Graduate Student Seminar: Geometrically Nonlinear Wave Propagation in a 3D Elastic Medium

The most general way of doing linear elasticity (Hooke's law) is to
allow for a nonlinear description of the deformation. For most applications in
seismology, the displacements are small, and we can afford to use a linearized
description of the deformation. In the near-field, however, the displacements
can be large and we need a nonlinear description of the deformation. I have
been working on modifying SPECFEM3D, a software package for modeling elastic
wave propagation based on a spectral element method, to use a nonlinear
description of deformation, and have used this to study effects in the
near-field. In this talk, we will see how the general formulation of linear
elasticity is obtained, and will look at a numerical example using the Southern
California model.