Scalable statistics of correlated random variables and extremes applied to deep borehole porosities

摘要: We analyze scale-dependent statistics of correlated random hydrogeological variables and their extremes using neutron porosity data from six deep boreholes, in three diverse depositional environments, as example. show that key increments behave scale manners typical many earth environmental (as well other) variables. These scaling behaviors include a tendency to have symmetric, non-Gaussian frequency distributions characterized by heavy tails decay with separation distance or lag; power-law sample structure functions (statistical moments absolute increments) midranges lags; linear relationships between log successive orders at all lags, known extended self-similarity ESS; nonlinear function exponents order, phenomenon commonly attributed the literature multifractals. Elsewhere we proposed, explored demonstrated new method geostatistical inference captures these phenomena within unified theoretical framework. The framework views samples fields constituting mixtures truncated (monofractal) fractional Brownian motion (tfBm) Gaussian noise (tfGn). Important questions not addressed previous studies concern distribution statistical extreme incremental values. Of special interest hydrology (and other areas) are exceeding given thresholds, peaks over threshold POTs. In this paper explore and, for first time, corresponding POTs associated tfBm tfGn. demonstrate possess properties such thus follow theory proposed. additional value revealing remarkable cross-over one regime another certain lags. uncover importance analysis fluid flow solute particulate transport complex hydrogeologic environments.