Sparse Reconstruction of Aliased Seismic Signals Recorded During the Insight Mars Mission

Abstract

The NASA InSight lander successfully placed a seismometer on the surface of Mars. Alongside, a hammering device was deployed that penetrated into the ground to attempt the first measurements of the planetary heat flow of Mars. The hammering generated repeated seismic signals that were registered by the seismometer. These signals can potentially be used to image the shallow subsurface just below the lander. However, the frequencies excited by the hammering probe widely exceed the Nyquist frequency dictated by the seismometer's sampling rate. Here, we propose an algorithm to reconstruct the seismic signals beyond the classical sampling theorem. We exploit the structure in the data due to thousands of repeated, only gradually varying hammering signals as the heat probe slowly penetrates into the ground. This allows us to reconstruct signals by enforcing a sparsity constraint in a modified Radon transform domain.