Title:

Theoretical problems in global seismology and geodynamics

In Chapter 2, we consider the hydrostatic equilibrium figure of a rotating earth model with arbitrary radial density profile. We derive an exact nonlinear partial differential equation describing the equilibrium figure. Perturbation theory is used to obtain approximate forms of this equation, and we show that the firstorder theory is equivalent to Clairaut's equation. In Chapter 3, a method for parametrizing the possible equilibrium stress fields of a laterally heterogeneous earth model is described. In this method a solution of the equilibrium equations is first found that satisfies some desirable physical property. All other solutions can be written as the sum of this equilibrium stress field and a divergencefree stress tensor field whose boundary tractions vanish. In Chapter 4, we consider the minor vector method for the stable numerical solution of systems of linear ordinary differential equations. Results are presented for the application of the method to the calculation of seismic displacement fields in spherically symmetric, selfgravitating earth models. In Chapter 5, we present a new implementation of the direct solution method for calculating normal mode spectra in laterally heterogeneous earth models. Numerical tests are presented to demonstrate the validity and effectiveness of this method for performing large mode coupling calculations. In Chapter 6, we consider the theoretical basis for the viscoelastic normal mode method which is used in studies of seismic wave propagation, postglacial rebound, and postseismic deformation. We show how the timedomain solution to the viscoelastodynamic equation can be written as a normal mode sum in a rigorous manner.
