An inversion method for HVSR spectral ratio curves based on the diffusion field theory

Abstract

The present invention is applicable to the field of geophysical exploration technology and provides an inversion method for HVSR spectral ratio curves based on the diffusion field theory, including the following steps: construction of a spectral ratio calculation equation based on the diffusion field theory; artificial synthesis of microtremor records with a random seismic source distribution; model setting and microtremor data acquisition; calculation of HVSR spectral ratio curves; construction and optimization of an inversion objective function; and output of inversion results. Based on the diffusion field theory, the present invention significantly reduces the limitations of traditional single-wavefield assumptions by comprehensively considering various wavefield components such as body waves and surface waves, and improves the inversion accuracy. This method shows excellent adaptability under shallow structure and complex medium conditions, and at the same time has strong noise robustness, and is applicable to complex environments such as urban underground space exploration. In addition, this method reduces the dependence on the initial model, avoids the problem of local optimum, and can be extended to fields such as engineering seismic safety assessment and underground water resource exploration, with broad application prospects.

Description

Technical Field

[0001] The present invention belongs to the technical field of geophysical exploration, and particularly relates to an inversion method for HVSR spectral ratio curves based on the diffusion field theory. Background Art

[0002] The exploration of urban underground space is an important application field of geophysical exploration, aiming to obtain geological information such as shallow underground soil, rocks, and groundwater through geophysical data signals. In recent years, the single-station microtremor detection technology, as a low-cost detection method without artificial seismic sources, has received extensive attention. This method records the surface microtremor signals and uses the HVSR method (the Fourier amplitude spectrum ratio of the horizontal component to the vertical component) to invert the underground structure. The HVSR spectral ratio method can capture various 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 various interpretation models based on the body wave hypothesis, surface wave hypothesis, and full wave field hypothesis. The spectral ratio method based on the body wave hypothesis has the advantages of a mature theoretical basis and strong deep exploration ability, but it performs poorly in the adaptability to shallow structures and complex media and is sensitive to noise. The spectral ratio method based on the surface wave hypothesis performs excellently in shallow exploration and noise suppression, but its deep exploration ability 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 inversion of HVSR spectral ratio curves still needs to be further optimized. Therefore, the present invention proposes an inversion method for HVSR spectral ratio curves based on the diffusion field theory, aiming to solve the applicability problem of traditional methods under complex medium conditions and improve the inversion accuracy and efficiency at the same time. Summary of the Invention

[0003] The purpose of the present invention is to provide an inversion method for HVSR spectral ratio curves based on the diffusion field theory, aiming to solve the problems proposed in the above background art.

[0004] The purpose of the present invention is achieved through the following technical solutions:

[0005] An inversion method for HVSR spectral ratio curves based on the diffusion field theory includes the following steps:

[0006] Step S1: Construction of the spectral ratio calculation equation based on the diffusion field theory;

[0007] Considering the information of P waves, SV waves, and SH waves in a homogeneous isotropic elastic medium, construct the HVSR spectral ratio calculation equation based on the diffusion field theory; in three-dimensional space, the displacement field satisfies the diffusion field equation, and the HVSR spectral ratio formula is expressed as the Fourier amplitude spectrum ratio of the horizontal component to the vertical component;

[0008] Step S2: Artificially synthesize the microtremor records of randomly distributed artificial seismic sources;

[0009] Set an artificial seismic source and randomly change the excitation time, source location, and dominant frequency parameters to simulate the random wavefield distribution; when simulating microtremor recordings, consider the noise source as a point source, and the wavefield recorded by the geophone is the simulated microtremor recording;

[0010] Step S3: Model setting and microtremor data acquisition;

[0011] Construct a two-layer medium model, given the acquisition parameters, and the geophone acquires microtremor data under the distribution of random seismic sources;

[0012] Step S4: HVSR spectral ratio curve calculation;

[0013] Calculate the spectral ratio of the horizontal direction to the vertical direction of the simulated microtremor recordings collected in step S3 to obtain 100 HVSR spectral ratio curves; average these 100 HVSR spectral ratio curves to obtain a representative HVSR spectral ratio curve;

[0014] Step S5: Inversion objective function construction and optimization;

[0015] Combined with the initial model parameters, set the inversion frequency band range to 5 - 20 Hz, construct an inversion objective function to minimize the difference between the observed data and the model predicted data; use the Monte Carlo algorithm to perform shear wave velocity and depth inversion on the representative HVSR spectral ratio curve;

[0016] Step S6: Output of inversion results;

[0017] Output the inversion results and generate a depth and velocity structure diagram, and compare the inversion results with the actual model to verify the accuracy of the inversion results.

[0018] Furthermore, in step S1, in three-dimensional space, the displacement field satisfies the diffusion field equation, where the displacement satisfies the equation:

[0019] ;

[0020] where, is the shear wave velocity, is the compressional 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;

[0021] The HVSR spectral ratio formula is expressed as the Fourier amplitude spectral ratio of the horizontal component to the vertical component, and the specific formula is:

[0022] ;

[0023] Among them, is the energy spectrum ratio in the horizontal and vertical directions, 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's 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 a complex number.

[0024] Furthermore, in the step S3, the size of the two-layer medium model is 70m × 100m; the source wavelet adopts a Ricker wavelet, 20 random sources are set, and the main frequencies of the sources are distributed between 10 - 40Hz; the starting channel of the geophones is 1m, the ending channel is 100m, the channel interval is 1m, there are 100 channels in total, and the acquisition time is 1s.

[0025] Furthermore, in the step S5, the inversion objective function is as follows:

[0026] ;

[0027] Among them, E is the objective function, N represents the number of sampling points of the curve, is the synthetic HVSR spectrum ratio curve, is the HVSR spectrum ratio curve to be fitted during the inversion process, is the standard deviation of the HVSR spectrum ratio curve to be fitted.

[0028] Compared with the prior art, the beneficial effects of the present invention are:

[0029] 1. Comprehensive consideration of wavefield components: Traditional body wave assumptions and surface wave assumptions only consider single wavefield components, ignoring the influence of other wavefields, resulting in inaccurate inversion results in complex wavefield environments. Based on the diffusion field theory, the present invention comprehensively considers various wavefield components such as body waves and surface waves, effectively reducing the uncertainty brought by single wavefield assumptions and enhancing the stability of inversion results.

[0030] 2. Adaptability to complex media: The diffusion field theory on which the present invention is based can better describe the wavefield characteristics in complex media. Especially under shallow layer structures and complex media conditions, the inversion results can be more accurate and reliable.

[0031] 3. Noise robustness: The diffusion field theory on which the present invention is based has strong robustness to noise, can provide stable inversion results in a noisy environment, and is applicable to complex environments such as urban underground space exploration.

[0032] 4. Wide application range: The present invention overcomes the shortcomings of the traditional method, such as strong dependence on the initial model and easy to fall into local optimum, improves the accuracy and reliability of the inversion results, is not only applicable to urban underground space exploration, but also can be used in fields such as seismic safety evaluation of engineering sites and underground water resource exploration, and has broad application prospects. Brief Description of the Drawings

[0033] Figure 1 It is a flowchart of the method of the present invention.

[0034] Figure 2 They are the model parameters and source distributions used in the simulation; among them, a is the two-layer medium model used in the simulation; b is the random source distribution situation.

[0035] Figure 3 They are the HVSR spectral ratio curves of 100 simulated microtremors.

[0036] Figure 4 They are the comparison of inversion results under three different assumptions; among them, a is the inversion result based on the body wave assumption, represented by P / S; b is the inversion result based on the surface wave assumption, represented by SW; c is the inversion result based on the diffusion field theory assumption, represented by DW.

[0037] Figure 5 They are the comparison of the fitting degrees of the inversion results under three different assumptions with the velocity and depth of the actual given two-layer medium model; among them, a is the comparison of the number of iterations of the objective function; b is the comparison of the fitting degrees of the inversion results under three different assumptions.

[0038] Figure 6 They are the comparison of the inversion results of the measured data in the work area under three different assumptions; among them, a is the HVSR spectral ratio curves under three different assumptions; b is the comparison of the inversion results. Detailed Implementation Manner

[0039] In order to have a clearer understanding of the technical features, objectives and beneficial effects of the present invention, the technical solution of the present invention will be described in detail below, but it should not be construed as a limitation on the implementable scope of the present invention.

[0040] The following describes the specific implementation of the present invention in detail in combination with specific embodiments.

[0041] The present invention provides a method for inverting the HVSR spectral ratio curve based on the diffusion field theory, and its flowchart is as Figure 1 shown, including the following steps:

[0042] Step S1: Construction of the spectral ratio calculation equation based on the diffusion field theory;

[0043] Considering the P-wave, SV-wave, and SH-wave information in a homogeneous isotropic elastic medium, the HVSR spectral 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 spectral ratio formula can be expressed as the Fourier amplitude spectrum ratio of the horizontal component to the vertical component.

[0044] Specifically, in three-dimensional space, the displacement satisfies the equation:

[0045] ;

[0046] where is the shear wave velocity, is the P-wave velocity, is the spatial displacement at one point, is the spatial displacement at another point, , is the corresponding spatial point position, t is the time variable.

[0047] The specific formula for the HVSR spectral ratio is:

[0048] ;

[0049] ;

[0050] where is the energy spectral ratio between the horizontal and vertical directions, is the energy density in the horizontal direction, is the energy density in another horizontal direction, is the energy density in the vertical direction, is a component of the Green's function tensor in the horizontal direction, is another component of the Green's 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.

[0051] Step S2: Synthetic generation of microtremor records with a random seismic source distribution;

[0052] By setting multiple groups of artificial seismic sources and randomly changing parameters such as the excitation time, seismic source location, and dominant frequency, the random wave field distribution is simulated. When simulating the microtremor records, the noise source is regarded as a point seismic source, and the wave field recorded by the geophone is the simulated microtremor record.

[0053] Step S3: Model setup and microtremor data acquisition;

[0054] Construct a two-layer medium model, given the acquisition parameters, and the geophones collect the microseismic data under the random source distribution. Figure 2 Figure a in it shows the two-layer medium model used in the simulation. Figure 2 Figure b in it shows the random source distribution. The size of the model is 70m×100m, and Table 1 gives the parameter information of the two-layer medium model. The source wavelet uses the Ricker wavelet, and a total of 20 random sources are set, and the main frequencies of the sources are distributed between 10 - 40Hz. The starting channel of the geophones is 1m, the ending channel is 100m, the channel interval is 1m, there are 100 channels in total, and the acquisition time is 1s.

[0055] Table 1 Parameters of the two-layer medium model

[0056]

[0057] Step S4: Calculate the HVSR spectral ratio curve;

[0058] Perform the spectral ratio calculation in the horizontal and vertical directions on the simulated microseismic records collected in Step S3 to obtain 100 HVSR spectral ratio curves (as shown in Figure 3 ). By averaging these 100 HVSR spectral ratio curves, a representative HVSR spectral ratio curve is obtained. Figure 3 The black line in it is the average of the 100 HVSR spectral ratio curves, which is a general result. As shown in the figure, the main peak of the HVSR spectral ratio curve of the two-layer medium model is around 10Hz.

[0059] Step S5: Construct and optimize the inversion objective function;

[0060] Combined with the initial model parameters (as shown in Table 2), set the inversion frequency band range to 5 - 20Hz, and construct the inversion objective function , where E is the objective function, N represents the number of sampling points of the curve, is the synthetic HVSR spectral ratio curve, is the HVSR spectral ratio curve to be fitted during the inversion process, is the standard deviation of the HVSR spectral ratio curve to be fitted. This function aims to minimize the difference between the observed data and the model prediction data. Use the Monte Carlo algorithm to perform the shear wave velocity and depth inversion on the representative HVSR spectral ratio curve in Step S4. Figure 4 Figures a - c in it respectively show the inversion results based on the body wave hypothesis, the surface wave hypothesis, and the diffusion field theory hypothesis.

[0061] Table 2 Initial model parameters for inversion

[0062]

[0063] Step S6: Output of inversion result;

[0064] Output the inversion result and generate the depth and velocity structure diagrams. Compare the inversion result with the actual model for analysis to verify the accuracy of the inversion result.

[0065] Figure 5 The consistencies of the inversion results using three different assumptions with the velocities and depths of the actually given two-layer medium model are compared. The objective function is used to measure the difference between the observed data and the model predicted data. The lower its value, the closer the model predicted data is to the observed data, which also means that the correlation between the inversion result and the actual model is better. As can be seen from Figure 5 Figure a, the objective function value based on the diffusion field theory assumption is the lowest, which indicates that during the inversion process, the model constructed based on the diffusion field theory assumption has the best fitting effect on the data, the difference between its predicted data and the observed data is the smallest, thus reflecting that there is a good correlation between the HVSR spectral ratio curve parameters based on the diffusion field theory assumption and the parameters of the synthetic model. As can be seen from Figure 5 Figure b, the inversion result based on the diffusion field theory assumption is closer to the actually given two-layer medium model in terms of shear wave velocity and depth. This high degree of consistency further proves that the HVSR spectral ratio curve parameters based on the diffusion field theory assumption and the parameters of the synthetic model have a good correlation and can more accurately reflect the characteristics of the actual model.

[0066] Example 1: To further verify the potential of the present invention in practical applications, it is 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 result in this example. The measured data is collected using three-component geophones with a sampling interval of 2 ms and a collection time of 20 min. The initial inversion parameters are shown in Table 3.

[0067] Table 3 Initial inversion model parameters for the actual working area

[0068]

[0069] Use the HVSR spectral ratio curve inversion method to process the measured data to obtain the inversion results under three different assumptions (as shown in Figure 6 Figures a and b). As can be seen from Figure 6 Figures, compared with the inversion results based on the surface wave assumption and the body wave assumption, the inversion result based on the diffusion field theory assumption has better consistency with the forward model parameters and borehole information, and this result fully verifies the effectiveness and reliability of the present invention.

[0070] Conclusion: The present invention provides an inversion method for HVSR spectral ratio curves based on the diffusion field theory. Through innovation at the theoretical level and optimization and improvement of the algorithm, the problems existing in the traditional method during the exploration of urban underground space are effectively solved, which has important theoretical value and practical application significance.

[0071] The above are only the preferred embodiments 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 practicability of the patent.

Claims

1. An inversion method for HVSR spectral ratio curves based on the diffusion field theory, characterized in that, It includes the following steps: Step S1: Construction of the spectral ratio calculation equation based on the diffusion field theory; Considering the P-wave, SV-wave, and SH-wave information in a homogeneous and isotropic elastic medium, construct the HVSR spectral ratio calculation equation based on the diffusion field theory; in three-dimensional space, the displacement field satisfies the diffusion field equation, and the HVSR spectral ratio formula is expressed as the Fourier amplitude spectral ratio of the horizontal component to the vertical component; Step S2: Artificially synthesize the microtremor records of the random seismic source distribution; Set artificial seismic sources, randomly change the excitation time, source position, and dominant frequency parameters to simulate the random wave field distribution; when simulating the microtremor records, regard the noise source as a point source, and the wave field recorded by the geophone is the simulated microtremor record; Step S3: Model setting and microtremor data acquisition; Construct a two-layer medium model, given the acquisition parameters, and the geophone acquires the microtremor data under the random seismic source distribution; Step S4: Calculation of the HVSR spectral ratio curve; Perform spectral ratio calculations in the horizontal and vertical directions on the simulated microtremor records collected in Step S3 to obtain 100 HVSR spectral ratio curves; average these 100 HVSR spectral ratio curves to obtain a representative HVSR spectral ratio curve; Step S5: Construction and optimization of the inversion objective function; Combined with the initial model parameters, set the inversion frequency band range to 5 - 20 Hz, construct the inversion objective function to minimize the difference between the observed data and the model predicted data; use the Monte Carlo algorithm to perform shear wave velocity and depth inversion on the representative HVSR spectral ratio curve; Step S6: Output of the inversion result; In the step S1, in a three-dimensional space, the displacement field satisfies the diffusion field equation, where the displacement satisfies the equation: ； Among them, is the shear wave velocity, is the compressional wave velocity, is the spatial displacement of a point position, is the spatial displacement of another point position, , is the corresponding spatial point position, t is the time variable; Output the inversion result and generate the depth and velocity structure diagrams, compare the inversion result with the actual model for analysis, and verify the accuracy of the inversion result; ； Among them, is the energy spectrum ratio in the horizontal direction and 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, is a component of the Green's function tensor in the horizontal direction, is another component of the Green's 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 a complex number; The HVSR spectral ratio formula is expressed as the Fourier amplitude spectral ratio of the horizontal component to the vertical component, and the specific formula is: ； Among them, E is the objective function, N represents the number of sampling points of the curve, is the artificially synthesized HVSR spectral ratio curve, is the HVSR spectral ratio curve to be fitted during the inversion process, is the standard deviation of the HVSR spectral ratio curve to be fitted.

2. The HVSR spectral ratio curve inversion method based on the diffusion field theory according to claim 1, characterized in that In the said Step S5, the inversion objective function is as follows: In the said Step S3, the size of the two-layer medium model is 70m × 100m; the seismic source wavelet uses a Ricker wavelet, set 20 random seismic sources, and the dominant frequency of the sources is distributed between 10 - 40 Hz; the starting channel of the geophone is 1m, the ending channel is 100m, the channel spacing is 1m, there are 100 channels in total, and the acquisition time is 1s.

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