Recovery of the sound speed for the Acoustic wave equation from\n phaseless measurements

2015/09/24 by Joonas Ilmavirta, Ilmavirta, Joonas, Alden Waters +1
Earth and Planetary Sciences · Engineering · Mathematics · #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #Electrical and Bioimpedance Tomography #FOS: Mathematics #Numerical methods in inverse problems #Seismic Imaging and Inversion Techniques

paper · pdf · doi:10.48550/arxiv.1509.07292

openalex publication_date 2015/09/24 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

We recover the higher order terms for the acoustic wave equation from\nmeasurements of the modulus of the solution. The recovery of these coefficients\nis reduced to a question of stability for inverting a Hamiltonian flow\ntransform, not the geodesic X-ray transform encountered in other inverse\nboundary problems like the determination of conformal factors. We obtain new\nstability results for the Hamiltonian flow transform, which allow to recover\nthe higher order terms.\n

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