Paper Info
Title
An augmented time reversal method for source and scatterer identification.
Abstract
We propose a computational method which improves the identification of sources and scatterers in a two-dimensional elastic medium using the Time Reversal (TR) technique. The identification procedure makes use of partial numerical data available at a small number of sensors. While in realistic applications these data are obtained by lab or field measurements, in the present work they are synthesized by solving the corresponding forward problem. We introduce an “augmentation” procedure that is utilized in addition to the TR technique and investigate its benefits. The augmentation procedure involves the solution of a suitable elliptic problem at selected time steps. In practice, one needs to solve, as a pre-process, a small number of “fundamental” elliptic problems which is equal to the number of measured quantities. A version of the augmentation procedure, which is easier to implement and involves almost no computational cost, is also presented. The local elastic energy in the domain is employed to decide whether the TR solution has properly refocused at the source. Cost functionals, whose minima are sought, are constructed for the source and scatterer identification problems. We conclude that augmentation improves the identification performance, in particular in the presence of noisy measurements. In some cases augmented TR succeeds in the identification whereas non-augmented TR fails.
Year
DOI
Venue
2018
10.1016/j.jcp.2018.08.026
Journal of Computational Physics
Keywords
Field
DocType
Time reversal,Source identification,Scatterer identification,Refocusing,Inverse problems,Elastodynamics
Small number,Mathematical optimization,Augmentation procedure,Algorithm,Maxima and minima,Elastic energy,Mathematics
Journal
Volume
ISSN
Citations 
375
0021-9991
0
PageRank 
References 
Authors
0.34
3
3
Name
Order
Citations
PageRank
Daniel Rabinovich131.12
Eli Turkel28414.00
Dan Givoli3829.91