Particle Motion Induced by Elastic Waves Radiating from Subsurface, Penny-Shaped Cracks and Mapping of Subsurface Cracks

Abstract

Dynamic, elastic responses of rocks against the sudden growth of a subsurface penny-shaped reservoir crack ane analyzed in order to study the characteristics of elastic waves from the crack and particle motions observed at observation stations in an intermediate region where the distance from the crack is several ten times the size of the crack. In the analysis, a singular intergrodifferential equation was derived in Laplace image space, and the equation was solved numerically by a collocation method. The results show that the radial and circumferential displacements rise steeply just after P and S wave arrivals, respectively, where small oscillations are superimposed on the steeply rising portions. It is also shown that the displacement vectors are pointing to the crack tip where the crack growth is taking place, not the center of the crack.