有限尺寸声学孔径的全波形近似：正向与共轭波场
A Regularized Finite-Difference Approximation of Surface-restricted Emission and Reception Process in Acoustics with Application to Inverse Problems
AI总结：
本文通过建立单极子和偶极子积分公式与全波形近似的等价性，提出接收算子将自由空间压力波场映射到边界测量场，并推导了正向算子的共轭，用于提升声学正向问题和逆问题的近似与求解能力。
摘要：
声学波方程 governs 波传播，由体积辐射源或表面单极子或偶极子源引起。对于表面源，边界值问题通过Kirchhoff-Helmholtz或Rayleigh-Sommerfeld积分给出波场表示。本文首先建立单极子和偶极子积分公式与全波形近似的等价性。利用此等价性，引入接收算子将通过求解波方程得到的自由空间压力波场映射到边界限制的测量场。基于此迹映射，推导出正向算子的共轭。在Dirichlet型边界数据的常见假设下，共轭算子与偶极子积分公式在接收表面上的内场时间反转形式（除常数因子外）一致。本文旨在提升声学正向问题的近似和逆问题的求解能力，尤其关注需要精确幅值建模的应用，如治疗超声优化、衰减重建和光电声学成像。
英文摘要：
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 examining the equivalence between the analytic expressions of the associated monopole and dipole integral formulations and their regularized approximations. Leveraging these regularized formulations, 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 time-reversed form of the dipole integral formula, evaluated on the receiver surfaces. This study aims to advance the numerical approximation of forward problems and the solution of inverse problems in acoustics, with a particular focus on applications that require accurate amplitude modeling, including attenuation reconstruction and photoacoustic tomography.
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