The Physical Basis for the Modeling of HVSR Under the Diffuse Fields Assumption
The Horizontal to Vertical Spectral Ratio (HVSR) for Ambient Seismic Noise (ASN) is a popular measurement that typically determines the dominant period at a given soil site. Proposed by Nakamura in 1989, quickly gained adept practitioners around the world. The measurement is easy and economical and the results allow for microzonation with unprecedented resolution. The ideas of receiver functions seemed to be the basis of this method but the proposed explanations were not convincing. Arai and Tokimatsu (2004) proposed to compute HVSR as the ratio of averages that, using the concept of diffuse fields in dynamic elasticity firmly established by Weaver (1982), can be seen as ratios of directional energy densities. Within a diffuse field, occupying a half-space, composed of equipartitioned sets of plane P, S and Rayleigh waves, the Green’s function of dynamic elasticity is exactly retrieved from correlations. The full space with a circular cylindrical inclusion allowed to demonstrate exactly the Green’s function retrieval within a heterogeneous medium. In all these results, a common relationship was the proportionality of the average autocorrelation (the directional energy density) with the imaginary part of the system Green´s function.
Consequently, Sánchez-Sesma et al. (2011) proposed to model HVSR in terms of the imaginary part of system’s Green’s function and applied it to layered media. The approach has been extended to borehole measurements with and without a liquid layer. Lateral irregularities have been studied in pioneering test cases, but still they are the next frontier as the numerical burden requires further scrutiny. On the other hand, we rely on multiple scattering as a primary factor for field equilibration but the search for reliable indicators of a diffuse nature of ASN is part of our quest. This research is partially supported by DGAPA-UNAM grants IN105523 and IG100626. J. G. González is supported by the UNAM Postdoctoral Program (POSDOC).
Session: On the State of Knowledge/Art/Practice for mHVSR Analyses; A Prelude to the ESG7-COSMOS mHVSR Pre-Event Forum - II
Type: Oral
Room: Ballroom A
Date: 4/17/2026
Presentation Time: 10:30 AM (local time)
Presenting Author: Francisco Sánchez-Sesma
Student Presenter: No
Invited Presentation:
Poster Number:
Additional Authors
Francisco Sánchez-Sesma Presenting Author Corresponding Author sesma@unam.mx National Autonomous University of Mexico |
Richard Weaver r-weaver@illinois.edu University of Illinois |
Michel Campillo michel.campillo@obs.ujf-grenoble.fr Joseph Fourier University |
Mathieu Perton mathieu.perton@gmail.com McGill University |
Marcela Baena-Rivera mbaenar@gmail.com National Autonomous University of Mexico |
Josué González jgonzalezf@iingen.unam.mx National Autonomous University of Mexico |
José Piña-Flores jpina@uv.mx Veracruzana University |
Ursula Iturrarán ursula@ciencias.unam.mx National Autonomous University of Mexico |
Francisco Luzón fluzon@ual.es University of Almería |
Antonio García-Jerez ant16garje@gmail.com University of Almería, Almería, , Spain |
Agostiny M Lontsi agostiny.lontsi@ubuea.cm University of Buea, Buea, , Cameroon |
Shinichi Matsushima matsushima@sds.dpri.kyoto-u.ac.jp Kyoto University, Kyoto, , Japan |
Hiroshi Kawase h-kawase@gbrc.or.jp General Building Research Corporation of Japan, Kyoto, , Japan |
The Physical Basis for the Modeling of HVSR Under the Diffuse Fields Assumption
Category
On the State of Knowledge/Art/Practice for mHVSR Analyses; A Prelude to the ESG7-COSMOS mHVSR Pre-Event Forum
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