Prediction of true classes of surficial and deep earth materials using multivariate spatial data is a common challenge for geoscience modelers. Most geological processes leave a footprint that can be explored by geochemical data analysis. These footprints are normally complex statistical and spatial patterns buried deep in the high-dimensional compositional space. This paper proposes a spatial predictive model for classification of surficial and deep earth materials derived from the geochemical composition of surface regolith. The model is based on a combination of geostatistical simulation and machine learning approaches. A random forest predictive model is trained, and features are ranked based on their contribution to the predictive model. To generate potential and uncertainty maps, compositional data are simulated at unsampled locations via a chain of transformations (isometric log-ratio transformation followed by the flow anamorphosis) and geostatistical simulation. The simulated results are subsequently back-transformed to the original compositional space. The trained predictive model is used to estimate the probability of classes for simulated compositions. The proposed approach is illustrated through two case studies. In the first case study, the major crustal blocks of the Australian continent are predicted from the surface regolith geochemistry of the National Geochemical Survey of Australia project. The aim of the second case study is to discover the superficial deposits (peat) from the regional-scale soil geochemical data of the Tellus Project. The accuracy of the results in these two case studies confirms the usefulness of the proposed method for geological class prediction and geological process discovery.
In the field of mineral resources extraction, one main challenge is to meet production targets in terms of geometallurgical properties. These properties influence the processing of the ore and are often represented in resource modeling by coregionalized variables with a complex relationship between them. Valuable data are available about geometalurgical properties and their interaction with the beneficiation process given sensor technologies during production monitoring. The aim of this research is to update resource models as new observations become available. A popular method for updating is the ensemble Kalman filter. This method relies on Gaussian assumptions and uses a set of realizations of the simulated models to derive sample covariances that can propagate the uncertainty between real observations and simulated ones. Hence, the relationship among variables has a compositional nature, such that updating these models while keeping the compositional constraints is a practical requirement in order to improve the accuracy of the updated models. This paper presents an updating framework for compositional data based on ensemble Kalman filter which allows us to work with compositions that are transformed into a multivariate Gaussian space by log-ratio transformation and flow anamorphosis. This flow anamorphosis, transforms the distribution of the variables to joint normality while reasonably keeping the dependencies between components. Furthermore, the positiveness of those variables, after updating the simulated models, is satisfied. The method is implemented in a bauxite deposit, demonstrating the performance of the proposed approach.
Mathematical Geosciences - In the geosciences it is still uncommon to include measurement uncertainties into statistical methods such as discriminant analysis, but, especially for trace elements,... 相似文献
Mathematical Geosciences - This paper presents an overview of results for the geostatistical analysis of collocated multivariate data sets, whose variables form a composition, where the components... 相似文献
Nowadays, numerical modeling is a common tool used in the study of sedimentary basins, since it allows to quantify the processes simulated and to determine interactions among them. One of such programs is SIMSAFADIM-CLASTIC, a 3D forward-model process-based code to simulate the sedimentation in a marine basin at a geological time scale. It models the fluid flow, siliciclastic transport and sedimentation, and carbonate production. In this article, we present the last improvements in the carbonate production model, in particular about the usage of Generalized Lotka-Volterra equations that include logistic growth and interaction among species. Logistic growth is constrained by environmental parameters such as water depth, energy of the medium, and depositional profile. The environmental parameters are converted to factors and combined into one single environmental value to model the evolution of species. The interaction among species is quantified using the community matrix that captures the beneficial or detrimental effects of the presence of each species on the other. A theoretical example of a carbonate ramp is computed to show the interaction among carbonate and siliciclastic sediment, the effect of environmental parameters to the modeled species associations, and the interaction among these species associations. The distribution of the modeled species associations in the theoretical example presented is compared with the carbonate Oligocene-Miocene Asmari Formation in Iran and the Miocene Ragusa Platform in Italy. 相似文献
Frequently, regionalized positive variables are treated by preliminarily applying a logarithm, and kriging estimates are back-transformed
using classical formulae for the expectation of a lognormal random variable. This practice has several problems (lack of robustness,
non-optimal confidence intervals, etc.), particularly when estimating block averages. Therefore, many practitioners take exponentials
of the kriging estimates, although the final estimations are deemed as non-optimal. Another approach arises when the nature
of the sample space and the scale of the data are considered. Since these concepts can be suitably captured by an Euclidean
space structure, we may define an optimal kriging estimator for positive variables, with all properties analogous to those
of linear geostatistical techniques, even for the estimation of block averages. In this particular case, no assumption on
preservation of lognormality is needed. From a practical point of view, the proposed method coincides with the median estimator
and offers theoretical ground to this extended practice. Thus, existing software and routines remain fully applicable. 相似文献
Indicator kriging (IK) is a spatial interpolation technique aimed at estimating the conditional cumulative distribution function
(ccdf) of a variable at an unsampled location. Obtained results form a discrete approximation to this ccdf, and its corresponding
discrete probability density function (cpdf) should be a vector, where each component gives the probability of an occurrence
of a class. Therefore, this vector must have positive components summing up to one, like in a composition in the simplex.
This suggests a simplicial approach to IK, based on the algebraic-geometric structure of this sample space: simplicial IK
actually works with log-odds. Interpolated log-odds can afterwards be easily re-expressed as the desired cpdf or ccdf. An
alternative but equivalent approach may also be based on log-likelihoods. Both versions of the method avoid by construction
all conventional IK standard drawbacks: estimates are always within the (0,1) interval and present no order-relation problems
(either with kriging or co-kriging). Even the modeling of indicator structural functions is clarified. 相似文献
The aim of this paper is to compare four different methods for binary classification with an underlying Gaussian process with
respect to theoretical consistency and practical performance. Two of the inference schemes, namely classical indicator kriging
and simplicial indicator kriging, are analytically tractable and fast. However, these methods rely on simplifying assumptions
which are inappropriate for categorical class labels. A consistent and previously described model extension involves a doubly
stochastic process. There, the unknown posterior class probability f(·) is considered a realization of a spatially correlated Gaussian process that has been squashed to the unit interval, and
a label at position x is considered an independent Bernoulli realization with success parameter f(x). Unfortunately, inference for this model is not known to be analytically tractable. In this paper, we propose two new computational
schemes for the inference in this doubly stochastic model, namely the “Aitchison Maximum Posterior” and the “Doubly Stochastic
Gaussian Quadrature”. Both methods are analytical up to a final step where optimization or integration must be carried out
numerically. For the comparison of practical performance, the methods are applied to storm forecasts for the Spanish coast
based on wave heights in the Mediterranean Sea. While the error rate of the doubly stochastic models is slightly lower, their
computational cost is much higher. 相似文献
Mathematical Geosciences - Spatial data mining helps to find hidden but potentially informative patterns from large and high-dimensional geoscience data. Non-spatial learners generally look at the... 相似文献
Three independent single‐grain geochronometers applied to detrital minerals from Central Dinaride sediments constrain the timing of felsic magmatism that associated the Jurassic evolution of the Neotethys. The Lower Cretaceous clastic wedge of the Bosnian Flysch, sourced from the Dinaride ophiolitic thrust complex, yields magmatic monazite and zircon grains with dominant age components of 164 ± 3 and 152 ± 10 Ma respectively. A unique tephra horizon within the Adriatic Carbonate Platform was dated at 148 ± 11 Ma by apatite fission track analysis. These consistent results suggest that leucocractic melt generation in the Central Dinaride segment of the Neotethys culminated in Middle to Late Jurassic times, coeval with and slightly post‐dating subophiolitic sole metamorphism. Growth of magmatic monazite and explosive volcanism call for supra‐subduction‐zone processes at the convergent Neotethyan margin. New compilation of geochronological data demonstrates that such Jurassic felsic rocks are widespread in the entire Dinaride–Hellenide orogen. 相似文献
