ALBERT

Description: A new implementation of indirect boundary element method allows simulating the elastic wave propagation in complex configurations made of embedded regions that are homogeneous with irregular boundaries or flat layers. In an older implementation, each layer of a flat layered region would have been treated as a separated homogeneous region without taking into account the flat boundary information. For both types of regions, the scattered field results from fictitious sources positioned along their boundaries. For the homogeneous regions, the fictitious sources emit as in a full-space and the wave field is given by analytical Green's functions. For flat layered regions, fictitious sources emit as in an unbounded flat layered region and the wave field is given by Green's functions obtained from the discrete wavenumber (DWN) method. The new implementation allows then reducing the length of the discretized boundaries but DWN Green's functions require much more computation time than the full-space Green's functions. Several optimization steps are then implemented and commented. Validations are presented for 2-D and 3-D problems. Higher efficiency is achieved in 3-D.

Description: The H/V spectral ratio has emerged as a single station method within the seismic ambient noise analysis field by its capability to quickly estimate the frequency of resonance at a site and through inversion the average profile information. Although it is easy to compute from experimental data, its counter theoretical part is not obvious when building a forward model which can help in reconstructing the derived H/V spectrum. This has led to the simplified assumption that the noise wavefield is mainly composed of Rayleigh waves and the derived H/V often used without further correction. Furthermore, only the right (and left) flank around the H/V peak frequency is considered in the inversion for the subsurface 1-D shear wave velocity profile. A new theoretical approach for the interpretation of the H/V spectral ratio has been presented by Sánchez-Sesma et al. In this paper, the fundamental idea behind their theory is presented as it applies to receivers at depth. A smooth H/V( z , f ) spectral curve on a broad frequency range is obtained by considering a fine integration step which is in turn time consuming. We show that for practical purposes and in the context of inversion, this can be considerably optimized by using a coarse integration step combined with the smoothing of the corresponding directional energy density (DED) spectrum. Further analysis shows that the obtained H/V( z , f ) spectrum computed by the mean of the imaginary part of Green's function method could also be recovered using the reflectivity method for a medium well illuminated by seismic sources. Inversion of synthetic H/V( z , f ) spectral curve is performed for a single layer over a half space. The striking results allow to potentially use the new theory as a forward computation of the H/V( z , f ) to fully invert the experimental H/V spectral ratio at the corresponding depth for the shear velocity profile ( Vs ) and additionally the compressional velocity profile ( Vp ) using receivers both at the surface and in depth. We use seismic ambient noise data in the frequency range of 0.2–50 Hz recorded at two selected sites in Germany where borehole information is also available. The obtained 1-D Vs and Vp profiles are correlated with geological log information. Results from shallow geophysical experiment are also used for comparison.

Description: A method is presented to simulate the propagation of elastic waves in a 2-D piecewise homogeneous domain composed of several regions of arbitrary shapes. The regions can be isolated within an elastic background or also embedded among themselves. The method is based on the indirect boundary element method (IBEM) in which the diffracted field is obtained as the contributions of distributed sources along the regions boundaries. This is somehow reminiscent of Huygens's Principle for wave fronts. The fields emitted by the sources are computed in frequency domain using analytical expressions of Green's functions for displacements and tractions. This approach is validated, in the antiplane case, by comparing against a semi-analytical solution for a basin composed of concentric semi-circular layers and embedded in a half-space. Finally, an example of in-plane wave propagation is given for a complex configuration involving five interlocked regions.

Description: In order to evaluate the site effects on seismic ground motion and establish preventive measures to mitigate these effects, the dynamic characterization of sites is mandatory. Among the various geophysical tools aimed to this end, the horizontal to vertical spectral ratio (H/V) is a simple way to assess the dominant frequency of a site from seismic ambient noise. The aim of this communication is contributing to enhance the potential of this measurement with a novel method that allows extracting from the H/V the elastic properties of the subsoil, assumed here as a multilayer medium. For that purpose, we adopt the diffuse field assumption from both the experimental and the modelling perspectives. At the experimental end, the idea is to define general criteria that make the data processing closely supported by theory. On the modelling front, the challenge is to compute efficiently the imaginary part of Green's function. The Cauchy's residue theory in the horizontal wavenumber complex plane is the selected approach. This method allows both identifying the contributions of body and surface waves and computing them separately. This permits exploring the theoretical properties of the H/V under different compositions of the seismic ambient noise. This answers some questions that historically aroused and gives new insights into the H/V method. The efficient forward calculation is the prime ingredient of an inversion scheme based on both gradient and heuristic searches. The availability of efficient forward calculation of H/V allows exploring some relevant relationships between the H/V curves and the parameters. This allows generating useful criteria to speed up inversion. As in many inverse problems, the non-uniqueness issues also emerge here. A joint inversion method that considers also the dispersion curves of surface waves extracted from seismic ambient noise is presented and applied to experimental data. This joint scheme mitigates effectively the non-uniqueness.