Introduction

Abstract

Seismic waves are the most powerful tool geophysicists have at their disposal to investigate the in situ physical properties of the Earth’s deep interior. The theory of elasticity is the basic theoretical framework upon which seismological methods are developed. The theory was already well advanced in the mid-nineteenth century, before it was proven that the Earth was a quasi perfectly elastic body for short time constants. The mechanical behavior of a linear elastic material depends primarily on Hooke’s law which relates the stress to the strain. After the setting of the first general equations of elasticity by Navier, Cauchy, and Poisson in the 1820s, a controversy arose on the number of independent parameters needed to relate the stress to the strain. It was finally concluded, after the work of Green and Stokes in the 1830s and 1840s, that 21 independent elastic coefficients were required to describe the elastic properties of a solid in the most general case. This number reduces to 2 for isotropic solids and to 1 for fluids. The basic theoretical framework of the theory of elastic-wave propagations had then been set up a long time before geophysicists started exploring the Earth’s interior with seismic waves.