Two perspectives on equipartition in diffuse elastic fields in three dimensions.

Area of Science:

• Seismology and Solid Earth Geophysics
• Wave Propagation and Elasticity Theory

Background:

• The elastodynamic Green function is crucial for understanding wave propagation.
• Retrieving the Green function relies on cross-correlating motions within a diffuse wave field.
• Perfect field diffuseness, characterized by energy equipartition, is a prerequisite for exact Green function extraction.

Purpose of the Study:

• To theoretically investigate diffuse elastic fields in three-dimensional (3D) full-space and extend these findings to the half-space problem.
• To reconcile different viewpoints on energy equipartition in elastic wave fields.
• To derive benchmark results for diffuse energy densities applicable to Green function retrieval.

Main Methods:

• Gathering and extending theoretical results for diffuse elastic fields in 3D full-space.
• Analyzing energy density fluctuations in the elastic half-space, particularly within one Rayleigh wavelength depth.
• Deriving diffuse energy densities using two distinct approaches related to energy equipartition.

Main Results:

• Established the equivalence of two approaches to energy equipartition in elastic media.
• Demonstrated that derived diffuse energy densities are equal for both theoretical viewpoints.
• Identified conspicuous depth-dependent energy fluctuations in the elastic half-space.

Conclusions:

• The study provides benchmark theoretical results for diffuse elastic fields under the assumption of perfect diffuseness.
• Findings have practical implications for normalizing correlations in Green function retrieval.
• The results offer insights relevant to seismic imaging and understanding wave propagation in complex media.