Acoustic head wave on the borehole wall in a porous formation and the causes for its accompanying electromagnetic field

To understand the propagation mechanism of the acoustic head wave and its accompanying electromagnetic field during logging in a porous formation, we studied the displacement characteristics of the wave. Calculations by both the fast compressional branch-cut-integral and the real-wavenumber-integral methods show that the head wave travels along the borehole wall with the fast compressional wave velocity, but it differs from a plane compressional wave in two aspects. First, the head wave causes radial displacement as well as axial displacement. Second, it is composed of the gradients of the fast and slow compressional potentials and the rotation of the shear potential. The gradient of the slow compressional potential constitutes the dominating part of the fluid filtration. It is the slow compressional potential that induces electric field that accompanies the acoustic head wave during acousto-electric well logging. And it is the shear potential that induces magnetic field that accompanies the acoustic head wave.