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κ-statistics approach to optimal transport waveform inversion.
Sérgio Luiz E F da Silva1, G Kaniadakis1
1Department of Applied Science and Technology, Politecnico di Torino, 10129 Torino, Italy.
Physical Review. E
|October 21, 2022
Summary
This study introduces a new method combining optimal transport theory and κ-statistical thermodynamics to solve phase ambiguity in waveform analysis. The approach enhances physical parameter extraction in complex scientific and geophysical problems.
Area of Science:
- Physics
- Geophysics
- Statistical Thermodynamics
Background:
- Extracting unmeasurable physical parameters from data is challenging.
- Phase ambiguity in waveforms hinders physical model construction.
Purpose of the Study:
- To present a novel approach for mitigating phase ambiguity in waveform-driven problems.
- To improve the accuracy of physical parameter extraction.
Main Methods:
- Combining optimal transport theory with κ-statistical thermodynamics.
- Constructing an energy function using a κ-Gaussian distribution to create an optimal transport metric.
Main Results:
- The proposed method outperforms classical frameworks in geophysical inverse problems.
- Demonstrated effectiveness on a nonlinear, wave-equation-based numerical solution.
Conclusions:
- The κ-generalized optimal transport metric offers a versatile solution for various inverse problems.
- Applicable to power-law exponent estimation and quantum mechanics machine learning.
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