Earthquakes

A model for earthquake ground motion is developed in this dissertation using principles of geophysics and stochastics. The earth is idealized as being composed of horizontally stratified layers, with uniform physical properties for each layer. The seismic source is assumed to be the result of shear dislocation propagating on a fault line, which is further discretized into a series of point sources at equal intervals. The fundamental problem of the ground motion in a layered medium due to a point source at a given source location is first considered. The governing equations of three-dimensional wave motion in a uniform layer are presented and solved in both Cartesian and cylindrical coordinates. Wave propagation in a multi-layered medium is then analyzed in detail, in which the wave scattering matrices are introduced so that stability and accuracy in numerical calculation can be guaranteed. A detailed review of the mechanism of seismic point source is also provided. Based on the fundamental solution for a point source, an earthquake model is constructed by superposing the solutions associated with a series of point sources along a line which are activated sequentially at random times. Statistical characteristics of earthquake ground motion is then obtained by applying a generalized version of the random-pulse-train theory and its evolutionary spectral representation. Finally the effects of uneven interface on the earthquake ground motion is also analyzed using a first-order perturbation approach.