Estimating uncertainties on net erosion from well-log porosity data

Estimating the amount of erosion experienced by a sedimentary basin during its geological history plays a key role in basin modelling. In this paper, we present a novel probabilistic approach to estimate net erosion from porosity-depth data from a single well. Our approach uses a Markov chain Monte Carlo algorithm which readily allows us to deal with imprecise knowledge of the lithology-dependent compaction parameters in a joint inversion scheme using multiple lithologies. The results using synthetic data highlight the advantages of our approach over conventional techniques for net erosion estimation: (a) uncertainties on compaction parameters can be effectively mapped into a probabilistic solution for net erosion; (b) posterior uncertainties are easy to quantify; (c) the joint inversion scheme can automatically reconcile porosity data from different lithologies. Our results also underscore the critical role of prior assumptions on controlling the retrieved estimates for net erosion. Using real data from a well in the Barents Sea, we simulate three possible scenarios of variable prior assumptions on compaction parameters to demonstrate the general applicability of our approach. Strong prior assumptions on the compaction parameters led to unrealistic estimates of net erosion for the target well, indicating the assumptions are probably inappropriate. Our preferred strategy for this dataset is to include additional data to constrain the normal compaction trend of the sediments. This provides a net erosion estimate for the target well of about 2300 m with a standard deviation of 140 m which is in line with previous studies. Finally, we discuss potential guidelines to deal with real applications in which data from normally compacted sediments are not available. One is to use our algorithm as a hypothesis-testing tool to evaluate the results under a large set of assumed compaction parameters. A second is to infer compaction parameters and net erosion simultaneously from the target well porosity data. Although appealing and successful with synthetic data, this strategy provides results which are strongly dependent on the calibration data and the geological history of the sediments sampled by the target well.