Non-linear conjugate gradient-based surface wave frequency dispersion data inversion method and system
The shear wave velocity model is optimized by nonlinear conjugate gradient iterative inversion method, which solves the problem of strong dependence on the initial model in linear inversion method. It realizes high-precision and stable surface wave dispersion data inversion and is suitable for various engineering explorations and geological surveys.
Patent Information
- Application Number
- CN202511790012.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-01
- Publication Date
- 2026-03-27
AI Technical Summary
Existing linear inversion methods are highly dependent on the initial model, are prone to getting trapped in local extrema, cannot accurately identify complex geological structures, and perform poorly under low signal-to-noise ratio conditions, resulting in unreasonable or failed inversion results, and cannot meet the requirements of high accuracy and universality.
A nonlinear conjugate gradient iterative inversion method is adopted. By constraining the dispersion data with signal-to-noise ratio and dispersion curve smoothness, and combining regularization term and nonlinear conjugate gradient optimization, the shear wave velocity model is iteratively updated until the preset convergence condition is met.
It improves the stability and accuracy of inversion, can more accurately characterize the underground shear wave velocity distribution, is suitable for various surface wave dispersion inversion application scenarios, reduces the dependence on the initial model, and improves the reliability and resolution of the inversion results.
Smart Images
Figure CN121744847A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of surface wave dispersion data inversion technology, specifically to a surface wave dispersion data inversion method and system based on nonlinear conjugate gradient. Background Technology
[0002] Surface waves are elastic waves that propagate along the Earth's surface. Their unique dispersion characteristics make them an important tool for revealing subsurface structures, especially since shear wave velocity has a decisive influence on the morphology of dispersion curves. In recent years, surface wave dispersion inversion technology has been widely applied in fields ranging from engineering surveys to global Earth structure research, including near-surface geological surveys, oil and gas resource exploration, earthquake hazard assessment, and deep Earth structure detection. With the increasing utilization of underground space in engineering construction and the continuous growth in demand for energy resources, the requirements for the accuracy and resolution of subsurface structure imaging are constantly increasing, greatly promoting the technological innovation and theoretical progress of surface wave dispersion inversion methods.
[0003] In current surface wave dispersion inversion practices, inversion methods based on linearization theory constitute the mainstream of industry applications. These methods include a series of inversion techniques based on local linear approximations, such as the least squares method and the generalized inverse algorithm. The core idea of these methods is to linearize the inherently nonlinear surface wave dispersion inversion problem near the initial model through methods such as Taylor expansion, and then gradually approximate the true solution by iteratively solving a system of linear equations. The main advantages of linear inversion methods are high computational efficiency, good numerical stability, and relatively simple implementation, which makes them widely used in commercial software and engineering practices. However, while this linearization process brings computational convenience, it also comes at a heavy theoretical cost. The most prominent issue is the heavy dependence of linear inversion methods on the initial model. Since linear methods essentially perform local linear approximations near the initial model, when the initial model deviates significantly from reality, the inversion process is prone to getting trapped in erroneous local extrema, producing physically unreasonable solutions, or even causing the inversion to fail completely. This characteristic makes linear inversion methods highly dependent on the operator's experience and prior knowledge, greatly limiting the universality and standardized application of the methods. The second key issue lies in the inherent limitations of linear approximations when dealing with complex geological structures. When the relationship between the surface wave dispersion curve and model parameters exhibits strong nonlinear characteristics, such as in complex geological conditions with low-velocity interlayers, sharp velocity interfaces, or dramatic lateral variations, the effectiveness of linear approximations drops sharply, leading to reduced inversion resolution and an inability to accurately identify these important geological features. The third prominent issue concerns the uniqueness and stability of the solution. Surface wave dispersion inversion is inherently an ill-posed problem with severe multiple solutions. Linear inversion methods typically require the introduction of strong regularization constraints to obtain stable solutions. These artificial constraints often over-smooth the actual subsurface structure, obscuring important geological details, and cannot fundamentally guarantee the uniqueness and geological plausibility of the solution.
[0004] Furthermore, existing technologies have revealed other limitations in practical applications. For example, most linear inversion methods are sensitive to noise in the observation data and perform poorly under low signal-to-noise ratio conditions. The adaptability of existing linear inversion methods also needs improvement when dealing with common engineering scenarios such as small offsets and non-plane wave assumptions. These problems collectively limit the effectiveness of surface wave dispersion inversion technology in practical applications, necessitating the development of new inversion strategies to overcome these technical bottlenecks. Summary of the Invention
[0005] The purpose of this invention is to provide a surface wave dispersion data inversion method and system based on nonlinear conjugate gradients, so as to achieve high-precision inversion of shear wave velocity models.
[0006] To address the aforementioned technical problems, this invention provides a surface wave dispersion data inversion method based on nonlinear conjugate gradients, comprising: S1. Acquire observed surface wave data and extract dispersion data; S2. Input the observation system parameters and dispersion data, and preprocess the dispersion data; S3. Set the initial shear wave velocity model; S4. Starting with the initial shear wave velocity model, optimize the shear wave velocity model using the nonlinear conjugate gradient iterative inversion method to minimize the objective function. Stop iterating when the shear wave velocity model meets the preset convergence condition. The objective function takes the shear wave velocity model as a variable and represents the residual between the synthetic data and the dispersion data output by the optimized shear wave velocity model. S5. Output the transverse wave velocity model obtained after iteration.
[0007] According to the above scheme, the dispersion data is a dispersion curve. The preprocessing in step S2 includes: constraining the dispersion curve by the signal-to-noise ratio and the physical smoothness of the dispersion curve, and identifying and removing unreliable dispersion data points in the dispersion curve.
[0008] According to the above scheme, the objective function is the L2 norm based on the residual between the extracted dispersion data and the theoretical dispersion data, and includes a regularization term for stable inversion.
[0009] According to the above scheme, the initial shear wave velocity model is either a uniform half-space model or a gradient model set according to regional geological information.
[0010] According to the above scheme, step S4 includes: S401. Based on the observation system parameters, perform forward modeling under the shear wave velocity model to obtain theoretical dispersion data; S402. Calculate the gradient of the objective function with respect to the shear wave velocity model; S403. Calculate the descent direction of the objective function based on the nonlinear conjugate gradient iterative inversion method; S404. Perform a line search along the descent direction to determine the optimal step size; S405. Iteratively update the parameters of the shear wave velocity model based on the descent direction and optimal step size.
[0011] The present invention also provides a surface wave dispersion data inversion system based on nonlinear conjugate gradients, comprising: The data interaction module is used to receive input observation surface wave data and observation system parameters; The core inversion module starts with a set initial shear wave velocity model and optimizes the initial shear wave velocity model using a nonlinear conjugate gradient iterative inversion method to minimize the objective function. The iteration stops when the initial shear wave velocity model meets the preset convergence condition. The objective function takes the subsurface shear wave velocity model to be inverted as the variable and represents the residual between the synthetic data and the dispersion data output by the optimized shear wave velocity model. The model management module is used to store and retrieve parameters of the shear wave velocity model during the inversion process; The output module is used to output the transverse wave velocity model obtained after iteration.
[0012] According to the above scheme, the core inversion module executes as follows: Based on the observation system parameters, forward modeling is performed under the shear wave velocity model to obtain theoretical dispersion data; Calculate the gradient of the objective function with respect to the shear wave velocity model; The descent direction of the objective function is calculated based on the nonlinear conjugate gradient iterative inversion method. Perform a line search along the descent direction to determine the optimal step size; The parameters of the shear wave velocity model are updated iteratively based on the descent direction and the optimal step size.
[0013] According to the above scheme, the output module includes a display mechanism, which visualizes the output transverse wave velocity model.
[0014] The present invention also provides a computer, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the surface wave dispersion data inversion method based on nonlinear conjugate gradient described above.
[0015] The present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the surface wave dispersion data inversion method based on nonlinear conjugate gradient described above.
[0016] Beneficial effects This invention employs a nonlinear conjugate gradient iterative inversion method to optimize the initial shear wave velocity model. This overcomes the limitations of traditional linear inversion methods that rely on local linear approximations, effectively reducing the dependence on the initial model and avoiding problems such as local extrema, physical inconsistencies, or even inversion failure caused by the initial model deviating from reality. This significantly improves the stability and reliability of the inversion process. Simultaneously, the objective function directly uses the shear wave velocity model to be inverted as a variable, precisely focusing on minimizing the residual between the synthetic data and dispersion data output by the optimized shear wave velocity model. This allows for a more direct and accurate depiction of the true distribution of subsurface shear wave velocities, greatly improving the inversion accuracy of surface wave dispersion data and making the inversion results more closely match the actual subsurface geological structure. Furthermore, by preprocessing the dispersion data and setting a stop condition after iteration to a preset convergence point, a reliable data foundation and reasonable iteration boundaries are provided for the inversion, ensuring the validity of the inversion results. This makes the method widely applicable to various surface wave dispersion inversion applications such as near-surface geological surveys and oil and gas resource exploration, demonstrating strong practicality and universality. Attached Figure Description
[0017] Figure 1 This is a real model in one embodiment of the present invention; Figure 2 This is the initial shear wave velocity model in one embodiment of the present invention; Figure 3 This is the dispersion data obtained by forward modeling using a real model in one embodiment of the present invention; Figure 4 This is the dispersion data obtained by forward modeling an initial shear wave velocity model in one embodiment of the present invention; Figure 5 The result is the surface wave dispersion data inversion method of nonlinear conjugate gradient according to an embodiment of the present invention; Figure 6 The results were inverted using the steepest descent method; Figure 7 This refers to the residual between the inversion result dispersion curve and the true model dispersion curve in one embodiment of the present invention. Figure 8 The residual between the dispersion curve of the steepest descent method inversion result and the dispersion curve of the true model; Figure 9 This is a flowchart of a surface wave dispersion data inversion method based on nonlinear conjugate gradient according to an embodiment of the present invention. Detailed Implementation
[0018] To make the objectives, technical solutions, and advantages of the embodiments of this disclosure clearer, the technical solutions of the embodiments of this disclosure will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this disclosure. All other embodiments obtained by those skilled in the art based on the described embodiments of this disclosure without creative effort are within the scope of protection of this disclosure.
[0019] This embodiment designs and implements an automated surface wave dispersion inversion software system based on a nonlinear conjugate gradient algorithm. Through a standardized data processing and inversion workflow, the system transforms the complex mathematical inversion process into a stable and efficient software operation, providing users with high-precision imaging results of underground structures.
[0020] See Figure 9 This embodiment discloses a surface wave dispersion data inversion method based on nonlinear conjugate gradients, including: S1. Acquire observed surface wave data and extract dispersion data; S2. Input the observation system parameters and dispersion data, and preprocess the dispersion data; S3. Set the initial shear wave velocity model; S4. Starting with the initial shear wave velocity model, optimize the shear wave velocity model using the nonlinear conjugate gradient iterative inversion method to minimize the objective function. Stop iterating when the shear wave velocity model meets the preset convergence condition. The objective function takes the shear wave velocity model as a variable and represents the residual between the synthetic data and the dispersion data output by the optimized shear wave velocity model. S5. Output the shear wave velocity model obtained after iteration. (See below) Figure 5 .
[0021] This embodiment uses model data for implementation description; therefore, the dispersion data acquisition in step S1 is achieved by... Figure 1 The model shown was obtained through forward modeling. The actual model size (number of grids) was 1300×400, with a grid spacing of 0.5km. The actual model consisted of five anomalies uniformly distributed in the shallow medium with a transverse gradient, and a deep uniform half-space, with the velocity discontinuity located at a depth of 60km. The observation system included 129 stations uniformly distributed on the surface, ranging from 5 to 645km; the observation period was 3 to 59s, with a period sampling interval of 2s; the surface wave dispersion data was synthesized from a local 1D layered model below the stations. Simultaneously, in step S2, the dispersion curves and the observation system were input into the system.
[0022] See Figure 2In this embodiment, the initial model for the shear wave velocity (Vs) is constructed using empirical formulas, while the initial model for the longitudinal wave velocity (Vp) is related to density and Vs. Figure 3 , Figure 4 It can be seen that the initial phase velocity map differs significantly from the observed phase velocity map.
[0023] Furthermore, the dispersion data is a dispersion curve. The preprocessing in step S2 includes: constraining the dispersion curve by the signal-to-noise ratio and the physical smoothness of the dispersion curve, and identifying and removing unreliable dispersion data points in the dispersion curve.
[0024] Furthermore, the objective function is based on the L2 norm of the residual between the extracted dispersion data and the theoretical dispersion data, and includes a regularization term for stable inversion.
[0025] Specifically, an objective function is constructed to minimize the observed data. Synthetic data corresponding to the model The residuals between the data are used to introduce a regularization term into the optimization problem of the stable inversion system, transforming the inversion objective into minimizing the data residuals. With model residuals The objective function of the inversion problem can be expressed as a weighted combination of the following:
[0026] in, As regularization parameters, the data residual function and the model residual function are defined as follows:
[0027]
[0028] In the formula, users can select data weights based on data quality or sensitivity analysis. With model weights ; This represents the current shear wave velocity model. This serves as a reference model estimated based on prior information. For linear operators that act on the model.
[0029] Furthermore, the initial shear wave velocity model is either a uniform half-space model or a gradient model set according to regional geological information.
[0030] Further, step S4 includes: S401. Based on the observation system parameters, perform forward modeling under the shear wave velocity model to obtain theoretical dispersion data; S402. Calculate the gradient of the objective function with respect to the shear wave velocity model; S403. Based on the nonlinear conjugate gradient iterative inversion method, calculate the descent direction of the objective function (to avoid the model getting trapped in local minima in a specific direction). S404. Perform a line search along the descent direction to determine the optimal step size; S405. Iteratively update the parameters of the shear wave velocity model based on the descent direction and optimal step size.
[0031] Specifically, the expression for the descent direction in step S503 is:
[0032] Where k represents the number of iterations. This represents the gradient of the objective function calculated by the current model. Represents the nonlinear conjugate gradient factor. Representing the descent direction of the previous iteration, this embodiment also selects... A nonlinear conjugate gradient method is constructed, and a Powell restart condition is introduced to accelerate inversion convergence:
[0033] in, This represents the amount of gradient update between two consecutive iterations.
[0034] In step S405, since surface waves are less sensitive to Vp and density, these two parameters are not updated during the inversion process; instead, Vs is updated using a parabolic fitting method. The iteration form of the Vs model update is as follows:
[0035] In the formula, positive coefficients The step size is as important as the descent direction.
[0036] This embodiment also provides a surface wave dispersion data inversion system based on nonlinear conjugate gradients, including: The data interaction module is used to receive input observation surface wave data and observation system parameters; The core inversion module starts with a set initial shear wave velocity model and optimizes the initial shear wave velocity model using a nonlinear conjugate gradient iterative inversion method to minimize the objective function. The iteration stops when the initial shear wave velocity model meets the preset convergence condition. The objective function takes the subsurface shear wave velocity model to be inverted as the variable and represents the residual between the synthetic data and the dispersion data output by the optimized shear wave velocity model. The model management module is used to store and retrieve parameters of the shear wave velocity model during the inversion process; The output module is used to output the transverse wave velocity model obtained after iteration.
[0037] Furthermore, the core inversion module executes: Based on the observation system parameters, forward modeling is performed under the shear wave velocity model to obtain theoretical dispersion data; Calculate the gradient of the objective function with respect to the shear wave velocity model; The descent direction of the objective function is calculated based on the nonlinear conjugate gradient iterative inversion method. Perform a line search along the descent direction to determine the optimal step size; The parameters of the shear wave velocity model are updated iteratively based on the descent direction and the optimal step size.
[0038] Furthermore, the output module includes a display mechanism that visualizes the output transverse wave velocity model.
[0039] To verify the accuracy and effectiveness of the calculation results of the method proposed in this invention, the results of another nonlinear inversion method were compared with those of this invention. The resolution of the inversion results obtained by the nonlinear conjugate gradient method of this invention is slightly higher than that of the steepest descent method. See [link to relevant documentation]. Figure 6 .
[0040] Simultaneously, the inversion results are used as the dispersion data for forward modeling of this model, and the residuals are calculated with the input dispersion data. The residuals obtained by the surface wave dispersion data inversion method based on nonlinear conjugate gradients provided by this invention are significantly smaller than the residuals calculated by the steepest descent method. See [link to related documentation]. Figure 7 , Figure 8 Therefore, the nonlinear conjugate gradient surface wave dispersion data inversion method can obtain relatively reliable and high-resolution results.
[0041] This embodiment also provides a computer, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps of the surface wave dispersion data inversion method based on nonlinear conjugate gradient described above.
[0042] The memory is used to store the computer program. Specifically, its function is to preserve a series of instruction codes, i.e., the computer program that implements the surface wave dispersion data inversion method in this embodiment, even when the device is powered off. These program instructions constitute the core logic and steps of the method.
[0043] The processor is communicatively connected to the memory and configured to execute computer programs stored in the memory. Specifically, after the device starts and loads the program, the processor reads, interprets, and executes the program instructions one by one. During this process, the processor calls its arithmetic logic unit to perform calculations, controls the data flow according to the program's logic, and ultimately completes a series of inversion operations such as forward simulation, gradient calculation, conjugate direction determination, and model updating, thereby realizing the surface wave dispersion data inversion method based on nonlinear conjugate gradients of this invention.
[0044] This embodiment also provides a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of the surface wave dispersion data inversion method based on nonlinear conjugate gradients described above.
[0045] The storage medium itself is a physical entity that serves to provide a portable and transferable storage medium for the computer program. This medium can be non-volatile, meaning that the stored program content will not be lost even without a power supply.
[0046] The computer program is carried on the storage medium, and when the program is read and executed by one or more processors, it causes the processors to execute all or predetermined steps of the aforementioned surface wave dispersion data inversion method based on nonlinear conjugate gradients.
[0047] This invention successfully transforms an advanced mathematical tool into a practical technique for solving specific exploration problems by software-izing and systematizing the nonlinear conjugate gradient algorithm. The software system is easy to operate, greatly reducing reliance on the user's professional experience; the inversion results are robust and highly accurate, effectively overcoming the inherent defects of linear methods; the automated process frees technicians from tedious parameter adjustments, significantly improving the efficiency and reliability of surface wave data processing, and providing a powerful tool for engineering exploration and geological research.
[0048] This invention introduces the nonlinear conjugate gradient method, a highly efficient nonlinear optimization algorithm validated in other fields, into surface wave dispersion inversion. This method retains the theoretical advantages of nonlinear inversion in handling complex problems, while maintaining reasonable computational efficiency through its efficient convergence characteristics. It achieves a better balance between inversion accuracy, stability, and practicality, thus promoting the development of surface wave exploration technology to a deeper level.
[0049] It should be noted that, depending on the implementation needs, the various steps / components described in this application can be broken down into more steps / components, or two or more steps / components or parts of the operation of steps / components can be combined into new steps / components to achieve the purpose of this invention.
[0050] Those skilled in the art will readily understand that the above description is merely 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 scope of protection of the present invention.
Claims
1. A surface wave dispersion data inversion method based on nonlinear conjugate gradient, characterized in that, include: S1. Acquire observed surface wave data and extract dispersion data; S2. Input the observation system parameters and dispersion data, and preprocess the dispersion data; S3. Set the initial shear wave velocity model; S4. Starting with the initial shear wave velocity model, optimize the shear wave velocity model using the nonlinear conjugate gradient iterative inversion method to minimize the objective function. Stop iterating when the shear wave velocity model meets the preset convergence condition. The objective function takes the shear wave velocity model as a variable and represents the residual between the synthetic data and the dispersion data output by the optimized shear wave velocity model. S5. Output the transverse wave velocity model obtained after iteration.
2. The surface wave dispersion data inversion method based on nonlinear conjugate gradient according to claim 1, characterized in that, The dispersion data is a dispersion curve. The preprocessing in step S2 includes: constraining the dispersion curve by the signal-to-noise ratio and the physical smoothness of the dispersion curve, and identifying and removing unreliable dispersion data points in the dispersion curve.
3. The surface wave dispersion data inversion method based on nonlinear conjugate gradient according to claim 1, characterized in that, The objective function is based on the L2 norm of the residuals between the extracted dispersion data and the theoretical dispersion data, and includes a regularization term for stable inversion.
4. The surface wave dispersion data inversion method based on nonlinear conjugate gradient according to claim 1, characterized in that, The initial shear wave velocity model is either a uniform half-space model or a gradient model set according to regional geological information.
5. The surface wave dispersion data inversion method based on nonlinear conjugate gradient according to claim 1, characterized in that, Step S4 includes: S401. Based on the observation system parameters, perform forward modeling under the shear wave velocity model to obtain theoretical dispersion data; S402. Calculate the gradient of the objective function with respect to the shear wave velocity model; S403. Calculate the descent direction of the objective function based on the nonlinear conjugate gradient iterative inversion method; S404. Perform a line search along the descent direction to determine the optimal step size; S405. Iteratively update the parameters of the shear wave velocity model based on the descent direction and optimal step size.
6. A surface wave dispersion data inversion system based on nonlinear conjugate gradients, characterized in that, include: The data interaction module is used to receive input observation surface wave data and observation system parameters; The core inversion module starts with a set initial shear wave velocity model and optimizes the initial shear wave velocity model using a nonlinear conjugate gradient iterative inversion method to minimize the objective function. The iteration stops when the initial shear wave velocity model meets the preset convergence condition. The objective function takes the subsurface shear wave velocity model to be inverted as the variable and represents the residual between the synthetic data and the dispersion data output by the optimized shear wave velocity model. The model management module is used to store and retrieve parameters of the shear wave velocity model during the inversion process; The output module is used to output the transverse wave velocity model obtained after iteration.
7. The surface wave dispersion data inversion system based on nonlinear conjugate gradient according to claim 6, characterized in that, Core inversion module execution: Based on the observation system parameters, forward modeling is performed under the shear wave velocity model to obtain theoretical dispersion data; Calculate the gradient of the objective function with respect to the shear wave velocity model; The descent direction of the objective function is calculated based on the nonlinear conjugate gradient iterative inversion method. Perform a line search along the descent direction to determine the optimal step size; The parameters of the shear wave velocity model are updated iteratively based on the descent direction and the optimal step size.
8. The surface wave dispersion data inversion system based on nonlinear conjugate gradient according to claim 6, characterized in that, The output module includes a display mechanism that visualizes the output transverse wave velocity model.
9. A computer, 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 steps of the surface wave dispersion data inversion method based on nonlinear conjugate gradient as described in claim 1.
10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the surface wave dispersion data inversion method based on nonlinear conjugate gradient as described in claim 1.