On the crack inverse problem for pressure waves in half-space

After formulating the pressure wave equation in half-space minus a crack with a zero Neumann condi-tion on the top plane, we introduce a related inverse problem. That inverse problem consists of identifying the crack and the unknown forcing term on that crack from overdetermined boundary data on a relatively open set of the top plane. This inverse problem is not uniquely solvable unless some additional assump-tion is made. However, we show that we can differentiate two cracks P1 and P2 under the assumption that R3 \ P1 ? P2 is connected. If that is not the case we provide counterexamples that demonstrate non -uniqueness, even if P1 and P2 are smooth and "almost" flat. Finally, we show in the case where R3 \P1 ? P2 is not necessarily connected that after excluding a discrete set of frequencies, P1 and P2 can again be dif-ferentiated from overdetermined boundary data. (c) 2023 Elsevier Inc. All rights reserved.