The seismic exploration problem can be expressed as a linear integral relating the Earth model and the recorded data. An estimated Earth model may be recovered from observed data by inversion. A 2D acoustic, constant, density inversion algorithm is presented.; Standard smooth constraints deal well with noise, but blur material boundaries. In contrast, a blocky solution will encourage sharp discontinuities. This is enforced by placing sparse constraints on the model gradient. A non-linear sparse constraint found to be especially suited for blocky medical imaging by Charbonnier et al. (1997) is tested for exploration seismology.; The non-linear sparse/blocky constraint is tested for 1D seismic impedance inversion. It is then applied to the 2D migration/inversion problem. In both instances, it consistently recovers accurate, piecewise continuous profiles. Higher resolution images are obtained than those recovered by standard solutions.
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