Energy landscape interpretation of universal linearly increasing absorption with frequency

Abstract

Absorption of elastic waves in complex media is commonly found to increase linearly with frequency, for both longitudinal and shear waves. This ubiquitous property is observed in media such as rocks, unconsolidated sediments, and human tissue. Absorption is due to relaxation processes at the level of atomic scales and up to the sub-micron scale of biological materials. The effect of these processes is usually expressed as an integral over relaxation frequencies or relaxation times. Here we argue that these processes are thermally activated. Unusual for ultrasonics and seismics, we can therefore transform the expression for absorption from the frequency or time domains to an integral over an activation energy landscape weighted by an energy distribution. The universal power-law property surprisingly corresponds to a flat activation energy landscape. This is the solution which maximizes entropy or randomness. Therefore the linearly increasing absorption corresponds to the energy landscape with the fewest possible constraints.

9 pages, 4 figures

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