A theoretical investigation of average H/V ratios

The mode summation method and a finite difference technique are applied to investigate the spectral ratio between the horizontal and vertical components (H/V ratio) of ambient vibrations and to explore the variation of the resonance frequency and the amplitude and shape of polarization as a function of the structure and the source positions. Layered structural models are used by assuming a large number of sources distributed around a receiver, with shallow source depths that are randomly assigned. We identify stable parts of the H/V ratios that are independent of the source distance and are dominated by the ellipticity of the fundamental-mode Rayleigh wave in the frequency band between the fundamental frequency of resonance of the unconsolidated sediments and the first minimum of the average H/V ratio. The ellipticity in this frequency band is determined by the layering of the sediments. The numerical simulations are compared with observations at a site where the thickness and velocity structure of the unconsolidated sediments are known from S-wave and surface wave measurements. Two methods are applied to compute the H/V ratio, the classical method in the frequency domain and a method based on frequency-time analysis that allows us to locate P-SV wavelets in the time-series. The main problem in comparing synthetics with observations is the contribution of SH waves in the observed H/V ratios. We propose a method to minimize these effects and the effects of the superposition of different incoming P-SV waves. An inversion scheme is applied to the stable parts of the observed H/V ratio, based on a genetic algorithm, to retrieve the S-wave velocity structure from a single ambient vibration record.