Multi-modal surface wave frequency dispersion curve extraction method and system
By adaptively separating the fundamental and higher-order signals using Shearlet transform and ADMM algorithm, and constructing a Radon transform model with multiple regularization constraints, the problem of multimodal surface wave dispersion curve extraction under low signal-to-noise ratio conditions is solved. This achieves high-precision and robust dispersion curve extraction, improving the accuracy of near-surface shear wave velocity inversion.
Patent Information
- Application Number
- CN202511708270.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-11-20
- Publication Date
- 2026-02-17
AI Technical Summary
Under low signal-to-noise ratio conditions, traditional methods are difficult to effectively extract the dispersion curves of multimodal surface waves. In particular, the energy response of higher-order modes is weakened and easily interfered with by noise, affecting the accuracy and stability of near-surface shear wave velocity inversion.
Shearlet transform is used for adaptive signal separation, a high-precision linear Radon transform inversion model with multiple regularization constraints is constructed, and the alternating direction multiplier method (ADMM) is used to solve it to generate the basic and higher order dispersion energy maps. Multimodal surface wave dispersion curves are extracted by combining automatic and manual correction.
It improves the resolution and noise resistance of higher-order modes, ensures the reliability and authenticity of dispersion curves, and enhances the accuracy and stability of near-surface shear wave velocity inversion.
Smart Images
Figure CN121541255A_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the field of active source surface wave exploration, in particular to a multi-modal surface wave dispersion curve extraction method and system. BACKGROUND
[0002] With the increasing demand for underground space information in the exploration field, accurately obtaining the characteristics of the underground geological structure has become a key link in geophysical exploration. Surface wave exploration is an important means to obtain near-surface shear wave velocity structure. Among them, the extraction of Rayleigh wave dispersion curve is the core link of surface wave exploration. The accuracy of the result directly affects the precision and reliability of the near-surface shear wave velocity inversion. However, under the condition of low signal-to-noise ratio, the energy of high-order mode is weak and the resolution is low in the dispersion diagram, and it is difficult to accurately identify. Therefore, how to effectively improve the distinguishability and noise resistance of the base and high-order modes under noise interference has become a key problem in multi-modal surface wave dispersion curve extraction.
[0003] In surface wave exploration, the base mode of Rayleigh wave mainly represents the overall shear wave velocity structure of the underground medium, and the high-order mode has a significant effect on optimizing the shear wave velocity structure, improving the resolution and stability of the inversion. Compared with using only the base mode, joint introduction of high-order mode information can more effectively constrain the near-surface shear wave velocity structure, reduce the inversion multi-solution, and significantly improve the accuracy and longitudinal resolution of the result. However, the energy of the base mode usually dominates in the dispersion energy spectrum, and the energy response of the high-order mode is therefore often weakened or blurred. When faced with low signal-to-noise ratio surface wave seismic data, the high-order dispersion energy group is easily covered, increasing the difficulty of multi-modal dispersion curve extraction. The extraction of multi-modal dispersion curve is still affected by the weak energy of high-order mode and noise interference. Improving the resolution of high-order mode and enhancing its noise resistance are the core challenges to realize robust multi-modal dispersion curve extraction and high-precision near-surface shear wave inversion. At present, the traditional high-precision linear Radon surface wave dispersion curve extraction method has limitations: first, the multi-window selection strategy lacks an adaptive mechanism, making it difficult to dynamically adjust the window parameters according to the signal characteristics; second, it does not discuss the processing of noisy surface wave data. The applicability of this method under low signal-to-noise ratio conditions has not been fully verified. Noise interference may lead to a decrease in the quality of dispersion curve extraction, thereby reducing the stability and reliability of the near-surface shear wave velocity inversion result. SUMMARY
[0004] The purpose of the present application is to provide a multi-modal surface wave dispersion curve extraction method and system to solve the problems raised in the background art.
[0005] To achieve the above purpose, the present application provides the following technical solutions: A multi-modal surface wave dispersion curve extraction method, the method comprising: The surface wave seismic record is acquired, based on the apparent velocity difference of base mode and high mode, adaptive signal separation is performed on the surface wave seismic record by using Shearlet transform to obtain a first signal mainly containing base mode signal and a second signal containing high mode signal; A high-precision linear Radon transform inversion model based on multiple regularization constraints is constructed, and an objective function of the inversion model includes a data fidelity term, a regularization term of base mode signal and a regularization term of high mode signal; The inversion model is solved by using an alternating direction multiplier method to obtain base mode signal and high mode signal in the Radon domain; The base mode signal and the high mode signal in the Radon domain are converted to the frequency-velocity domain to generate base mode and high mode dispersion energy maps; Based on the dispersion energy map, multi-mode surface wave dispersion curves are extracted.
[0006] As a further scheme of the present application, the step of using Shearlet transform to perform adaptive signal separation on the surface wave seismic record based on the apparent velocity difference of base mode and high mode to obtain a first signal mainly containing base mode signal and a second signal containing high mode signal specifically includes: The NSST transform is performed on the surface wave seismic record to obtain multi-scale and multi-direction sub-band sparse coefficients; Based on the apparent velocity difference, the similarity coefficients and their standard deviations between sub-bands are calculated; The sparse coefficients containing high mode signal are adaptively selected according to the standard deviations; Inverse NSST transform is performed on the selected sparse coefficients to obtain the second signal; The difference between the original seismic signal and the second signal is taken as the first signal.
[0007] As a further scheme of the present application, the objective function of the high-precision linear Radon transform inversion model is: ; Wherein, is a penalty parameter, L is a linear Radon transform operator, is base mode surface wave data in the Radon domain, is high mode surface wave data in the Radon domain, represents an actual seismic record, and are regularization parameters of base mode signal and high mode signal, respectively.
[0008] As a further scheme of the present application, the step of solving the inversion model by using an alternating direction multiplier method to obtain base mode signal and high mode signal in the Radon domain specifically includes: The objective function is reconstructed into an augmented Lagrangian form by introducing auxiliary variables; The base order signal, the high order signal, the auxiliary variables and the dual variables are alternately updated; The convergence condition is judged, and the base order signal and the high order signal in the Radon domain are output.
[0009] As a further scheme of the present application, the reconstructed augmented Lagrangian function is specifically: ; Wherein, and are dual variables. , is a penalty parameter, and are auxiliary variables.
[0010] As a further scheme of the present application, the step of extracting the multimodal surface wave dispersion curve based on the dispersion energy map specifically comprises: Automatic peak picking is performed on the dispersion energy map; The automatic picking result is manually corrected.
[0011] The present application also provides a multimodal surface wave dispersion curve extraction system for realizing a multimodal surface wave dispersion curve extraction method, and the system comprises: A signal separation module is configured to acquire a surface wave seismic record, perform adaptive signal separation on the surface wave seismic record by using a Shearlet transform based on the apparent velocity difference between base order and high order modes, and obtain a first signal mainly containing a base order signal and a second signal containing a high order signal; A model construction module is configured to construct a high-precision linear Radon transform inversion model based on multiple regularization constraints, and an objective function of the inversion model comprises a data fidelity term, a regularization term of the base order signal and a regularization term of the high order signal; A solving module is configured to solve the inversion model by using an alternating direction multiplier method, and obtain a base order signal and a high order signal in a Radon domain; A signal conversion module is configured to convert the base order signal and the high order signal in the Radon domain to a frequency-velocity domain, and generate base order and high order dispersion energy maps; An extraction module is configured to extract a multimodal surface wave dispersion curve based on the dispersion energy map.
[0012] Compared with the prior art, the beneficial effects of the present invention are: by using an adaptive basis-higher-order signal separation mechanism as the starting input of the process, and constructing a high-basis-order signal inversion system based on Radon domain sparse representation, the invention highlights the dispersion energy of higher-order modes while improving the noise resistance of high-precision Radon transform, thereby ensuring the reliability and authenticity of the extracted dispersion curve. To address the ill-qualitative nature of the inverse problem, the following methods are employed: Regularization constraint on base order signals, Regularization constrains higher-order signals by adjusting q 1. q 2 and regularization parameters , Achieving a balance between fitting accuracy and sparsity; In the solution process, the ADMM algorithm is used to decompose the complex inverse problem under multiple regularization constraints into multiple subproblems that are easy to solve, thereby efficiently obtaining the optimal solution. Attached Figure Description
[0013] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention.
[0014] Figure 1 The following are seismic record diagrams of simulated data from a velocity model containing soft interlayers provided in an embodiment of the present invention. Figure (a) is a surface wave seismic record diagram with -5dB random noise added; Figure (b) is a seismic record diagram with the basic order as the main component after adaptive signal separation; and Figure (c) is a seismic record diagram containing higher-order information after adaptive separation.
[0015] Figure 2 The following are surface wave dispersion energy spectra and dispersion curves of a velocity model containing soft interlayers provided in the embodiments of the present invention. Figure (a) is the surface wave dispersion energy spectrum of the conventional method; Figure (b) is the multi-mode surface wave dispersion curve picked from Figure (a).
[0016] Figure 3 The surface wave dispersion curve energy diagram of the velocity model containing soft interlayer provided in the embodiments of the present invention is shown in Figure (a), which is related to the energy diagram of the surface wave dispersion curve of the present invention. Figure 1 (b) Energy map of surface wave dispersion curves corresponding to earthquake records; Figure (b) is a comparison with... Figure 1 (c) Energy map of surface wave dispersion curves corresponding to earthquake records.
[0017] Figure 4 The following are extraction diagrams of the surface wave dispersion curves using the scheme of the present invention for the velocity model data containing soft interlayers provided in the embodiments of the present invention. In the figure, (a) is the basic order dispersion energy point; and (b) is the higher order surface wave dispersion energy point.
[0018] Figure 5 The surface wave dispersion curves obtained using the scheme of the present invention for the velocity model data containing soft interlayer provided in the embodiments of the present invention are shown in Figure (a), which is the basic order surface wave dispersion curve; Figure (b) is the higher order surface wave dispersion curve; and Figure (c) is the multimode surface wave dispersion curve. Detailed Implementation
[0019] To make the technical problems to be solved, the technical solutions, and the beneficial effects of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the present invention and are not intended to limit the present invention.
[0020] In this embodiment of the invention, a method for extracting multimodal surface wave dispersion curves is provided, the method comprising: A method for extracting dispersion curves of multimodal surface waves, the method comprising: Surface wave seismic records are acquired, and based on the apparent velocity difference between the fundamental and higher-order modes, the Shearlet transform is used to adaptively separate the surface wave seismic records to obtain a first signal dominated by the fundamental signal and a second signal containing higher-order signals. A high-precision linear Radon transform inversion model based on multiple regularization constraints is constructed. The objective function of the inversion model includes a data fidelity term, a regularization term for the basic signal, and a regularization term for the higher-order signal. The inversion model is solved using the alternating direction multiplier method to obtain the basic and higher-order signals in the Radon domain; The fundamental and higher-order signals in the Radon domain are converted to the frequency-velocity domain to generate fundamental and higher-order dispersion energy maps. Multimodal surface wave dispersion curves are extracted based on the dispersion energy map.
[0021] like Figures 1 to 5 As shown, in this embodiment, an adaptive basis-higher-order signal separation mechanism is proposed as the starting input of the process, and a high-basis-order signal inversion system based on Radon domain sparse representation is constructed. While highlighting the dispersion energy of higher-order modes, the noise resistance of the high-precision Radon transform is improved, thereby ensuring the reliability and authenticity of the extracted dispersion curve. To address the ill-posedness of the inverse problem, the following methods are employed: Regularization constraint on base order signals, Regularization constrains higher-order signals by adjusting q 1. q 2 and regularization parameters , The balance between fitting accuracy and sparsity is achieved. In the solving process, the ADMM algorithm is used to decompose the complex inverse problem under the multi-regularization term constraint into multiple sub-problems which are easy to solve, so as to efficiently obtain the optimal solution.
[0022] As a preferred embodiment of the present application, the difference in apparent velocity based on the fundamental and high-order modes is used to adaptively separate the surface wave seismic record by Shearlet transform to obtain a first signal mainly containing the fundamental signal and a second signal containing the high-order signal. The NSST transform is performed on the surface wave seismic record to obtain multi-scale and multi-directional sub-band sparse coefficients. Based on the difference in apparent velocity, the similarity coefficients and their standard deviations between sub-bands are calculated. The sparse coefficients containing the high-order signal are adaptively selected according to the standard deviation. The selected sparse coefficients are inversely NSST transformed to obtain the second signal. The difference between the original seismic signal and the second signal is taken as the first signal.
[0023] In this embodiment, according to the difference in apparent velocity between the fundamental and high-order modes in the surface wave record, the adaptive multi-modal signal separation strategy is used to decompose the original seismic record by using the sparse representation characteristics of Shearlet domain in multi-scale and multi-direction. ; where y is the surface wave data, is the sub-band sparse coefficient of the surface wave signal after NSST forward transformation, is the high-order signal component extracted after apparent velocity filtering, is the sub-band sparse coefficient of the high-order signal after NSST transformation, and S represents the NSST transformation operator. The similarity coefficients and their standard deviations between sub-bands in the Shearlet domain are combined to realize adaptive signal separation of the fundamental and high-order mode signals.
[0024] Similarity coefficient The calculation formula is as follows: ; And use the standard deviation As a measure, the sparse coefficients containing the high-order signal can be adaptively selected, and finally the selected sparse coefficients are summarized and inversely NSST transformed: ; ; where d represents the seismic signal, represents the high-order signal, denotes the base-order signal. This step extracts the relatively independent base-order and high-order modal signals, i.e., the second signal and the first signal, to provide reliable input for the subsequent Radon transform.
[0025] Constructing the inversion problem of high-precision Radon transform based on multiple regularization constraints.
[0026] This approach allows appropriate and independent sparsification constraints to be imposed on the base-order and high-order energy, and takes into account the robust recovery of the base-order signal and the objective function representation of the weak high-order signal. ; wherein, is a penalty parameter, L is a linear Radon transform operator, is the base-order surface wave data in the Radon domain, is the high-order surface wave data in the Radon domain, denotes the actual seismic record, and are regularization parameters of the base-order and high-order signals, respectively. This multi-regularization item inversion strategy can effectively recover the weak high-order dispersion curve without losing the base-order information, and is of great significance for improving the accurate extraction of multi-modal surface wave dispersion curves. The multi-regularization item objective function belongs to a non-convex high-dimensional optimization problem, and direct use of traditional optimization methods for solving has problems such as high computational complexity, easy to fall into local optimum, and high parameter sensitivity. Therefore, introducing the alternating direction multiplier method (ADMM) framework becomes an effective solution. ADMM uses a decomposition-coordination process to naturally decouple the variables to solve the regularization problem. Specifically, using two auxiliary variables and , the objective function can be re-expressed as: ; The overall optimization problem is decomposed into multiple sub-problems, each of which independently processes the regularization of single-order energy, while maintaining global consistency through multiplier updates. This mechanism not only improves the numerical stability and convergence of the solution, but also allows the effective extraction of base-order and weak high-order signals under the same framework.
[0027] As a preferred embodiment of the present application, the alternating direction multiplier method is used to solve the inversion model to obtain the base-order signal and the high-order signal in the Radon domain. The step specifically comprises: introducing auxiliary variables to reconstruct the objective function into an augmented Lagrangian form; alternately updating the base-order signal, the high-order signal, the auxiliary variable, and the dual variable; judging the convergence condition and outputting the base-order signal and the high-order signal in the Radon domain.
[0028] In this embodiment, an augmented Lagrangian function is constructed including the data fidelity term and the regularization term, and the Lagrange multiplier is updated according to the following formula, aiming to force the constraint condition to be satisfied , and the augmented Lagrangian function of which is as follows: ; wherein, and are dual variables. , is a penalty parameter.
[0029] Under the ADMM framework, the model parameters of the base order and the high order modal are updated by the proximal operator respectively, and the gradient descent method is used to optimize the data fidelity term in each iteration, so as to realize the alternating optimization under multiple regularization terms. The iteration update of the primal variable and the dual variable of ADMM mainly includes the following three steps: Update: Since 0<q<1, the proximal operator needs to obtain a sparse solution by solving a nonlinear equation.
[0030] ; ; Update: According to the gradient descent method, the update formula of , is obtained by minimizing the weighted sum of the data fidelity term and the regularization term. The main problem to be solved in this step is a least square problem including the data fidelity term, and this process itself has certain smoothing and noise averaging effect.
[0031] ; ; Dual variable update: by the dual gradient ascent method, the is updated along the constraint direction, and in this iteration process, the condition is gradually satisfied.; ; ; The update process, the algorithm is iterated until the convergence criterion (such as residual or objective function change less than threshold) is satisfied, or the maximum iteration number is reached, and finally the stable Radon domain inversion result is obtained.
[0032] The separated time Radon domain data base order signal and the high order signal are obtained. The (t-p) domain data , Fourier transform is performed to obtain (fp) domain data , By introducing the relationship between slowness and velocity, p=1 / v, we obtain the (fv) domain data. , The data is then normalized along the frequency to obtain the final dispersion energy map, which describes the relationship between frequency f and phase velocity c.
[0033] In a preferred embodiment of the present invention, the step of extracting the multimodal surface wave dispersion curve based on the dispersion energy map specifically includes: Automatic peak picking is performed on the dispersion energy map; Manual correction is performed on the automatically picked results.
[0034] In this embodiment, a method combining automatic picking and manual correction is used to extract the surface wave dispersion curve: first, automatic picking is performed by calculating the energy peak value of each frequency, and then manual correction is performed on some details to improve the continuity and accuracy of the curve.
[0035] This invention also provides a multimodal surface wave dispersion curve extraction system, the system comprising: The signal separation module is used to acquire surface wave seismic records. Based on the apparent velocity difference between the fundamental and higher-order modes, the module uses Shearlet transform to perform adaptive signal separation on the surface wave seismic records to obtain a first signal dominated by the fundamental signal and a second signal containing higher-order signals. The model building module is used to build a high-precision linear Radon transform inversion model based on multiple regularization constraints. The objective function of the inversion model includes a data fidelity term, a regularization term for the basic signal, and a regularization term for the higher-order signal. The solution module is used to solve the inversion model using the alternating direction multiplier method to obtain the basic and higher-order signals in the Radon domain; The signal conversion module is used to convert the fundamental and higher-order signals in the Radon domain to the frequency-velocity domain, generating fundamental and higher-order dispersion energy maps. The extraction module is used to extract the multimodal surface wave dispersion curve based on the dispersion energy map.
[0036] This method has been applied to a four-layer horizontal velocity model containing soft interlayers. The medium parameters of this model are shown in the table below. The seismic record has 1024 sampling points with a sampling interval of 0.1 ms. Receiver points are uniformly distributed along the surface with a trace spacing of 1 m, totaling 121 receiver points. The final surface wave seismic data is then supplemented with -5 dB of random noise, resulting in the following image. Figure 1 (a) shows the noisy surface wave seismic record f.
[0037] The final dispersion energy diagram is obtained as follows: Figure 3 As shown in the figure, this graph illustrates the relationship between frequency f and phase velocity c, where Figure 3 (a) represents the dispersion energy map of the fundamental-order surface wave obtained by the improved method. Figure 3 (b) represents the high-order surface wave dispersion energy map obtained by the improved method.
[0038] The surface wave dispersion energy points picked from the surface wave dispersion energy map are as follows: Figure 4 As shown. Combining the two sets of dispersion curves yields the following result: Figure 5 (c) shows the multimodal surface wave dispersion curve.
[0039] The results of extracting surface wave dispersion curves using traditional methods are as follows: Figure 2 As shown. Among them, Figure 2 (a) shows the surface wave dispersion energy map obtained using the traditional method, and the surface wave dispersion curve obtained by combining automatic picking and manual correction methods, as shown in the figure. Figure 2 As shown in (b), the improved method yields results that are more consistent with the theoretical curve and provide more complete dispersion information, verifying its high accuracy and robustness in multimodal dispersion energy spectrum extraction.
[0040] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.
Claims
1. A method for extracting the dispersion curve of multimodal surface waves, characterized in that, The method includes: Surface wave seismic records are acquired, and based on the apparent velocity difference between the fundamental and higher-order modes, the Shearlet transform is used to adaptively separate the surface wave seismic records to obtain a first signal dominated by the fundamental signal and a second signal containing higher-order signals. A high-precision linear Radon transform inversion model based on multiple regularization constraints is constructed. The objective function of the inversion model includes a data fidelity term, a regularization term for the basic signal, and a regularization term for the higher-order signal. The inversion model is solved using the alternating direction multiplier method to obtain the basic and higher-order signals in the Radon domain; The fundamental and higher-order signals in the Radon domain are converted to the frequency-velocity domain to generate fundamental and higher-order dispersion energy maps. Multimodal surface wave dispersion curves are extracted based on the dispersion energy map.
2. The method for extracting multimodal surface wave dispersion curves according to claim 1, characterized in that, The step of adaptively separating the surface wave seismic record based on the apparent velocity difference between the fundamental and higher-order modes using Shearlet transform to obtain a first signal dominated by the fundamental signal and a second signal containing higher-order signals specifically includes: The surface wave seismic record was subjected to NSST transformation to obtain multi-scale, multi-directional subband sparsity coefficients; Based on the apparent velocity difference, the similarity coefficient and its standard deviation between each sub-band are calculated; The sparse coefficients containing higher-order signals are adaptively selected based on the standard deviation. The second signal is obtained by performing an inverse NSST transform on the selected sparse coefficients. The difference between the original seismic signal and the second signal is used as the first signal.
3. The method for extracting multimodal surface wave dispersion curves according to claim 1, characterized in that, The objective function of the high-precision linear Radon transform inversion model is: ； in, Here, L is the penalty parameter, and L is the linear Radon transform operator. These are fundamental-order surface wave data in the Radon domain. It is high-order surface wave data in the Radon domain. Represents actual earthquake records. and These are the regularization parameters for the base and higher-order signals, respectively.
4. The method for extracting multimodal surface wave dispersion curves according to claim 3, characterized in that, The steps for solving the inversion model using the alternating direction multiplier method to obtain the basic and higher-order signals in the Radon domain specifically include: Introducing auxiliary variables reconstructs the objective function into an augmented Lagrange form; Alternately update the basic signal, higher-order signals, auxiliary variables, and dual variables; Determine the convergence condition and output the fundamental and higher-order signals in the Radon domain.
5. The method for extracting multimodal surface wave dispersion curves according to claim 4, characterized in that, The reconstructed augmented Lagrangian function is specifically as follows: ； in, and These are dual variables. , For penalty parameters, and It is an auxiliary variable.
6. The method for extracting multimodal surface wave dispersion curves according to claim 1, characterized in that, The step of extracting the multimodal surface wave dispersion curve based on the dispersion energy map specifically includes: Automatic peak picking is performed on the dispersion energy map; Manual correction is performed on the automatically picked results.
7. A multimodal surface wave dispersion curve extraction system, used to implement the multimodal surface wave dispersion curve extraction method according to any one of claims 1-6, characterized in that, The system includes: The signal separation module is used to acquire surface wave seismic records. Based on the apparent velocity difference between the fundamental and higher-order modes, the module uses Shearlet transform to perform adaptive signal separation on the surface wave seismic records to obtain a first signal dominated by the fundamental signal and a second signal containing higher-order signals. The model building module is used to build a high-precision linear Radon transform inversion model based on multiple regularization constraints. The objective function of the inversion model includes a data fidelity term, a regularization term for the basic signal, and a regularization term for the higher-order signal. The solution module is used to solve the inversion model using the alternating direction multiplier method to obtain the basic and higher-order signals in the Radon domain; The signal conversion module is used to convert the fundamental and higher-order signals in the Radon domain to the frequency-velocity domain, generating fundamental and higher-order dispersion energy maps. The extraction module is used to extract the multimodal surface wave dispersion curve based on the dispersion energy map.