| In PART I of this dissertation, a new method is presented for computing the complete elastic response of a vertically heterogeneous halfspace. The method utilizes a discrete wavenumber decomposition for the horizontal dependence of the wave motion in terms of a Fourier-Bessel series. The series representation is exact and consequently eliminates the need to numerically integrate a continuous Bessel transform. The vertical and time dependence of the wave motion is obtained as the solution to a system of partial differential equations. These equations are solved numerically by a combination of finite element and finite difference methods which accommodate arbitrary vertical heterogeneities. By using a reciprocity relation, the wave motion is computed simultaneously for all source-observer combinations of interest so that the differential equations need only be solved once. A comparison is made, for layered media, between the solutions obtained by discrete wavenumber/finite element, wavenumber integration, axisymmetric finite element, and generalized rays.; In PART II of this dissertation, subsurface slip on a known fault is formulated as the solution to an inverse problem in which recorded surface ground motion is the data. Two methods of solution are presented: the least squares method, which minimizes the squared differences between theory and data, and the constrained least squares method which simultaneously maintains a set of linear inequalities. Instabilities in the solution are effectively eliminated in both methods and the sensitivity of the solution to small changes in the data is quantitatively stated. The inversion methodology is applied to 77 components of near-field ground acceleration recorded during the October 15, 1979 Imperial Valley earthquake. The faulting is constrained to propagate bilaterally away from the epicenter at an average velocity of 90 percent of the shear wave speed on a vertical fault plane extending from the surface to ten kilometers depth. Inequality constraints are used to keep the faulting sequence physically reasonable by maintaining right lateral motion and positive slip velocity. The preferred solution is stable and provides a good fit to the data; it is also realistic and consistent with observed surface offsets and independent estimates of seismic moment. |
