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Unified Green's function retrieval by cross-correlation; connection with energy principles.
Roel Snieder1, Kees Wapenaar, Ulrich Wegler
1Center for Wave Phenomena and Department of Geophysics, Colorado School of Mines, Golden, Colorado 80401, USA. rsnieder@mines.edu
Summary
Scientists can now extract the Green's function, a key wave property, from system fluctuations. This method works for many linear systems, even those not time-reversible, by using volume sources for energy balance.
Area of Science:
- Physics
- Applied Mathematics
- Wave Phenomena
Background:
- The Green's function is crucial for understanding wave propagation in various physical systems.
- Previous methods successfully retrieved the Green's function for acoustic and elastic waves using cross-correlation of ambient noise.
Purpose of the Study:
- To generalize the extraction of the Green's function to a broader range of scalar linear systems.
- To identify conditions and methods for Green's function retrieval in non-time-reversible systems.
Main Methods:
- Theoretical extension of Green's function retrieval techniques.
- Analysis of energy balance (equipartitioning) requirements using volume sources for non-time-reversible systems.
- Application of the general theory to diverse systems like diffusion, Schrödinger, and wave equations.
Main Results:
- A generalized theory for Green's function extraction from system fluctuations is established.
- The necessity of volume sources for energy balance in non-time-reversible systems is demonstrated.
- The theory is validated across multiple physical examples, including wave, diffusion, and advection equations.
Conclusions:
- The developed theory enables Green's function extraction for a wide array of scalar linear systems.
- New applications are identified in fields such as fluid dynamics in porous media, quantum mechanics, and structural mechanics.
- The method provides a powerful tool for analyzing system responses from recorded fluctuations.
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