论文标题
部分可观测时空混沌系统的无模型预测
Full-waveform Approximation of Finite-Sized Acoustic Apertures: Forward and Adjoint Wavefields
论文作者
论文摘要
声波方程控制着由体积辐射源或单极或偶极类型的表面源引起的波传播。对于表面源，边界价值问题通过Kirchhoff-Helmholtz或Rayleigh-Sommerfeld积分产生波场表示。这项研究首先建立了单极和偶极积分制剂的分析表达式与其全波形近似之间的等效性。利用这种等价性，我们介绍了接收操作员，该接收器映射了通过求解波动方程的自由时空压力波场，即限制在边界上的测量场。在此跟踪映射的基础上，我们得出了向前操作员的伴随。我们表明，在Dirichlet型边界数据的常见实际假设下，伴随操作员与在边界上评估的内部偶极子积分公式的时间转换形式相吻合 - 与反相反的因子相吻合。这些发现对声学中的前进和反问题都具有重要意义，尤其是在需要准确的振幅建模的应用中，例如治疗性超声优化，衰减重建和光声断层扫描。
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 monopole and dipole integral formulations and their full-waveform approximations. Leveraging this equivalence, we introduce 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 an inverse constant factor--with the time-reversed form of the interior-field dipole integral formula, evaluated on the boundary. These findings have 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.
