Marc Wathelet

Surface-wave inversion using a direct search algorithm and its application to ambient vibration measurements

Passive recordings of seismic noise are increasingly used in earthquake engineering to measure in situ the shear-wave velocity profile at a given site. Ambient vibrations, which are assumed to be mainly composed of surface waves, can be used to determine the Rayleigh-wave dispersion curve, with the advantage of not requiring artificial sources. Due to the data uncertainties and the non-linearity of the problem itself, the solution of the dispersion-curve inversion is generally non-unique. Stochastic search methods such as the neighbourhood algorithm allow searches for minima of them is fit function by investigating the whole parameter space. Due to the limited number of parameters in surface-wave inversion, they constitute an attractive alternative to linearized methods. An efficient tool using the neighbourhood algorithm was developed to invert the one-dimensional V s profile from passive or active source experiments. As the number of generated models is usually high in stochastic techniques, special attention was paid to the optimization of the forward computations. Also, the possibility of inserting a priori information into the parametrization was introduced in the code. This new numerical tool was successfully tested on synthetic data, with and without a priori information. We also present an application to real-array data measured at a site in Brussels (Belgium), the geology of which consists of about 115 m of sand and clay layers overlying a Palaeozoic basement. On this site, active and passive source data proved to be complementary and the method allowed the retrieval of a V s profile consistent with borehole data available at the same location.

Effects of Love Waves on Microtremor H/V Ratio

Abstract The horizontal-to-vertical (H/V) method has the potential to significantly contribute to site effects evaluation, in particular in urban areas. Within the European project, site effects assessment using ambient excitations (SESAME), we investigated the nature of ambient seismic noise in order to assess the reliability of this method. Through 1D seismic noise modeling, we simulated ambient noise for a set of various horizontally stratified structures by computing efficiently the displacement and stress of dynamic Green’s functions for a viscoelastic-layered half-space. We performed array analysis using the conventional semblance-based frequence-wavenumber method and the three-component modified spatial autocorrelation method on both vertical and horizontal components and estimated the contribution of different seismic waves (body/surface waves, Rayleigh/Love waves) at the H/V peak frequency. We show that the very common assumption that almost all the ambient noise energy would be carried by fundamental-mode Rayleigh waves is not justified. The relative proportion of different wave types depends on site conditions, and especially on the impedance contrast. For the 1D horizontally layered structures presented here, the H/V peak frequency always provides a good estimate of the fundamental resonance frequency whatever the H/V peak origin (Rayleigh wave ellipticity, Airy phase of Love waves, S -wave resonance). We also infer that the relative proportion of Love waves in ambient noise controls the amplitude of the H/V peak.

Deriving Wavefield Characteristics and Shear-Velocity Profiles from Two- Dimensional Small-Aperture Arrays Analysis of Ambient Vibrations in a Small-Size Alluvial Basin, Colfiorito, Italy

We analyze the dispersion characteristics of ambient noise vibrations. For this purpose, two-dimensional (2d) seismic array data were acquired in four different sites in the Colfiorito plain, an alluvial intramountain basin that exhibits strong site effects. Assuming seismic noise being mainly composed of surface waves, we derive one-dimensional (1d) shallow shear-velocity profiles through the inversion of dispersion curves measured by frequency–wavenumber ( f-k ) methods. The inverted shear-wave velocity profiles are consistent with a priori information for those sites that can be approximated by 1d simple models. In these cases, the use of passive records of seismic vibrations can be a valuable tool for determining the shallow velocity profile if a detailed depiction of velocity structure is not required. The theoretical dispersion curves for Rayleigh and Love waves were compared with the measured dispersion curves for vertical and horizontal components, respectively. This allows us to discuss qualitatively the composition of ambient vibrations (outlining a large proportion of Love waves in the noise wave field) and the effects of higher modes. We also use the single-station method for investigating the origin of the horizontal-to-vertical (h/v) peak in the plain of Colfiorito in terms of ellipticity of the fundamental Rayleigh mode.

Direct Inversion of Spatial Autocorrelation Curves with the Neighborhood Algorithm

Ambient vibration techniques are promising methods for assessing the subsurface structure, in particular the shear-wave velocity profile ( Vs ). They are based on the dispersion property of surface waves in layered media. Therefore, the penetration depth is intrinsically linked to the energy content of the sources. For ambient vibrations, the spectral content extends in general to lower frequency when compared to classical artificial sources. Among available methods for processing recorded signals, we focus here on the spatial autocorrelation method. For stationary wavefields, the spatial autocorrelation is mathematically related to the frequency-dependent wave velocity c ( ω ). This allows the determination of the dispersion curve of traveling surface waves, which, in turn, is linked to the Vs profile. Here, we propose a direct inversion scheme for the observed autocorrelation curves to retrieve, in a single step, the Vs profile. The powerful neighborhood algorithm is used to efficiently search for all solutions in an n -dimensional parameter space. This approach has the advantage of taking into account the existing uncertainty over the measured curves, thus generating all Vs profiles that fit the data within their experimental errors. A preprocessing tool is also developed to estimate the validity of the autocorrelation curves and to reject parts of them if necessary before starting the inversion itself. We present two synthetic cases to test the potential of the method: one with ideal autocorrelation curves and another with autocorrelation curves computed from simulated ambient vibrations. The latter case is more realistic and makes it possible to figure out the problems that may be encountered in real experiments. The Vs profiles are correctly retrieved up to the depth of the first major velocity contrast unless low-velocity zones are accepted. We demonstrate that accepting low-velocity zones in the parameterization has a dramatic influence on the result of the inversion, with a considerable increase in the nonuniqueness of the problem. Finally, a real data set is processed with the same method.

Influence of parameterization on inversion of surface wave dispersion curves and definition of an inversion strategy for sites with a strong VS contrast

Inversion of the fundamental mode of the Rayleigh wave dispersion curve does not provide a unique solution and the choice of the parameterization (number of layers, range of velocity, and thickness values for the layers) is of prime importance for obtaining reliable results. We analyzed shear-wave velocity profiles derived from borehole tests at 10 sites where soil layers overlay bedrock in various geologic contexts. One to three seismic layers with linear velocity laws could model all of them. Three synthetic models defined from this preliminary study were used to understand the influence of parameterization on the dispersion curve inversion. This analysis resulted in the definition of a two-step inversion procedure for sites exhibiting a strong impedance con-trast. In the first step, the dispersion curve is inverted with an increasing number of layers over half space. The evolution of the minimum misfit and bedrock depth with number of layers allows the estimation of the true bedrock depth range. In the...

Investigation of a fractured limestone cliff (Chartreuse Massif, France) using seismic tomography and ground-penetrating radar

Evaluating the stability state of a rock slope is a complex problem, mainly due to the lack of knowledge of the real state of the rock mass. Geophysical methods appear to be useful for investigating the deep discontinuity pattern, which may be poorly interpreted from surface observations. However, they have seldom been applied on steep rock slopes. The aim of this study is to test seismic tomography and ground-penetrating radar on near-vertical cliffs, and assess the quality of information that they can provide when investigating the characteristics of the fracture pattern inside the massif. The test site is located in the Chartreuse massif, 20 km north-west of Grenoble, France. It is a 15 m high limestone cliff, characterized by one main near-vertical discontinuity set, including some wide open fractures. Seismic tomography has been conducted between the vertical free surface and the plateau above, along three parallel profiles. Results show strong velocity gradients, from 800 to 3500 m/s. Some triangular low-velocity zones can be correlated with field observation of open fractures, but different tests on synthetic models and on real data show that the method is too sensitive to such heterogeneous conditions to provide accurate information on the fracture pattern. Ground-penetrating radar surveys have also been acquired along vertical profiles on the cliff. We used three different antennae with centre frequencies of 35, 120 and 500 MHz. The penetration depth varied from 10 m (500 MHz) to about 20 m (35 MHz). The main reflectors are near-vertical and most of them can be correlated with fractures observed on the site. The reflectivity varies strongly along one single reflector, indicating changes in the aperture and/or filling characteristics.

Multimethod Characterization of the French-Pyrenean Valley of Bagnères-de-Bigorre for Seismic-Hazard Evaluation: Observations and Models

A narrow rectilinear valley in the French Pyrenees, affected in the past by damaging earthquakes, has been chosen as a test site for soil response characteriza- tion. The main purpose of this initiative was to compare experimental and numerical approaches. A temporary network of 10 stations has been deployed along and across the valley during two years; parallel various experiments have been conducted, in particular ambient noise recording, and seismic profiles with active sources for struc- ture determination at the 10 sites. Classical observables have been measured for site amplification evaluation, such as spectral ratios of horizontal or vertical motions between site and reference stations using direct S waves and S coda, and spectral ratios between horizontal and vertical (H/V) motions at single stations using noise and S-coda records. Vertical shear-velocity profiles at the stations have first been obtained from a joint inversion of Rayleigh wave dispersion curves and ellipticity. They have subsequently been used to model the H/V spectral ratios of noise data from synthetic seismograms, the H/V ratio of S-coda waves based on equipartition theory, and the 3D seismic response of the basin using the spectral element method. General good agreement is found between simulations and observations. The 3D simulation reveals that topography has a much lower contribution to site effects than sedimentary filling, except at the narrow ridge crests. We find clear evidence of a basin edge effect, with an increase of the amplitude of ground motion at some distance from the edge inside the basin and a decrease immediately at the slope foot.

Geoacoustic inversion with two source-receiver arrays in shallow water

A geoacoustic inversion scheme based on a double beamforming algorithm in shallow water is proposed and tested. Double beamforming allows identification of multi-reverberated eigenrays propagating between two vertical transducer arrays according to their emission and reception angles and arrival times. Analysis of eigenray intensities yields the bottom reflection coefficient as a function of angle of incidence. By fitting the experimental reflection coefficient with a theoretical prediction, values of the acoustic parameters of the waveguide bottom can be extracted. The procedure was initially tested in a small-scale tank experiment for a waveguide with a Plexiglas bottom. Inversion results for the speed of shear waves in Plexiglas are in good agreement with the table values. A similar analysis was applied to data collected during an at-sea experiment in shallow coastal waters of the Mediterranean. Bottom reflection coefficient was fitted with the theory in which bottom sediments are modeled as a multi-layered system. Retrieved bottom parameters are in quantitative agreement with those determined from a prior inversion scheme performed in the same area. The present study confirms the interest in processing source-receiver array data through the double beamforming algorithm, and indicates the potential for application of eigenray intensity analysis to geoacoustic inversion problems.

Geoacoustic inversion performed from two source‐receive arrays in shallow‐water waveguide.

Raylike propagation of acoustic waves in a shallow‐water waveguide between two vertical line arrays is investigated by applying a double beamforming algorithm, which performs time‐delay beamforming on both emitting and receiving arrays and allows identification of eigenrays by their emission and reception angles and arrival times. From the intensity of each eigenray, it is possible to determine reflection coefficient from the bottom of the waveguide as a function of an angle of incidence. The procedure was initially tested in a small‐scale tank experiment for an acoustic waveguide with either steel or Plexiglas bottom. By fitting an experimentally found reflection coefficient with a corresponding theoretical expression, an estimate for the speed of shear waves in the bottom material was obtained. Similar analysis was subsequently applied to the data obtained during an at‐sea experiment, which was performed between two vertical transducer arrays in shallow‐coastal waters of the Mediterranean. An angle‐depe...