Multivariate prediction equations in geology

Conclusion It is suggested that in geology the estimated values Ŷ_T, Ŷ_B, and, in particular, Ŷ_G may provide useful information in multivariate prediction problems where the outcome will be determined mainly by mutually interrelated, local anomalies for many geological variables.     

A conceptual model for kimberlite emplacement by solitary interfacial mega-waves on the core mantle boundary

If convection in the Earth's liquid outer core is disrupted, degrades to turbulence and begins to behave in a chaotic manner, it will destabilize the Earth's magnetic field and provide the seeds for kimberlite melts via turbulent jets of silicate rich core material which invade the lower mantle. These (proto-) melts may then be captured by extreme amplitude solitary nonlinear waves generated through interaction of the outer core surface with the base of the mantle. A pressure differential behind the wave front then provides a mechanism for the captured melt to ascend to the upper mantle and crust so quickly that emplacement may indirectly promote a type of impact fracture cone within the relatively brittle crust. These waves are very rare but of finite probability. The assumption of turbulence transmission between layers is justified using a simple three-layer liquid model. The core derived melts eventually become frozen in place as localised topographic highs in the Mohorovicic discontinuity (Moho), or as deep rooted intrusive events. The intrusion's final composition is a function of melt contamination by two separate sources: the core contaminated mantle base and subducted Archean crust. The mega-wave hypothesis offers a plausible vehicle for early stage emplacement of kimberlite pipes and explains the age association of diamondiferous kimberlites with magnetic reversals and tectonic plate rearrangements.     

Application of Fractal Models to Distinguish between Different Mineral Phases

Fractal modeling is demonstrated to be an effective and rapid tool to distinguish between mineral phases in rock samples. It supplements work that previously could be performed only by observing the interpenetrational or metasomatic phenomena between different minerals with the aid of mineralographic microscope. The Gejiu tin district in southwestern China was chosen as a study area for the recognition and characterization of the spatial distribution of two phases (Types I and II) of cassiterite. Vector patterns used for this study were extracted from digital photomicrographs and analyzed with the aid of MapGIS. Perimeter–area fractal dimension, cumulative number–area exponent, and shape index were determined in order to quantify geometrical irregularities and spatial cassiterite phase distribution characteristics. The results show that fractal dimensions based on area and perimeter are larger for crystals of Type I than for those of Type II. The mean shape index (SI) increases from 0.54 (Type I) to 0.64 (Type II), indicating an increase in regularity. The number–area exponent also increases from 0.88 to 1.15, indicating the smaller crystals of Type II. The cumulative number–shape index log–log plot shows two separate straight-line segments. One of these probably represents a background shape realized during the original process of natural crystallization, whereas the other likely represents anomalous shapes because of weathering or other superimposed processes. Two parallel lines can be constructed on the perimeter–area log–log plots. The upper line, with a larger intercept, represents crystals with lower SI. The lower line represents crystals with higher SI, indicating that the intercept provides a measure of the irregularity of grains. By combining the perimeter–area model with cumulative number–area plot and shape index, the two phases of cassiterite can be distinguished and characterized. One phase has fewer crystals of large size, and the other has smaller crystals. This difference can be explained by assuming that under higher-temperature conditions, the large cassiterite crystals formed earlier than the smaller crystals. Consequently, the large cassiterites underwent longer, high-intensive weathering than the small crystals so that their shapes became more irregular. The younger, more abundant small cassiterites retained their original regular shapes.     

Combining indicator patterns in weights of evidence modeling for resource evaluation

The weights of evidence model for combining indicator patterns in mineral resource evaluation is briefly explained with emphasis on the effect of undiscovered deposits on the estimation of the weights and posterior probabilities. A group of six statistical tests is proposed for analyzing the interaction of two or three indicator patterns with the point pattern for mineral deposits. A distinction is made between statistics that depend on choice of unit cell size and those that are approximately or completely independent of it. Finally, weights of evidence are compared to regression coefficients obtained by means of the logistic model.     

Age refinement of the Messinian salinity crisis onset in the Mediterranean

We propose a revised age calibration of the Messinian salinity crisis onset in the Mediterranean at 5.971 Ma based on the recognition of an extra gypsum cycle in the transitional interval of the Perales section (Sorbas basin, Spain) and the revision of the magnetostratigraphy of the Monticino section (Vena del Gesso basin, Italy). This age re‐calibration allows to state more accurately that: (i) the interval encompassing the MSC‐onset is continuous, thus ruling out any erosional feature or stratigraphic hiatus related to a major sea‐level fall affecting the Mediterranean; (ii) the first gypsum was deposited during the summer insolation peak at 5.969 Ma associated with an eccentricity minimum and roughly coincident with glacial stage TG32; (iii) the MSC‐onset was preconditioned by the tectonically‐driven reduction of the hydrological exchanges with the Atlantic Ocean and finally triggered by glacial conditions in the northern hemisphere and by arid conditions in northern Africa.     

Evaluation of the uncertainty in estimation of metal resources of skarn tin in Southern China

This study is concerned with the problem of how many undiscovered mineral deposits can be expected to occur in the vicinity of any known deposit, especially if the deposit is nearly mined out. Skarn tin deposits in southern China were chosen to demonstrate that fractal modeling can be a useful tool to characterize the spatial–temporal distribution of mineral deposits, and to quantify their grades and tonnages. The results show that the spatial–temporal distribution of skarn tin deposits as well as their grades and tonnages satisfy fractal statistic, and suggest that 14 skarn tin deposits could be found around a known skarn tin deposit within a radius of 80 km. Monte Carlo simulation was used to combine the number of deposits and the frequency distributions of grade and tonnage and to capture the uncertainty in estimation of metal resources. At the 90%, 50% and 10% confidence levels, tin metal resources amount to 6 ton, 200 ton, and 1.0 × 10⁴ ton around a known tin deposit within a radius of 80, respectively.