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| Titel |
Scalable statistics of correlated random variables and extremes applied to deep borehole porosities |
| VerfasserIn |
A. Guadagnini, S. P. Neuman, T. Nan, M. Riva, C. L. Winter |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1027-5606
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| Digitales Dokument |
URL |
| Erschienen |
In: Hydrology and Earth System Sciences ; 19, no. 2 ; Nr. 19, no. 2 (2015-02-04), S.729-745 |
| Datensatznummer |
250120619
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| Publikation (Nr.) |
 copernicus.org/hess-19-729-2015.pdf |
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| Zusammenfassung |
| 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. We show
that key statistics of porosity increments behave and scale in manners
typical of many earth and environmental (as well as other) variables. These
scaling behaviors include a tendency of increments to have symmetric,
non-Gaussian frequency distributions characterized by heavy tails that decay
with separation distance or lag; power-law scaling of sample structure
functions (statistical moments of absolute increments) in midranges of lags;
linear relationships between log structure functions of successive orders at
all lags, known as extended self-similarity or ESS; and nonlinear scaling of
structure function power-law exponents with function order, a phenomenon
commonly attributed in the literature to multifractals. Elsewhere we
proposed, explored and demonstrated a new method of geostatistical inference
that captures all of these phenomena within a unified theoretical framework.
The framework views data as samples from random fields constituting
scale mixtures of truncated (monofractal) fractional Brownian motion (tfBm)
or fractional Gaussian noise (tfGn). Important questions not addressed in
previous studies concern the distribution and statistical scaling of extreme
incremental values. Of special interest in hydrology (and many other areas)
are statistics of absolute increments exceeding given thresholds, known as
peaks over threshold or POTs. In this paper we explore the statistical
scaling of data and, for the first time, corresponding POTs associated with
samples from scale mixtures of tfBm or tfGn. We demonstrate that porosity
data we analyze possess properties of such samples and thus follow the
theory we proposed. The porosity data are of additional value in revealing a
remarkable cross-over from one scaling regime to another at certain lags.
The phenomena we uncover are of key importance for the analysis of fluid
flow and solute as well as particulate transport in complex hydrogeologic
environments. |
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