A computer code for forward calculation and inversion of the H/V spectral ratio under the diffuse field assumption

Abstract

During a quarter of a century, the main characteristics of the horizontal-to-vertical spectral ratio of ambient noise HVSRN have been extensively used for site effect assessment. In spite of the uncertainties about the optimum theoretical model to describe these observations, over the last decade several schemes for inversion of the full HVSRN curve for near surface surveying have been developed.In this work, a computer code for forward calculation of H/V spectra based on the diffuse field assumption (DFA) is presented and tested. It takes advantage of the recently stated connection between the HVSRN and the elastodynamic Green's function which arises from the ambient noise interferometry theory.The algorithm allows for (1) a natural calculation of the Green's functions imaginary parts by using suitable contour integrals in the complex wavenumber plane, and (2) separate calculation of the contributions of Rayleigh, Love, P-SV and SH waves as well. The stability of the algorithm at high frequencies is preserved by means of an adaptation of the Wang's orthonormalization method to the calculation of dispersion curves, surface-waves medium responses and contributions of body waves.This code has been combined with a variety of inversion methods to make up a powerful tool for passive seismic surveying.

Antarctic ice sheet thickness estimation using the horizontal-to-vertical spectral ratio method with single-station seismic ambient noise

“…These assumptions differentiate themselves in the scheme of forward calculation of the H / V spectrum. In this study, a more recently developed H / V spectrum forward calculation and inversion method based on the DFA was employed (García-Jerez et al, 2016). The DFA was proposed on the basis of the recently stated connection between the diffuse fields and the Green's function which arises from the ambient noise interferometry theory.…”

The inversion of spectral ratio H/V in a layered system using the diffuse field assumption (DFA)

“…In fact, the H/V ratio considering only the body waves contributions (see figure 4-a) is very similar to the transfer function for vertical S waves, in partial agreement with Nakamura's (1989) interpretation. Finally, when all the wave types are considered (Spica et al 2015;Rivet et al 2015García-Jerez et al 2016, the H/V ratio is usually dominated by surface wave contributions for frequencies higher than the first maximum, whereas it is dominated by body waves below that frequency (see figure 4-a) .…”

“…We applied this approach to interpret data gathered in Almería (Spain) including joint inversion. A computer code, based on this formulation is described elsewhere (García-Jerez et al 2016).…”

“…These positions are evaluated rapidly as they correspond to points of the dispersion curves at a given frequency (see e.g. García-Jerez et al 2016). Even for a fine discretization the poles are likely to be lost and the computed integrals be wrong.…”

“…Its main advantage is the possibility to explore an extended parameter space, which may present several local minima, and to converge toward an optimum model. This method has already been successfully employed in seismology to invert the fundamental Rayleigh mode dispersion curves (Martínez et al 2000;Iglesias et al 2001;Beaty et al 2002;Xia et al 2002;Pei et al 2007) and H/V (Spica et al 2015;García-Jerez et al 2016). When the misfit is already close to an acceptable value, or when enough a priori information is available, the inversion can be made using a local optimization scheme (e.g.…”