Remote sensing of fractures with elastic waves is important in fields ranging from seismology to nondestructive testing. In many geophysical applications, fractures control the flow of fluids such as water, hydrocarbons or magma. While previous analytic descriptions of scattering mostly deal with very large or very small fractures (compared to the dominant wavelength), we present an analytic solution for the scattering of elastic waves from a fracture of arbitrary size. Based on the linear slip model for a dry fracture, we derive the scattering amplitude in the frequency domain under the Born approximation for all combinations of incident and scattered wave modes. Our analytic results match laser-based ultrasonic laboratory measurements of a single fracture in clear plastic, allowing us to quantify the compliance of a fracture.
Blum, Thomas E.; Snieder, Roel; van Wijk, Kasper; and Willis, Mark E.. (2011). "Theory and Laboratory Experiments of Elastic Wave Scattering by Dry Planar Fractures". Journal of Geophysical Research: Solid Earth, 116B08218. http://dx.doi.org/10.1029/2011JB008295