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Extracting the Green function from diffuse, equipartitioned waves.

Alison E Malcolm1, John A Scales, Bart A van Tiggelen

  • 1Physical Acoustics Laboratory and Center for Wave Phenomena, Department of Geophysics, Colorado School of Mines, Golden, Colorado 80401, USA. amalcolm@dix.ines.edu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 25, 2004
PubMed
Summary

A ballistic pulse in a scattering medium transitions to diffusive behavior. Eventually, the wave-field correlation reveals the Green function, indicating energy equipartition.

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Area of Science:

  • Physics
  • Wave Propagation
  • Random Media

Background:

  • Wave propagation in random media is complex, transitioning from ballistic to diffusive regimes.
  • Understanding energy distribution and wave-field correlations is key in these regimes.

Purpose of the Study:

  • To investigate the transition of a ballistic pulse to diffusive propagation in a strongly scattering medium.
  • To observe the emergence of the Green function from wave-field correlations in the equipartitioned regime.

Main Methods:

  • Simulating or experimentally analyzing a ballistic pulse in a heterogeneous medium.
  • Measuring wave-field correlations over time and distance.
  • Comparing correlations to theoretical Green functions of the average medium.

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Main Results:

  • A ballistic pulse becomes diffusive after a few mean-free times.
  • The wave-field correlation approaches the sum of advanced and retarded Green functions in the equipartitioned regime.
  • The Green function emerges from the correlation at approximately 9 mean-free times in a heterogeneous rock sample.

Conclusions:

  • The study demonstrates the transition to diffusive wave propagation and energy equipartition in random media.
  • Observing the Green function from wave-field correlations validates theoretical predictions for strongly scattering environments.
  • This finding has implications for understanding wave transport in complex natural materials like rocks.