This paper considers the Westervelt equation, one of the most widely used models in nonlinear acoustics, and seeks to recover two spatially-dependent parameters of physical importance from time-trace boundary measurements. Specifically, these are the nonlinearity parameter $\kappa(x)$ often referred to as $B/A$ in the acoustics literature and the wave speed $c_0(x)$. The determination of the spatial change in these quantities can be used as a means of imaging. We consider identifiability from one or two boundary measurements as relevant in these applications. For a reformulation of the problem in terms of the squared slowness $\mathfrak{s}=1/c_0^2$ and the combined coefficient $\eta=\frac{B/A+2}{\varrho_0 c_0^4}$ we devise a frozen Newton method and prove its convergence. The effectiveness (and limitations) of this iterative scheme are demonstrated by numerical examples.

翻译：本文研究非线性声学中最广泛使用的模型之一——Westervelt方程，旨在通过时间迹边界测量恢复两个具有物理重要性的空间依赖参数。具体而言，这两个参数分别为声学文献中常记为$B/A$的非线性参数$\kappa(x)$以及波速$c_0(x)$。这些量空间变化的测定可作为一种成像手段。我们考虑与这些应用场景相关的单次或两次边界测量的可辨识性问题。针对以平方慢度$\mathfrak{s}=1/c_0^2$和组合系数$\eta=\frac{B/A+2}{\varrho_0 c_0^4}$重新表述的问题，我们设计了一种冻结牛顿法并证明了其收敛性。数值算例展示了该迭代方案的有效性及其局限性。