Asymptotic Theory of Electroseismic Prospecting

Abstract

In a porous medium such as the earth's subsurface, electromagnetic (EM) waves and mechanical waves are coupled through the phenomenon of electrokinetics, for which a complete set of partial differential equations was derived by S. Pride. In this paper, we derive from Pride's equations an asymptotic theory that enables forward modeling of the seismic response to an EM source in fully three-dimensional geometries on a scale that is relevant to exploration. For simplicity, we consider piecewise homogeneous media separated by interfaces which are curved surfaces in three dimensions. The following physical picture emerges: An EM source excites an EM wave which propagates into the earth, stirring up local mechanical movement. At an interface, EM energy is converted to seismic waves, which may be described by ray theory. Instantly, on the seismic time scale, every interface becomes a wavefront for both compressional and shear waves; that is, seismic P- and S-waves explode from both sides of each interface, at every point on it. The rays for these waves leave the interface in the orthogonal direction and propagate up and down into the homogeneous media on both sides of the surface. We derive formulas for the initial amplitudes of these waves. Conventional seismic ray theory then describes propagation of the P- and S-waves, including reflection, transmission, and mode conversion at any other interfaces that they may encounter. Thus, three-dimensional electroseismic modeling may be accomplished with conventional EM and conventional seismic modeling tools, using the present theory to provide the link between them.