Energy partition of seismic coda waves in layered media: theory and application to Pinyon Flats Observatory

TL;DR

This study analyzes seismic coda wave energy partitioning at Pinyon Flats Observatory, revealing deviations from homogeneous models and developing a layered media theory that aligns well with observed energy ratios.

Contribution

The paper introduces a new theoretical framework for energy partition in layered elastic media, explaining observed seismic wave energy ratios.

Findings

Shear to compressional energy ratio stabilizes around 2.8 in the coda.

Vertical to horizontal kinetic energy ratio increases from 0.1 to 0.8 across 5-25Hz.

Layer resonance significantly affects energy partition, matching observations.

Abstract

We have studied the partition of shear, compressional and kinetic energies in the coda of ten earthquakes recorded on a dense array, located at Pinyon Flats Observatory (PFO), California. We observe a clear stabilization of the shear to compressional ($W^s/W^p$) energy ratio in the coda, with an average value of about 2.8. The ratio between the vertical and horizontal kinetic energies ($V^2/H^2$) can be measured from 5 to 25Hz and shows an abrupt transitionfrom 0.1 in the 5-10Hz band, to about 0.8 in the 15-25Hz band. These measured values are in sharp contrast with the theoretical prediction for equipartitioned elastic waves in a homogeneous half-space. To explain these observations, we have developed a theory of equipartition in a layered elastic half-space. Using a rigorous spectral decomposition of the elastic wave equation, we define equipartition as a white noise distributed over the complete set of eigenfunctions. The theory predicts that close to the resonance frequency of a low-velocity layer, the ratio between shear and compressional energies strongly decreases. Using a detailed model of the subsurface at PFO, this conterintuitive result is found to be in good qualitative and quantitative agreement with the observations.