Scatterer identification in a 2D geophysical medium using an augmented computational time reversal method

Abstract

The problem of identifying an obstacle (scatterer) in the form of a cavity in a 2D geophysical medium is considered. This is posed as an inverse wave problem, where the location of the cavity is sought based on measurements of the elastic waves recorded by sensors located at certain points in the domain. The sensor measurements are noisy, and are generated synthetically as a first step. The inverse problem is solved by seeking the minimum of a specially designed cost functional, based on a computational time reversal (TR) procedure, where waves are radiated back in time from the sensors. The cost functional is defined to measure, for each scatterer candidate in the search space, the quality of the refocusing of the backward‐propagating waves on the given wave source at the end of the TR process. While the basic idea has appeared in previous publications, here it is applied to a 2D heterogeneous geophysical model (albeit a relatively simple one), and is enhanced by using several auxiliary techniques. These include (a) an “augmentation” technique, which is used to strengthen the coherent information (and thus to weaken the noncoherent information) by solving an elliptic problem at each time step; (b) experimentation with both instantaneous (impact) sources and time‐harmonic sources of finite duration; (c) combining the identification results of several sources and several source wavelengths to enhance identification; (d) reducing the size of the search space by a special “zooming in” technique; and (e) defining a performance index to assess the method's success and to provide a measure of confidence in the identification result in each specific case. Several numerical experiments are presented that demonstrate the performance of the proposed schemes. The sensitivity of the identification process to various parameters of the scatterer, the measurements, and the medium is investigated.

Single‐field identification of inclusions and cavities in an elastic medium

“…We wish to find 𝜇(x) such that the functional Π in ( 8) is minimized subject to Equations (6). In the spirit of the tutorial, 21 we discretize 𝜇 from the outset, using a finite element shape-function expansion, that is,…”

“…subject to the elastodynamics equations (6). Note that we do not include a regularization term in the definition of the objective functional as in (1).…”

“…In the context of wave‐based techniques, these are sometimes called obstacle identification or scatterer identification problems. Four well‐known classes of computational methods for scatterer identification are linear sampling method (LSM), 4 arrival time imaging (ATI), 5 also called Kirchhoff migration, time reversal (TR) 6 and full waveform inversion (FWI) 7,8 . Rabinovich et al 9 compare between the TR and FWI‐adjoint methods through a sequence of numerical experiments and point to the relative advantages of each.…”