Energy landscape interpretation of universal linearly increasing absorption with frequency

TL;DR

This paper proposes that the universal linear increase in wave absorption with frequency across various media can be explained by a flat activation energy landscape, linking thermally activated relaxation processes to a maximum entropy state.

Contribution

It introduces a novel interpretation of absorption as an integral over an energy landscape, revealing that the universal linear trend corresponds to a maximally unconstrained, flat landscape.

Findings

Absorption increases linearly with frequency in diverse media.

A flat activation energy landscape explains the universal power-law behavior.

Thermally activated relaxation processes underpin the observed absorption properties.

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.