Calculation of seismic displacement fields in self-gravitating earth models—applications of minors vectors and symplectic structure

An account is given of the minor vector method that allows for the stable numerical integration of the systems of linear ordinary differential equations occurring in a number of geophysical problems. In particular, new results are presented that allow for the application of the method to the solution of 6-D inhomogeneous boundary value problems, such as those encountered in the calculation of seismic displacement fields in spherically symmetric, self-gravitating earth models. In addition, the symplectic structure possessed by many of the ordinary differential equations of interest is described. It is shown how this structure can be used to simplify the numerical implementation of the minor vector method and also to concisely derive a number of theoretical results about the eigenfrequencies and eigenfunctions of a linearly anelastic earth model.