Surface Wave Dispersion Data Research Articles

Improving the Uniqueness of Surface Wave Inversion Using Multiple-Mode Dispersion Data

The use of multiple-mode dispersion data in surface wave inversion to derive shear-wave velocity ( vs ) profiles has increased in the past decade as the inclusion of higher mode data can improve the accuracy of the inversion results. However, the error associated with nonuniqueness in the multiple-mode inversion has not been clarified and quantified. This research focuses on the attempt to improve the accuracy of multiple-mode surface wave inversion result by optimizing the use of multiple-mode dispersion data to reduce the error associated with the nonuniqueness in inversion. In this research, an alternative approach was used where inversion of surface wave dispersion data was performed using three distinct modes. Four different vs profiles, representing regular and irregular cases, were used, and multiple-mode dispersion data were synthesized from these profiles using the dynamic stiffness matrix method as the theoretical model. The dispersion data were then inverted using the Levenberg–Marquardt method...

Multi-station joint inversion of receiver function and surface-wave phase velocity data for exploration of deep sedimentary layers

In this study, we propose a joint inversion method, using genetic algorithms, to estimate an S-wave velocity structure for deep sedimentary layers from receiver functions and surface-wave phase velocity observed at several sites. The method takes layer continuity over a target area into consideration by assuming that each layer has uniform physical properties, especially an S-wave velocity, at all the sites in a target area in order to invert datasets acquired at different sites simultaneously. Numerical experiments with synthetic data indicate that the proposed method is effective in reducing uncertainty in deep structure parameters when modelling only surface-wave dispersion data over a limited period range. We then apply the method to receiver functions derived from earthquake records at one site and two datasets of Rayleigh-wave phase velocity obtained from microtremor array surveys performed in central Tokyo, Japan. The estimated subsurface structure is in good agreement with the results of previous seismic refraction surveys and deep borehole data. We also conclude that the proposed method can provide a more accurate and reliable model than individual inversions of either receiver function data only or surface-wave dispersion data only.

Reconciling a geophysical model to data using a Markov chain Monte Carlo algorithm: An application to the Yellow Sea–Korean Peninsula region

In an effort to build seismic models that are the most consistent with multiple data sets we have applied a new probabilistic inverse technique. This method uses a Markov chain Monte Carlo (MCMC) algorithm to sample models from a prior distribution and test them against multiple data types to generate a posterior distribution. While computationally expensive, this approach has several advantages over deterministic models, notably the seamless reconciliation of different data types that constrain the model, the proper handling of both data and model uncertainties, and the ability to easily incorporate a variety of prior information, all in a straightforward, natural fashion. A real advantage of the technique is that it provides a more complete picture of the solution space. By mapping out the posterior probability density function, we can avoid simplistic assumptions about the model space and allow alternative solutions to be identified, compared, and ranked. Here we use this method to determine the crust and upper mantle structure of the Yellow Sea and Korean Peninsula region. The model is parameterized as a series of seven layers in a regular latitude‐longitude grid, each of which is characterized by thickness and seismic parameters (Vp, Vs, and density). We use surface wave dispersion and body wave traveltime data to drive the model. We find that when properly tuned (i.e., the Markov chains have had adequate time to fully sample the model space and the inversion has converged), the technique behaves as expected. The posterior model reflects the prior information at the edge of the model where there is little or no data to constrain adjustments, but the range of acceptable models is significantly reduced in data‐rich regions, producing values of sediment thickness, crustal thickness, and upper mantle velocities consistent with expectations based on knowledge of the regional tectonic setting.

Development of a Velocity Model for Black Mesa, Arizona, and the Southern Colorado Plateau from Multiple Data Sets

During the summer of 2003, a consortium of scientific institutions conducted a set of seismic experiments on Black Mesa, Arizona, in the southern Colorado Plateau to determine the velocity structure and crustal thickness below the mesa. We detonated a series of explosions, which were recorded by 130 near-source, vertical-component sensors and 25 broadband seismometers. The broadband stations, deployed in a linear array to the south of the mesa, also recorded earthquakes at regional and teleseismic distances during the duration of the deployment. Prior to the explosion series, we conducted a shallow refraction study at the site by using 20 three-component geophones. We utilized the multiple data sets recorded by the experiment to develop a new velocity model for Black Mesa. We analyzed the shallow refraction and explosion data to generate P - and S -velocity models for the upper crust. The P velocities ( α ) were determined by examining first-arrival times as a function of distance from the source. In addition, we performed ground-roll and surface-wave studies to develop a shear-wave velocity ( β ) structure for the upper crust. The results indicate an upper-crustal velocity structure that consists of very slow velocity sediments ( α β α and β , respectively. For the deeper-crustal and upper-mantle velocity, we used refraction data from broadband stations and inverted surface-wave dispersion data. We were not able to confidently determine the depth of the Moho, as our results indicate it to be between 37 and 46 km. The velocity model developed for Black Mesa was validated using comparisons between observed and synthetic waveforms and small ground-truth explosion location studies.

Possible effects of misidentified mode number on Rayleigh wave inversion

Surface wave dispersion data obtained in field surveys are inherently incomplete. Poorly constrained dispersion curves and inclusion of data from higher-mode dispersion curves can be shown to produce erroneous inversion results. The present study evaluates the effects of cross-mode data mixing, and limited data and frequency range on inversion models. Multimodal dispersion curves were generated from synthetic velocity profiles using the forward modeling method. Subsets of the data points obtained by sampling the resulting dispersion curves using different sample intervals, frequency ranges, and by mixing fundamental-mode data with portion of the data from the higher-mode dispersion curves were inverted. The inversion results show that small sample intervals over a wide frequency range and an unambiguous identification of the fundamental-mode dispersion curve are essential factors for the reconstruction of accurate inversion models. The penetration range and accuracy of the inversion models are particularly sensitive to phase velocities at low frequencies of the dispersion curve. The theoretical results were tested with data from a roadbed survey in northern China. Ground model obtained from dispersion data derived by using the F-K method, which contained many cross-mode data points, was found to deviate substantially from the borehole record. A better agreement with the geotechnical record was obtained by inverse modeling of the dispersion data obtained from the fundamental-mode curve of the MASW spectral image.

Crustal shear velocity structure of the south Indian shield

The south Indian shield is a collage of Precambrian terrains gathered around and in part derived from the Archean‐age Dharwar craton. We operated seven broadband seismographs on the shield along a N‐S corridor from Nanded (NND) to Bangalore (BGL) and used data from these to determine the seismic characteristics of this part of the shield. Surface wave dispersion and receiver function data from these sites and the Geoscope station at Hyderabad (HYB) give the shear wave velocity structure of the crust along this 600 km long transect. Inversion of Rayleigh wave phase velocity measured along the profile shows that the crust has an average thickness of 35 km and consists of a 3.66 km s−1, 12 km thick layer overlying a 3.81 km s−1, 23 km thick lower crust. At all sites, the receiver functions are extremely simple, indicating that the crust beneath each site is also simple with no significant intracrustal discontinuities. Joint inversion of the receiver function and surface wave phase velocity data shows the seismic characteristics of this part of the Dharwar crust to be remarkably uniform throughout and that it varies within fairly narrow bounds: crustal thickness (35 ± 2 km), average shear wave speed (3.79 ± 0.09 km s−1), and Vp/Vs ratio (1.746 ± 0.014). There is no evidence for a high velocity basal layer in the receiver function crustal images of the central Dharwar craton, suggesting that there is no seismically distinct layer of mafic cumulates overlying the Moho and implying that the base of the Dharwar crust has remained fairly refractory since its cratonization.

Simultaneous measurement and inversion of surface wave dispersion and attenuation curves

Surface wave tests are non-invasive seismic techniques that have traditionally been used to determine the shear wave velocity (i.e. shear modulus) profile of soil deposits and pavement systems. Recently, Rix et al. [J. Geotech. Geoenviron. Engng 126 (2000) 472] developed a procedure to obtain near-surface values of material damping ratio from measurements of the spatial attenuation of Rayleigh waves. To date, however, the shear wave velocity and shear damping ratio profiles have been determined separately. This practice neglects the coupling between surface wave phase velocity and attenuation that arises from material dispersion in dissipative media. This paper presents a procedure to measure and invert surface wave dispersion and attenuation data simultaneously and, thus, account for the close coupling between the two quantities. The methodology also introduces consistency between phase velocity and attenuation measurements by using the same experimental configuration for both. The new approach has been applied at a site in Memphis, TN and the results obtained are compared with independent measurements.

Monte-Carlo inversion for a global shear-velocity model of the crust and upper mantle

SUMMARY We describe a method to invert surface wave dispersion data for a model of shear velocities with uncertainties in the crust and uppermost mantle. The inversion is a multistep process, constrained by a priori information, that culminates in a Markov-chain Monte-Carlo sampling of model space to yield an ensemble of acceptable models at each spatial node. The model is radially anisotropic in the uppermost mantle to an average depth of about 200 km and is isotropic elsewhere. The method is applied on a 2 ◦ × 2 ◦ grid globally to a large data set of fundamental mode surface wave group and phase velocities (Rayleigh group velocity, 16‐200 s; Love group velocity, 16‐150 s; Rayleigh and Love phase velocity, 40‐150 s). The middle of the ensemble (Median Model) defines the estimated model and the half-width of the corridor of models provides the uncertainty estimate. Uncertainty estimates allow the identification of the robust features of the model which, typically, persist only to depths of ∼250 km. We refer to the features that appear in every member of the ensemble of acceptable models as ‘persistent’. Persistent features include sharper images of the variation of oceanic lithosphere and asthenosphere with age, continental roots, extensional tectonic features in the upper mantle, the shallow parts of subducted lithosphere, and improved resolution of radial anisotropy. In particular, we find no compelling evidence for ‘negative anisotropy’ (vsv >v sh) anywhere in the world’s lithosphere.

Constraints on the S wave velocity structure in a continental shield from surface wave data: Comparing linearized least squares inversion and the direct search Neighbourhood Algorithm

In their study of upper mantle structure beneath the Paraná Basin of SE Brazil, Snoke and James [1997] concluded, on the basis of a linearized least squares inversion (LLSI) of surface wave dispersion data, that a strong (5% contrast) low‐velocity zone (LVZ) beginning at a depth less than ∼150 km was not required to fit the data. They were unable to establish a quantitative estimate, however, on the maximum depth at which such a LVZ could be resolved by their data. Sambridge [1999a, 1999b] has introduced the Neighbourhood Algorithm (NA), a direct search method for nonlinear inversion which can be tuned to extract information from an ensemble of models in addition to finding a single best fit model. Applying NA to the Brazilian dispersion data quantifies the statistics of the ensemble of models classified as “acceptable” based on a data misfit criterion and a smoothness constraint. The NA best fit model is not significantly different from the LLSI best fit model, but the analysis of the ensemble of models provides new insights regarding how well constrained the model is. Synthetics runs show that for this data set, our modeling procedures could resolve a strong LVZ that began at a depth of 120 km but could not rule out such an LVZ beginning at a depth of 180 km.

APPLICATION OF A GLOBAL 3D MODEL TO IMPROVE REGIONAL EVENT LOCATIONS

Accurate location of weak seismic events is crucial for monitoring clandestine nuclear tests, for studying local seismic structures, and for assessing possible seismic hazards. Outside of a few regions with dense seismic networks, weak seismic events (with magnitude less than 4) are usually sparsely recorded at epicentral distances less than 20°. Because of lateral variations in crustal and upper mantle structures, observed travel times of seismic phases deviate significantly from predictions based on 1-dimensional (1D) seismic models. Accurately locating weak seismic events remains a difficult task for modern seismology. Perhaps the most promising solution to this problem is the use of a 3-dimensional (3D) model of the Earth. Here we present the results of a validation test in which, using the 3D model SR2002 of the crust and upper mantle and regional phase data alone, we relocate ~ 200 earthquakes and nuclear explosions in Eurasia. The 3D model is constructed using surface wave dispersion data. The event locations using the 3D model are compared with so-called Ground Truth data, either known by non-seismic means or validated by cluster analysis, with location accuracy mostly 5 km or better. Typically, the 3D model reduces the location errors to about half the values attained with the 1D model; i.e., ~ 18 km location errors are reduced to about 9 km. This test indicates that the location of regional events can be significantly improved by using a global 3D model.

An attempt at 3-D imaging of a small domain (Almeria, southern Spain)

When applying a methodology for obtaining the 3-D shear-wave velocity structure of a medium from surface wave dispersion data, the problem must be considered with caution since one inverts path-averaged velocities and the use of any inversion method entails some drawbacks such as lack of uniqueness, unwarranted stability and constraints affecting the data. Several imaging techniques aimed at volumetric modeling and the visualization of data can be used to overcome these drawbacks. Actually, some spatial prediction techniques are especially useful for analyzing short-range variability between scattered points. We use here a pathwise reconstruction by means of an algorithm that, from a mathematical viewpoint, can be understood through the application of the orthogonal projection theorem onto convex sets (POCS). In particular, we are interested in exploring the possibilities of a POCS algorithm operating on a very unfavorable case constrained by a lack of available data. In this paper, we have tackled a small-sized problem and we present the results based on ray-path seismic velocities that we have obtained in the case of a sparsely sampled study area like Almeria (southeastern Spain) by way of tomographic images obtained by application of such an algorithm. The main goal of this procedure is the reconstruction of the very shallow Rg-wave velocity structure of a small domain strongly constrained by the data. The method has allowed us to examine the sharply contrasting geology between neighboring geological formations. Although the relationship between lateral changes in Rg-wave dispersion and geologic structure may not be straightforward, we have observed a correlation between the velocity structure of very shallow soils and the local geology at surface. The good agreement between our results and the field observations prove the versatility of the method and the reliability of the imaging.

Inversion of Rayleigh wave phase and group velocities by simulated annealing

A joint inversion of regionalized phase and group velocities of fundamental mode Rayleigh waves is performed by means of a simulated annealing scheme which makes use of some thermodynamic analogies based on the Gibbs’ distribution. The correlations and the uncertainties on shear-wave velocities defining the elastic model are estimated by using a procedure based on the same thermodynamic analogies. As a relevant feature, the simulated annealing algorithm permits reducing the usual dependence of the solution on the sometimes arbitrary starting model. A shortcoming linked to the use of this procedure for solving an inversion problem is the necessity of a previous empirical determination of some parameters controlling the annealing process. With this aim, a simulation of a joint inversion of synthetic surface wave dispersion data has been performed. After that, path-averaged velocity dispersion curves corresponding to a Hercynian area of the Iberian Peninsula have been inverted to derive two possible crust and upper mantle elastic structures. Whereas, the first structure has been deduced by considering as unknown variables the shear velocities of the stratified Earth model, the second has been obtained also including the respective layer thicknesses. Both structures are compared with shear velocity and Q β models derived by the stochastic inversion procedure in previous studies and from the same Rayleigh waves dataset. Finally, advantages and shortcomings of the inversion of phase and group velocity data by means of simulated annealing are discussed.

Rapid assessment of S-wave profiles from the inversion of multichannel

The importance of detailed knowledge of the shear-wave velocity structure of the upper geological layers was recently stressed in strong motion studies. In this work we describe an algorithm which we have developed to infer the 1D shear wave velocity structure from the inversion of multichannel surface wave dispersion data (ground-roll). Phase velocities are derived from wavenumber-frequency stacks while the inversion process is speeded up by the use of Householder transformations. Using synthetic and experimental data, we examined the applicability of the technique in deducing S-wave profiles. The comparison of the obtained results with those derived from cross-hole measurements and synthesized wave fields proved the reliability of the technique for the rapid assessment of shear wave profiles during microzonation investigations.

A proper methodology aimed at surface wave tomography

When applying a methodology for obtaining the 3D shear-wave velocity structure of a medium from surface wave dispersion data, the problem must be considered with caution since one inverts path-averaged velocities and the use of any inversion method entails some drawbacks such as lack of uniqueness, unwarranted stability and constraints affecting the data. In order to avoid the application of consecutive inversions and to overcome these drawbacks, we propose alternative mapping methods, for example spatial prediction methods, or else the use of an algorithm that, from a mathematical viewpoint, can be understood through the application of the orthogonal projection theorem onto convex sets (POCS). Among the first ones, we try inverse weighted distance interpolation. The POCS algorithm we have used discretises a second order differential equation for the velocity field with boundary conditions. All these imaging techniques aimed at volumetric modelling and the visualisation of data are discussed, and finally we show some results based on ray path velocities obtained previously by inversion of phase and group velocities of Rayleigh waves propagating across the Iberian peninsula.

Constraints for upper mantle shear-wave models of the basin and range from surface-wave inversion

Abstract Several earthquakes in a limited region on the coast of Northern California and off the coast of Oregon have provided a set of broadband regional seismograms at Lajitas (LTX). The significant Love and Rayleigh waves contained in these waveforms have repetitively sampled the same source-receiver path within the Basin and Range province. Previous studies for this path (using a subset of these sources) of mantle S waves suggest a smoothly varying S velocity structure above 400 km followed by a strong gradient between 400 and 700 km. These data are unable to uniquely constrain the shear velocity at shallower depths. Surface-wave inversions are performed in order to refine the upper mantle S-wave model using group- and phase-velocity dispersion for periods between 10 and 100 sec. This period range gives good resolution for sub-Moho depths extending into the low-velocity zone. Group velocities are extracted by multiple filter analysis and show significant differences for events on- and off-shore at periods around 50 sec. This effect can be shown to be an interference pattern with the mantle S body-wave arrivals. As single-station data were used, phase velocities are estimated by phase-matched filtering. The recovered surface-wave dispersion data are used in an inversion procedure to recover a shear-wave structure for the Basin and Range path to LTX that consists of a relatively thin mantle lid underlain by a low-velocity channel extending to a depth of 200 km. Structure below 200 km is poorly resolved and trades off with shallower structure. The Rayleigh-wave group-velocity data favor shear-velocity models with a ridge within the low-velocity zone with velocities 0.05 to 0.2 km/sec higher than the background.

Application of genetic algorithms to an inversion of surface-wave dispersion data

Abstract A new method for inversion of surface-wave dispersion data is introduced. This method successfully utilizes recently developed genetic algorithms as a global optimization method. Such algorithms usually consist of selection, crossover, and mutation of individuals in a population. To facilitate convergence to an optimal solution, we added elite selection, which ensures that the “best” individual with the smallest misfit value is not excluded from the succeeding generation, and dynamic mutation, which contains a generation-variant mutation probability. Using synthetic and observed earthquake data, we examined the applicability of this genetic surface-wave inversion method in deducing an S-wave profile for sedimentary layers from short- and intermediate-period surface-wave dispersion data. We demonstrated that the method is robust and can be used to interpret surface-wave dispersion data.

Resolving a low-velocity zone with surface-wave data

SUMMARY The main purpose of seismic inversion is the retrieval of seismic velocities and densities in the earth. Inversion of body-wave traveltimes cannot uniquely determine the seismic velocities as a function of depth when a low-velocity layer is present. It is generally assumed that surface waves do not suffer from the same non-uniqueness. The issue is addressed whether it is possible to remove the non-uniqueness of traveltime inversions with a realistic set of surface-wave data. This requires the exact determination of the velocity distribution within and around the low-velocity zone. Waveforms, phase velocities as well as group velocities are investigated qualitatively. Synthetic Love-wave phase and group velocities are actually inverted. Waveforms are shown to be sensitive to the exact velocity distribution of a low-velocity layer, but it is concluded that the removal of the non-uniqueness with the use of waveforms is difficult because the differences of the waveforms are generally small and because complications such as lateral heterogeneity and poorly known source parameters reduce the accuracy of waveform inversions. The inversions of Love phase and group velocities indicate that it is difficult to determine the velocity distribution of a low-velocity layer in a statistically significant way with a realistic set of dispersion data. Group velocities are shown to be more sensitive to the low-velocity structure than phase velocities. Unfortunately, group-velocity data suffers from a practical non-uniqueness because in general only fundamental-mode group velocities can be measured. It is concluded that the non-uniqueness in the detailed structure caused by a low-velocity layer cannot readily be resolved by using surface-wave dispersion data.

Short-period surface-wave dispersion and shallow crustal structure of central and eastern Tennessee

AbstractGroup velocity dispersion of explosion-generated seismic surface waves with periods ranging from 0.2 to 1.5 sec is used to investigate shallow crustal structure of eastern and central Tennessee. Several modes of both Rayleigh and Love waves can be identified and separated on the seismograms of seven SARSN regional network stations by zero-phase digital filtering. Dispersion data for sinusoidal wave motion were based on digitized zero-crossing times.By forward modeling, we find that a wave guide of at least two layers over a half-space can adequately represent our particular multi-mode, narrow-band observations. In a layered section about 3 km thick, lower velocities characterize outcropping clastic rocks of the Cumberland plateau, and higher velocities correspond to shallow carbonate rocks of the Nashville Dome. Half-space shear velocities of about 3.9 km/sec appear to represent lower Paleozoic carbonate lithology deeper than 2 to 4 km on most of the observed paths.Our best data, interpreted jointly with earlier data of Oliver and Ewing (1958) and of Chen et al. (1989), have a composite period range of 0.2 to 40 sec, but they represent different Appalachian paths. Group velocities over this broad spectrum are satisfied by a complex model with two low-velocity layers. The uniqueness of this model cannot be demonstrated, but it represents important hypotheses concerning regional geologic features that can be tested more rigorously by improved surface-wave dispersion data.

Crustal and upper mantle structure of the Mediterranean area derived from surface-wave data

Abstract A summary of results based mainly on the inversion of available surface-wave dispersion data is given for the Mediterranean area both for crustal and upper mantle structure. The results are presented on maps outlining the regionalization of the crust and the lithosphere-asthenosphere system in the area. It is possible to distinguish several types of crust with average S-wave velocities in the range 2.8–3.8 km s −1 and thickness varying from a minimum of about 10–16 km, in the Western Mediterranean, to a maximum of about 50 km (including a possible transitional layer) beneath the Ionian Sea. The average properties of the crust and of the lithospheric part of the mantle indicate a possible continuous structure extending from North Africa through the Ionian Sea to the Adriatic Sea, characterized by the presence of a transitional layer at the crust-mantle boundary. Strong lateral variations are present in the lithosphere-asthenosphere system both in thickness, from 30 km in the Western Mediterranean, to about 130 km, under the Alps, and in S-wave velocity, from 4.1–4.2 km s −1 up to 4.7 km s −1 . The relatively high position of low resistivity material that seems to characterize the Mediterranean area agrees fairly well with the shallower average top of the asthenosphere found in this area from the study of the elastic properties. The usefulness of combining seismological and electromagnetic studies is stressed.

Crustal structure in the southern Bering Shelf and the Alaska Peninsula from inversion of surface-wave dispersion data

AbstractDispersion of surface waves in the southern Bering Shelf (Bristol Bay) and the Alaska Peninsula is investigated for a study of the regional crustal structure. Our data consist of five shallow earthquakes located along the Aleutian Arc and recorded by long-period, three-component seismographs sited in south-central Alaska. Both Love and Rayleigh group velocities are obtained through the application of the phase-matched filtering technique. The results are converted to equivalent pure-path data by appropriate adjustment using the published information for the continental Alaska.Treating the shear velocity of each layer as an independent parameter, the pure-path group velocities of Love and Rayleigh waves are jointly inverted in order to obtain a satisfactory agreement between the theoretical and the observed dispersion characteristics. Estimates of the resolving power of the inversion and uncertainty of the final velocity structure show substantial improvement over the previously published models.With their crustal thicknesses ranging between 33 and 36 km, none of the final models displays structural characteristics reminiscent of an oceanic crust. Over the northernmost path across the Bristol Bay, we found an indication of a weak low-velocity zone (five per cent reduction relative to the lid velocity) whose prominence diminishes towards the south.