A Full-waveform Approximation of Finite-Sized Acoustic Apertures: Forward and Adjoint Wavefields

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Hauptverfasser: Javaherian, Ashkan, Setarehdan, Seyed Kamaledin
Format: Preprint
Veröffentlicht: 2022
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author Javaherian, Ashkan
Setarehdan, Seyed Kamaledin
author_facet Javaherian, Ashkan
Setarehdan, Seyed Kamaledin
contents The acoustic wave equation governs wave propagation induced by either volumetric radiation sources, or by surface sources of monopole or dipole type. For surface sources, boundary value problems yield wavefield representations via the Kirchhoff-Helmholtz or Rayleigh-Sommerfeld integrals. This study begins by establishing an equivalence between the analytic expressions of the associated monopole and dipole integral formulations and their full-waveform approximations. Leveraging this equivalence, we introduce reception operators that map free space pressure wavefields-obtained by solving the wave equation-onto measured fields restricted to the boundary. Building on this trace mapping, we derive the adjoint of the forward operator. We show that, under the common practical assumption of Dirichlet-type boundary data, the adjoint operator coincides-up to a constant factor-with the interior-field time-reversed form of the dipole integral formula, evaluated on the receiver surfaces. This study aims to advance the approximation of forward problems and the solution of inverse problems in acoustics, with a particular focus on applications that require accurate amplitude modeling, including therapeutic ultrasound optimization, attenuation reconstruction, and photoacoustic tomography.
format Preprint
id arxiv_https___arxiv_org_abs_2212_04466
institution arXiv
publishDate 2022
record_format arxiv
spellingShingle A Full-waveform Approximation of Finite-Sized Acoustic Apertures: Forward and Adjoint Wavefields
Javaherian, Ashkan
Setarehdan, Seyed Kamaledin
Numerical Analysis
35L05, 45Q05, 65R20, 65R32, 65N21
G.1.8; G.1.9
The acoustic wave equation governs wave propagation induced by either volumetric radiation sources, or by surface sources of monopole or dipole type. For surface sources, boundary value problems yield wavefield representations via the Kirchhoff-Helmholtz or Rayleigh-Sommerfeld integrals. This study begins by establishing an equivalence between the analytic expressions of the associated monopole and dipole integral formulations and their full-waveform approximations. Leveraging this equivalence, we introduce reception operators that map free space pressure wavefields-obtained by solving the wave equation-onto measured fields restricted to the boundary. Building on this trace mapping, we derive the adjoint of the forward operator. We show that, under the common practical assumption of Dirichlet-type boundary data, the adjoint operator coincides-up to a constant factor-with the interior-field time-reversed form of the dipole integral formula, evaluated on the receiver surfaces. This study aims to advance the approximation of forward problems and the solution of inverse problems in acoustics, with a particular focus on applications that require accurate amplitude modeling, including therapeutic ultrasound optimization, attenuation reconstruction, and photoacoustic tomography.
title A Full-waveform Approximation of Finite-Sized Acoustic Apertures: Forward and Adjoint Wavefields
topic Numerical Analysis
35L05, 45Q05, 65R20, 65R32, 65N21
G.1.8; G.1.9
url https://arxiv.org/abs/2212.04466