Hierarchical model for the scale-dependent velocity of seismic waves

TL;DR

This paper introduces a hierarchical model from polymer physics to explain the scale-dependent velocity of seismic waves, successfully capturing the saturation behavior observed in simulations.

Contribution

It presents a novel application of polymer physics models to seismology, addressing the limitation of perturbation theories in predicting velocity saturation.

Findings

Velocity saturation scales with the four-third power of fluctuation amplitude.

Model accurately predicts the saturation behavior seen in simulations.

Provides a new theoretical framework for seismic wave velocity analysis.

Abstract

Elastic waves of short wavelength propagating through the upper layer of the Earth appear to move faster at large separations of source and receiver than at short separations. This scale dependent velocity is a manifestation of Fermat's principle of least time in a medium with random velocity fluctuations. Existing perturbation theories predict a linear increase of the velocity shift with increasing separation, and cannot describe the saturation of the velocity shift at large separations that is seen in computer simulations. Here we show that this long-standing problem in seismology can be solved using a model developed originally in the context of polymer physics. We find that the saturation velocity scales with the four-third power of the root-mean-square amplitude of the velocity fluctuations, in good agreement with the computer simulations.