Application of ray methods to one-dimensional site response of inhomogeneous soil deposits

The technique referred as ray approximation treats wave propagation in a heterogeneous medium at the infinitely small wavelength limit. This classic simplification allows useful approximate analytical results to be obtained in cases where complete description of the waveform behaviour is virtually unattainable, hence its wide use in physics. In seismology, this approximation has been widely applied. This paper presents an application in one-dimensional site response (1DSR) analysis: it is used herein, first to explain and elucidate the generality of some previous observations as to the use of the harmonic mean of a shear-wave velocity profile to represent the global behaviour of a site; and second to partially settle an open question in 1DSR, namely ‘What are the equivalent homogeneous properties that yield the same response, in terms of natural frequencies and resonance amplitude, for a given inhomogeneous site?’, providing a few assumptions are met – chiefly, that excitations of sufficiently high frequency are considered.