the above data set and each station in the sub-array, and obtain all the spatial autocorrelation coefficients;
[0009] The third step is to fit all the above spatial autocorrelation coefficients through Bessel function to obtain the dispersion curve;
[0010] The fourth step is to process the dispersion curve through the inversion algorithm, and then obtain the shear wave velocity structure of the underground medium under the sub-array;
[0011] Step 5. Repeat steps 1 to 4 for each station until the sub-array covers the monitoring area, and obtain the shear wave velocity structure of the underground medium of each sub-array. Then, summarize the shear wave velocity structures of the underground medium of all sub-arrays to obtain a velocity structure set. According to the velocity structure set, a three-dimensional velocity model of the underground medium in the monitoring area is constructed through spatial interpolation.
[0012] In the second step, the spatial autocorrelation method is used to calculate the distance relationship between the above data set and each station in the sub-array, and all spatial autocorrelation coefficients are obtained, specifically:
[0013] The polar coordinate form of the frequency spectrum of the micro-motion signal is:
[0014]
[0015] In the formula, ω and k form a functional relationship, ζ = r (cosθ, sinθ), k = k (cosφ, sinφ), usually the spectrum of micro-motion is continuously differentiable with respect to frequency and propagation direction, so the above formula can be rewritten as:
[0016] E[|dz(ω,φ| 2 ]=dH(ω,φ)=h(ω,φ)dωdφ;
[0017] Where H(ω, φ) is the integrated spectrum of X(t, r, θ) with respect to orientation, and h(ω, φ) is the frequency-orientation density.
[0018] The frequency spectra of the micro-motion records at points O(0, 0) and A(r, θ) on the circular array are:
[0019]
[0020] Where ω is the angular frequency, k is the wave number, φ is the incident angle of the micro-motion signal, and ζ(ω, φ) is an orthogonal random process.
[0021] The spatial autocorrelation function S(r;θ) of points O and A is defined as:
[0022]
[0023] Where g(ω, r; θ) is the spatial covariance function, h(ω, φ) is the frequency-azimuth spectral density, and taking the azimuth average of the spatial covariance function g(ω, r; θ) yields:
[0024]
[0025] Where J0 is the first kind zero-order Bessel function;
[0026] Define ρ(ω, r) as the spatial autocorrelation coefficient of angular frequency ω:
[0027]
[0028] Substituting k = ω / c(ω), ω = 2πf, c(ω) is the Rayleigh wave phase velocity, we can get:
[0029]
[0030] The Fourier transform of O(0,0) and A(r,θ) are respectively expressed as S O (0, ω), S A (r, ω), then the spatial autocorrelation coefficient between two points in the frequency domain can be expressed as:
[0031]
[0032] In the formula, Re(·) represents the real part, and * represents the complex conjugate.
[0033] The number of stations in the seismic network is greater than forty.
[0034] In the third step, all the spatial autocorrelation coefficients are fitted by Bessel function, and the fitting methods include least square method, nonlinear least square method and piecewise fitting.
[0035] In the first step, a preset radius is set for the central station, and the preset radius is set according to geological structure, detection depth and signal attenuation factors.
[0036] The detection depth is 4-10 times the distance between stations, and the size of the sub-array is set in proportion to the target detection depth.
[0037] In the fourth step, the dispersion curve is first processed by an inversion algorithm, and then the shear wave velocity structure of the underground medium below the sub-array is obtained. Specifically, the dispersion curve is the relationship between the phase velocity and frequency of the underground medium, the abscissa is the frequency, and the ordinate is the surface wave phase velocity. The fitting of the theoretical dispersion curve calculated by the preset velocity structure and the observed dispersion curve is compared, and the best fitting shear wave velocity structure is gradually adjusted, that is, the relationship between the shear wave velocity and depth of the underground medium.
[0038] The fifth step summarizes the shear wave velocity structures of the underground media of all sub-arrays to obtain a velocity structure set, and also includes quality control of the shear wave velocity structure, eliminating outliers, and ensuring data consistency.
[0039] Compared with the prior art, the present invention has the following beneficial effects:
[0040] 1. In a method for dynamically monitoring underground structure changes in a target area using regional earthquakes, the shear wave velocity structure of the underground medium of each sub-array is obtained, and then the shear wave velocity structures of the underground medium of all sub-arrays are summarized to obtain a velocity structure set. A three-dimensional velocity model of the underground medium of the region is constructed by spatial interpolation based on the velocity structure set. The SPAC method can utilize existing seismic array data without the need for additional source excitation. Through continuous or repeated observations, SPAC coefficients and dispersion curves at different time points are collected to monitor their changes, thereby dynamically obtaining changes in underground structures, and thus real-time or near-real-time underground structure change information is essential for rapid response to emergencies such as geological disasters. Therefore, the present invention can dynamically obtain changes in the underground three-dimensional structure below the network.
[0041] 2. In the method of using regional earthquakes to dynamically monitor underground structural changes in a target area, the SPAC method is suitable for monitoring in complex environments such as cities because it does not require artificial seismic sources. It can also use existing seismic array data without the need for additional source excitation, so it has flexibility in data acquisition. In addition, high-resolution underground structure images can be obtained, which helps to more accurately understand the properties of underground media. Therefore, the present invention has higher acquisition flexibility and more intuitive display of underground structures.
[0042] 3. In the method of using regional earthquake dynamics to monitor underground structural changes in the target area, the SPAC coefficient deviation is clustered and analyzed to distinguish changes caused by factors such as human activities and environmental changes, and changes caused by underground structural changes. The monitored underground structural changes are associated with surface phenomena to better understand the impact of underground structural changes on surface stability. Therefore, the analysis of the present invention is more comprehensive and the monitoring effect is better. BRIEF DESCRIPTION OF THE DRAWINGS
[0043] Figure 1 It is a schematic diagram of the array of the present invention.
[0044] Figure 2 It is a schematic diagram of the spatial autocorrelation coefficient of the present invention.
[0045] Figure 3 It is the observation data diagram of the present invention.
[0046] Figure 4 It is the calculation power diagram of the present invention.
[0047] Figure 5 It is a schematic diagram of calculation coefficients of the present invention.
[0048] Figure 6 It is the phase velocity diagram of the present invention.
[0049] Figure 7 It is a dispersion curve diagram of the present invention.
[0050] Figure 8 It is a shear wave velocity structure diagram below the underground array of the present invention. DETAILED DESCRIPTION
[0051] The present invention is further described in detail below in conjunction with the accompanying drawings and specific implementation methods.
[0052] See also Figures 1 to 8 A method for dynamically monitoring underground structure changes in a target area using regional earthquakes, the method comprising the following steps:
[0053] The first step is to select a station in the seismic network in the monitoring area as the central station, then set a preset radius for the central station, identify and select all stations within the preset radius, and then form all the stations into a sub-array, obtain the seismic surface wave data of each station in the corresponding sub-array, and form a data set;
[0054] The second step is to use the spatial autocorrelation method to calculate the distance relationship between the above data set and each station in the sub-array, and obtain all the spatial autocorrelation coefficients;
[0055] The third step is to fit all the above spatial autocorrelation coefficients through Bessel function to obtain the dispersion curve;
[0056] The fourth step is to process the dispersion curve through the inversion algorithm, and then obtain the shear wave velocity structure of the underground medium under the sub-array;
[0057] Step 5. Repeat steps 1 to 4 for each station until the sub-array covers the monitoring area, and obtain the shear wave velocity structure of the underground medium of each sub-array. Then, summarize the shear wave velocity structures of the underground medium of all sub-arrays to obtain a velocity structure set. According to the velocity structure set, a three-dimensional velocity model of the underground medium in the monitoring area is constructed through spatial interpolation.
[0058] In the second step, the spatial autocorrelation method is used to calculate the distance relationship between the above data set and each station in the sub-array, and all spatial autocorrelation coefficients are obtained, specifically:
[0059] The polar coordinate form of the frequency spectrum of the micro-motion signal is:
[0060]
[0061] In the formula, ω and k form a functional relationship, ζ = r (cosθ, sinθ), k = k (cosφ, sinφ), usually the spectrum of micro-motion is continuously differentiable with respect to frequency and propagation direction, so the above formula can be rewritten as:
[0062] E[|dz(ω,φ)| 2 ]=dH(ω,φ)=h(ω,φ)dωdφ;
[0063] Where H(ω, φ) is the integrated spectrum of X(t, r, θ) with respect to orientation, and h(ω, φ) is the frequency-orientation density.
[0064] The frequency spectra of the micro-motion records at points O(0, 0) and A(r, θ) on the circular array are:
[0065]
[0066] Where ω is the angular frequency, k is the wave number, φ is the incident angle of the micro-motion signal, and ζ(ω, φ) is an orthogonal random process.
[0067] The spatial autocorrelation function S(r, θ) of points O and A is defined as:
[0068]
[0069] Where g(ω, r, θ) is the spatial covariance function, h(ω, φ) is the frequency-azimuth spectral density, and taking the azimuth average of the spatial covariance function g(ω, r, θ) yields:
[0070]
[0071] Where J0 is the first kind zero-order Bessel function;
[0072] Define ρ(ω, r) as the spatial autocorrelation coefficient of angular frequency ω:
[0073]
[0074] Substituting k = ω / c(ω), ω = 2πf, c(ω) is the Rayleigh wave phase velocity, we can get:
[0075]
[0076] The Fourier transform of O(0,0) and A(r,θ) are respectively expressed as S O (0, ω), S A (r, ω), then the spatial autocorrelation coefficient between two points in the frequency domain can be expressed as:
[0077]
[0078] In the formula, Re(·) represents the real part, and * represents the complex conjugate.
[0079] The number of stations in the seismic network is greater than forty.
[0080] In the third step, all the spatial autocorrelation coefficients are fitted by Bessel function, and the fitting methods include least square method, nonlinear least square method and piecewise fitting.
[0081] In the first step, a preset radius is set for the central station, and the preset radius is set according to geological structure, detection depth and signal attenuation factors.
[0082] The detection depth is 4-10 times the distance between stations, and the size of the sub-array is set in proportion to the target detection depth.
[0083] In the fourth step, the dispersion curve is first processed by an inversion algorithm, and then the shear wave velocity structure of the underground medium below the sub-array is obtained. Specifically, the dispersion curve is the relationship between the phase velocity and frequency of the underground medium, the abscissa is the frequency, and the ordinate is the surface wave phase velocity. The fitting of the theoretical dispersion curve calculated by the preset velocity structure and the observed dispersion curve is compared, and the best fitting shear wave velocity structure is gradually adjusted, that is, the relationship between the shear wave velocity and depth of the underground medium.
[0084] The fifth step summarizes the shear wave velocity structures of the underground media of all sub-arrays to obtain a velocity structure set, and also includes quality control of the shear wave velocity structure, eliminating outliers, and ensuring data consistency.
[0085] The supplementary description of the present invention is as follows:
[0086] Each seismograph in the array has recorded data for each earthquake. The array layout is fixed, that is, the observations between each station are calculated. This distance information is used to extract the dispersion curve from the spatial autocorrelation coefficient. The data recorded by all stations for each earthquake can obtain a three-dimensional velocity structure. Earthquakes that affect the array occur frequently but not simultaneously around the array. Therefore, by comparing the three-dimensional velocity structure obtained from each earthquake data, some changes in the underground structure can be discovered, such as where the mine is excavated and where the water stored in the reservoir has seeped. Earthquakes of magnitude 6 or above 1,000 km away from the network, magnitude 5 or above 500 km away, magnitude 4 200 km away, and small earthquakes nearby occur intermittently, and the surface wave data sets of these earthquakes are processed.
[0087] Embodiment 1:
[0088] A method for dynamically monitoring underground structure changes in a target area using regional earthquakes, the method comprising the following steps:
[0089] The first step is to select a station in the seismic network in the monitoring area as the central station, then set a preset radius for the central station, identify and select all stations within the preset radius, and then form all the stations into a sub-array, obtain the seismic surface wave data of each station in the corresponding sub-array, and form a data set;
[0090] The second step is to use the spatial autocorrelation method to calculate the distance relationship between the above data set and each station in the sub-array, and obtain all the spatial autocorrelation coefficients;
[0091] The third step is to fit all the above spatial autocorrelation coefficients through Bessel function to obtain the dispersion curve;
[0092] The fourth step is to process the dispersion curve through the inversion algorithm, and then obtain the shear wave velocity structure of the underground medium under the sub-array;
[0093] Step 5. Repeat steps 1 to 4 for each station until the sub-array covers the monitoring area, and obtain the shear wave velocity structure of the underground medium of each sub-array. Then, summarize the shear wave velocity structures of the underground medium of all sub-arrays to obtain a velocity structure set. According to the velocity structure set, a three-dimensional velocity model of the underground medium in the monitoring area is constructed through spatial interpolation.
[0094] Embodiment 2:
[0095] Embodiment 2 is substantially the same as Embodiment 1, except that:
[0096] The spatial autocorrelation method is used to calculate the distance relationship between the above data set and the stations in the sub-array to obtain the spatial autocorrelation coefficient, which is:
[0097] The polar coordinate form of the frequency spectrum of the micro-motion signal is:
[0098]
[0099] In the formula, ω and k form a functional relationship, ζ = r (cosθ, sinθ), k = k (cosφ, sinφ), usually the spectrum of micro-motion is continuously differentiable with respect to frequency and propagation direction, so the above formula can be rewritten as:
[0100] E[|dz(ω,φ)| 2 ]=dH(ω,φ)=h(ω,φ)dωdφ;
[0101] Where H(ω, φ) is the integrated spectrum of X(t, r, θ) with respect to orientation, and h(ω, φ) is the frequency-orientation density.
[0102] like Figure 1 As shown, the frequency spectra of the micro-motion records of the two points O(0, 0) and A(r, θ) on the circular array are:
[0103]
[0104] Where ω is the angular frequency, k is the wave number, φ is the incident angle of the micro-motion signal, and ζ(ω, φ) is an orthogonal random process.
[0105] The spatial autocorrelation function S(r, θ) of points O and A is defined as:
[0106]
[0107] Where g(ω, r, θ) is the spatial covariance function, h(ω, φ) is the frequency-azimuth spectral density, and taking the azimuth average of the spatial covariance function g(ω, r, θ) yields:
[0108]
[0109] Where J0 is the first kind zero-order Bessel function;
[0110] Define ρ(ω, r) as the spatial autocorrelation coefficient of angular frequency ω:
[0111]
[0112] Substituting k = ω / c(ω), ω = 2πf, c(ω) is the Rayleigh wave phase velocity, we can get:
[0113]
[0114] This formula shows that the Rayleigh wave phase velocity can be obtained by the first-kind zero-order Bessel function and the spatial autocorrelation coefficient. The corresponding spatial autocorrelation coefficient is Figure 2 As shown;
[0115] The Fourier transform of O(0,0) and A(r,θ) are respectively expressed as S O (0, ω), S A (r, ω), then the spatial autocorrelation coefficient between two points in the frequency domain can be expressed as:
[0116]
[0117] In the formula, Re(·) represents the real part, and * represents the complex conjugate.
[0118] Embodiment 3:
[0119] Embodiment 3 is substantially the same as Embodiment 1, except that:
[0120] The preset radius is set according to the geological structure, detection depth and signal attenuation factors. The detection depth is 4-10 times the station spacing. The size of the sub-array is set in proportion to the target detection depth. The data of a sub-array is processed to obtain an underground structure profile, similar to a borehole profile. This result is a comprehensive average result of the structure within the sub-array range. Therefore, the sub-array should not be too large or too small. If it is too large, it cannot reflect the lateral details; if it is too small, the detection depth may not be enough. When processing data, you can try to select the most appropriate sub-array size to determine the number of seismographs in the sub-array.
[0121] Embodiment 4:
[0122] Embodiment 4 is substantially the same as Embodiment 1, except that:
[0123] By determining the lowest frequency according to the detection depth, the lowest frequency also limits the depth that can be detected. After the lowest frequency is determined, the reciprocal is used to know the maximum period. According to the Nyquist theorem, the data length must be at least twice the period for the frequency to be undistorted. In general, a length of more than 10 times is used as the segment length for data processing. For example, if the lowest frequency is 0.2Hz and the corresponding period is 5s, then the segment data length can be 50s. In order for the data volume to be a power of 2, since the sampling rate is generally 100Hz, 40.96s, 81.92s or 163.84s can be used. This is conducive to fast Fourier transform (FFT). Usually the observed data length reaches several minutes or even hours. Generally, such long data is divided into time periods. After cross-correlation calculation is performed in each time period, superposition and averaging are performed to improve the signal-to-noise ratio. The averaged result is used to fit the Bessel function and then extract the dispersion curve.
[0124] Embodiment 5:
[0125] Embodiment 5 is substantially the same as Embodiment 1, except that:
[0126] Seismic surface waves are plane waves that propagate on the surface of the earth due to earthquake excitation. They generally have dispersion characteristics, that is, waves of different frequencies propagate at different speeds. The relationship curve between the propagation speed and the frequency is the dispersion curve. Therefore, by extracting the dispersion curve through observation, the underground velocity structure can be inverted or inferred based on empirical formulas. The magnitude of the velocity at various locations in the underground structure reflects the following situations. For example, if the velocity at a certain location is obviously low, it may be a tunnel excavated by a mine, a cavity caused by karst collapse, or an artificially excavated air-raid shelter, etc. The possible reasons can be inferred by the high and low velocities at the location reflected by the underground three-dimensional velocity structure and the shapes formed by these high and low values.
[0127] The above description is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above embodiment. Any equivalent modifications or changes made by ordinary technicians in this field based on the contents disclosed by the present invention should be included in the protection scope recorded in the claims.
Claims
1. A method for dynamically monitoring underground structural changes in a target area using regional earthquakes, characterized in that: The method for dynamically monitoring underground structure changes in a target area using regional earthquakes comprises the following steps: The first step is to select a station in the seismic network in the monitoring area as the central station, then set a preset radius for the central station, identify and select all stations within the preset radius, and then form all the stations into a sub-array, obtain the seismic surface wave data of each station in the corresponding sub-array, and form a data set; The second step is to use the spatial autocorrelation method to calculate the distance relationship between the above data set and each station in the sub-array, and obtain all the spatial autocorrelation coefficients; The third step is to fit all the above spatial autocorrelation coefficients through Bessel function to obtain the dispersion curve; The fourth step is to process the dispersion curve through the inversion algorithm, and then obtain the shear wave velocity structure of the underground medium under the sub-array; Step 5. Repeat steps 1 to 4 for each station until the sub-array covers the monitoring area, and obtain the shear wave velocity structure of the underground medium of each sub-array. Then, summarize the shear wave velocity structures of the underground medium of all sub-arrays to obtain a velocity structure set. According to the velocity structure set, a three-dimensional velocity model of the underground medium in the monitoring area is constructed through spatial interpolation.
2. A method for dynamically monitoring underground structural changes in a target area using regional earthquakes according to claim 1, characterized in that: In the second step, the spatial autocorrelation method is used to calculate the distance relationship between the above data set and each station in the sub-array, and all spatial autocorrelation coefficients are obtained, specifically: The polar coordinate form of the frequency spectrum of the micro-motion signal is: In the formula, ω and k form a functional relationship, ζ = r (cosθ, sinθ), k = k (cosφ, sinφ), usually the spectrum of micro-motion is continuously differentiable with respect to frequency and propagation direction, so the above formula can be rewritten as: E[|dz(ω,φ)| 2 ]=dH(ω,φ)=h(ω,φ)dωdφ; Where H(ω, φ) is the integrated spectrum of X(t, r, θ) with respect to orientation, and h(ω, φ) is the frequency-orientation density.
3. The method of using regional earthquakes to dynamically monitor underground structural changes in a target area according to claim 2, characterized in that: The frequency spectra of the micro-motion records at points O(0, 0) and A(r; θ) on the circular array are: Where ω is the angular frequency, k is the wave number, φ is the incident angle of the micro-motion signal, and ζ(ω, φ) is an orthogonal random process.
4. The method of using regional earthquakes to dynamically monitor underground structural changes in a target area according to claim 3, characterized in that: The spatial autocorrelation function S(r;θ) of points O and A is defined as: Where g(ω, r; θ) is the spatial covariance function, h(ω, φ) is the frequency-azimuth spectral density, and taking the azimuth average of the spatial covariance function g(ω, r; θ) yields: Where J0 is the first kind zero-order Bessel function; Define ρ(ω, r) as the spatial autocorrelation coefficient of angular frequency ω: Substituting k = ω / c(ω), ω = 2πf, c(ω) is the Rayleigh wave phase velocity, we can get: The Fourier transform of O(0,0) and A(r,θ) are respectively expressed as S O (0, ω), S A (r, ω), then the spatial autocorrelation coefficient between two points in the frequency domain can be expressed as: In the formula, Re(·) represents the real part, and * represents the complex conjugate.
5. The method of using regional earthquakes to dynamically monitor underground structural changes in a target area according to claim 1, characterized in that: The number of stations in the seismic network is greater than forty.
6. The method of using regional earthquakes to dynamically monitor underground structural changes in a target area according to claim 1, characterized in that: In the third step, all the spatial autocorrelation coefficients are fitted by Bessel function to obtain the dispersion curve, and the fitting methods include least square method, nonlinear least square method and piecewise fitting.
7. The method of using regional earthquakes to dynamically monitor underground structural changes in a target area according to claim 1, characterized in that: In the first step, a preset radius is set for the central station, and the preset radius is set according to geological structure, detection depth and signal attenuation factors.
8. The method of using regional earthquakes to dynamically monitor underground structural changes in a target area according to claim 7, characterized in that: The detection depth is 4-10 times the distance between stations, and the size of the sub-array is set in proportion to the target detection depth.
9. The method of using regional earthquakes to dynamically monitor underground structural changes in a target area according to claim 1, characterized in that: In the fourth step, the dispersion curve is first processed by an inversion algorithm, and then the shear wave velocity structure of the underground medium below the sub-array is obtained. Specifically, the dispersion curve is the relationship between the phase velocity and frequency of the underground medium, the abscissa is the frequency, and the ordinate is the surface wave phase velocity. The fitting of the theoretical dispersion curve calculated by the preset velocity structure and the observed dispersion curve is compared, and the best fitting shear wave velocity structure is gradually adjusted, that is, the relationship between the shear wave velocity and depth of the underground medium.
10. The method of using regional earthquakes to dynamically monitor underground structural changes in a target area according to claim 1, characterized in that: The fifth step summarizes the shear wave velocity structures of the underground media of all sub-arrays to obtain a velocity structure set, and also includes quality control of the shear wave velocity structure, eliminating outliers, and ensuring data consistency.
Citation Information
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