The Determination of Q, Dynamic Viscosity and Transient Creep Curves from Wave Propagation Measurements

Perhaps the best theoretical approximation to the experimentally observed attenuation and spreading of seismic body waves is due to Futterman. Wuenschel has utilized the Pierre shale field data of McDonal et al. as well as his own two-dimensional model work using plexiglas sheet, to obtain remarkable confirmation of Futterman's approach. However, Futterman's assumption of a linear attenuation—frequency relation requires truncation at both ends of the frequency spectrum. The arbitrariness of this truncation leads to unnecessary parameters which make his approximation awkward to use. We discuss a power-law approximation to the attenuation characteristic which does not have this difficulty. Emphasis will be on computation of mechanical properties such as spatial 'Q', magnitude and loss angle of the modulus, dynamic viscosity and transient creep. These computations which are based upon the wave propagation measurements of Jordan will be seen to be in remarkable agreement with independent measurements by Lethersich, who utilized direct experimental procedures.