Constraining stochastic 3-D structural geological models with topology information using Approximate Bayesian Computation in GemPy 2.1

Structural geomodeling is a key technology for the visualization and quantification of subsurface systems. Given the limited data and the resulting necessity for geological interpretation to construct these geomodels, uncertainty is pervasive and traditionally unquantified. Probabilistic geomodeling allows for the simulation of uncertainties by automatically constructing geomodel ensembles from perturbed input data sampled from probability distributions. But random sampling of input parameters can lead to construction of geomodels that are unrealistic, either due to modeling artefacts or by not matching known
information about the regional geology of the modeled system. We present here a method to incorporate geological information in the form of known geomodel topology into stochastic simulations to constrain resulting probabilistic geomodel ensembles using the open-source geomodeling software GemPy. Simulated geomodel realisations are checked against topology information using Approximate Bayesian Computation approach, to avoid the specification of a likelihood function. We demonstrate how we can infer the posterior distributions of the model parameters using topology information in two experiments: (1) A
synthetic geomodel using a rejection sampling scheme (ABC-REJ) to demonstrate the approach; (2) A geomodel of a subset of the Gullfaks field in the North Sea, comparing both rejection sampling and a Sequential Monte Carlo sampler (ABC-SMC). Possible improvements to processing speed of up to 10.1x are discussed, focusing on the use of more advanced sampling techniques to avoid the simulation of unfeasible geomodels in the first place. Results demonstrate the feasibility of using topol ogy graphs as a summary statistic, to restrict the generation of geomodel ensembles with known geological information and to obtain improved ensembles of probable geomodels which respect the known topology information and exhibits reduced uncertainty using stochastic simulation methods.