Subsurface target illumination in elastic hosts: a comparison of time-reversal and inverse-source approaches

Abstract

The need for focusing wave energy to selected targets embedded within a host is commonly shared among various engineering fields, whether for stimulation and imaging in exploration geophysics, for contaminant removal in geo-environmental engineering, or for diagnostic/therapeutic purposes in medicine. In this presentation, we discuss the problem of focusing wave energy to multiple subsurface targets embedded within a semi-infinite heterogeneous elastic host. We review the advantages and disadvantages of two distinct approaches: first, using the apparatus of PDE-constrained optimization, we describe an inverse source (IS) approach, where we seek to design optimal excitations (both in space and time) in order to maximize target illumination. The second approach is rooted on the time-reversibility (TR) of the lossless wave equation; however the unboundness of the host, and equipment limitations that necessitate that recorded Dirichlet data be time reversed as Neumann data, create particularly adverse conditions for time-reversal. To overcome, we discuss a switching time-reversing mirror, and report on numerical experiments that show illumination resolution improvement. We define target illumination metrics to assess the relative performance of the IS and TR methods, and, using numerical experiments, we show that both approaches have similar efficiency.