Surface wave dispersion energy spectrum imaging method based on ista high-resolution radon transform

Abstract

The application relates to the field of surface wave exploration, and discloses a surface wave dispersion energy spectrum imaging method based on high-resolution radon transformation of an ista, which comprises the following steps: acquiring surface wave data in a d(x, t) field collected in the field, wherein t is time; performing time-domain dimension Fourier transformation on each channel of the surface wave data to obtain a d(x, f) field, wherein f is frequency; transforming the d(x, f) field into an m(p, f) field based on a high-resolution Radon model of an iterative shrinkage threshold algorithm to obtain a high-resolution imaging result, wherein p is slowness. The high-resolution surface wave dispersion spectrum energy imaging can be realized, the precision of dispersion curve picking is improved, the subsequent accurate inversion of transverse wave velocity is guaranteed, the method has good applicability to low signal-to-noise ratio surface wave data, and especially provides a reliable processing method for increasingly increasing urban low signal-to-noise ratio surface wave data.

Description

Technical Field

[0001] This invention relates to the field of surface wave exploration, and specifically to a high-resolution Radon transform-based surface wave dispersion energy spectrum imaging method based on ISTA. Background Technology

[0002] Surface wave exploration is a rapidly developing shallow surface exploration method in recent years. This technology boasts advantages such as high detection accuracy, strong stratification capability, and low economic cost. Surface wave exploration technology can be used for geotechnical engineering investigations, non-destructive testing of shallow surface geology, real-time monitoring of urban underground environments, and solving other related geological problems.

[0003] Surface wave energy dominates the seismic wave field energy and contains rich information on the shear wave velocity of the subsurface medium. In the late 1990s, a near-surface multichannel surface wave analysis technique was proposed, which has advantages such as strong noise resistance and convenient construction, and has therefore been widely used in surface wave exploration. Its main process includes four aspects: field surface wave data acquisition, surface wave dispersion spectrum energy imaging, dispersion curve picking, and inversion of the shear wave velocity structure. Accurate surface wave dispersion spectrum imaging is a crucial step in inverting the shear wave velocity structure from the surface wave dispersion curve; currently, traditional research methods have relatively low resolution. Summary of the Invention

[0004] The purpose of this invention is to provide a high-resolution Radon transform-based surface wave dispersive energy spectrum imaging method based on ista, which solves the problem of low resolution in existing surface wave dispersive energy spectrum imaging.

[0005] To achieve the above-mentioned objectives, the technical solution adopted by this invention is: a surface wave dispersive energy spectrum imaging method based on ISTA high-resolution Radon transform, the method comprising:

[0006] Acquire surface wave data in the d(x,t) domain collected in the field, where t is time;

[0007] Perform a time-domain Fourier transform on each surface wave data to obtain the d(x, f) domain, where f is the frequency;

[0008] The high-resolution Radon model based on the iterative shrinkage threshold algorithm transforms the d(x,f) domain into the m(p,f) domain to obtain high-resolution imaging results, where p is the slowness.

[0009] Preferably, the method further includes: constructing a high-resolution dispersive energy spectrum, including:

[0010] The speed is calculated based on the slowness.

[0011] A high-resolution dispersive energy spectrum fv is constructed based on the slowness and velocity.

[0012] Preferably, the method further includes: finding a high-resolution Radon model solution in the d(x, f) domain, including:

[0013] Determine the minimum objective function Φ:

[0014] Φ=||d-Lm|| 2 +β||m || 1 ;

[0015] In the formula: d represents seismic data; L represents the positive transform operator; β represents the regularization parameter; m represents the τ-p domain data;

[0016] The objective function Φ is solved using the steepest descent method.

[0017] Preferably, the objective function Φ is solved using the steepest descent method, including:

[0018] Determine the gradient direction: g = L T *r i-1 Where, L = e i2πfpx f is the frequency, p is the slowness, x is the offset distance, and r0 = d;

[0019] Step size selection: k = (g*g) / ((L*g)*(L*g));

[0020] Model update: m i =T0*m i-1 +k*g, where T0 is the contraction operator;

[0021] Where a is the threshold, I is the maximum number of iterations, i is the current number of iterations, and m0 = 0;

[0022] Data residual term: r i =dm i ;

[0023] Loop iteration: Repeat the above steps until the maximum number of iterations is reached, then terminate the loop and output the high-resolution solution of model m.

[0024] Preferably, the method further includes: preprocessing the acquired surface wave data, wherein the preprocessing includes selection processing and filtering processing.

[0025] The present invention also provides a surface wave dispersive energy spectrum imaging system based on ISTA high-resolution Radon transform. This system is used to implement the aforementioned method for calculating the surface wave dispersive energy spectrum based on ISTA high-resolution Radon transform. The system comprises:

[0026] The acquisition module is used to acquire surface wave data in the d(x,t) domain collected in the field, where t is time;

[0027] The first transformation module is used to perform a time-domain Fourier transform on each surface wave data to obtain the d(x, f) domain, where f is the frequency;

[0028] The second transformation module is used to transform the d(x,f) domain to the m(p,f) domain based on the high-resolution Radon model using the iterative shrinkage threshold algorithm, so as to obtain high-resolution imaging results, where p is the slowness.

[0029] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the processor executes the computer program to implement the above-mentioned high-resolution Radon transform surface wave dispersion energy spectrum calculation method based on ISTA.

[0030] The present invention also provides a computer-readable storage medium storing a computer program thereon, characterized in that the computer program, when executed by the processor, implements the above-mentioned high-resolution Radon transform surface wave dispersion energy spectrum calculation method based on ISTA.

[0031] The beneficial effects of this invention are mainly reflected in:

[0032] 1. The dispersion energy imaging method based on iterative shrinkage threshold high-resolution Radon transform proposed in this invention can realize high-resolution surface wave dispersion spectrum energy imaging, improve the accuracy of dispersion curve picking, and provide a guarantee for subsequent accurate inversion of shear wave velocity.

[0033] 2. This invention has good applicability to low signal-to-noise ratio surface wave data, and in particular provides a reliable processing method for the ever-increasing amount of low signal-to-noise ratio surface wave data in cities. Attached Figure Description

[0034] Figure 1 A flowchart illustrating a high-resolution Radon transform surface wave dispersion energy spectrum calculation method based on ISTA provided in one embodiment of the present invention;

[0035] Figure 2 A schematic diagram of the original input surface wave shot record provided in an optional embodiment of the present invention;

[0036] Figure 3 This represents low-resolution imaging results from existing technologies.

[0037] Figure 4 This is a schematic diagram of the high-resolution imaging results of the present invention. Detailed Implementation

[0038] To enable those skilled in the art to better understand the technical solutions of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0039] Figure 1 This is a flowchart illustrating the calculation of high-resolution Radon transform surface wave dispersion energy spectrum based on ISTA, according to one embodiment of the present invention. Figure 1 As shown, this invention provides a high-resolution Radon transform-based surface wave dispersion energy spectrum imaging method based on ISTA, the method comprising:

[0040] Step S101: Obtain surface wave data in the d(x,t) domain collected in the field, where t is time, i.e., obtain surface wave data in the spatial-temporal domain.

[0041] As a further optimization of this embodiment, the acquired surface wave data is preprocessed, including selection processing and filtering processing.

[0042] Step S102: Perform a time-domain Fourier transform on each selected surface wave data to obtain the d(x, f) domain, where f is the frequency; that is, transform the surface wave data in the spatial-time domain to the frequency-space domain.

[0043] Step S103: The high-resolution Radon model based on the iterative shrinkage threshold algorithm transforms the d(x,f) domain into the m(p,f) domain, i.e. the slow frequency domain, where the relationship between slowness p and velocity v is v = 1 / p, thereby constructing a high-resolution dispersive energy spectrum fv, which can obtain high-resolution imaging results.

[0044] In the process of transforming the d(x, f) domain to the m(p, f) domain, in order to obtain a sparse, high-resolution Radon model solution, as a further optimization in this embodiment, it is preferable to use the L1 norm as the regularization term and the L2 norm as the data error term, that is, to determine the minimum objective function; the method further includes: finding the high-resolution Radon model solution in the d(x, f) domain, including:

[0045] Step A1: Determine the minimum objective function Φ:

[0046] Φ=||d-Lm|| 2 +β||m|| 1 ;

[0047] In the formula: d represents seismic data; L represents the positive transform operator; β represents the regularization parameter; m represents the τ-p domain data; 2 represents the error term; and 1 represents the regularization term.

[0048] Step A2: Solve for the objective function Φ using the steepest descent method.

[0049] As a further optimization of this embodiment, in step A2, the objective function Φ is solved using the steepest descent method, including:

[0050] A201: Determine the gradient direction: g = L T *r i-1 Where, L = e i2πfpx f is the frequency, p is the slowness, x is the offset distance, and r0 = d;

[0051] A202: Step size selection: k = (g*g) / ((L*g)*(L*g));

[0052] A203: Model Update: m i =T0*m i-1 +k*g, where T0 is the contraction operator;

[0053] Where a is the threshold, I is the maximum number of iterations, i is the current number of iterations, and m0 = 0;

[0054] A204: Data Residual Term: r i =dm i ;

[0055] A205: Iterative Loop: Repeat steps A201-A204 until the maximum number of iterations is reached, at which point the loop terminates and outputs a high-resolution solution for model m.

[0056] As a further optimization of this embodiment, the method further includes: constructing a high-resolution dispersive energy spectrum, including:

[0057] The speed is calculated based on the slowness; where the relationship between slowness p and speed v is: v = 1 / p;

[0058] A high-resolution dispersive energy spectrum fv is constructed based on the slowness and velocity.

[0059] like Figure 2-4 As shown, Figure 2 This is a schematic diagram of the original input surface wave shot record provided in an optional embodiment of the present invention. Figure 3 For low-resolution imaging results of existing technologies, from Figure 3 As can be seen, the dispersion curve has low resolution, and it is obvious that there is a lot of noise in the low-frequency part, which affects the picking of the dispersion curve. Figure 4 This is a schematic diagram of the high-resolution imaging results of the present invention. The noise is significantly reduced, the dispersion curve is clearly visible, and it is easy to pick up.

[0060] The present invention also provides a surface wave dispersive energy spectrum imaging system based on ISTA high-resolution Radon transform. This system is used to implement the aforementioned method for calculating the surface wave dispersive energy spectrum based on ISTA high-resolution Radon transform. The system comprises:

[0061] The acquisition module is used to acquire surface wave data in the d(x,t) domain collected in the field, where t is time;

[0062] The first transformation module is used to perform a time-domain Fourier transform on each surface wave data to obtain the d(x, f) domain, where f is the frequency;

[0063] The second transformation module is used to transform the d(x,f) domain to the m(p,f) domain based on the high-resolution Radon model using the iterative shrinkage threshold algorithm, so as to obtain high-resolution imaging results, where p is the slowness.

[0064] The dispersion energy imaging method based on iterative shrinkage threshold high-resolution Radon transform proposed in this invention can realize high-resolution surface wave dispersion spectrum energy imaging, improve the accuracy of dispersion curve picking, and provide a guarantee for subsequent accurate inversion of shear wave velocity.

[0065] This invention is well applicable to low signal-to-noise ratio surface wave data, and in particular provides a reliable processing method for the ever-increasing amount of low signal-to-noise ratio surface wave data in cities.

[0066] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the processor executes the computer program to implement the above-mentioned high-resolution Radon transform surface wave dispersion energy spectrum calculation method based on ISTA.

[0067] The present invention also provides a computer-readable storage medium storing a computer program thereon, characterized in that the computer program, when executed by the processor, implements the above-mentioned high-resolution Radon transform surface wave dispersion energy spectrum calculation method based on ISTA.

[0068] The optional embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the embodiments of the present invention are not limited to the specific details in the above embodiments. Within the scope of the technical concept of the embodiments of the present invention, various simple modifications can be made to the technical solutions of the embodiments of the present invention, and these simple modifications all fall within the protection scope of the embodiments of the present invention.

[0069] It should also be noted that the various specific technical features described in the above embodiments can be combined in any suitable manner without contradiction. To avoid unnecessary repetition, the embodiments of the present invention will not describe the various possible combinations separately.

[0070] Those skilled in the art will understand that all or part of the steps in the methods of the above embodiments can be implemented by a program instructing related hardware. This program is stored in a storage medium and includes several instructions to cause a microcontroller, chip, or processor to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as a USB flash drive, a portable hard drive, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk.

[0071] Furthermore, various different implementations of the present invention can be combined arbitrarily, as long as they do not violate the spirit of the present invention, they should also be regarded as the content disclosed in the present invention.

Claims

1. A high-resolution Radon transform-based surface wave dispersive energy spectrum imaging method based on ISTA, characterized in that, The method includes: Acquire surface wave data in the d(x,t) domain collected in the field, where t is time; Perform a time-domain Fourier transform on each surface wave data to obtain the d(x, f) domain, where f is the frequency; The high-resolution Radon model based on the iterative shrinkage threshold algorithm transforms the d(x,f) domain into the m(p,f) domain to obtain high-resolution imaging results, where p is the slowness. The method further includes: finding a high-resolution Radon model solution in the d(x, f) domain, including: Determine the minimum objective function : + ； In the formula: d represents seismic data; L represents the positive transform operator; β represents the regularization parameter; m represents the τ-p domain data; Solving the objective function using the steepest descent method ,include: Determine the gradient direction: ,in, f is the frequency, p is the slowness, and x is the offset distance. ; Step size selection: ; Model update: ,in, For contraction operators; Where a is the threshold and I is the maximum number of iterations. This represents the current iteration number. ; Data residuals: ; Loop iteration: Repeat the above steps until the maximum number of iterations is reached, then terminate the loop and output the high-resolution solution of model m.

2. The high-resolution Radon transform-based surface wave dispersive energy spectrum imaging method based on ISTA according to claim 1, characterized in that, The method further includes: constructing a high-resolution dispersive energy spectrum, including: The speed is calculated based on the slowness. A high-resolution dispersive energy spectrum fv is constructed based on the slowness and velocity.

3. The high-resolution Radon transform-based surface wave dispersive energy spectrum imaging method based on ISTA according to claim 1, characterized in that, The method further includes: preprocessing the acquired surface wave data, wherein the preprocessing includes selection processing and filtering processing.

4. A high-resolution Radon transform-based surface wave dispersion energy spectrum imaging system based on ISTA, the system being used to implement the high-resolution Radon transform-based surface wave dispersion energy spectrum calculation method according to any one of claims 1-3, characterized in that, The system includes: The acquisition module is used to acquire surface wave data in the d(x,t) domain collected in the field, where t is time; The first transformation module is used to perform a time-domain Fourier transform on each surface wave data to obtain the d(x, f) domain, where f is the frequency; The second transformation module is used to transform the d(x,f) domain to the m(p,f) domain using the high-resolution Radon model based on the iterative shrinkage threshold algorithm, so as to obtain high-resolution imaging results, where p is the slowness.

5. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the high-resolution Radon transform surface wave dispersion energy spectrum calculation method based on ISTA as described in any one of claims 1-3.

6. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the computer program implements the high-resolution Radon transform surface wave dispersion energy spectrum calculation method based on ISTA as described in any one of claims 1-3.

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