Frequency-independent background internal friction in heterogeneous solids

A source of elastic wave internal friction is proposed for complex, randomly heterogeneous solids. It arises from the dissipation of long-range thermal currents due to temperature waves excited by dilatational strain fluctuations between extended elastically dissimilar regions in a solid containing multiple heterogeneities. Dissipation of thermal currents driven by temperature waves across grain boundaries is a part of conventional theory in the high-frequency limit where only individual anisotropies immediately adjacent to each other are considered, and the range of the waves is small compared to a grain size. It is argued that such dissipation will also become important toward low frequency if a random distribution of elastic heterogeneity exists on a scale exceeding both the thermal skin depth and the grain size. In this event, nearly adiabatic temperature differences arise, in response to an incident elastic wave, between contiguous regions the size of the skin depth due to the difference in average elastic properties. Fast local relaxation on the scale of the grain size as described by prior theory equalizes temperature over such regions, but the relaxation between them is controlled by the skin depth rather than the structure of the inhomogeneities. Dissipation due to this long-range relaxation produces a figure of merit Q of magnitude 100-1000 for most rocks which is independent of (or nearly independent of) frequency, depending upon the properties and distribution of the inhomogeneities. Qualitative comparison with experiment is given for five types of rock, three glasses, and several other complex solids in the kilocycle frequency region which supports the hypotheses. For sufficiently small grain or effective crystallite size, the effect persists well into the megacycle range. Existing attenuation data for solids with granular or disordered molecular structure, or pure crystalline materials with high concentrations of dislocations, appear consistent with the predictions of the theory.