INTRODUCTION

Feynman: "You know, I couldn't do it. I couldn't reduce it to the freshman level. That means we really don't understand it." Richard Feynman

SCOPE of this COURSE

The purpose of these notes is (1) to provide the necessary mathematical and physical background for an undergraduate senior or beginning graduate student in science to (2) engage the uses of applied seismology. I hope that through the various exercises the student will gain a personal understanding of the subjects and the computational skills to continue learning seismology on their own.

DIFFERENT PHYSICAL MODELS for the EARTH

In seismology we are primarily interested in the use of the wave equation at a sophisticated level. Quite often seismology alone is insufficient to understand a physical process in the earth and other physical models for the earth are required. Electromagnetic models employ Maxwell’s equations and give us a simplified view (model) of the earth in terms of electrical conductivity. A third manner of observing the world is to model the behavior of moving fluids through its connected pores. For this objective we employ the diffusion equation. Other views of the earth exist based on how heat flows, how the lithosphere bends, and based on the distribution of the density of matter.

VEC T ORS

Powerpoint link

Herein, we will deal mainly with the humble wave equation,

, where u is the displacement, and is the Laplacian operator.

A conceptual, physical interpretation of this equation can be that the acceleration experienced by the passing of a wave is a function of the difference between the local and average surrounding displacements (Laplacian). The constant of proportionality depends on the speed of the wave through the material.

VEC T ORS

VEC T ORS