Modeling noise horizontal-to-vertical spectral ratio in irregular layers
By Francisco J Sánchez-Sesma
Professor at the Institute of Engineering, UNAM, Mexico
ABSTRACT
For relatively flat environments the modeling and inversion of measured noise horizontal-to-vertical spectral ratio HVSR in terms of the imaginary parts of Green tensor, using the diffuse field theory, lead to successful retrieval of vertical profiles of mechanical properties. Lateral irregularity introduces bias when HVSR is used to characterize a site. Certainly, the easiest thing to do is interpolation but in order to get the best results the directional character of H/V should be accounted for. The field experiment of Matsushima et al (2017) in Onahama, Japan, and the ensuing modeling revealed the great potential of directional differences in HVSR. They used the spectral element method to compute the time domain response and detailed Fourier analysis allowed retrieval of the imaginary part of Green’s function. The modeling of HVSR showed improved matching of calculations and observations when the known irregularity was accounted for. Similarly, the exposed layering at the crater rim allowed Perton et al. (2017) to model HVSR for the Ijen volcano, Indonesia,
In this work we present a practical approach and use the indirect boundary element method (IBEM) in 3D to study the case of a single layer over a half-space. This problem has a numerical solution and we reproduced it using an adaptive mesh that changes with frequency. Our results is based upon the important diffraction at low frequencies and the asymptotic behavior in high frequencies. We model HVSR for a layer over a half space with lateral variations and obtained the directional HVSR detecting both the changes in peak frequency and the variations in amplitude for both longitudinal and transverse directions.