Eshelby transformations, pore pressure and fluid mass changes, and subsidence

This paper is motivated by a recent analysis by Walsh (2002) of subsidence above a planar reser- voir. Although the problem has been treated previously by Geertsma (1966, 1973a, b) and Segall (1992), Walsh (2002) uses a different approach. In particular, he uses a cut and weld procedure, originated by Eshelby (1957), and the reciprocal theorem of elasticity. Walsh obtains the same results as Geertsma and Segall but the connec- tion between the two approaches is not evident. The purpose of this paper is to generalize the approach used by Walsh (2002) and to develop the connection to the approach of Geertsma and Segall.