We introduce a joint geophysical inversion workflow that aims to improve subsurface imaging and decrease uncertainty by integrating petrophysical constraints and geological data. In this framework, probabilistic geological modeling is used as a source of information to condition the petrophysical constraints spatially and to derive starting models. The workflow then utilizes petrophysical measurements to constrain the values retrieved by geophysical joint inversion. The different sources of constraints are integrated into a least-square framework to capture and integrate information related to geophysical, petrophysical and geological data. This allows us to quantify the posterior state of knowledge and to calculate posterior statistical indicators. To test this workflow, using geological field data we have generated a set of geological models, which we used to derive a probabilistic geological model. In this synthetic case study, we show that the integration of geological information and petrophysical constraints in geophysical joint inversion can reduce uncertainty and improve imaging. In particular, the use of petrophysical constraints retrieves sharper boundaries and better reproduces the statistics of the observed petrophysical measurements. The integration of probabilistic geological modeling permits more accurate retrieval of model geometry, and better constrains the solution 2 while still satisfying the statistics derived from geological data. The analysis of statistical indicators at each step of the workflow shows that 1) the inversion methodology is effective when applied to complex geology, and 2) the integration of prior information and constraints from geology and petrophysics significantly improves the inversion results while decreasing uncertainty. Lastly, the analysis of uncertainty to the integration of the conditioned petrophysical constraints also shows that, for this example, the best results are obtained for joint inversion using petrophysical constraints spatially conditioned by geological modeling. * i-th geological model cell Conditioning of petrophysical constraints

Abstract. We introduce a workflow integrating geological modelling uncertainty information to constrain gravity inversions. We test and apply this approach to the Yerrida Basin (Western Australia), where we focus on prospective greenstone belts beneath sedimentary cover. Geological uncertainty information is extracted from the results of a probabilistic geological modelling process using geological field data and their inferred accuracy as inputs. The uncertainty information is utilized to locally adjust the weights of a minimum-structure gradient-based regularization function constraining geophysical inversion. Our results demonstrate that this technique allows geophysical inversion to update the model preferentially in geologically less certain areas. It also indicates that inverted models are consistent with both the probabilistic geological model and geophysical data of the area, reducing interpretation uncertainty. The interpretation of inverted models reveals that the recovered greenstone belts may be shallower and thinner than previously thought.

Abstract. Three-dimensional (3-D) geological structural modeling aims to determine geological information in a 3-D space using structural data (foliations and interfaces) and topological rules as inputs. This is necessary in any project in which the properties of the subsurface matters; they express our understanding of geometries in depth. For that reason, 3-D geological models have a wide range of practical applications including but not restricted to civil engineering, the oil and gas industry, the mining industry, and water management. These models, however, are fraught with uncertainties originating from the inherent flaws of the modeling engines (working hypotheses, interpolator's parameterization) and the inherent lack of knowledge in areas where there are no observations combined with input uncertainty (observational, conceptual and technical errors). Because 3-D geological models are often used for impactful decision-making it is critical that all 3-D geological models provide accurate estimates of uncertainty. This paper's focus is set on the effect of structural input data measurement uncertainty propagation in implicit 3-D geological modeling. This aim is achieved using Monte Carlo simulation for uncertainty estimation (MCUE), a stochastic method which samples from predefined disturbance probability distributions that represent the uncertainty of the original input data set. MCUE is used to produce hundreds to thousands of altered unique data sets. The altered data sets are used as inputs to produce a range of plausible 3-D models. The plausible models are then combined into a single probabilistic model as a means to propagate uncertainty from the input data to the final model. In this paper, several improved methods for MCUE are proposed.The methods pertain to distribution selection for input uncertainty, sample analysis and statistical consistency of the sampled distribution. Pole vector sampling is proposed as a more rigorous alternative than dip vector sampling for planar features and the use of a Bayesian approach to disturbance distribution parameterization is suggested. The influence of incorrect disturbance distributions is discussed and propositions are made and evaluated on synthetic and realistic cases to address the sighted issues. The distribution of the errors of the observed data (i.e., scedasticity) is shown to affect the quality of prior distributions for MCUE. Results demonstrate that the proposed workflows improve the reliability of uncertainty estimation and diminish the occurrence of artifacts.

To reduce uncertainties in reconstructed images, geological information must be introduced in a numerically robust and stable way during the geophysical data inversion procedure. In the context of potential (gravity) data inversion, it is important to bound the physical properties by providing probabilistic information on the number of lithologies and ranges of values of possibly existing related rock properties (densities). For this purpose, we introduce a generalization of bounding constraints for geophysical inversion based on the alternating direction method of multipliers (ADMM). The flexibility of the proposed technique enables us to take into account petrophysical information as well as probabilistic geological modeling, when it is available. The algorithm introduces a priori knowledge in terms of physically acceptable bounds of model parameters based on the nature of the modeled lithofacies in the region under study. Instead of introducing only one interval of geologically acceptable values for each parameter representing a set of rock properties, we define sets of disjoint intervals using the available geological information. Different sets of intervals are tested, such as quasi-discrete (or narrow) intervals as well as wider intervals provided by geological information obtained from probabilistic geological modeling. Narrower intervals can be used as soft constraints encouraging quasi-discrete inversions. The algorithm is first applied to a synthetic 2D case for proof-of-concept validation and then to the 3D inversion of gravity data collected in the Yerrida basin (Western Australia). Numerical convergence tests show the robustness and stability of the bound constraints we apply, which is not always trivial for constrained inversions. This technique can be a more reliable uncertainty reduction method as well as an alternative to other petrophysically or geologically constrained inversions based on more classical “clustering” or Gaussian-mixture approaches.