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Register a new userFast Automatic Detection of Geological Boundaries from Multivariate Log Data Using Recurrence
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Manual interpretation of data collected from drill holes for mineral or oil and gas exploration is time-consuming and subjective. Identification of geological boundaries and distinctive rock physical property domains is the first step of interpretation. We introduce a multivariate technique, that can identify geological boundaries from petrophysical or geochemical data. The method is based on time-series techniques that have been adapted to be applicable for detecting transitions in geological spatial data. This method allows for the use of multiple variables in detecting different lithological layers. Additionally, it reconstructs the phase space of a single drill-hole or well to be applicable for further investigations across other holes or wells. The computationally cheap method shows efficiency and accuracy in detecting boundaries between lithological layers, which we demonstrate using examples from mineral exploration boreholes and an offshore gas exploration well.
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In this paper we present maps of K, eU, and eTh abundances of Elba Island (Italy) obtained with a multivariate spatial interpolation of airborne {gamma}-ray data using the constraints of the geologic map. The radiometric measurements were performed by a module of four NaI(Tl) crystals of 16 L mounted on an autogyro. We applied the collocated cokriging (CCoK) as a multivariate estimation method for interpolating the primary under-sampled airborne {gamma}-ray data considering the well-sampled geological information as ancillary variables. A random number has been assigned to each of 73 geological formations identified in the geological map at scale 1:10,000. The non-dependency of the estimated results from the random numbering process has been tested for three distinct models. The experimental cross-semivariograms constructed for radioelement-geology couples show well-defined co-variability structures for both direct and crossed variograms. The high statistical correlations among K, eU, and eTh measurements are confirmed also by the same maximum distance of spatial autocorrelation. Combining the smoothing effects of probabilistic interpolator and the abrupt discontinuities of the geological map, the results show a distinct correlation between the geological formation and radioactivity content. The contour of Mt. Capanne pluton can be distinguished by high K, eU and eTh abundances, while different degrees of radioactivity content identify the tectonic units. A clear anomaly of high K content in the Mt. Calamita promontory confirms the presence of felsic dykes and hydrothermal veins not reported in our geological map. Although we assign a unique number to each geological formation, the method shows that the internal variability of the radiometric data is not biased by the multivariate interpolation.
Geometrical properties of landscapes result from the geological processes that have acted through time. The quantitative analysis of natural relief represents an objective form of aiding in the visual interpretation of landscapes, as studies on coastlines, river networks, and global topography, have shown. Still, an open question is whether a clear relationship between the quantitative properties of landscapes and the dominant geomorphologic processes that originate them can be established. In this contribution, we show that the geometry of topographic isolines is an appropriate observable to help disentangle such a relationship. A fractal analysis of terrestrial isolines yields a clear identification of trenches and abyssal plains, differentiates oceanic ridges from continental slopes and platforms, localizes coastlines and river systems, and isolates areas at high elevation (or latitude) subjected to the erosive action of ice. The study of the geometrical properties of the lunar landscape supports the existence of a correspondence between principal geomorphic processes and landforms. Our analysis can be easily applied to other planetary bodies.
We report an empirical determination of the probability density functions P(r) of the number r of earthquakes in finite space-time windows for the California catalog, over fixed spatial boxes 5 x 5 km^2 and time intervals dt =1, 10, 100 and 1000 days. We find a stable power law tail P(r) ~ 1/r^{1+mu} with exponent mu approx 1.6 for all time intervals. These observations are explained by a simple stochastic branching process previously studied by many authors, the ETAS (epidemic-type aftershock sequence) model which assumes that each earthquake can trigger other earthquakes (``aftershocks). An aftershock sequence results in this model from the cascade of aftershocks of each past earthquake. We develop the full theory in terms of generating functions for describing the space-time organization of earthquake sequences and develop several approximations to solve the equations. The calibration of the theory to the empirical observations shows that it is essential to augment the ETAS model by taking account of the pre-existing frozen heterogeneity of spontaneous earthquake sources. This seems natural in view of the complex multi-scale nature of fault networks, on which earthquakes nucleate. Our extended theory is able to account for the empirical observation satisfactorily. In particular, the adjustable parameters are determined by fitting the largest time window $dt=1000$ days and are then used as frozen in the formulas for other time scales, with very good agreement with the empirical data.
A promising method for real time early warning of gravity driven rupture that considers both the heterogeneity of natural media and characteristics of acoustic emissions attenuation is proposed. The method capitalizes on co-detection of elastic waves emanating from micro-cracks by multiple and spatially separated sensors. Event co-detection is considered as surrogate for large event size with more frequent co-detected events marking imminence of catastrophic failure. Using a spatially explicit fiber bundle numerical model with spatially correlated mechanical strength and two load redistribution rules, we constructed a range of mechanical failure scenarios and associated failure events (mapped into AE) in space and time. Analysis considering hypothetical arrays of sensors and consideration of signal attenuation demonstrate the potential of the co-detection principles even for insensitive sensors to provide early warning for imminent global failure.
In this work, we introduce a new methodology for inferring the interaction structure of discrete valued time series which are Poisson distributed. While most related methods are premised on continuous state stochastic processes, in fact, discrete and counting event oriented stochastic process are natural and common, so called time-point processes (TPP). An important application that we focus on here is gene expression. Nonparameteric methods such as the popular k-nearest neighbors (KNN) are slow converging for discrete processes, and thus data hungry. Now, with the new multi-variate Poisson estimator developed here as the core computational engine, the causation entropy (CSE) principle, together with the associated greedy search algorithm optimal CSE (oCSE) allows us to efficiently infer the true network structure for this class of stochastic processes that were previously not practical. We illustrate the power of our method, first in benchmarking with synthetic datum, and then by inferring the genetic factors network from a breast cancer micro-RNA (miRNA) sequence count data set. We show the Poisson oCSE gives the best performance among the tested methods anfmatlabd discovers previously known interactions on the breast cancer data set.
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