Frequency dependence of elasticity of rock—test of seismic velocity dispersion

Abstract

LINEAR theories of attenuation of acoustic or seismic waves in media, such as rocks, which are characterised by constant or nearly constant Q factors (fractional energy loss per cycle equals 2π/Q) imply velocity dispersion and, therefore, frequency dependence of elasticity. The effect is small, corresponding to a change of order 1 % over the period range of seismological interest (1 s to 1 h), and is consequently difficult to observe. However, it leads to an internal inconsistency in the development of earth models by inversion of free oscillation data and to discrepancies between these models and body wave data^1–3. It is a matter of considerable geophysical interest to resolve the problem. Validity of the linearity assumption has been questioned⁴ but we are now observing elliptical hysteresis loops in basalt and granite samples subjected to sinusoidal strains of order 10⁻⁶ and this is strong evidence that attenuation does become a linear phenomenon at low strain amplitudes. But whether or not perfect linearity applies, a direct demonstration of body wave dispersion is the most satisfying indication that earth model studies need revision.