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Abstract

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 \emph{reception operators} that map free space-time 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 has significant implications for both forward and inverse problems in acoustics, particularly in applications requiring accurate amplitude modeling, such as therapeutic ultrasound optimization, attenuation reconstruction, and photoacoustic tomography.