Inversion Of Rayleigh Wave Dispersion Curves Research Articles

Near-Surface Rayleigh Wave Dispersion Curve Inversion Algorithms: A Comprehensive Comparison

Near-Surface Rayleigh Wave Dispersion Curve Inversion Algorithms: A Comprehensive Comparison

Deep learning inversion of Rayleigh-wave dispersion curves with geological constraints for near-surface investigations

SUMMARY With the emergence of massive seismic data sets, surface wave methods using deep learning (DL) can effectively obtain shear wave velocity (Vs) structure for non-invasive near-surface investigations. Previous studies on DL inversion for deep geophysical investigation have a reference model to generate the training data set, while near-surface investigations have no model. Therefore, we systematically give a set of training data set generation processes. In the process, we use both prior information and the observed data to constrain the data set so that the DL inversion model can learn the local geological characteristics of the survey area. Because the space of inverted Vs models is constrained and thus narrowed, the inversion non-uniqueness can be reduced. Furthermore, the mean squared error, which is commonly used as loss function, may cause a poor fitting accuracy of phase velocities at high frequencies in near-surface applications. To make the fitting accuracy evenly in all frequency bands, we modify the loss function into a weighted mean squared relative error. We designed a convolutional neural network (CNN) to directly invert fundamental-mode Rayleigh-wave phase velocity for 1-D Vs models. To verify the feasibility and reliability of the proposed algorithm, we tested and compared it with the Levenberg–Marquardt (L-M) inversion and neighbourhood algorithm (NA) using field data from the Lawrence experiment (USA) and the Wuwei experiment (China). In both experiments, the inverted Vs models by CNN are consistent with the borehole information and are similar to that from existing methods after fine tuning of model parameters. The average root mean squares errors (RMSEs) of the CNN, NA and L-M methods are also similar, except in the Lawrence experiment, the RMSE of CNN is 17.33 m s−1 lower than previous studies using the L-M method. Moreover, the comparison of different loss functions for the Wuwei experiment indicates that the modified loss function can achieve higher accuracy than the traditional one. The proposed CNN is therefore ideally suited for rapid, repeated near-surface subsurface imaging and monitoring under similar geological settings.

Rayleigh Wave Dispersion Curve Inversion with the Artificial Bee Colony Algorithm

Rayleigh wave dispersion curve inversion is a non-linear iterative optimization process with multi-parameter and multi-extrema. It is difficult to carry out inversion and reconstruction of stratigraphic parameters quickly and accurately with a single linear or non-linear inversion for the data processing of Rayleigh waves with complex seismic geological conditions. We proposed a new method that combines artificial bee colony algorithm (ABC) and damped least squares algorithm (DLS) to invert Rayleigh wave dispersion curve. First, food sources are initialized in a large scale of the model based on the prior geological information. Then, after three kinds of bee operators (employed bees, onlooker bees and scout bees) transform each other and perform search optimization with several iterations, the targets are converged near the optimal solution to obtain an initial S-wave velocity model. Finally, the final S-wave velocity model is obtained by local optimization of DLS inversion with fast convergence and strong stability. The correctness of the method has been verified by one high-velocity interlayer model, and it was further applied to a real Rayleigh wave dataset. The results show that our method not only absorbs the advantages of ABC global search optimization and strong adaptability, but also makes full use of the advantages of DLS inversion, such as high accuracy and fast convergence speed. The inversion strategy can effectively suppress the inversion falling into local extrema, get rid of the dependence on an initial model, enhance the inversion stability, further improve the convergence speed and inversion accuracy, while has good anti-noise ability.

Velocity modeling based on Rayleigh wave dispersion curve and sparse optimization inversion

<p style='text-indent:20px;'>This paper studies the S wave velocity modeling based on the Rayleigh wave dispersion curve inversion. We first discuss the forward simulation, and present a fast root-finding method with cubic-order of convergence speed to obtain the Rayleigh wave dispersion curve. With the Rayleigh wave dispersion curve as the observation data, and considering the prior geological anomalies structural information, we establish a sparse constraint regularization model, and propose an iterative solution method to solve for the S wave velocity. Experimental tests are performed both on the theoretical models and on the field data. It indicates from the experimental results that our new inversion scheme possesses the characteristics of easy calculation, high computational efficiency and high precision for model characterization.</p>

Wave-equation dispersion inversion of Love waves

We present a theory for wave-equation inversion of Love-wave dispersion curves, in which the misfit function is the sum of the squared differences between the wavenumbers along the predicted and observed dispersion curves. Similar to inversion of Rayleigh-wave dispersion curves, the complicated Love-wave arrivals in traces are skeletonized as simpler data, namely, the picked dispersion curves in the [Formula: see text] domain. Numerical solutions to the SH-wave equation and an iterative optimization method are then used to invert these dispersion curves for the S-wave velocity model. This procedure, denoted as wave-equation dispersion inversion of Love waves (LWD), does not require the assumption of a layered model or smooth velocity variations, and it is less prone to the cycle-skipping problems of full-waveform inversion. We demonstrate with synthetic and field data examples that LWD can accurately reconstruct the S-wave velocity distribution in a laterally heterogeneous medium. Compared with Rayleigh waves, inversion of the Love-wave dispersion curves empirically exhibits better convergence properties because they are completely insensitive to the P-velocity variations. In addition, Love-wave dispersion curves for our examples are simpler than those for Rayleigh waves, and they are easier to pick in our field data with a low signal-to-noise ratio.

An Interactive Integrated Interpretation of GPR and Rayleigh Wave Data Based on the Genetic Algorithm

Ground-penetrating radar (GPR) and the seismic surface wave method are two geophysical techniques commonly used in near-surface surveys up to a depth of tens of meters. GPR can be utilized to clearly distinguish lithologic interfaces, while the seismic surface wave method (hereby referred to as the Rayleigh wave) is employed for its high sensitivity to the shear (S) wave velocity. However, the propagation velocity of the electromagnetic (EM) wave which is both initiated and tracked by GPR is difficult to determine within the stratum. Unfortunately, this can affect the time–depth conversion and interpretation of the radargram. Moreover, both the horizontal resolution and the detectability of the properties of the shallow stratum are limited by the seismic geometry of the Rayleigh wave data. It is important to note that the non-uniqueness of geophysical inversion problem also generates additional biases. To overcome the problems mentioned above, we put forward an interactive integrated geophysical system that utilizes the thickness as a bridge to connect GPR and the Rayleigh wave data in the data processing and inversion. In this study, we employed the velocity of a radagram and the Rayleigh wave dispersion curve inversion based on a genetic algorithm to reconstruct the near-surface distribution. Then, we set the thickness derived from the GPR data as limit of the Rayleigh wave dispersion curve inversion. Hence, we applied the constrained inversion result to determine the most accurate EM wave velocity. As expected, both the constrained inversion of the Rayleigh wave dispersion curve and the velocity correction of the radargram performed better than did the geophysical method alone, both in the numerical models and in the field. Finally, we found the interactive integrated geophysical system to be more conducive for geological interpretation in near-surface surveys.

Crustal and upper mantle structures of Makran subduction zone, SE Iran by combined surface wave velocity analysis and gravity modeling

The inversion of Rayleigh wave group velocity dispersion curves is challenging, because it is non-linear and multimodal. In this study, we develop and test a new Rayleigh wave dispersion curve inversion scheme using the Shuffled Complex Evolution (SCE) algorithm. Incorporating this optimization algorithm into the inverse procedure not only can effectively locate the promising areas in the solution space for a global minimum but also avoids its wandering near the global minimum in the final stage of search. In addition, our approach differs from others in the model parameterization: Instead of subdividing the model into a large number of thin layers, we invert for thickness, velocities and densities and their vertical gradients of four layers, sediments, upper-crust, lower-crust and upper mantle. The proposed inverse procedure is applied to non-linear inversion of fundamental mode Rayleigh wave group dispersion curves for shear and compressional wave velocities. At first, to determine the efficiency and stability of the SCE method, two noise-free and two noisy synthetic data sets are inverted. Then real data for Makran region in SE Iran are inverted to examine the usage and robustness of the proposed approach on real surface wave data. In a second step, we applied 3D Gravity Modeling based on surface wave analysis results to obtain the density structure and thickness of each layer. The reason for using both types of data sets, is that gravity anomaly has a bad vertical resolution and surface wave group velocities are good for placing layer limits at depth, but they are not very sensitive to densities. Therefore, using gravity data increases the overall resolution of density distribution. In a final step, we used again the SCE method to invert the fundamental mode Rayleigh wave group dispersion curves based on the gravity results. Gravity results like thicknesses and sediment densities have been used to constrain the limit of search space in the SCE method. Results show a high shear and compressional velocity under the Gulf of Oman which reduce to the North of the Makran region. The Moho depth of the Oman Gulf is about 18–28 km and it increases to 46–48 km under the Taftan-Bazman volcanic-arc. The density image shows an average crustal density with maximum values under the Gulf of Oman decreasing northward to the Makran.

Nonlinear Rayleigh wave inversion based on the shuffled frog-leaping algorithm

At present, near-surface shear wave velocities are mainly calculated through Rayleigh wave dispersion-curve inversions in engineering surface investigations, but the required calculations pose a highly nonlinear global optimization problem. In order to alleviate the risk of falling into a local optimal solution, this paper introduces a new global optimization method, the shuffle frog-leaping algorithm (SFLA), into the Rayleigh wave dispersion-curve inversion process. SFLA is a swarm-intelligence-based algorithm that simulates a group of frogs searching for food. It uses a few parameters, achieves rapid convergence, and is capability of effective global searching. In order to test the reliability and calculation performance of SFLA, noise-free and noisy synthetic datasets were inverted. We conducted a comparative analysis with other established algorithms using the noise-free dataset, and then tested the ability of SFLA to cope with data noise. Finally, we inverted a real-world example to examine the applicability of SFLA. Results from both synthetic and field data demonstrated the effectiveness of SFLA in the interpretation of Rayleigh wave dispersion curves. We found that SFLA is superior to the established methods in terms of both reliability and computational efficiency, so it offers great potential to improve our ability to solve geophysical inversion problems.

Perturbational and nonperturbational inversion of Rayleigh-wave velocities

The inversion of Rayleigh-wave dispersion curves is a classic geophysical inverse problem. We have developed a set of MATLAB codes that performs forward modeling and inversion of Rayleigh-wave phase or group velocity measurements. We describe two different methods of inversion: a perturbational method based on finite elements and a nonperturbational method based on the recently developed Dix-type relation for Rayleigh waves. In practice, the nonperturbational method can be used to provide a good starting model that can be iteratively improved with the perturbational method. Although the perturbational method is well-known, we solve the forward problem using an eigenvalue/eigenvector solver instead of the conventional approach of root finding. Features of the codes include the ability to handle any mix of phase or group velocity measurements, combinations of modes of any order, the presence of a surface water layer, computation of partial derivatives due to changes in material properties and layer boundaries, and the implementation of an automatic grid of layers that is optimally suited for the depth sensitivity of Rayleigh waves.

Rayleigh wave inversion using heat-bath simulated annealing algorithm

The dispersion of Rayleigh waves can be used to obtain near-surface shear (S)-wave velocity profiles. This is performed mainly by inversion of the phase velocity dispersion curves, which has been proven to be a highly nonlinear and multimodal problem, and it is unsuitable to use local search methods (LSMs) as the inversion algorithm. In this study, a new strategy is proposed based on a variant of simulated annealing (SA) algorithm. SA, which simulates the annealing procedure of crystalline solids in nature, is one of the global search methods (GSMs). There are many variants of SA, most of which contain two steps: the perturbation of model and the Metropolis-criterion-based acceptance of the new model. In this paper we propose a one-step SA variant known as heat-bath SA. To test the performance of the heat-bath SA, two models are created. Both noise-free and noisy synthetic data are generated. Levenberg–Marquardt (LM) algorithm and a variant of SA, known as the fast simulated annealing (FSA) algorithm, are also adopted for comparison. The inverted results of the synthetic data show that the heat-bath SA algorithm is a reasonable choice for Rayleigh wave dispersion curve inversion. Finally, a real-world inversion example from a coal mine in northwestern China is shown, which proves that the scheme we propose is applicable.

Backtracking search algorithm for effective and efficient surface wave analysis

Surface wave dispersion analysis is widely used in geophysics to infer near-surface shear (S)-wave velocity profiles for a wide variety of applications. However, inversion of surface wave data is challenging for most local-search methods due to its high nonlinearity and to its multimodality. In this work, we proposed and implemented a new Rayleigh wave dispersion curve inversion scheme based on backtracking search algorithm (BSA), a novel and powerful evolutionary algorithm (EA). Development of BSA is motivated by studies that attempt to develop an algorithm that possesses desirable features for different optimization problems which include the ability to reach a problem's global minimum more quickly and successfully with a small number of control parameters and low computational cost, as well as robustness and ease of application to different problem models.The proposed inverse procedure is applied to nonlinear inversion of fundamental-mode Rayleigh wave dispersion curves for near-surface S-wave velocity profiles. To evaluate calculation efficiency and effectiveness of BSA, four noise-free and four noisy synthetic data sets are firstly inverted. Then, the performance of BSA is compared with that of genetic algorithms (GA) by two noise-free synthetic data sets. Finally, a real-world example from a waste disposal site in NE Italy is inverted to examine the applicability and robustness of the proposed approach on real surface wave data. Furthermore, the performance of BSA is compared against that of GA by real data to further evaluate scores of BSA.Results from both synthetic and actual data demonstrate that BSA applied to nonlinear inversion of surface wave data should be considered good not only in terms of the accuracy but also in terms of the convergence speed. The great advantages of BSA are that the algorithm is simple, robust and easy to implement. Also there are fewer control parameters to tune.

An implementation of differential search algorithm (DSA) for inversion of surface wave data

Surface wave dispersion analysis is widely used in geophysics to infer near-surface shear (S)-wave velocity profiles for a wide variety of applications. However, inversion of surface wave data is challenging for most local-search methods due to its high nonlinearity and to its multimodality. In this work, we proposed and implemented a new Rayleigh wave dispersion curve inversion scheme based on differential search algorithm (DSA), one of recently developed swarm intelligence-based algorithms. DSA is inspired from seasonal migration behavior of species of the living beings throughout the year for solving highly nonlinear, multivariable, and multimodal optimization problems.The proposed inverse procedure is applied to nonlinear inversion of fundamental-mode Rayleigh wave dispersion curves for near-surface S-wave velocity profiles. To evaluate calculation efficiency and stability of DSA, four noise-free and four noisy synthetic data sets are firstly inverted. Then, the performance of DSA is compared with that of genetic algorithms (GA) by two noise-free synthetic data sets. Finally, a real-world example from a waste disposal site in NE Italy is inverted to examine the applicability and robustness of the proposed approach on surface wave data. Furthermore, the performance of DSA is compared against that of GA by real data to further evaluate scores of the inverse procedure described here.Simulation results from both synthetic and actual field data demonstrate that differential search algorithm (DSA) applied to nonlinear inversion of surface wave data should be considered good not only in terms of the accuracy but also in terms of the convergence speed. The great advantages of DSA are that the algorithm is simple, robust and easy to implement. Also there are fewer control parameters to tune.

Differential evolution algorithm for nonlinear inversion of high-frequency Rayleigh wave dispersion curves

Abstract In recent years, Rayleigh waves are gaining popularity to obtain near-surface shear (S)-wave velocity profiles. However, inversion of Rayleigh wave dispersion curves is challenging for most local-search methods due to its high nonlinearity and to its multimodality. In this study, we proposed and tested a new Rayleigh wave dispersion curve inversion scheme based on differential evolution (DE) algorithm. DE is a novel stochastic search approach that possesses several attractive advantages: (1) Capable of handling non-differentiable, non-linear and multimodal objective functions because of its stochastic search strategy; (2) Parallelizability to cope with computation intensive objective functions without being time consuming by using a vector population where the stochastic perturbation of the population vectors can be done independently; (3) Ease of use, i.e. few control variables to steer the minimization/maximization by DE's self-organizing scheme; and (4) Good convergence properties. The proposed inverse procedure was applied to nonlinear inversion of fundamental-mode Rayleigh wave dispersion curves for near-surface S-wave velocity profiles. To evaluate calculation efficiency and stability of DE, we firstly inverted four noise-free and four noisy synthetic data sets. Secondly, we investigated effects of the number of layers on DE algorithm and made an uncertainty appraisal analysis by DE algorithm. Thirdly, we made a comparative analysis with genetic algorithms (GA) by a synthetic data set to further investigate the performance of the proposed inverse procedure. Finally, we inverted a real-world example from a waste disposal site in NE Italy to examine the applicability of DE on Rayleigh wave dispersion curves. Furthermore, we compared the performance of the proposed approach to that of GA to further evaluate scores of the inverse procedure described here. Results from both synthetic and actual field data demonstrate that differential evolution algorithm applied to nonlinear inversion of high-frequency surface wave data should be considered good not only in terms of the accuracy but also in terms of the convergence speed.

A hybrid inversion method of damped least squares with simulated annealing used for Rayleigh wave dispersion curve inversion

Surface wave methods are becoming increasingly popular in many geotechnical applications and in earthquake seismology due to their noninvasive characteristics. Inverse surface wave dispersion curves are a crucial step in most surface wave methods. Many inversion methods have been applied to surface wave dispersion curve inversion, including linearized inversion and nonlinearized inversion methods. In this study, a hybrid inversion method of Damped Least Squares (DLS) with Very Fast Simulated Annealing (VFSA) is developed for multi-mode Rayleigh wave dispersion curve inversion. Both synthetic and in situ field data were used to verify the validity of the proposed method. The results show that the proposed method is superior to the conventional VFSA method in aiming at global minimum, especially when parameter searching space is adjacent to real values of the parameters. The advantage of the new method is that it retains both the merits of VFSA for global search and DLS for local search. At high temperatures, the global search dominates the runs, while at a low temperatures, the local search dominates the runs. Thus, at low temperatures, the proposed method can almost directly approach the actual model.

Application of particle swarm optimization to interpret Rayleigh wave dispersion curves

Abstract Rayleigh waves have been used increasingly as an appealing tool to obtain near-surface shear (S)-wave velocity profiles. However, inversion of Rayleigh wave dispersion curves is challenging for most local-search methods due to its high nonlinearity and to its multimodality. In this study, we proposed and tested a new Rayleigh wave dispersion curve inversion scheme based on particle swarm optimization (PSO). PSO is a global optimization strategy that simulates the social behavior observed in a flock (swarm) of birds searching for food. A simple search strategy in PSO guides the algorithm toward the best solution through constant updating of the cognitive knowledge and social behavior of the particles in the swarm. To evaluate calculation efficiency and stability of PSO to inversion of surface wave data, we first inverted three noise-free and three noise-corrupted synthetic data sets. Then, we made a comparative analysis with genetic algorithms (GA) and a Monte Carlo (MC) sampler and reconstructed a histogram of model parameters sampled on a low-misfit region less than 15% relative error to further investigate the performance of the proposed inverse procedure. Finally, we inverted a real-world example from a waste disposal site in NE Italy to examine the applicability of PSO on Rayleigh wave dispersion curves. Results from both synthetic and field data demonstrate that particle swarm optimization can be used for quantitative interpretation of Rayleigh wave dispersion curves. PSO seems superior to GA and MC in terms of both reliability and computational efforts. The great advantages of PSO are fast in locating the low misfit region and easy to implement. Also there are only three parameters to tune (inertia weight or constriction factor, local and global acceleration constants). Theoretical results exist to explain how to tune these parameters.

Shuffled complex evolution approach for effective and efficient surface wave analysis

Inversion of Rayleigh wave dispersion curves is challenging for most local-search methods due to its high nonlinearity and to its multimodality. In this paper, we proposed and tested a new Rayleigh wave dispersion curve inversion scheme called the shuffled complex evolution (SCE) approach, which is based on a synthesis of four global optimization strategies that have proved successful for global optimization: (a) combination of probabilistic and deterministic approaches; (b) the strategy of clustering; (c) systematic evolution of a complex of points spanning the space, in the direction of global improvement; and (d) competitive evolution. Incorporating these four global optimization strategies into the inverse procedure greatly enhances the performance of the SCE method because these steps not only can effectively locate the promising areas in the solution space for a global minimum but also avoid its wandering near the global minimum in the final stage of search.The proposed inverse procedure was applied to nonlinear inversion of fundamental-mode Rayleigh wave dispersion curves for near-surface shear (S)-wave velocity profiles. The calculation efficiency and stability of the inversion scheme are tested on four synthetic models and a real-world example from a waste disposal site in NE Italy. A comparative analysis with genetic algorithms (GA), marginal posterior probability density (MPPD) estimation, and simulated annealing (SA) is also made in the present study to further evaluate the performance of the proposed approach.Results from both synthetic and actual field data demonstrate that shuffled complex evolution algorithm promises to be robust, effective, and efficient for high-frequency surface wave analysis.

Pattern search algorithms for nonlinear inversion of high-frequency Rayleigh-wave dispersion curves

Inversion of Rayleigh wave dispersion curves is challenging for most local-search methods due to its high nonlinearity and to its multimodality. In this paper, we implemented and tested a Rayleigh wave dispersion curve inversion scheme based on GPS Positive Basis 2N, a commonly used pattern search algorithm. Incorporating complete poll and complete search strategies based on GPS Positive Basis 2N into the inverse procedure greatly enhances the performance of pattern search algorithms because the two steps can effectively locate the promising areas in the solution space containing the global minima and significantly reduce the computation cost, respectively.The proposed inverse procedure was applied to nonlinear inversion of fundamental-mode Rayleigh wave dispersion curves for a near-surface shear (S)-wave velocity profile. The calculation efficiency and stability of the inversion scheme are tested on three synthetic models and a real example from a roadbed survey in Henan, China. Effects of the number of data points, the reduction of the frequency range of the considered dispersion curve, errors in P-wave velocities and density, the initial S-wave velocity profile as well as the number of layers and their thicknesses on inversion results are also investigated in the present study to further evaluate the performance of the proposed approach.Results demonstrate that pattern search algorithms applied to nonlinear inversion of high-frequency surface wave data should be considered good not only in terms of accuracy but also in terms of the computation effort due to their global and deterministic search process.