Hydrocarbon extraction leads to compaction of the gas reservoir, which is visible on the surface as subsidence. Subsidence measurements therefore give information on the hydrocarbon extraction and can thus be used to better estimate uncertain reservoir parameters. Normally, optical height difference measurements are taken between benchmarks, adjusted and tested to arrive at estimated height differences (or subsequently, heights relative to a reference benchmark) and are differenced between epochs to arrive at subsidence estimates. These can subsequently be used in inversions for reservoir parameters. We have designed, implemented and applied a new algorithm that uses measured optical height differences directly in the geophysical inversion. This eliminates the problems introduced by insufficient knowledge of the full covariance matrix of the subsidence estimates. The procedure was applied to invert for compaction of the Groningen gas reservoir in the Netherlands. We used a linear inversion procedure to update an existing reservoir compaction field. This yielded areas of increased and reduced compaction relative to the existing compaction field, which correspond with observed discrepancies in porosity and aquifer activity.