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应用最广泛的模型之一——韦斯特韦尔特方程，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相关参数。具体而言，这两个参数为非线性参数 $\kappa(x)$（声学文献中常称为 $B/A$）和波速 $c_0(x)$。这些量空间变化的确定可作为成像手段。我们考虑与这些应用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（及局限性）。