Constant Q attenuation of subsurface radar pulses

Abstract

Q is a measure of the energy stored to the energy dissipated in a propagating wave and can be estimated from the ratio of attenuation and frequency. For seismic waves, Q has been found to be essentially independent of frequency. As a result, attenuation is an approximately linear function of frequency and the impulse response function of the earth. Hence, the distortion of a seismic pulse as it propagates can be described by a single parameter. Laboratory measurements show that the attenuation of radio waves in some geological materials can also be approximated by a linear function of frequency over the bandwidths of typical subsurface radar pulses. We define a new parameter Q* to describe the slope of this linear region. The impulse response of the transfer function for a given value of Q* differs from that of the same value of Q only in total amplitude. Thus the change of shape of a radar pulse as it travels through these materials can also be described by a single parameter. The constant Q* model successfully describes the distortion of radar pulses propagated through a laboratory water tank and through weathered granite in a borehole field study.