TY - JOUR
T1 - Inverse Obstacle Scattering in an Unbounded Structure
AU - Bao , Gang
AU - Liu , Huayan
AU - Li , Peijun
AU - Zhang , Lei
JO - Communications in Computational Physics
VL - 5
SP - 1274
EP - 1306
PY - 2019
DA - 2019/08
SN - 26
DO - http://doi.org/10.4208/cicp.2019.js60.01
UR - https://global-sci.org/intro/article_detail/cicp/13265.html
KW - Helmholtz's equation, inverse scattering problem, unbounded rough surface, domain derivative, uniqueness, local stability.
AB - <p style="text-align: justify;">This paper is concerned with the acoustic scattering of a point incident wave
by a sound hard obstacle embedded in a two-layered lossy background medium which
is separated by an infinite rough surface. Given the point incident wave, the direct
scattering problem is to determine the acoustic wave field for the given obstacle and
infinite rough surface; the inverse scattering problem is to determine both the obstacle
and the infinite rough surface from the reflected and transmitted wave fields measured
on two plane surfaces enclosing the structure. For the direct scattering problem, the
well-posedness is studied by using the method of boundary integral equations. For the
inverse scattering problem, we prove that the obstacle and the infinite rough surface
can be uniquely determined by the measured wave fields corresponding to a single
point incident wave. To prove the local stability, the domain derivative of the wave
field with respect to the change of the shapes of the obstacle and the infinite rough
surface is examined. The local stability indicates that the Hausdorff distance of two
domains is bounded above by the distance of corresponding wave fields if the two
domains are close enough.</p>