Volker Michel

A Multiscale Method for the Modelling and Interpolation of Earthquake Wave Propagation

Earthquake waves can be modelled by the Cauchy-Navier equation. In the simplified case of a homogeneous, isotropic, and ball-shaped Earth a fundamental system is known for the Fourier-transformed equation. This system of Hansen vectors is used to derive the theoretical eigenfrequencies of the Earth. In case of major earthquakes such as the 1960 Chile event such eigenoscillations, which can last several days after the event, have already been found in seismograms.
In this talk the inverse Fourier-transformed function system is derived yielding a time-dependent function system to describe not only the eigenoscillations but also the propagation of regular earthquake waves. Based on this result scaling functions and wavelets are constructed to obtain a multiresolution of the solution space of the time-dependent Cauchy-Navier equation. This method offers a new approach to analyse the propagation of seismic waves at different (temporal and spatial) resolution scales. Moreover, the obtained kernels have a localising character. This is important since the distribution of seismographs over the Earth is extremely inhomogeneous. Hence, the new method will allow the interpolation of waves at comparatively high resolution in regions with high seismograph density such as California without being seriously influenced by areas with less data.

back to main page