This work addresses the possibility of using a set of relocatable moving receivers for on the fly bottom inversion. The moving receivers form an array which shape may change along time according to the specific geo-acoustic features and characteristics of the area being surveyed, required resolution, water depth, etc. Previous work in this field used either pre-determined fixed receiving arrays or acoustic receivers at random positions. In the latter case, the random positions may change along time (e.g. drifters) or be fixed (e.g. in the bottom). Our case differs in the sense that the received array may take any shape (linear, planar, volumetric, etc), under practical limitations, and may adaptively change along time and space at user request. In all cases the receiver position is assumed known to a given accuracy which relates to the frequency band being used, and thus to the required resolution and bottom penetration. This work uses compressed sensing inspired techniques to obtain an optimal or near-optimal array geometry that adaptively samples the bottom return acoustic field. Realistic simulations using environmental information and configurations of previous experiments show that the estimation gain obtained in certain specific cases by array shape optimization is marginal with a tendency to a “one-size-fits-all” situation. However, from an optimality point of view, the results also show that there are classes of cases characterized by specific bottom features for which array configurations provide near-optimal results, leading to the situation of “a-few-sizes-fit-almost-all” [work supported by EU H2020 under project WiMUST ICT-645141].