Inversion Of Surface Wave Data Research Articles

Integrated analysis of surface wave velocity and gravity data for the development of new density-velocity models of the crust and upper mantle in SE Iran

Inversion of Rayleigh wave dispersion curves is challenging due to its nonlinearity and multimodality. In this paper, a Simulated Annealing (SA) algorithm is applied to the nonlinear inversion of fundamental-mode Rayleigh wave group dispersion curves for shear and compressional wave velocities. In our approach, we invert thickness, velocities and densities and their vertical gradients of four layers, sediments, upper-crust, lower-crust and lithospheric mantle.At first, to determine the efficiency and stability of the method, noise-free and noisy synthetic data sets are inverted. Results from the synthetic data demonstrate that the SA applied to the nonlinear inversion of surface wave data is interesting not only in terms of accuracy but also in terms of the convergence speed. In fact, the SA method is suitable for large-scale optimization problems, especially for those in which a desired global minimum is hidden among many local minima. In a second step, real data in SE Iran are inverted to examine the usage and robustness of the proposed approach on real surface wave data. Then, we applied 3D gravity modeling based on surface wave analysis results to obtain the density structure of each layer. The reason for using both types of data sets is that the gravity anomaly does not have a good vertical resolution and surface wave group velocities are more appropriate for placing layer limits at depth, but they are not very sensitive to density variations. Therefore, the use of gravity data increases the overall resolution of density distribution. Compared with the Shuffle Complex Evolution (SCE) method that was implemented in a previous study, we found out that the SA method is more stable and has less variability of model parameter values in successive tests. In the final step, we reapplied the SA method to invert the fundamental-mode Rayleigh wave group velocities based on the results of gravity modeling. Gravity results, such as thicknesses and densities were used to limit the search space in the SA method.Our results show that the Moho depth across the Makran subduction zone is increasing from the Oman seafloor (24–30 km) and Makran forearc setting (34–42 km) to the Taftan-Bazman volcanic arc (47–49 km). Also, the results show high shear and compressional velocities under the Gulf of Oman, decreasing to the north of the Makran region. The density image shows an average crustal density with maximum values under the Gulf of Oman, decreasing northward to the Makran region.

Deep shear wave velocity profiles in the Mississippi embayment from surface wave measurements

Local geology in the Mississippi embayment is a significant source of site effects due to the deep unconsolidated sediments and basin effects near the edge of the embayment. Proper characterization of the velocity structure of the embayment is crucial for site response and seismic hazard studies. In this paper, deep dynamic site characterization was conducted in the Mississippi embayment to develop shear wave velocity profiles down to bedrock at 24 sites using active and passive source surface wave methods. Study sites cover parts of Arkansas, Missouri, Kentucky, and Tennessee, with bedrock depths ranging from 250 to 1115 m. Multimodal joint inversion of surface wave data, which included both Rayleigh and Love wave dispersion and site fundamental frequency was utilized to develop the shear wave velocity profiles (VS profiles). The developed VS profiles provided reasonable site characterization solution and captured the site signature from experimental dispersion data and fundamental frequency. Average shear wave velocity down to bedrock ranges from 462 to 686 m/s and is proportionally related with the site period and depth to bedrock of the site. Average shear wave velocities estimated by previous studies using the resonance period-sediment thickness relationship tend to systematically overestimate the average shear wave velocity in the embayment by 25–40%. Formation velocities calculated for the commonly found geologic units in the embayment, Quaternary, Upper Tertiary, Memphis sand, Paleocene, Cretaceous, and Paleozoic bedrock are approximately 214, 418, 607, 665, 967, and 2211 m/s, respectively. Comparison of the developed VS profiles demonstrated better agreement with related VS profiles generated from direct measurements, but differences up to 30% are observed with the current velocity models of the Embayment.

Measured vs. predicted site response at the Garner Valley Downhole Array considering shear wave velocity uncertainty from borehole and surface wave methods

This paper compares measured and predicted site response at the Garner Valley Downhole Array (GVDA) using a wide range of shear wave velocity (Vs) profiles developed from both borehole methods and inversion of surface wave data. Only low amplitude ground motions, resulting in approximately linear-viscoelastic site response between the downhole accelerometer and the surface accelerometers, were considered in this study. Thus, uncertainties associated with the small-strain Vs profiles used for site response predictions play a considerable role in attempting to match the recorded site response and its associated variability. Prior to our study, two borehole Vs profiles extending into rock were available for the site. However, their predicted/theoretical transfer functions (TTFs) were quite different and in poor agreement with the measured/empirical transfer functions (ETFs). These differences provided motivation to collect and interpret an extensive set of active-source and passive-wavefield surface wave measurements in an attempt to develop deep Vs profiles for the site that might be used to more accurately model the measured site response and its associated variability. Suites of non-unique Vs profiles developed from inversion of the surface wave data visually exhibited considerable differences, yet their predicted TTFs matched the measured ETFs very well. These results provide further evidence that surface wave dispersion data and horizontal-to-vertical spectral ratio curves represent an experimental “site signature” that can be used as a quantitative means of assessing whether candidate Vs profiles are appropriate for use in site response analyses.

Inversion of surface wave data for subsurface shear wave velocity profiles characterized by a thick buried low-velocity layer

The study formed part of the SIMIT project (Integrated Italy-Malta Cross-Border System of Civil Protection) (B1-2.19/11) part-financed by the European Union under the ItaliaMalta Cross-Border Cooperation Programme, 2007–2013.

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.

Laterally constrained inversion of surface wave data at Najaf city (Iraq)

A case history is reported to outline a possible strategy for the construction of a pseudo-2D model of shear-wave velocity for seismic site response studies. Experimental data have been collected using the Multichannel Analysis of Surface Wave technique (MASW) at six sites in the city of Najaf (Southern Iraq). The sites are aligned along the route of a proposed subway. The dataset has been processed to extract the dispersion curves of each site and then it has been inverted by using a Laterally Constrained Inversion (LCI) algorithm. The initial model for the local search algorithm has been obtained with a preliminary Monte Carlo Inversion (MCI). A priori information from borehole logs and lateral constraints between neighbors 1D models are used to mitigate the non-uniqueness of the solution. The result is a pseudo-2D shear-wave velocity model of the area which is in good agreement with sediment lithology and thicknesses obtained from borehole logs.

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.

Seismic characterization of shallow bedrock sites with multimodal Monte Carlo inversion of surface wave data

Sites with a limited overburden over a stiff basement are of particular relevance for seismic site response. The characterization of such stratigraphies by means of surface wave methods poses some difficulties in interpretation. Indeed the presence of sharp seismic contrasts between the sediments and the shallow bedrock is likely to cause a relevance of higher modes in the surface wave apparent dispersion curve, which must be properly taken into account in order to provide reliable results. In this study a Monte Carlo algorithm based on a multimodal misfit function has been used for the inversion of experimental dispersion curves. Case histories related to the characterization of stations of the Italian accelerometric network are reported. Spectral ratios and amplification functions associated to each site are moreover evaluated to provide an independent benchmark test. The results show the robustness of the inversion method in such non-trivial conditions and the possibility of getting an estimate of uncertainty related to solution non-uniqueness.

Improved Monte Carlo inversion of surface wave data

ABSTRACTInversion of surface wave data suffers from solution non‐uniqueness and is hence strongly biased by the initial model. The Monte Carlo approach can handle this non‐uniqueness by evidencing the local minima but it is inefficient for high dimensionality problems and makes use of subjective criteria, such as misfit thresholds, to interpret the results. If a smart sampling of the model parameter space, which exploits scale properties of the modal curves, is introduced the method becomes more efficient and with respect to traditional global search methods it avoids the subjective use of control parameters that are barely related to the physical problem. The results are interpreted drawing inference by means of a statistical test that selects an ensemble of feasible shear wave velocity models according to data quality and model parameterization. Tests on synthetic data demonstrate that the application of scale properties concentrates the sampling of model parameter space in high probability density zones and makes it poorly sensitive to the initial boundary of the model parameters. Tests on synthetic and field data, where boreholes are available, prove that the statistical test selects final results that are consistent with the true model and which are sensitive to data quality. The implemented strategies make the Monte Carlo inversion efficient for practical applications and able to effectively retrieve subsoil models even in complex and challenging situations such as velocity inversions.

Global crustal thickness from neural network inversion of surface wave data

SUMMARY We present a neural network approach to invert surface wave data for a global model of crustal thickness with corresponding uncertainties. We model the a posteriori probability distribution of Moho depth as a mixture of Gaussians and let the various parameters of the mixture model be given by the outputs of a conventional neural network. We show how such a network can be trained on a set of random samples to give a continuous approximation to the inverse relation in a compact and computationally efficient form. The trained networks are applied to real data consisting of fundamental mode Love and Rayleigh phase and group velocity maps. For each inversion, performed on a 2°× 2° grid globally, we obtain the a posteriori probability distribution of Moho depth. From this distribution any desired statistic such as mean and variance can be computed. The obtained results are compared with current knowledge of crustal structure. Generally our results are in good agreement with other crustal models. However in certain regions such as central Africa and the backarc of the Rocky Mountains we observe a thinner crust than the other models propose. We also see evidence for thickening of oceanic crust with increasing age. In applications, characterized by repeated inversion of similar data, the neural network approach proves to be very efficient. In particular, the speed of the individual inversions and the possibility of modelling the whole a posteriori probability distribution of the model parameters make neural networks a promising tool in seismic tomography.

Waveform inversion of surface wave data: test of a new tool for systematic investigation of upper mantle structures

SUMMARY In most tomographic inversion of surface wave data, the long-period seismograms are first interpreted in terms of dispersion and/or attenuation curves before performing an inversion in terms of laterally and depth-varying properties. An alternative to this approach is to perform a direct waveform inversion or, as in Cara & Levěque, (1987), to use another set of secondary observables built up from the seismograms. In this paper, we systematically test with actual Rayleigh wave records this latter technique by considering laterally homogeneous models. We use for this purpose a set of recent long-period digital records from the Geoscope station Dumont d'Urville, Antarctica, for surficial events in the south Indian Ocean and the southeast Pacific Ocean, and for intermediate-depth events in the Vanuatu and Kermadec trenches. In addition to the obvious advantages of being able to deal with situations where overtones are present in the seismogram, it is found that the waveform inversion procedure allows us to reach a better depth resolution than in classical inversion of dispersion curves, even when only the fundamental mode is present in the seismogram. Quite good resolution is obtained to depth as large as 300km for S velocity when using surficial events located at a few thousand kilometres from the station, while classical surface wave studies do not allow us to resolve S velocity at depth larger than 150 km for these events. When intermediate-depth events are used at distances of about 5000 km, the presence of overtones in the signal allows us to get resolution to depth as large as 600 km for S velocity. Poorer resolution is obtained in both situations for the attenuation factor. S velocity appears furthermore to be more robust than attenuation at depth where good resolution is achieved. Due to the great sensitivity of surface wave amplitude to departure from the assumption of lateral homogeneity, more sophisticated direct modelling would be required to get more confidence in the inverted attenuation models.

A Fast and Reliable Method for Surface Wave Tomography

— We describe a method to invert regional or global scale surface-wave group or phase-velocity measurements to estimate 2-D models of the distribution and strength of isotropic and azimuthally anisotropic velocity variations. Such maps have at least two purposes in monitoring the nuclear Comprehensive Test-Ban Treaty (CTBT): (1) They can be used as data to estimate the shear velocity of the crust and uppermost mantle and topography on internal interfaces which are important in event location, and (2) they can be used to estimate surface-wave travel-time correction surfaces to be used in phase-matched filters designed to extract low signal-to-noise surface-wave packets.¶The purpose of this paper is to describe one useful path through the large number of options available in an inversion of surface-wave data. Our method appears to provide robust and reliable dispersion maps on both global and regional scales. The technique we describe has a number of features that have motivated its development and commend its use: (1) It is developed in a spherical geometry; (2) the region of inference is defined by an arbitrary simple closed curve so that the method works equally well on local, regional, or global scales; (3) spatial smoothness and model amplitude constraints can be applied simultaneously; (4) the selection of model regularization and the smoothing parameters is highly flexible which allows for the assessment of the effect of variations in these parameters; (5) the method allows for the simultaneous estimation of spatial resolution and amplitude bias of the images; and (6) the method optionally allows for the estimation of azimuthal anisotropy.¶We present examples of the application of this technique to observed surface-wave group and phase velocities globally and regionally across Eurasia and Antarctica.

Direct Solution Method による地球内部3次元構造の決定

We summarize recent results of our work on inversion for laterally heterogeneous earth structure using the Direct Solution Method (DSM). We obtained a 3-D upper mantle S-wave velocity model, PUM0 (Preliminary Upper Mantle model, version 0) by iterative linearized waveform inversion of surface wave data. The deep roots of ridges and cratons can be identified as the geological features responsible for the lateral heterogeneity of PUM0 at depths of 300-400km. We discuss the necessity of iterative linearized waveform inversion based on our calculations. We also discuss the future prospects for application of the DSM to waveform inversion of body wave data for the 3-D structure of the earth's deep interior.

Deep structure of the Alps—what do we really know?

In the last five decades the deep structure of the Alps has been probed by every geophysical method applicable, and the resulting amount of data is unmatched for any other orogen. In this study, an attempt is made to review the data and the proposed structural models with the aim of separating the certain from the probable and from the speculative information. This can be achieved by first reviewing the theoretical resolving power and ambiguity of the applied interpretation methods and then analysing the proposed models. The methods reviewed are inversion of surface wave data, teleseismic and local earthquake seismic tomography, near-vertical reflection seismology, wide-angle reflection and refraction seismology, and gravity modelling. All information about the Moho rated as certain is combined to give a Moho map of the Alpine area. The information rated as certain and probable, and additional qualitative arguments, are used to discuss a crustal model of the Western and Central Alps represented by two cross-sections. Major structural elements in this crustal model are a thick overthrust Penninic nappe system, wedging at mid- to lower-crustal levels, a discontinuous Moho and strong variations along the strike of the orogen. Whereas the structures of the European upper crust and of the Penninic nappe system are well constrained, only few and isolated lower-crustal structural elements are rated as certain. Finally, the shape of the lower lithosphere in the Alps is discussed by review and comparison of the results from surface-wave, teleseismic travel-time residual and tomographic studies. Qualitative arguments suggest the existence of a lithospheric root or slab beneath the Alps. Probable tomographic information suggests a south-vergent European lithospheric slab beneath the Southern Alps and the Po Plain. Despite the considerable number of studies aimed at resolving the deepest part of Alpine orogeny, the available quantitative information on the sub-Moho structure cannot be rated as certain.

Line focus acoustic microscopy to measure anisotropic acoustic properties of thin films

Propagation characteristics of surface acoustic waves on thin film coated elastic materials have been investigated by the use of an acoustic microscope with a line focus beam. Measurements were carried out for thin films of various thicknesses deposited on the (001) plane of cubic crystals. The phase velocities measured as functions of the angle of propagation display the anisotropy and confirm the advantage of directional measurement by the line focus acoustic microscope. Dispersion curves of surface waves propagating along the symmetry axes were obtained for various film thicknesses and frequencies. A systematic inversion of surface wave data based on a comparison of theoretical and experimental results has been used to obtain the thin film material constants.

Alfred Wegener Conference

From August 28–31, 1982, the Alfred Wegener‐Stiftung held its 1st Alfred Wegener Conference on ‘Geophysical, Geochemical and Petrological Evidence on Deformation and Composition of the Continental Subcrustal Lithosphere’ at Seeheim/F.R. Germany. It was convened by K. Fuchs (University of Karlsruhe) and H. Wanke (Max‐Planck‐Institut Mainz).The main results and questions from this conference may be summarized as follows: Geophysical, petrological, and geochemical models of the earth's continental lithosphere have been refined recently so far that they are no longer independent of one another. From an analysis of xenoliths the compositions proposed for this part of the earth were confronted with seismic velocities measured in situ at depth. Both observations are not compatible unless seismic anisotropy is present in the upper mantle. Triaxial anisotropy was also required in the asthenosphere from a world‐wide inversion of surface wave data. Seismic anisotropy was recognized as a possible tracer of mantle convection. Whether it signifies a paleomotion or is generated by recent flow patterns depends on a number of material parameters that require future research in the field, in the laboratory, and in numerical modeling, e.g., experiments on stress relations at low strain rates, on seismic velocities and their partial derivatives at seismic frequencies under upper‐mantle conditions, and on field experiments to map anisotropy in the mantle and lower crust. The conference showed that geophysical, petrological, and geochemical models can and should be integrated, since they offer mutual constraints.

Inversion of surface wave data in source mechanism studies

A least squares method is proposed to invert Rayleigh and Love wave observations in source mechanism studies. When complex spectra is available the inversion scheme is linear and it is carried out in a single step. When only amplitude spectra is available the inversion scheme may be linearized and it converges to a unique solution independent of the orientation of the initial trial source. Source depth is found by minimizing errors in repeated application of the method at different trial depths. Application to real data requires a careful weighting of observations when the path structure is not well-known. The source representation in term of seismic moment tensor components allows for a simple analysis of the surface wave data resolving power. Complex spectra of Rayleigh waves render a unique solution, but complex spectra of Love waves admit infinite solutions. If a double-couple source is assumed, the Love wave data may have either one or three equally satisfactory solutions. When only absolute values of surface wave spectra are available, any solution may be rotated 180° in azimuth and/or all the source tensor components may be changed in sign.

The inversion of surface wave data

Observations of surface waves depend both on the structure traversed and the nature of the source, and therefore inversion of surface wave data can yield information about both structure and sources. The available methods for structural inversion are compared and discussed and a suggestion made for improved source inversion.

Partial derivatives of surface wave phase velocity with respect to physical parameter changes within the Earth

By using energy equations, which are equivalent to fundamental equations and boundary conditions in surface wave problems, we can get analytical expressions for partial derivatives of phase velocity with respect to changes of physical parameters within the earth. These derivatives can be calculated by knowing only the eigenfunction corresponding to the phase velocity. Numerical examples are worked out for CANSD (a model proposed by Brune and Dorman for the Canadian shield), the Jeffreys model, and the Gutenberg model for crustmantle structure. An application of the present result to numerical inversion of surface wave data is demonstrated by an example.