SOLUTION OF PRIDE'S EQUATIONS THROUGH POTENTIALS

Abstract

In 1994, S. Pride offered a system of equations describing interdependent propagation of acoustic and electromagnetic (EM) fields in porous media saturated by a fluid electrolyte (electrokinetic effect). We proved that the displacement vectors of frame and of pore fluid can be represented as a linear combinations of gradients of two scalar potentials and rotors of two vector potentials provided the coefficients of Pride's equations are independent of spatial coordinates. Each of these potentials satisfies Helmholtz equation with appropriate complex velocity. This representation underlies the computer code created by us for exploring borehole acoustics logging problems in axial-symmetric radially layered medium. Noteworthy, layers can be of any of the following types: uniform porous medium saturated by fluid electrolyte, uniform nonporous elastic medium, compressible nonviscous fluid or compressible viscous fluid. Results of numerical experiments are presented and discussed. The most important of them is that the back influence on acoustic disturbance of EM field excited by this disturbance is negligibly small in usually used frequency band and for realistic formation parameters. The mechanism of generation and propagation of different types of EM waves during acoustic logging is discussed as well.