Approximate formula of peak frequency of H/V ratio curve in multilayered model and its use in H/V ratio technique

The main peak frequency of the Horizontal to Vertical (H/V) ratio curve is the key factor used in the H/V ratio technique since the resonace frequency of the transmission response of the site is estimated from this frequency. However, there has not been explicit formula of the main peak frequency of the H/V ration curve in multiplayered models. In the present study, an approximate explicit equation of the peak frequency of H/V ratio is devired of the multiplayered models of high impedance contrast between the half-space and surface layers. This approximate equation is then generalized for model of an functionally graded material (FGM) layer over half-space. Then, the approximate equation is used to obtain an explicit approxiamte formula of the main peak frequency of H/V ration curve. The principle formula of H/V ratio technique is used along with the obtained approximate formula of the main peak frequency to formulate a new average formula of the shear-wave velocity of a composite layer composed 
    of an arbitrary number of horizontal, homogeneous layers. The new average formula is shown to be more suitable in the use of H/V ratio technique than the currently used ones in the sense that it takes into account the effect of the mass density and the position of sublayers. Finally, some numerical caculation to illustrate the application of the peak formula and the new average formula of shear-wave velocity is presented.