Optimal Transport and Seismic Rays

Article Geochemistry & Geophysics

Capturing seismic velocity changes in receiver functions with optimal transport

Jared Bryan et al.

Summary: Temporal changes in seismic velocities are crucial for tracking structural changes within the crust. We propose a deep seismic monitoring method based on teleseismic receiver functions, which provide information about crustal velocity structures from the bottom-up. Using synthetic waveform modelling, we demonstrate that receiver functions are uniformly sensitive to velocity changes throughout the crust and can determine the depth of perturbations. We introduce a novel method using optimal transport for measuring non-linear time-amplitude signal variations in receiver function monitoring, enabling comparison of full waveform distributions.

GEOPHYSICAL JOURNAL INTERNATIONAL (2023)

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Article Mathematics, Applied

Optimal Transport Based Seismic Inversion:Beyond Cycle Skipping

Bjorn Engquist et al.

Summary: Full-waveform inversion is a standard process for seismic imaging inverse problems, using PDE-constrained optimization to determine unknown geophysical parameters. Introducing the Wasserstein metric can help mitigate cycle skipping and improve inversion accuracy.

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS (2022)

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Article Geochemistry & Geophysics

Geophysical inversion and optimal transport

Malcolm Sambridge et al.

Summary: In this paper, a new approach is proposed to measure the agreement between two oscillatory time-series, such as seismic waveforms, and it is demonstrated that this approach can be effectively used in inverse problems. The proposed measure is based on Optimal Transport theory and the Wasserstein distance, with a novel transformation of the time-series to meet necessary normalization and positivity conditions. The measure is differentiable and can be readily used within an optimization framework. The performance of the approach is demonstrated with various synthetic examples, including seismic source inversion, showing significantly better convergence properties than conventional L-2 misfits. The relationship between Optimal Transport and Bayesian inference is also briefly discussed.

GEOPHYSICAL JOURNAL INTERNATIONAL (2022)

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Article Mathematics, Applied

FAST ITERATIVE SOLUTION OF THE OPTIMAL TRANSPORT PROBLEM ON GRAPHS

Enrico Facca et al.

Summary: This paper discusses the numerical solution of the optimal transport problem on undirected weighted graphs, proposing an effective method that combines backward Euler time stepping scheme with inexact Newton-Raphson method. Experimental results show that solving linear systems involving weighted Laplacian matrices efficiently using algebraic multigrid methods leads to an accurate solver for the optimal transport problem on graphs.

SIAM JOURNAL ON SCIENTIFIC COMPUTING (2021)

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Article Biochemical Research Methods