A Novel Characterization of Seismic Site Response: Time–Frequency Transfer Function

ABSTRACT

Fourier transfer function FTF(f), defined as a Fourier transform of the impulse response of the medium between a source and receiver, fully characterizes transfer properties in the frequency domain. Modulus of FTF(f) is one of the most used characteristics of seismic site response in both theoretical and numerical analyses of effects of local surface structures on seismic motion. It is especially useful for identifying resonance peaks and/or the amplified frequency bands. By definition, however, |FTF(f)| cannot provide information on temporal development of the site response. In this article, we introduce a novel characterization of seismic site response—time–frequency transfer function TFTF(t, f) that properly characterizes temporal development of frequency content of transfer function. This feature significantly helps in interpretating wavefield composition. We present theory that is readily applicable to any time-dependent output signal. We demonstrate superior properties of TFTF(t, f) in comparison with standard |FTF(f)| for selected quasi-1D canonical models of local surface sedimentary structures. In the model of a semi-infinite layer, TFTF(t, f) made it possible to distinguish modes of vertical resonance and modes of surface waves, which is impossible based on standard |FTF(f)|.