非均匀流体介质内部散射声场重建的逐层计算方法*

入射声波激励下非均匀流体介质内部散射声场的重建方法对超声层析成像具有重要意义。以往采用矩量法求解，但该方法全域离散形成的复数满秩矩阵规模随着分辨率与计算精度的提高而急剧增大，对算力具有很高的要求，一定程度上限制了其在实际中的应用。为克服上述缺陷，本文以逐层离散、逐层计算为核心思想，以声散射基本公式与近场声全息理论为基础，推导出逐层计算非均匀流体介质内部散射声场的理论公式并给出对应的几何离散模型。为验证该方法的可行性，以矩量法为参照，对同样的介质模型进行介质内部声场重构仿真。结果表明，逐层算法不仅可以有效地重建非均匀流体介质内部散射声场，且大幅度减小了求解规模。

The layer-by-layer calculation method for reconstruction of scattered sound field in inhomogeneous fluid media

The reconstruction of scattered sound fields in inhomogeneous fluid media under the excitation of incoming sound waves is of great importance to ultrasonic tomography. In the past, the method of moments was used to solve the problem. However, the size of the complex full rank matrix formed by the method of global discretization increases sharply with the improvement of resolution and calculation accuracy, which has high requirements for computing power and limits its practical application to some extent. In order to overcome these shortcomings, based on the basic formulas of acoustic scattering and near-field acoustic holography, the theoretical formulas for calculating the scattered sound field in inhomogeneous fluid media layer by layer are deduced and the corresponding geometric dispersion models are given. To verify the feasibility of this method, the internal acoustic field reconstruction of the same media model is simulated with the method of moments as the reference. The results show that the layer-by-layer algorithm can not only effectively reconstruct the scattered sound field in non-uniform media, but also greatly reduce the solution size.