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.

We have developed a joint geophysical inversion workflow that aims to improve subsurface imaging and decrease uncertainty by integrating petrophysical constraints and geologic data. In this framework, probabilistic geologic modeling is used as a source of information to condition the petrophysical constraints spatially and to derive starting models. The workflow then uses petrophysical measurements to constrain the values retrieved by geophysical joint inversion. The different sources of constraints are integrated into a least-squares framework to capture and integrate information related to geophysical, petrophysical, and geologic data. This allows us to quantify the posterior state of knowledge and to calculate posterior statistical indicators. To test this workflow, using geologic field data, we have generated a set of geologic models, which we used to derive a probabilistic geologic model. In this synthetic case study, we found that the integration of geologic information and petrophysical constraints in geophysical joint inversion could 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 geologic modeling permits more accurate retrieval of model geometry, and it better constrains the solution while still satisfying the statistics derived from geologic data. The analysis of statistical indicators at each step of the workflow indicates 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. Finally, the analysis of uncertainty to the integration of the conditioned petrophysical constraints also indicates that, for this example, the best results are obtained for joint inversion using petrophysical constraints spatially conditioned by geologic modeling.

Unlike some other well-known challenges such as facial recognition, where machine learning and inversion algorithms are widely developed, the geosciences suffer from a lack of large, labelled data sets that can be used to validate or train robust machine learning and inversion schemes. Publicly available 3D geological models are far too restricted in both number and the range of geological scenarios to serve these purposes. With reference to inverting geophysical data this problem is further exacerbated as in most cases real geophysical observations result from unknown 3D geology, and synthetic test data sets are often not particularly geological or geologically diverse. To overcome these limitations, we have used the Noddy modelling platform to generate 1 million models, which represent the first publicly accessible massive training set for 3D geology and resulting gravity and magnetic data sets (https://doi.org/10.5281/zenodo.4589883, Jessell, 2021). This model suite can be used to train machine learning systems and to provide comprehensive test suites for geophysical inversion. We describe the methodology for producing the model suite and discuss the opportunities such a model suite affords, as well as its limitations, and how we can grow and access this resource.

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.