ALBERT

Description: Summary We explore here the benefits of using constraints from seismic tomography in gravity data inversion and how inverted density distributions can be improved by doing so. The methodology is applied to a real field case in which we reconstruct the density structure of the Pyrenees along a southwest-northeast transect going from the Ebro basin in Spain to the Arzacq basin in France. We recover the distribution of densities by inverting gravity anomalies under constraints coming from seismic tomography. We initiate the inversion from a prior density model obtained by scaling a pre-existing compressional seismic velocity Vp model using a Nafe-Drake relationship : the Vp model resulting from a full-waveform inversion of teleseismic data. Gravity data inversions enforce structural similarities between Vp and density by minimizing the norm of the cross-gradient between the density and Vp models. We also compare models obtained from 2.5D and 3D inversions. Our results demonstrate that structural constraints allow us to better recover the density contrasts close to the surface and at depth, without degrading the gravity data misfit. The final density model provides valuable information on the geological structures and on the thermal state and composition of the western region of the Pyrenean lithosphere.

Description: 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.

Description: This paper proposes and demonstrates improvements for the Monte Carlo simulation for uncertainty propagation (MCUP) method. MCUP is a type of Bayesian Monte Carlo method aimed at input data uncertainty propagation in implicit 3-D geological modeling. In the Monte Carlo process, a series of statistically plausible models is built from the input dataset of which uncertainty is to be propagated to a final probabilistic geological model or uncertainty index model. Significant differences in terms of topology are observed in the plausible model suite that is generated as an intermediary step in MCUP. These differences are interpreted as analogous to population heterogeneity. The source of this heterogeneity is traced to be the non-linear relationship between plausible datasets' variability and plausible model's variability. Non-linearity is shown to mainly arise from the effect of the geometrical rule set on model building which transforms lithological continuous interfaces into discontinuous piecewise ones. Plausible model heterogeneity induces topological heterogeneity and challenges the underlying assumption of homogeneity which global uncertainty estimates rely on. To address this issue, a method for topological analysis applied to the plausible model suite in MCUP is introduced. Boolean topological signatures recording lithological unit adjacency are used as n-dimensional points to be considered individually or clustered using the density-based spatial clustering of applications with noise (DBSCAN) algorithm. The proposed method is tested on two challenging synthetic examples with varying levels of confidence in the structural input data. Results indicate that topological signatures constitute a powerful discriminant to address plausible model heterogeneity. Basic topological signatures appear to be a reliable indicator of the structural behavior of the plausible models and provide useful geological insights. Moreover, ignoring heterogeneity was found to be detrimental to the accuracy and relevance of the probabilistic geological models and uncertainty index models. Highlights. Monte Carlo uncertainty propagation (MCUP) methods often produce topologically distinct plausible models. Plausible models can be differentiated using topological signatures. Topologically similar probabilistic geological models may be obtained through topological signature clustering.

Description: 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.

Description: Three-dimensional (3D) geological modeling aims to determine geological information in a 3D space using structural data (foliations and interfaces) and topological rules as inputs. They are necessary in any project where the properties of the subsurface matters, they express our understanding of geometries in depth. For that reason, 3D geological models have a wide range of practical applications including but not restrained to civil engineering, oil and gas industry, 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) combined with input uncertainty (observational-, conceptual- and technical errors). Because 3D geological models are often used for impactful decision making it is critical that all 3D geological models provide accurate estimates of uncertainty. This paper’s focus is set on the effect of structural input data uncertainty propagation in implicit 3D geological modeling using GeoModeller API. This aim is achieved using Monte Carlo simulation uncertainty estimation (MCUE), a heuristic 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 3D 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 inappropriate 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 diminishes the occurrence of artefacts.

Description: We introduce a workflow integrating geological uncertainty information in order to constrain gravity inversions. We test and apply this approach to data from 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 uncertainty as input. It 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 finally reveals that the recovered greenstone belts may be shallower and thinner than previously thought.

Description: This paper proposes and demonstrates improvements for the Monte Carlo simulation for Uncertainty Estimation (MCUE) method. MCUE is a type of Bayesian Monte Carlo aimed at input data uncertainty propagation in implicit 3D geological modeling. In the Monte Carlo process, a series of statistically plausible models are built from the input data set which uncertainty is to be propagated to a final probabilistic geological model (PGM) or uncertainty index model (UIM). Significant differences in terms of topology are observed in the plausible model suite that is generated as an intermediary step in MCUE. These differences are interpreted as analogous to population heterogeneity. The source of this heterogeneity is traced to be the non-linear relationship between plausible datasets’ variability and plausible model’s variability. Non-linearity is shown to arise from the effect of the geometrical ruleset on model building which transforms lithological continuous interfaces into discontinuous piecewise ones. Plausible model heterogeneity induces geological incompatibility and challenges the underlying assumption of homogeneity which global uncertainty estimates rely on. To address this issue, a method for topological analysis applied to the plausible model suite in MCUE is introduced. Boolean topological signatures recording lithological units’ adjacency are used as n-dimensional points to be considered individually or clustered using the Density-Based Spatial Clustering of Applications with Noise (DBSCAN) algorithm. The proposed method is tested on two challenging synthetic examples with varying levels of confidence in the structural input data. Results indicate that topological signatures constitute a powerful discriminant to address plausible model heterogeneity. Basic topological signatures appear to be a reliable indicator of the structural behavior of the plausible models and provide useful geological insights. Moreover, ignoring heterogeneity was found to be detrimental to the accuracy and relevance of the PGMs and UIMs.

Description: The integration of petrophysical data and probabilistic geological modelling in geophysical joint inversion is a powerful tool to solve exploration challenges. Models obtained from geologically and/or petrophysically constrained inversions are the result of complex interactions between correspondingly diverse data sets. Therefore, it is important to understand how non-geophysical input uncertainty impacts inverted models. In this paper, we propose to study the influence of uncertainty in geological and petrophysical measurements used to derive prior information and constraints onto geophysical inversion. Starting from geological field data from the Mansfield area (Victoria, Australia), we simulate low, medium and high uncertainty levels in geological measurements and petrophysical data, combined into a series of nine realistic case scenarios. This allows us to investigate the impact and propagation of uncertainty from non-geophysical measurements into geophysical inversion. We calculate misfit indicators and reconstruct lithological models a posteriori to analyse inversion results. We complement the examination of inverted models with topological analysis of lithological models in order to quantify the geological resemblance between the recovered and reference models. Our work reveals that the influence of uncertainty in geological measurements over the recovered lithological models is significantly stronger than it is for petrophysical data. Our posterior analysis indicates that intermediate petrophysical uncertainty provides optimum results.

Description: Monte Carlo Uncertainty Estimation (MCUE) is an emerging heuristic uncertainty propagation method designed to provide reliable and time/cost efficient estimates of geometrical uncertainties in 3D geological modeling. MCUE is a subtype of Bayesian Monte Carlo method similar to geostatistical simulation. The methods described here rely on disturbance probability distributions that are parameterized to best represent individual input uncertainty. Essentially, disturbance distributions quantify the error about the location (x, y, z) and orientation (dip and azimuth) of observed geological structures. The disturbance distributions are sampled either independently or via a Markov-Chain to produce many plausible alternative datasets. These plausible datasets are then input to a 3D geological modeling engine to build a series of plausible alternative model realizations. Further processing may be applied to the series of plausible models to provide valuable decision aids such as probabilistic models, reliability models, or uncertainty reduction hotspot maps.In this paper, a complete and comprehensive MCUE procedure for common drillhole path and log uncertainty propagation is proposed. Basic concepts of drillhole uncertainty are introduced and are applied to a Markov Chain scheme. Appropriate disturbance distributions for the different parts of the problem and their respective parameterization are discussed. The method proposed is demonstrated on three separate proof of concept case studies of increasing complexity. Results demonstrate that the method is able to propagate path and log uncertainty appropriately. First order interpretation indicates that both path and log uncertainty increase with depth and angle of attack to the geological interfaces. Ignoring drillhole uncertainty was found to be detrimental to the understanding of a modeled area which is most likely due to the over-constraining effect brought by “perfect” drillholes. The third case study (Mansfield) hints that uncertainty is better reduced when drillholes intersect the “triple line” that partitions three distinct lithologies. In cross-sections, triples lines appear as triple points.