Solving an inverse obstacle problem for the wave equation by using the boundary control method

Abstract

We introduced in [arXiv:1106.3204] a method to locate discontinuities of a wave speed in dimension two from acoustic boundary measuments modelled by the hyperbolic Neumann-to-Dirichlet operator. Here we extend the method for sound hard obstacles in arbitrary dimension. We present numerical experiments with simulated noisy data suggesting that the method is robust against measurement noise.

References in corpus (1)

• Inverse obstacle problem for the non-stationary wave equation with an unknown background

Cited by in corpus (11)

• Extracting the geometry of an obstacle and a zeroth-order coefficient of a boundary condition via the enclosure method using a single reflected wave over a finite time interval
• On the Construction of Virtual Interior Point Source Travel Time Distances from the Hyperbolic Neumann-to-Dirichlet Map
• The enclosure method for inverse obstacle scattering over a finite time interval: IV. Extraction from a single point on the graph of the response operator
• The reconstruction of sound speed in the Marmousi model by the boundary control method
• Dynamical and spectral Dirac systems: response function and inverse problems
• The enclosure method for inverse obstacle scattering over a finite time interval: V. Using time-reversal invariance
• A Linearized Boundary Control Method for the Acoustic Inverse Boundary Value Problem
• A Non-Iterative Reconstruction Algorithm for the Acoustic Inverse Boundary Value Problem
• The enclosure method for the heat equation using time-reversal invariance for a wave equation
• Inverse scattering on non-compact manifolds with general metric
• An Exact Redatuming Procedure for the Inverse Boundary Value Problem for the Wave Equation