THE EQUATION OF MOTION OF A GEOPHONE ON THE SURFACE OF AN ELASTIC EARTH

Abstract

The motion of a geophone case placed on the surface of an elastic earth does not follow faithfully the motion of the earth at high frequencies. In effect, a weight placed on the surface of an elastic solid constitutes a damped oscillating system. The elastic restoring forces are determined by the area of contact between the weight and the surface of the solid and by the elastic moduli of the solid. The damping force is due to emission of elastic waves by the oscillating weight. The motion of the solid also contributes to the inertia of the system. Equations are developed for these forces on the assumption that the wave length is long compared to the linear dimensions of the area of contact between the weight and the elastic solid. This leads to a determination of the frequency of oscillation and of the decrement of such a system.