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, several schemes for inversion of the full HVSRN curve for near surface surveying have been developed over the last decade. 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.

💡 Analysis

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, several schemes for inversion of the full HVSRN curve for near surface surveying have been developed over the last decade. 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.

📄 Content

a Departamento de Química y Física, Universidad de Almería. 04120 Almería, Spain. Emails: agarcia- jerez@ual.es, fluzon@ual.es
b Instituto Andaluz de Geofísica. Universidad de Granada. C/ Profesor Clavera, 12. 18071 Granada, Spain. c Instituto de Ingeniería, Universidad Nacional Autónoma de México, CU, Coyoacán, 04510 D.F., Mexico.
Emails: ead2009@hotmail.com, sesma@unam.mx, mathieu.perton@gmail.com
© 2016. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/

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

Antonio García-Jereza,b, José Piña-Floresc, Francisco J. Sánchez-Sesmac, Francisco Luzóna, and Mathieu Pertonc

Accepted for publication in Computers & Geosciences. doi:10.1016/j.cageo.2016.06.016

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.

1. Introduction

Since the early work of Kanai et al. (1954), many efforts have been devoted to the observation and interpretation of the seismic ambient noise (microtremor), consisting of background vibrations due to natural phenomena of atmospheric, oceanic, seismic and volcanic origins as well as human activities like traffic and industry. The possibility of using this ubiquitous natural illumination for exploration of ground structures with seismic arrays was soon recognized by Aki (1957).

Later, the capabilities of single-station measurements of this wavefield were enhanced by Nakamura (1989), who proposed that the ratio between the spectra of horizontal and vertical components of ambient noise allowed for identification of resonance peaks and for estimation of seismic amplifications of soils. After these early developments, several sophisticated tools have been introduced to take full advantage of these spectral ratios for seismic exploration, which are based on diverse and in some cases opposite theoretical approaches.

Fäh et al. (2003) and Wathelet (2005) studied the inversion of the Rayleigh wave ellipticity, sometimes considered as a rough proxy of the horizontal-to-vertical spectral ratio of ambient noise (HVSRN), using genetic algorithms and the neighborhood method as inversion procedures. Their method was not intended to be applied using energy ratios of raw microtremor records, because they consist of a complicated mixture of Rayleigh, Love and

body waves, but is better suited when used together with more advanced processing aimed at extracting the ellipticity (e.g. Poggi et al., 2012).

Arai and Tokimatsu (2004) introduced a method for inversion of the HVSRN accounting for surface waves generated by a continuum of uncorrelated shallow sources located far enough from the receiver. Their approximate expressions allow for a quick and suitable estimation of the power ratio in those models and frequency bands where surface waves are the dominant contribution. Related full-wavefield versions have been developed by Lachet and Bard (1994) and Lunedei and Albarello (2009). To the best of the authors’ knowledge, these two methods have not been incorporated into ground inversion tools. It is probably due to the intensive computing requirements.

On the other hand, a code for inversion of layered ground structures from horizontal-to- vertical spectral ratios of microtremor was published by Herak (2008). The algorithm models the HVSRN as the ratio between the ground responses for vertically incident S and P waves. In this approach, the anelastic attenuation plays a major role in order to make the H/V decay at high frequencies as observed in most experimen

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