Discrete Time Solution of Plane P - SV Waves in a Plane Layered Medium

DISCRETE TIME SOLUTION OF PLANE P-SV WAVES IN A PLANE LAYERED MEDIUM by Clint Wellington Frasier Submitted to the Department of Earth and Planetary Sciences in partial fulfillment of the requirement for the degree of Doctor of Philosophy. For plane waves at normal incidence to a layered, elastic medium both the forward and inverse discrete time problems have been previously solved. Here, the forward problem of calculating the waves in a medium of plane, homogeneous, isotropic layers is extended to P and SV body waves at non-normal incidence, where the horizontal phase velocity of each wave is greater than the shear and compressional waves of each layer. Vertical travel times for P and SV waves through each layer are rounded off to unequal integer multiples of a small time increment This gives a 4 x 4 layer matrix analagous to the 2 x 2 layer matrix for normal incidence obtained by previous authors. Reflection and transmission responses for layered media are derived as matrix series in integer powers of a Fourier transform variable z=e D 7 . These responses are generated recursively by polynomial division and include all multiply reflected P and SV waves with mode conversions. For a layered halfspace, the reflection response matrix for a source at the free surface equals the positive time part of the autocorrelation matrix of the transmission response matrix for a deep source. This can be used to convert surface records of teleseismic events to reflection seismograms for mapping the crust. For a known crustal structure, the reverberations contaminating a teleseismic event can be removed in time by a simple convolution, rather than by dividing spectra. Time domain transmission responses for two crustal models under LASA, and reflection responses for several core-mantle boundary models 3. are calculated as examples of the method. These responses are useful for studying the first motion and window length of transition layer responses. Finally, the method is extended to media containing any arrangement of solid and fluid layers. Thesis Supervisor: Keiiti Aki Title: Professor of Geophysics