Inverse modelling of surface subsidence to better understand the Earth's subsurface

Surface subsidence can have major repercussions. A classic example is the seabed above the Ekofisk oil field, offshore Norway, where excessive subsidence made it necessary to raise the production platform by 6 m in the 1980s. On land, subsidence may significantly increase the risk of damage to buildings and infrastructure. But, observations of subsidence can also give us a better handle on the subsurface processes like compaction behaviour of a reservoir, (un)drained compartments, or the strength of the aquifer. However, to get this information from subsidence data, you have to carefully follow an inversion procedure. This inversion exercise is a big challenge in which all the available knowledge has to be used to the fullest possible extent. Without the use of this prior knowledge the solution will be non-unique or very ill-conditioned. In our method we distinguish and quantify shallow and deep causes of subsidence in a time-resolved procedure. We take full advantage of all the available knowledge in the form of a prior model, the prior model covariance matrix, and the data covariance matrix. The covariances quantify the expected spatial and temporal relationships between the model points and the data points. As an example, the incorporation of the model covariance implicitly guarantees smoothness of the model estimate, while maintaining specific geological features like sharp boundaries. In two examples we demonstrate the strength of the method. The first example shows that prior knowledge in the form of a correct model parameterization (deep and shallow compaction) is crucial for a reliable result. The second example demonstrates the significant added value of fully accounting for the geology and the reservoir engineering information. Probabilistic information is entered using Monte Carlo simulations with a standard reservoir simulator, with several driving parameters being uncertain. The Monte Carlo runs deliver the prior model estimate and its covariance matrix. The inversion results in a good approximation of the driving parameters, even while their effects in terms of subsidence are highly correlated.