Geodynamics

In this Chapter

Numerical solutions to a variety of problems in geodynamics are given in this chapter utilizing MATLAB. In some cases, a specific boundary value problem given in a previous chapter is generalized to arbitrary boundary conditions. One example is the bending of the lithosphere under a load. The solution for a point load given in Chapter 3 is generalized to arbitrary load distributions. Solutions for lithospheric bending under axisymmetric loads are presented. The gravity anomaly over rectangular prisms is calculated, and a new formalism based on Fourier transforms is presented to solve for the gravity over arbitrary topography. Axisymmetric solutions for postglacial rebound and crater relaxation are developed. Finite amplitude thermal convection requires the solution of nonlinear partial differential equations. These solutions must be obtained using numerical methods. A MATLAB code for a two-dimensional steady solution is given. Finally, the discussion of faulting in Chapter 8 is extended to more complex geometries and faulting scenarios.

Bending of the Lithosphere under a Triangular Load

In Section 3.16 we solved for the bending of the elastic lithosphere under the load of a volcanic island chain by representing the island chain as a line load on the plate. With a numerical solution it is possible to represent the load on the plate more realistically, e. g., by a triangular load. We first develop the numerical approach by going back to the line load problem whose analytic solution provides a benchmark against which to evaluate the numerical solution.