Page 277 - Numerical Analysis and Modelling in Geomechanics

Chapter 9
Ground motion modelling using the 2-D

Chebyshev spectral element method
Enrico Priolo

Abstract
The 2-D Chebyshev spectral element method (SPEM) and its application to
engineering seismology problems is reviewed in this paper. The SPEM is a high-
order finite element technique, which is particularly suitable to compute
numerically accurate solutions of the full wave equations in complex media. The
chapter first gives an overview of the theoretical bases of the method and
discusses some methodological topics of interest for practical applications. Then,
the effectiveness of the method is illustrated through two case histories, i.e. the
ground shaking prediction in Catania (Sicily, Italy) for a catastrophic earthquake,
and the analysis of the ground motion in the presence of a massive structure.

Introduction
The spatial variability of the ground motion following an earthquake has been
observed in a large number of cases and is, nowadays, a widely accepted
phenomenon. Several studies have shown how it manifests itself (e.g.,
incoherent arrival phases, local amplifications in narrow frequency bands etc.,
especially for the acceleration field and frequencies higher than 2 Hz), and have
explained its possible causes. The great majority of the spatial ground motion
variability is tied to the rupture process at the source and the propagation of the
radiated wavefield through three-dimensionally complex, geologic structures. It
is also known that the ground structure and soils close to the surface (a 30 m
thickness is a widely accepted reference for “surface soils”) have the largest
influence on a local scale. The damage distribution to buildings and
infrastructures can be very mhomogeneous, with dramatic variations within a few
tens of metres (Hartzell et al., 1997). Only techniques that allow accurate
modelling of the seismic wavefield through complex geologic structures can
faithfully reproduce those phenomena, and this is one of the main reasons that
has led to the development of the spectral element method in its various forms.
The global Chebyshev spectral element method (SPEM), which is overviewed
here, is a high-order finite element technique, which solves the variational