Near field sampling type methods for the inverse fluid--solid interaction problem

The inverse fluid--solid interaction problem considered here is to determine the shape of an elastic body from pressure measurements made in the near field. In particular we assume that the elastic body is probed by pressure waves due to point sources, and the resulting scattered field and the normal derivative of the scattered field is available for every source and receiver combination on the source and measurement curves. We provide an analysis of the Reciprocity Gap (RG) method in this case, as well as the Linear Sampling Method (LSM). A novelty of our analysis is that we exhibit a connection between the RG method and a non--standard LSM using sources and receivers on different curves. We provide numerical tests of the algorithms using both synthetic and real data.