The Groningen gas field has been compacting since the start of gas extraction in the 1960s because of pressure depletion in the reservoir, causing subsidence in the Groningen region. Geodetic techniques, such as optical leveling and satellite-borne Interferometric Synthetic Aperture Radar (InSAR), provide displacement estimates for subsidence monitoring. InSAR displacement estimates provide observation points with a higher spatial density and temporal sampling than leveling. Whereas identifying leveling benchmarks with subsidence caused by the compaction reservoir is possible, the InSAR’s sensitivity to multiple subsidence sources (e.g., compacting reservoir, soil motion, and infrastructure instability) complicates the identification of subsidence-driving mechanisms in InSAR estimates. Combining physics-based subsurface models with InSAR estimates into data assimilation is an approach to estimating to what extent reservoir compaction and other subsurface processes contribute to the total subsidence.....

The particle filter is a data assimilation method based on importance sampling for state and parameter estimation. We apply a particle filter in two different quasi-static experiments with models of subsidence caused by a compacting reservoir. The first model considers uncorrelated model state variables and observations, with observed subsidence resulting from a single source of strain. In the second model, subsidence is a summation of subsidence contributions from multiple sources which causes spatial dependencies and correlations in the observed subsidence field. Assimilating these correlated subsidence fields may trigger weight collapse. With synthetic tests, we show in a model of subsidence with 50 independent state variables and spatially correlated subsidence a minimum of 10¹³ particles are required to have information in the posterior distribution identical to that in a model with 50 independent and spatially uncorrelated observations. Spatial correlations cause an information loss which can be quantified with mutual information. We illustrate how a stronger spatial correlation results in lower information content in the posterior and we empirically derive the required ensemble size for the importance sampling to remain effective. We furthermore illustrate how this loss of information is reflected in the log likelihood, and how this depends on the number of model state variables. Based on these empirical results, we propose criteria to evaluate the required ensemble size in data assimilation of spatially correlated observation fields.