TRAC method in dissipative media -Part I: Analysis in 1D and frequency domain
Résumé
In this paper, we propose to explore the Time-Reversed Absorbing Condition (TRAC) method in the case of dissipative homogeneous media. In previous work, the TRAC method was derived from the time-reversibility of the (undamped) wave equation and proved to be efficient in both the time-domain and the frequency-domain. Namely, two main utilisations of the TRAC method have been probed: (a) redatuming, i.e., moving virtually the measurements by reconstructing the wavefield and (b) tracking down the location of a possible inclusion inside the domain. However, many applications working with waves, and in need of redatuming for instance, require to add a dissipative component to their model. Accordingly, a study of the TRAC method in the case of dissipation is relevant and, in particular, we will see that performing the standard TRAC method, i.e., ignoring the dissipation, does not give satisfactory results. An analysis is provided in the frequency-domain and one-space dimension and shows satisfactory updated versions of the TRAC method. Numerical examples in 1D and 2D are presented to illustrate the results.
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