TRAC method in dissipative media—a first analysis in frequency domain and homogeneous media

Abstract

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.
In this paper, we focus on the redatuming application and investigate the feasibility of the TRAC method in the case of dissipation. In particular, we will see that performing the classical TRAC method, i.e., ignoring the dissipation, may give satisfactory results, even for larger values of dissipation.
An analysis is provided in the frequency-domain and one-space dimension and shows satisfactory updated versions of the TRAC method. Moreover, a systematic error study in two-space dimension is illustrated via numerical examples.