Non-uniqueness in surface-wave inversion and consequences on seismic site response analyses

Surface-wave tests are based on the solution of an inverse problem for shear-wave velocity profile identification from the experimentally measured dispersion curve. The main criticisms for these testing methodologies are related to the inverse problem solution and arise from the possible equivalence of different shear-wave velocity profiles. In this paper, some implications of solution non-uniqueness for seismic response studies are investigated using both numerical simulations and experimental data. A Monte Carlo approach for the inversion problem has been used to obtain a set of equivalent shear-wave velocity models. This selection is based on a statistical test which takes into account both data uncertainty and model parameterization. This set of solutions (i.e., soil profiles) is then used to evaluate the seismic response with a conventional one-dimensional analysis. It is shown that equivalent profiles with respect to surface-wave testing are equivalent also with respect to site amplification, thus countering the criticism related to inversion uncertainty for the engineering use of surface-wave tests.     

Tomography and velocity structure of the crust and uppermost mantle in southeastern Europe obtained from surface wave analysis

A set of two hundred shear-wave velocity models of the crust and uppermost mantle in southeast Europe is determined by application of a sequence of methods for surface-waves analysis. Group velocities for about 350 paths have been obtained after analysis of more than 600 broadband waveform records. Two-dimensional surface-wave tomography is applied to the group-velocity measurements at selected periods and after regionalisation, two sets of local dispersion curves (for Rayleigh and Love waves) are constructed in the period range 8–40 s. The shear-wave velocity models are derived by applying non-linear iterative inversion of local dispersion curves for grid cells predetermined by the resolving power of data. The period range of observations limits the velocity models to depths of 70 km in accordance to the penetration of the surface waves with a maximum period of 40 s. Maps of the Moho boundary depth, velocity distribution above and below Moho boundary, as well as velocity distribution at different depths are constructed. Well-known geomorphologic units (e.g. the Pannonian basin, southeastern Carpathians, Dinarides, Hellenides, Rodophean massif, Aegean Sea, western Turkey) are delineated in the obtained models. Specific patterns in the velocity models characterise the southeast Carpathians and adjacent areas, coast of Albania, Adriatic coast of southern Italy and the southern coast of the Black Sea. The models obtained in this study for the western Black Sea basin shows the presence of layers with shear-wave velocities of 3.5 km/s–3.7 km/s in the crust and thus do not support the hypothesis of existence of oceanic structure in this region.     

Application of passive source surface-wave method in site engineering seismic survey

Site engineering seismic survey provides basic data for seismic effect analysis. As an important parameter of soil, shear-wave velocity is usually obtained through wave velocity testing in borehole. In this paper, the passive source surface-wave method is introduced into the site engineering seismic survey and practically applied in an engineering site of Shijingshan District. By recording the ubiquitous weak vibration on the earth surface, extract the dispersion curve from the surface-wave components using the SPAC method and obtain the shear-wave velocity structure from inversion. Over the depth of 42 m underground, it totally consists of five layers with interface depth of 3.31, 4.50, 7.23, 17.41, and 42.00 m; and shear-wave velocity of 144.0, 198.3, 339.4, 744.2, and 903.7 m/s, respectively. The inversion result is used to evaluate site classification, determine the maximum shear modulus of soil, provide basis for further seismic hazard analysis and site assessment or site zoning, etc. The result shows that the passive source surface-wave method is feasible in the site engineering seismic survey and can replace boreholes, shorten survey period, and reduce engineering cost to some extent.     

地脉动空间自相关方法反演 浅层S波速度结构

在近地表地球物理领域, 基于地脉动(或称背景噪声)提取的面波频散曲线反演地下S波速度结构是一种简单经济的工程勘察方法. 本文基于地脉动的空间自相关方法对一个微型台阵观测的背景噪声记录进行处理, 介绍了一种简单易行的提取频散曲线的数据处理方法, 获得了6.7—23 Hz频段的可靠频散曲线; 通过对该观测频散曲线与预测模型的频散曲线进行拟合, 反演得到S波速度结构. 结果表明, 该速度结构与钻孔直接测试的结果相吻合.      

Application of the Spatial Auto-Correlation Method for Shear-Wave Velocity Studies Using Ambient Noise

Ambient seismic noise or microtremor observations used in spatial auto-correlation (SPAC) array methods consist of a wide frequency range of surface waves from the frequency of about 0.1 Hz to several tens of Hz. The wavelengths (and hence depth sensitivity of such surface waves) allow determination of the site S-wave velocity model from a depth of 1 or 2 m down to a maximum of several kilometres; it is a passive seismic method using only ambient noise as the energy source. Application usually uses a 2D seismic array with a small number of seismometers (generally between 2 and 15) to estimate the phase velocity dispersion curve and hence the S-wave velocity depth profile for the site. A large number of methods have been proposed and used to estimate the dispersion curve; SPAC is the one of the oldest and the most commonly used methods due to its versatility and minimal instrumentation requirements. We show that direct fitting of observed and model SPAC spectra generally gives a superior bandwidth of useable data than does the more common approach of inversion after the intermediate step of constructing an observed dispersion curve. Current case histories demonstrate the method with a range of array types including two-station arrays, L-shaped multi-station arrays, triangular and circular arrays. Array sizes from a few metres to several-km in diameter have been successfully deployed in sites ranging from downtown urban settings to rural and remote desert sites. A fundamental requirement of the method is the ability to average wave propagation over a range of azimuths; this can be achieved with either or both of the wave sources being widely distributed in azimuth, and the use of a 2D array sampling the wave field over a range of azimuths. Several variants of the method extend its applicability to under-sampled data from sparse arrays, the complexity of multiple-mode propagation of energy, and the problem of precise estimation where array geometry departs from an ideal regular array. We find that sparse nested triangular arrays are generally sufficient, and the use of high-density circular arrays is unlikely to be cost-effective in routine applications. We recommend that passive seismic arrays should be the method of first choice when characterizing average S-wave velocity to a depth of 30 m (V_s30) and deeper, with active seismic methods such as multichannel analysis of surface waves (MASW) being a complementary method for use if and when conditions so require. The use of computer inversion methodology allows estimation of not only the S-wave velocity profile but also parameter uncertainties in terms of layer thickness and velocity. The coupling of SPAC methods with horizontal/vertical particle motion spectral ratio analysis generally allows use of lower frequency data, with consequent resolution of deeper layers than is possible with SPAC alone. Considering its non-invasive methodology, logistical flexibility, simplicity, applicability, and stability, the SPAC method and its various modified extensions will play an increasingly important role in site effect evaluation. The paper summarizes the fundamental theory of the SPAC method, reviews recent developments, and offers recommendations for future blind studies.     

Probabilistic inversion of Rayleigh-wave dispersion data: an application to Mt. Etna, Italy

We present a methodology for determining the elastic properties of the shallow crust from inversion of surface wave dispersion characteristics through a fully nonlinear procedure. Using volcanic tremor data recorded by a small-aperture seismic array on Mount Etna, we measured the surface waves dispersion curves with the multiple signal classification technique. The large number of measurements allows the determination of an a priori probability density function without the need of making any assumption about the uncertainties on the observations. Using this information, we successively conducted the inversion of phase velocities using a probabilistic approach. Using a wave-number integration method, we calculated the predicted dispersion function for thousands of 1-D models through a systematic grid search investigation of shear-wave velocities in individual layers. We joined this set of theoretical dispersion curves to the experimental probability density function (PDF), thus obtaining the desired structural model in terms of an a posteriori PDF of model parameters. This process allowed the representation of the objective function, showing the non-uniqueness of the solutions and providing a quantitative view of the uncertainties associated with the estimation of each parameter. We then compared the solution with the surface wave group velocities derived from diffuse noise Green’s functions calculated at pairs of widely spaced (~5–10 km) stations. In their gross features, results from the two different approaches are comparable, and are in turn consistent with the models presented in several earlier studies.     

Site response in Tecoman,Colima, Mexico—II. Determination of subsoil structure and comparison with observations

In a companion paper local transfer functions were estimated at Tecoman using earthquake and microtremor data. In this paper, the subsoil structure at this city is investigated using seismic refraction and cross-correlation of noise records as a case study. P- and S-wave refraction profiles were measured at five sites within the city. Standard analysis constrained only very shallow layers. The P-wave refraction deployment was also used to record ambient vibration. These data were processed using an extension of the SPAC (SPatial AutoCorrelation (Aki, 1957) [1]) method; cross-correlation is computed between station pairs and the results are inverted to obtain a phase velocity dispersion curve. Penetration depth was larger than that from the refraction experiments but the shear-wave velocity of the basement could not be determined. For this reason, additional microtremor measurements were made using broad band seismometers with a larger spacing between stations. The results allowed to constrain the shear-wave velocity of the basement. Site amplification computed for the final profiles compare well with observed ground motion amplification at Tecoman. The case of Tecoman illustrates that even a simple subsoil structure may require crossing data from different experiments to correctly constrain site effects.     

From surface wave inversion to seismic site response prediction: Beyond the 1D approach

Surface wave methods consist of the extraction and inversion of the Rayleigh wave phase-velocity dispersion curve to recover the (usually 1D) shear-wave velocity profile. In the literature, uncertainty due to data error has not received much attention, but the discussion about uncertainty due to model error is even poorer. Even with an unrealistic noise-free dataset and an exact forward model, an inappropriate parameterization can generate solutions very far from the actual soil structure. In general, the model used for the dispersion curve interpretation is 1D. Hence, when the velocity distribution is laterally heterogeneous, model errors can have significant consequences on the reliability of the resulting shear-wave velocity distribution. From a poor velocity reconstruction, an unsatisfactory, and often dangerous site response analysis follows. In fact, shear wave measurements play a relevant role in seismic ground motion amplification estimation. In this paper, we discuss the possibility of processing the seismograms using a multi-offset phase analysis (MOPA), in order to derive soil elastic parameters for weak motion predictions. This technique allows the detection and location of the lateral discontinuities, and a better model parameterization. In fact, once the discontinuities are identified, we can split the profile into several, truly 1D, parts. The use of the standard 1D dispersion curve extraction and inversion for each side of the heterogeneity generates velocity profiles that we can put side by side to get correct 2D reconstructions of the shear-wave distributions. From 2D velocity reconstruction, we can calculate the site response that may be significantly different from the site response generated from a traditional 1D analysis of the same seismograms. In this work, we discuss the site responses of two synthetic examples with lateral heterogeneities. We show how misleading a 1D analysis may be if applied to a truly 2D velocity distribution, particularly in terms of site response prediction.     

3D soil structure of the Mygdonian basin for site response analysis

The 3D structure of the Mygdonian sedimentary basin (N. Greece) is investigated. The aim of this study is to propose a 3D model of this sedimentary structure that can later be used to model the seismic records currently being obtained by the permanent accelerograph network operating in the area. This model builds on previous efforts and incorporates new data. The geometry and dynamic properties of the soil layers were inverted using data from microtremor array measurements, seismic refraction profiles, boreholes, and geotechnical investigations. Phase-velocity dispersion curves of Rayleigh waves were determined at 27 sites in the basin using the spatial autocorrelation method (SPAC) introduced by Aki [1]. S-wave velocity profiles were inverted from these dispersion curves and the whole valley structure was interpolated using our new results and all previously available data. The proposed 3D model describes the geometry and shear-wave velocities of the Mygdonian and pre-Mygdonian sedimentary systems, and the top bedrock surface. Our results indicate that this 3D model correctly reflects the geometry and dynamic properties of the sedimentary layers. The case of Euroseistest, where the subsoil structure is the result of bringing together many disparate data, could be used as an example for similar alluvial basins throughout the world, where usually only scarce data is available.     

Shallow Seismic Velocity Structure of the Betic Cordillera (Southern Spain) from Modelling of Rayleigh Wave Dispersion

A detailed dispersion analysis of Rayleigh waves generated by local earthquakes and occasionally by blasts that occurred in southern Spain, was undertaken to obtain the shear-wave velocity structure of the region at shallow depth. Our database includes seismograms generated by 35 seismic events that were recorded by 15 single-component short-period stations from 1990 to 1995. All these events have focal depths less than 10 km and body-wave magnitudes between 3.0 and 4.0, and they were all recorded at distances between 40 and 300 km from the epicentre. We analysed a total of 90 source-station Rayleigh-wave paths. The collected data were processed by standard digital filtering techniques to obtain Rayleigh-wave group-velocity dispersion measurements. The path-averaged group velocities vary from 1.12 to 2.25 km/s within the 1.0-6.0 s period interval. Then, using a stochastic inversion approach we obtained 1-D shear-wave velocity–depth models across the study area, which were resolved to a depth of circa 5 km. The inverted shear-wave velocities range approximately between 1.0 and 3.8 km/s with a standard deviation range of 0.05–0.16 km/s, and show significant variations from region to region. These results were combined to produce 3-D images via volumetric modelling and data visualization. We present images that show different shear velocity patterns for the Betic Cordillera. Looking at the velocity distribution at various depths and at vertical sections, we discuss of the study area in terms of subsurface structure and S-wave velocity distribution (low velocity channels, basement depth, etc.) at very shallow depths (0–5 km). Our results characterize the region sufficiently and lead to a correlation of shear-wave velocity with the different geological units features.     

Addressing non-uniqueness in linearized multichannel surface wave inversion

The multichannel analysis of the surface waves method is based on the inversion of observed Rayleigh-wave phase-velocity dispersion curves to estimate the shear-wave velocity profile of the site under investigation. This inverse problem is nonlinear and it is often solved using 'local' or linearized inversion strategies. Among linearized inversion algorithms, least-squares methods are widely used in research and prevailing in commercial software; the main drawback of this class of methods is their limited capability to explore the model parameter space. The possibility for the estimated solution to be trapped in local minima of the objective function strongly depends on the degree of nonuniqueness of the problem, which can be reduced by an adequate model parameterization and/or imposing constraints on the solution.
In this article, a linearized algorithm based on inequality constraints is introduced for the inversion of observed dispersion curves; this provides a flexible way to insert a priori information as well as physical constraints into the inversion process. As linearized inversion methods are strongly dependent on the choice of the initial model and on the accuracy of partial derivative calculations, these factors are carefully reviewed. Attention is also focused on the appraisal of the inverted solution, using resolution analysis and uncertainty estimation together with a posteriori effective-velocity modelling. Efficiency and stability of the proposed approach are demonstrated using both synthetic and real data; in the latter case, cross-hole S-wave velocity measurements are blind-compared with the results of the inversion process.     

Inversion of SASW dispersion curves based on maximum flexibility coefficients in the wave number domain

Spectral analysis of surface waves (SASW) is a nondestructive in-situ testing method that is used to determine stiffness profiles of soil and pavement sites based on dispersion characteristics of Rayleigh-type surface waves.Inversion of the Rayleigh wave dispersion curve of a site provides information on the variation of shear-wave velocity with depth. In the inversion procedures currently used for SASW tests, the field dispersion curve is matched with a theoretical dispersion curve obtained for the fundamental mode of surface wave propagation.In order to overcome difficulties associated with the presence of multi-modes in SASW signals, a new inversion method based on the maximum vertical flexibility coefficient is introduced in this paper. Unlike root-searching methods, the new method easily identifies the predominant propagation modes. In this new approach, the simplex method is used to match field and theoretical dispersion curves automatically. The purpose of this paper is to present the details of the new method and to demonstrate its advantages.     

Crustal structure of northern Egypt from joint inversion of receiver functions and surface wave dispersion velocities

In this study, we used a combined inversion of body wave receiver functions and surface wave dispersion measurements to provide constraints on the crustal structure of northern Egypt. The two techniques are complementary to each other: receiver functions (RFs) are sensitive to shear-wave velocity contrasts, while surface wave dispersion (SWD) measurements are sensitive to finite variations of shear-wave velocity with depth. A database of 122 teleseismic events digitally recorded by the Egyptian National Seismological Network (ENSN) stations has been used as well. To enhance the resulting RFs at each ENSN station, the H-k stacking method was applied. A joint inversion process between the resulting receiver functions and the surface wave dispersion curves was applied as well. We have produced three averaged velocity structure models for distinct geographic and tectonic provinces namely Sinai, eastern desert, and western desert from east to the west respectively. These models will deeply help in estimation the epicenter distance of earthquake, focal mechanism solutions, and earthquake hazard analysis in northern Egypt. An obvious image of the subsurface structure has been determined which shows that generally the crustal structure of northern Egypt consists of three layers covered with a sequence of sediments that differs in thickness from across the region except in the Sharm area where the sedimentary cover is absent. The obtained results indicate that crustal thickness differs from east to west and reaches its maximum value of about 36 km at Siwa station (SWA) in the western desert and its minimum value of about 28 km at Sharm station (SHR) of the southern tip of the Sinai Peninsula. The Vp/Vs ratio varies between 1.71 and 2.07 in northern Egypt. Generally, the high values (1.93) of (Vp/Vs) at SWA station may reflect the well-known rich aquifer with fully saturated sediments of the Swia Oasis in the Western Desert. Moreover, the highest value (2.07) of (Vp/Vs) at BNS station may be attributed to the widespread recently discovered hydrocarbon fields at the Beni-Suef Basin along the Eastern Desert. Finally, an integrated geophysical and hydrological study of the dimensions and physical properties of the aquifer and hydrocarbon fields at SWA and BNS stations to confirm if they are sufficient to produce the elevated Vp/Vs ratios or not become essential and highly recommended.     

Shear-wave velocity estimation using a combination of ambient noise from small aperture array and small-scale active seismic measurements: a case study in the area of the natural gas fields of Northern Germany

In recent years, numerous induced seismic events have occurred in the proximity of the natural gas field in Northern Germany. To monitor the seismicity and to asses the seismic hazard potential, a local monitoring network was installed in the area. Focusing on the seismicity hazard assessment, a major challenge is the characterisation of potential site effects due to local soil characteristics. This is quantitatively performed by estimating the shear-wave velocity (V _s) variation with subsurface layer thickness. Such local effects can only be covered with a coarse spatial resolution due to the limited number of monitoring stations. Profiles were determined at three test sites (Langwedel, Walle and Bomlitz) by using a combined approach of small aperture 2D array ambient noise and small-scale active 1D measurements. The high-resolution frequency-wavenumber (HRFK), spatial autocorrelation (SPAC) and multichannel analysis of surface waves (MASW) methods were applied to the recorded ambient noise and active seismic data using various array sizes supplemented by the active measurements. This jointly allowed obtaining phase velocity dispersion curves covering a wide frequency range from 2 up to 32 Hz. The inversion of the obtained dispersion curves results in average S-wave velocity profiles down to depths of 70 m, identifying thin near-surface layers of a few meters as well as thicker layers of tens of meters in greater depth. A comparison with available borehole data shows a good correlation with the layering. Additionally, to asses the impact of a seismic event at the test sites, PGV estimations for various seismic events were performed. The final results of the test surveys demonstrate that the combined approach represents a suitable tool for near-surface characterisation, which can be used to improve the seismic hazard assessment in the area of the natural gas fields in Northern Germany.     

Shear-wave Velocity Structure around Teide Volcano: Results Using Microtremors with the SPAC Method and Implications for Interpretation of Geodetic Results

Deformation analysis and simulation of volcanic edifices require the construction of models of elastic properties of those structures. In this paper we present an analysis of microtremor measurements recorded during the performance tests of two temporary seismic arrays installed in the eastern portion of the Teide caldera in 1994. We take advantage of recent developments of the SPAC method and use spatial cross-correlation computations to estimate phase velocity dispersion of Rayleigh waves at the location of the arrays. We show that the extension of the standard SPAC method is valid in the case of our data, justifying its use and supporting the generalization of the SPAC method to single station pairs. The phase velocity dispersion curve obtained was inverted to recover the shear-wave profile at the site of the arrays. Our results indicate that the subsoil structure of the caldera is laterally homogeneous at the scale of a few km about the location of the arrays. We obtained about 315 m of volcanic sediments overlying rocks with a shear-wave velocity of 2 km/s. These results are robust and are a starting point to further modelling of deformation, permanent or transient, at this volcanic edifice, which can be useful in the interpretation of different observed fields. In fact, the computation of deformations and gravity changes due to possible volcanic intrusions in two models; one considering the volcanic sediments and the other without considering them, provided different results in the near field.     

Subsoil structure and site effects: A comparison between results from SPAC and HVSR in sites of complex geology

We present the results of the analysis of array recorded microtremors at 14 sites, close to the edges of the Mygdonian basin in northern Greece (Euroseistest). These measurements were made in order to better constrain the geometry and velocity structure of the basin as the soil layers taper out close to rock outcrop, where geology is complex and we may expect significant changes of the subsoil structure over short distances. The data were analysed using the SPAC method and HVSR. The first interprets the measurements as Rayleigh waves (for the vertical component we analysed) and allows to invert a phase velocity dispersion curve from computed correlation coefficients. The second estimates a local transfer function directly, from ratios of Fourier amplitude spectra. A phase velocity dispersion curve could be derived for 12 of the 14 measurement sites, and at three of the sites no resonant frequency was observed in the HVSR. It is encouraging that we obtained good results at most of our sites, in spite of the lateral heterogeneity expected close to the edges of Euroseistest. Our results allow us to obtain shear wave velocity models at most of the measurement sites (12 out of 14). They are also useful to explore the relation between size of the array and wavelength range for which a dispersion curve may be estimated, which in our case has strong limitations. We identify the frequency of resonance of the sediments as a small loss of coherency in SPAC’s correlation coefficients. Finally, we also consider the applicability of the joint inversion of the resonance frequency determined using HVSR and the phase velocity dispersion curve obtained from SPAC.     

Measurement of shallow shear wave velocities at a rock site using the ReMi technique

Shallow shear wave velocities beneath a rock site are characterized using the refraction microtremor (ReMi) technique developed by Louie [Faster, better: shear-wave velocity to 100 m depth from ReMi arrays. Bull Seism Soc Am 2001; 91: 347–64]. Ground motion from a passing train enabled capture of energy propagating parallel to the recording array. This allowed evaluation of the variation of the minimum phase-velocity of the dispersion curve envelope and better estimation of the true minimum velocity beneath the site. We use a new method to image and evaluate the dispersion curve envelope via power–slowness profiles through the slowness–frequency plots introduced by Louie [Faster, better: shear-wave velocity to 100 m depth from ReMi arrays. Bull Seism Soc Am 2001; 91: 347–64]. Data illustrated the frequency dependency of dispersion curve uncertainties, with greater uncertainty occurring at low frequencies. These uncertainties map directly into uncertainty of the inverted velocity–depth profile. Above 100 m depth velocities are well constrained with 10% variability. Variability is greatly reduced when the energy propagation is along the geophone array. Greater velocity variation is observed below 100 m depth.     

Advantages of Using Multichannel Analysis of Love Waves (MALW) to Estimate Near-Surface Shear-Wave Velocity

As theory dictates, for a series of horizontal layers, a pure, plane, horizontally polarized shear (SH) wave refracts and reflects only SH waves and does not undergo wave-type conversion as do incident P or Sv waves. This is one reason the shallow SH-wave refraction method is popular. SH-wave refraction method usually works well defining near-surface shear-wave velocities. Only first arrival information is used in the SH-wave refraction method. Most SH-wave data contain a strong component of Love-wave energy. Love waves are surface waves that are formed from the constructive interference of multiple reflections of SH waves in the shallow subsurface. Unlike Rayleigh waves, the dispersive nature of Love waves is independent of P-wave velocity. Love-wave phase velocities of a layered earth model are a function of frequency and three groups of earth properties: SH-wave velocity, density, and thickness of layers. In theory, a fewer parameters make the inversion of Love waves more stable and reduce the degree of nonuniqueness. Approximating SH-wave velocity using Love-wave inversion for near-surface applications may become more appealing than Rayleigh-wave inversion because it possesses the following three advantages. (1) Numerical modeling results suggest the independence of P-wave velocity makes Love-wave dispersion curves simpler than Rayleigh waves. A complication of “Mode kissing” is an undesired and frequently occurring phenomenon in Rayleigh-wave analysis that causes mode misidentification. This phenomenon is less common in dispersion images of Love-wave energy. (2) Real-world examples demonstrated that dispersion images of Love-wave energy have a higher signal-to-noise ratio and more focus than those generated from Rayleigh waves. This advantage is related to the long geophone spreads commonly used for SH-wave refraction surveys, images of Love-wave energy from longer offsets are much cleaner and sharper than for closer offsets, which makes picking phase velocities of Love waves easier and more accurate. (3) Real-world examples demonstrated that inversion of Love-wave dispersion curves is less dependent on initial models and more stable than Rayleigh waves. This is due to Love-wave’s independence of P-wave velocity, which results in fewer unknowns in the MALW method compared to inversion methods of Rayleigh waves. This characteristic not only makes Love-wave dispersion curves simpler but also reduces the degree of nonuniqueness leading to more stable inversion of Love-wave dispersion curves.     

Anisotropy in the Earth's crust and uppermost mantle in southeastern Europe obtained from Rayleigh and Love surface waves

Digital seismograms from 25 earthquakes located in the southeastern part of Europe, recorded by three-component very broadband seismometers at the stations Vitosha (Bulgaria) and Muntele Rosu (Romania), were processed to obtain the dispersion properties of Rayleigh and Love surface waves. Rayleigh and Love group-velocity dispersion curves were obtained by frequency–time analysis (FTAN). The path-averaged shear-wave velocity models were computed from the obtained dispersion curves. The inversion of the dispersion curves was performed using an approach based on the Backus–Gilbert inversion method. Finally, 70 path-averaged velocity models (35 R-models computed from Rayleigh dispersion curves and 35 L-models computed from Love dispersion curves) were obtained for southeastern Europe. For most of the paths, the comparison between each pair of models (R-model and L-models for the same path) shows that for almost all layers the shear-wave velocities in the L-models are higher than in the R-models. The upper sedimentary layers are the only exception. The analysis of both models shows that the depth of the Moho boundary in the L-models is shallower than its depth in the R-models. The existence of an anisotropic layer associated with the Moho boundary at depths of 30–45 km may explain this phenomenon. The anisotropy coefficient was calculated as the relative velocity difference between both R- and L-models at the same depths. The value of this coefficient varies between 0% and 20%. Generally, the anisotropy of the medium caused by the polarization anisotropy is up to 10–12%, so the maximum observed discrepancies between both types of models are also due to the lateral heterogeneity of the shear-wave velocity structure of the crust and the upper mantle in the region.     

Site response implications associated with using non-unique Vs profiles from surface wave inversion in comparison with other commonly used methods of accounting for Vs uncertainty

This paper discusses variability and accuracy of site response predictions performed using shear wave velocity (Vs) profiles derived from non-unique surface wave inversions and other commonly used statistical methods of accounting for epistemic uncertainty and aleatory variability in Vs. Specifically, linear and equivalent linear site response analyses were performed on the following three classes of Vs profiles: (1) 350 Vs profiles developed by performing multiple surface wave inversions, each with a unique set of layering parameters, on a common dispersion dataset, (2) two upper/lower range base-case Vs profiles developed by systematically increasing or decreasing the solution Vs profile by 20%, and (3) 100 Vs profiles developed using the Vs randomization procedure proposed by Toro (1995) [26]. Vs profiles derived from surface wave inversions generally yielded accurate site response estimates with minimal variability, so long as their theoretical dispersion data fit the experimental dispersion data well. On the other hand, the upper/lower range and randomized Vs profiles generally produced inaccurate and highly variable site response predictions, although the inclusion of site-specific parameters in the randomization model improved the results. At real sites where substantial aleatory variability is anticipated and/or the epistemic uncertainty is quite high, the site response estimates associated with the randomized and/or upper/lower range Vs profiles may be deemed acceptable. However, if the experimental dispersion data and horizontal-to-vertical spectral ratios are shown to be consistent over the footprint of a site, it may be possible to significantly reduce the uncertainty associated with the input Vs profile and the resulting uncertainty in the site response.