由低频散射声场重建有耗类流体柱体的三个力学材料常数
Reconstruction of the three mechanical material constants of a lossy fluid-like cylinder from low-frequency scattered acoustic fields
摘要：
本文以低频声波为探测辐射，研究了圆柱形区域的介质反问题。示出了对于$k_{0}a$中的二阶（$k_{0}$是主介质中的波数，$a$是圆柱体的半径），仅前三项（即，阶数为0、-1和+1）是非零的，并且材料参数以显式方式进入这些项。此外，零阶项仅包含两个未知材料常数（即，圆柱体的复数压缩率的实部和虚部$κ_{1}$）而$\pm 1$阶项包含其它材料常数（即，圆柱体的密度$ρ_{1}$）。一种方法，依赖于知识的远区散射场的整体和$ρ_{1}$和$κ_{1}$的显式表达式，设计和示出给这些数量的高度精确的估计，即使对于频率，使得$k_{0}a$是大到0.1。
英文摘要：
The inverse medium problem for a circular cylindrical domain is studied using low-frequency acoustic waves as the probe radiation. It is shown that to second order in $k_{0}a$ ($k_{0}$ the wavenumber in the host medium, $a$ the radius of the cylinder), only the first three terms (i.e., of orders 0, -1 and +1) in the partial wave representation of the scattered field are non-vanishing, and the material parameters enter into these terms in explicit manner. Moreover, the zeroth-order term contains only two of the unknown material constants (i.e., the real and imaginary parts of complex compressibility of the cylinder $κ_{1}$) whereas the $\pm 1$ order terms contain the other material constant (i.e., the density of the cylinder $ρ_{1}$). A method, relying on the knowledge of the totality of the far-zone scattered field and resulting in explicit expressions for $ρ_{1}$ and $κ_{1}$, is devised and shown to give highly-accurate estimates of these quantities even for frequencies such that $k_{0}a$ is as large as 0.1.
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