Series expansion of complex ground amplifications with a sequence of simple transfer functions

Abstract

Amplification of earthquake ground motions at actual deposit sites is an important factor to consider when assessing the risk of an earthquake disaster. In order to identify the amplification properties, several preprocessings such as the Fourier transform are required. I propose a series expansion of the amplification with simple ground transfer functions as a new preprocessing. I define a sequence of transfer functions based on a two-layered structure excluding an internal damping and a function space spanned by the set of the functions. I mathematically prove that the function space is equal to L2 space. This indicates that all the functions belonging to L2 space, that is, an arbitrary ground amplification, have a unique series expansion. This expansion is applied to the physics-based decomposition of the amplification. Some numerical examples indicate that the similarity between a target complex structure and a simple model is measured by the absolute value of each coefficient in the series expansion.