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.
Earth's near-surface mineralogy has diversified over more than 4.5 b.y. from no more than a dozen preplanetary refractory mineral species (what have been referred to as "ur-minerals" by Hazen et al., 2008) to ~5,000 species (based on the list of minerals approved by the International Mineralogical Association; http://rruff.info/ima). This dramatic diversification is a consequence of three principal physical, chemical, and biological processes: (1) element selection and concentration (primarily through planetary differentiation and fluidrock interactions); (2) an expanded range of mineral-forming environments (including temperature, pressure, redox, and activities of volatile species); and (3) the influence of the biosphere. Earth's history can be divided into three eras and ten stages of "mineral evolution" (Table 1; Hazen et al., 2008), each of which has seen significant changes in the planet's near-surface mineralogy, including increases in the number of mineral species; shifts in the distribution of those species; systematic changes in major, minor, and trace element and isotopic compositions of minerals; and the appearance of new mineral grain sizes, textures, and/or morphologies. Initial treatments of mineral evolution, first in Russia (e.g., Zhabin, 1979; Yushkin, 1982) and subsequently in greater detail by our group (Hazen et al., 2008, 2009, 2011, 2013a, b; Hazen and Ferry, 2010; Hazen, 2013), focused on key events in Earth history. The 10 stages we suggested are Earth's accretion and differentiation (stages 1, 2, and 3), petrologic innovations (e.g., the stage 4 initiation of granite magmatism), modes of tectonism (stage 5 and the commencement of plate tectonics), biological transitions (origins of life, oxygenic photosynthesis, and the terrestrial biosphere in stages 6, 7, and 10, respectively), and associated environmental changes in oceans and atmosphere (stage 8 "intermediate ocean" and stage 9 "snowball/hothouse Earth" episodes). These 10 stages of mineral evolution provide a useful conceptual framework for considering Earth's changing mineralogy through time, and episodes of metallization are often associated with specific stages of mineral evolution (Table 1). For example, the formation of complex pegmatites with Be, Li, Cs, and Sn mineralization could not have occurred prior to stage 4 granitization. Similarly, the appearance of large-scale volcanogenic sulfide deposits may postdate the initiation of modern-style subduction (stage 5). The origins and evolution of life also played central roles; for example, redox-mediated ore deposits of elements such as U, Mo, and Cu occurred only after the Great Oxidation Event (stage 7), and major Hg deposition is associated with the rise of the terrestrial biosphere (stage 10; Hazen et al., 2012).
Abstract. One of the main tasks in 3D geological modeling is the boundary parametrization of the subsurface from geological observations and geophysical inversions. Several approaches have been developed for geometric inversion and joint inversion of geophysical datasets. However, the robust, quantitative integration of models and datasets with different spatial coverage, resolution, and levels of sparsity remains challenging. One promising approach for recovering the boundary of the geological units is the utilization of a level set inversion method with potential field data. We focus on constraining 3D geometric gravity inversion with sparse lower-uncertainty information from a 2D seismic section. We use a level set approach to recover the geometry of geological bodies using two synthetic examples and data from the geologically complex Yamarna Terrane (Yilgarn Craton, Western Australia). In this study, a 2D seismic section has been used for constraining the location of rock unit boundaries being solved during the 3D gravity geometric inversion. The proposed work is the first we know of that automates the process of adding spatially distributed constraints to the 3D level set inversion. In many hard-rock geoscientific investigations, seismic data are sparse, and our results indicate that unit boundaries from gravity inversion can be much better constrained with seismic information even though they are sparsely distributed within the model. Thus, we conclude that it has the potential to bring the state of the art a step further towards building a 3D geological model incorporating several sources of information in similar regions of investigation.
AbstractOne of the major challenges for geophysical inversion schemes is to retain geological meaning during the inversion process. In voxel-based methods based on prior geological models we are typically forced into a manual reinterpretation of smooth petrophysical images in terms of discrete structures and lithostratigraphy.Recent work in the characterisation of geological uncertainty has demonstrated the inherent weaknesses in classical 3D geological model building strategies. The analysis of 3D geological uncertainty provides several pathways to improved geophysical inversion. The uncertainty can be characterised at the local scale to provide constraints on petrophysical inversions, and at the global scale to provide end-member geologically and topologically distinct prior models. Although in its infancy, geological uncertainty analysis shows promise in workflows aimed at integrating geological and geophysical constraints in 3D.
Abstract The univariate statistics of Potassium (K), thorium (Th), and uranium (U) concentrations, in the Earth’s oceanic and continental crust are examined by different techniques. The frequency distributions of the concentrations of these elements in the oceanic crust are derived from a global catalog of mid‐ocean ridge basalts. Their frequency distributions of concentrations in the continental crust are illustrated by the North Pilbara Craton, and the West Africa Craton. For these two cratons, the distributions of K, Th, and U derived from geochemical analyses of several thousand whole rock samples differ significantly from those derived from airborne radiometric surveys. The distributions from airborne surveys tends to be more symmetric with smaller standard deviations than the right‐skewed distributions inferred from whole rock geochemical analyses. Hypothetic causes of these differences include (a) bias in rock sampling or in airborne surveys, (b) the differences between the chemistry of superficial material and rocks, and (c) the differences in scales of measurements. The scale factor, viewed as consequence of the central limit theorem applied to K, Th, and U concentrations, appears to account for most of the observed differences in the distributions of K, Th, and U. It suggests that the three scales of auto‐correlation of K, Th, and U concentrations are of the same order of magnitude as the resolution of the airborne radiometric surveys (50–200 m). Concentrations of K, Th, and U are therefore generally heterogenous at smaller scales.
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