HVSR spectrum ratio curve inversion method based on diffusion field theory

Abstract

The invention is suitable for the technical field of geophysical exploration, and provides an HVSR spectrum ratio curve inversion method based on a diffusion field theory, which comprises the following steps: constructing a spectrum ratio calculation equation based on the diffusion field theory; artificially synthesizing a jogging record of random seismic source distribution; setting a model and acquiring micro-motion data; calculating an HVSR spectrum ratio curve; constructing and optimizing an inversion objective function; and outputting an inversion result. According to the invention, based on the diffusion field theory, by comprehensively considering various wave field components such as body waves and surface waves, the limitation of the traditional single wave field hypothesis is significantly reduced, and the inversion precision is improved. The method shows excellent adaptability under the conditions of a shallow structure and a complex medium, has strong noise robustness, and is suitable for complex environments such as urban underground space detection and the like. Besides, the method reduces dependence on an initial model, avoids a local optimum problem, can be expanded to the fields of engineering earthquake safety assessment, underground water resource exploration and the like, and has a wide application prospect.

Description

Technical Field

[0001] The invention belongs to the technical field of geophysical exploration, and in particular relates to an HVSR spectrum ratio curve inversion method based on diffusion field theory. Background Art

[0002] Urban underground space detection is an important application field of geophysical exploration, which aims to obtain geological information such as shallow underground soil, rock and groundwater through geophysical data signals. In recent years, single-station micromotion detection technology has attracted widespread attention as a low-cost detection method without artificial seismic sources. This method records surface micromotion signals and uses the HVSR method (Fourier amplitude spectrum ratio of horizontal component to vertical component) to invert underground structures. The HVSR spectral ratio method can capture multiple wave field components such as longitudinal waves, transverse waves and Rayleigh waves. However, due to the complexity of the wave field, different scholars have proposed a variety of interpretation models based on body wave hypothesis, surface wave hypothesis and full wave field hypothesis. The spectral ratio method based on body wave hypothesis has the advantages of mature theoretical basis and strong deep detection capability, but it performs poorly in adaptability to shallow structures and complex media and is more sensitive to noise. The spectral ratio method based on surface wave hypothesis performs well in shallow detection and noise suppression, but its deep detection capability and resolution are limited. The full wave field hypothesis based on the diffusion field can better describe the wave field characteristics in complex media and has strong robustness to noise. However, its application in the HVSR spectral ratio curve inversion still needs to be further optimized. To this end, the present invention proposes an HVSR spectral ratio curve inversion method based on the diffusion field theory, aiming to solve the applicability problem of traditional methods under complex media conditions and improve the inversion accuracy and efficiency. Summary of the invention

[0003] The object of the present invention is to provide a HVSR spectral ratio curve inversion method based on diffusion field theory, aiming to solve the problems raised in the above background technology.

[0004] The purpose of the present invention is achieved through the following technical solutions: A HVSR spectral ratio curve inversion method based on diffusion field theory includes the following steps: Step S1: constructing a spectrum ratio calculation equation based on diffusion field theory; Considering the information of P waves, SV waves and SH waves in homogeneous isotropic elastic media, the HVSR spectrum ratio calculation equation is constructed based on the diffusion field theory. In three-dimensional space, the displacement field satisfies the diffusion field equation, and the HVSR spectrum ratio formula is expressed as the Fourier amplitude spectrum ratio of the horizontal component to the vertical component. Step S2: artificially synthesizing micromotion records with random source distribution; An artificial source is set up, and the excitation time, source location and main frequency parameters are randomly changed to simulate the random wave field distribution; when simulating the micro-motion record, the noise source is regarded as a point source, and the wave field recorded by the geophone is the simulated micro-motion record; Step S3: model setting and micro-motion data collection; A two-layer medium model is constructed, and given acquisition parameters, the geophone collects micromotion data under random source distribution; Step S4: HVSR spectrum ratio curve calculation; Calculate the spectrum ratio of the simulated micro-motion record collected in step S3 in the horizontal direction and the vertical direction to obtain 100 HVSR spectrum ratio curves; average the 100 HVSR spectrum ratio curves to obtain a representative HVSR spectrum ratio curve; Step S5: constructing and optimizing the inversion objective function; Combined with the initial model parameters, the inversion frequency band is set to 5-20 Hz, and the inversion objective function is constructed to minimize the difference between the observed data and the model predicted data; the Monte Carlo algorithm is used to invert the shear wave velocity and depth of the representative HVSR spectral ratio curve; Step S6: output the inversion results; Output the inversion results and generate depth and velocity structure diagrams. Compare and analyze the inversion results with the actual model to verify the accuracy of the inversion results.

[0005] Furthermore, in step S1, in the three-dimensional space, the displacement field satisfies the diffusion field equation, where the displacement Satisfies the equation: ; in, is the shear wave velocity, is the longitudinal wave velocity, is the spatial displacement of a point, is the spatial displacement of another point, , is the corresponding spatial point position, t is the time variable; The HVSR spectral ratio formula is expressed as the Fourier amplitude spectrum ratio of the horizontal component to the vertical component. The specific formula is: ; in, is the energy spectrum ratio in the horizontal direction to the vertical direction, is the energy density in the horizontal direction, is the energy density in another horizontal direction, is the energy density in the vertical direction, A component of the Green's function tensor in the horizontal direction, is another component of the Green function tensor in the horizontal direction, is a component of the Green's function tensor in the vertical direction, and Im[ ] is the imaginary part of the complex number.

[0006] Furthermore, in step S3, the size of the two-layer medium model is 70m×100m; the source wavelet adopts the Ricker wavelet, 20 random sources are set, and the main frequency of the source is distributed between 10-40Hz; the starting channel of the detector is 1m, the ending channel is 100m, the channel spacing is 1m, a total of 100 channels, and the acquisition time is 1s.

[0007] Furthermore, in step S5, the inversion objective function is as follows: ; in, E is the objective function, N Indicates the number of sampling points of the curve, is the artificial HVSR spectrum ratio curve, is the HVSR spectral ratio curve that needs to be fitted during the inversion process, is the standard deviation of the HVSR spectral ratio curve to be fitted.

[0008] Compared with the prior art, the present invention has the following beneficial effects: 1. Comprehensive consideration of wave field components: The traditional body wave hypothesis and surface wave hypothesis only consider a single wave field component, ignoring the influence of other wave fields, resulting in inaccurate inversion results in complex wave field environments. Based on the diffusion field theory, the present invention comprehensively considers multiple wave field components such as body waves and surface waves, effectively reducing the uncertainty caused by a single wave field hypothesis and enhancing the stability of the inversion results.

[0009] 2. Adaptability to complex media: The diffusion field theory on which the present invention is based can better describe the wave field characteristics in complex media, especially under shallow structures and complex media conditions, which can make the inversion results more accurate and reliable.

[0010] 3. Noise robustness: The diffusion field theory on which the present invention is based is highly robust to noise and can provide stable inversion results in a noisy environment, and is suitable for complex environments such as urban underground space detection.

[0011] 4. Wide range of applications: The present invention overcomes the shortcomings of traditional methods such as strong dependence on the initial model and easy to fall into local optimality, improves the accuracy and reliability of the inversion results, and is not only suitable for urban underground space detection, but also can be used in engineering site earthquake safety evaluation, groundwater resource exploration and other fields, and has broad application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figure 1 The present invention is a flow chart of the method.

[0013] Figure 2 are the model parameters and earthquake source distribution used in the simulation; where a is the two-layer medium model used in the simulation; and b is the random earthquake source distribution.

[0014] Figure 3 HVSR spectral ratio curves of 100 simulated micromotions.

[0015] Figure 4 Comparison of inversion results based on three different assumptions; a is the inversion result based on the body wave assumption, expressed as P / S; b is the inversion result based on the surface wave assumption, expressed as SW; c is the inversion result based on the diffusion field theory assumption, expressed as DW.

[0016] Figure 5 The comparison of the consistency between the inversion results of three different assumptions and the actual given two-layer medium model velocity and depth; where a is the comparison of the number of iterations of the objective function; b is the comparison of the consistency of the inversion results of three different assumptions.

[0017] Figure 6 The figure shows the comparison of inversion results under three different assumptions for the measured data in the work area; a is the HVSR spectral ratio curve under three different assumptions; b is the comparison of inversion results. DETAILED DESCRIPTION

[0018] In order to have a clearer understanding of the technical features, purposes and beneficial effects of the present invention, the technical solution of the present invention is now described in detail below, but it should not be construed as limiting the applicable scope of the present invention.

[0019] The specific implementation of the present invention is described in detail below in conjunction with specific embodiments.

[0020] The present invention provides a HVSR spectrum ratio curve inversion method based on diffusion field theory, and its flow chart is as follows: Figure 1 As shown, the following steps are included: Step S1: constructing a spectrum ratio calculation equation based on diffusion field theory; Considering the information of P waves, SV waves and SH waves in homogeneous isotropic elastic media, the HVSR spectrum ratio calculation equation is constructed based on the diffusion field theory. In three-dimensional space, the displacement field satisfies the diffusion field equation, and the HVSR spectrum ratio formula can be expressed as the Fourier amplitude spectrum ratio of the horizontal component to the vertical component.

[0021] Specifically, in three-dimensional space, displacement Satisfies the equation: ; in, is the shear wave velocity, is the longitudinal wave velocity, is the spatial displacement of a point, is the spatial displacement of another point, , is the corresponding spatial point position, t is the time variable.

[0022] The specific formula of HVSR spectral ratio formula is: ; ; in, is the energy spectrum ratio in the horizontal direction to the vertical direction, is the energy density in the horizontal direction, is the energy density in another horizontal direction, is the energy density in the vertical direction, A component of the Green's function tensor in the horizontal direction, is another component of the Green function tensor in the horizontal direction, is a component of the Green's function tensor in the vertical direction, and Im[ ] is the imaginary part of the complex number.

[0023] Step S2: artificially synthesizing micromotion records with random source distribution; By setting multiple groups of artificial seismic sources and randomly changing parameters such as excitation time, source location and main frequency, random wave field distribution can be simulated. When simulating micro-seismic records, the noise source is regarded as a point source, and the wave field recorded by the geophone is the simulated micro-seismic record.

[0024] Step S3: model setting and micro-motion data collection; A two-layer medium model is constructed, and acquisition parameters are given. The geophone collects micromotion data under random source distribution. Figure 2 Figure a shows the two-layer medium model used in the simulation. Figure 2 Figure b shows the distribution of random earthquake sources. The size of the model is 70m×100m. Table 1 gives the parameter information of the two-layer medium model. The source wavelet adopts the Ricker wavelet, and a total of 20 random earthquake sources are set. The main frequency of the earthquake source is distributed between 10-40Hz. The starting channel of the detector is 1m, the ending channel is 100m, the channel spacing is 1m, a total of 100 channels, and the acquisition time is 1s.

[0025] Table 1 Parameters of the two-layer medium model

[0026] Step S4: HVSR spectrum ratio curve calculation; The simulated micromotion records collected in step S3 are used to calculate the spectral ratios in the horizontal and vertical directions to obtain 100 HVSR spectral ratio curves (such as Figure 3By averaging these 100 HVSR spectrum ratio curves, a representative HVSR spectrum ratio curve is obtained. Figure 3 The black line in the figure is the average value of 100 HVSR spectrum ratio curves, which is a general result. The figure shows that the main peak of the HVSR spectrum ratio curve of the two-layer medium model is around 10 Hz.

[0027] Step S5: constructing and optimizing the inversion objective function; Combined with the initial model parameters (as shown in Table 2), the inversion frequency band is set to 5-20 Hz, and the inversion objective function is constructed. ,in E is the objective function, N Indicates the number of sampling points of the curve, is the artificial HVSR spectrum ratio curve, is the HVSR spectral ratio curve that needs to be fitted during the inversion process, is the standard deviation of the HVSR spectral ratio curve to be fitted, and the function aims to minimize the difference between the observed data and the model predicted data. The Monte Carlo algorithm is used to perform shear wave velocity and depth inversion on the representative HVSR spectral ratio curve in step S4. Figure 4 Figures ac show the inversion results based on body wave hypothesis, surface wave hypothesis and diffusion field theory hypothesis respectively.

[0028] Table 2 Inversion initial model parameters

[0029] Step S6: output the inversion results; Output the inversion results and generate depth and velocity structure diagrams. Compare and analyze the inversion results with the actual model to verify the accuracy of the inversion results.

[0030] Figure 5 The inversion results using three different assumptions are compared to the actual given two-layer medium model velocity and depth. The objective function is used to measure the difference between the observed data and the model prediction data. The lower the value, the closer the model prediction data is to the observed data, which means that the correlation between the inversion results and the actual model is better. Figure 5 It can be seen from a that the objective function value based on the diffusion field theory hypothesis is the lowest, which indicates that in the inversion process, the model constructed based on the diffusion field theory hypothesis has the best fitting effect on the data, and the difference between its predicted data and the observed data is the smallest, which reflects that there is a good correlation between the HVSR spectrum ratio curve parameters based on the diffusion field theory hypothesis and the parameters of the synthetic model. Figure 5It can be seen from Figure b that the inversion results based on the diffusion field theory assumption are closer to the actual given two-layer medium model in terms of shear wave velocity and depth. This high degree of coincidence further proves that the HVSR spectral ratio curve parameters based on the diffusion field theory assumption have a good correlation with the parameters of the synthetic model and can more accurately reflect the characteristics of the actual model.

[0031] Example 1: To further verify the potential of the present invention in practical applications, it was applied to the measured data in a certain area of Jinan. In this area, the forward model parameters have been obtained, and the corresponding geological information has been obtained through boreholes. These data provide an important basis for verifying the inversion results in this example. The measured data was collected using a three-component geophone with a sampling interval of 2 ms and a collection time of 20 min. The initial inversion parameters are shown in Table 3.

[0032] Table 3 Initial inversion model parameters for the actual work area

[0033] The measured data was processed using the HVSR spectral ratio curve inversion method to obtain the inversion results under three different assumptions (as shown in Figures a and b). It can be seen from Figure that, compared with the inversion results based on the surface wave assumption and the body wave assumption, the inversion results based on the diffusion field theory assumption have better consistency with the forward model parameters and borehole information, which fully verifies the effectiveness and reliability of the present invention. Figure 6 Figure Figure 6 It can be seen from Figure that, compared with the inversion results based on the surface wave assumption and the body wave assumption, the inversion results based on the diffusion field theory assumption have better consistency with the forward model parameters and borehole information, which fully verifies the effectiveness and reliability of the present invention.

[0034] Conclusion: The present invention provides an HVSR spectral ratio curve inversion method based on the diffusion field theory. Through innovation at the theoretical level and optimization and improvement of the algorithm, it effectively solves the problems existing in the process of urban underground space detection by traditional methods, and has important theoretical value and practical application significance.

[0035] The above is only the preferred embodiment of the present invention. It should be noted that for those skilled in the art, without departing from the concept of the present invention, several modifications and improvements can still be made, which should also be regarded as the protection scope of the present invention, and these will not affect the implementation effect of the present invention and the practicality of the patent.

Claims

1. A HVSR spectrum ratio curve inversion method based on diffusion field theory, characterized in that: The following steps are involved: Step S1: constructing a spectrum ratio calculation equation based on diffusion field theory; Considering the information of P waves, SV waves and SH waves in homogeneous isotropic elastic media, the HVSR spectrum ratio calculation equation is constructed based on the diffusion field theory. In three-dimensional space, the displacement field satisfies the diffusion field equation, and the HVSR spectrum ratio formula is expressed as the Fourier amplitude spectrum ratio of the horizontal component to the vertical component. Step S2: artificially synthesizing micromotion records with random source distribution; An artificial source is set up, and the excitation time, source location and main frequency parameters are randomly changed to simulate the random wave field distribution; when simulating the micro-motion record, the noise source is regarded as a point source, and the wave field recorded by the geophone is the simulated micro-motion record; Step S3: model setting and micro-motion data collection; A two-layer medium model is constructed, and given acquisition parameters, the geophone collects micromotion data under random source distribution; Step S4: HVSR spectrum ratio curve calculation; Calculate the spectrum ratio of the simulated micro-motion record collected in step S3 in the horizontal direction and the vertical direction to obtain 100 HVSR spectrum ratio curves; average the 100 HVSR spectrum ratio curves to obtain a representative HVSR spectrum ratio curve; Step S5: constructing and optimizing the inversion objective function; Combined with the initial model parameters, the inversion frequency band is set to 5-20 Hz, and the inversion objective function is constructed to minimize the difference between the observed data and the model predicted data; the Monte Carlo algorithm is used to invert the shear wave velocity and depth of the representative HVSR spectral ratio curve; Step S6: output the inversion results; Output the inversion results and generate depth and velocity structure diagrams. Compare and analyze the inversion results with the actual model to verify the accuracy of the inversion results.

2. The HVSR spectral ratio curve inversion method based on diffusion field theory according to claim 1 is characterized in that: In step S1, in three-dimensional space, the displacement field satisfies the diffusion field equation, where the displacement Satisfies the equation: ； in, is the shear wave velocity, is the longitudinal wave velocity, is the spatial displacement of a point, is the spatial displacement of another point, , is the corresponding spatial point position, t is the time variable; The HVSR spectral ratio formula is expressed as the Fourier amplitude spectrum ratio of the horizontal component to the vertical component. The specific formula is: ； in, is the energy spectrum ratio in the horizontal direction to the vertical direction, is the energy density in the horizontal direction, is the energy density in another horizontal direction, is the energy density in the vertical direction, A component of the Green's function tensor in the horizontal direction, is another component of the Green function tensor in the horizontal direction, is a component of the Green's function tensor in the vertical direction, and Im[ ] is the imaginary part of the complex number.

3. The HVSR spectral ratio curve inversion method based on diffusion field theory according to claim 1 is characterized in that: In step S3, the size of the two-layer medium model is 70m×100m; the source wavelet adopts the Ricker wavelet, 20 random sources are set, and the main frequency of the source is distributed between 10-40Hz; the starting channel of the detector is 1m, the ending channel is 100m, the channel spacing is 1m, a total of 100 channels, and the acquisition time is 1s.

4. The HVSR spectral ratio curve inversion method based on diffusion field theory according to claim 1 is characterized in that: In step S5, the inversion objective function is as follows: ； in, E is the objective function, N Indicates the number of sampling points of the curve, is the artificially synthesized HVSR spectral ratio curve, is the HVSR spectral ratio curve that needs to be fitted during the inversion process, is the standard deviation of the HVSR spectral ratio curve to be fitted.

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