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| Titel |
Extended power-law scaling of air permeabilities measured on a block of tuff |
| VerfasserIn |
M. Siena, A. Guadagnini, M. Riva, S. P. Neuman |
| 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 ; 16, no. 1 ; Nr. 16, no. 1 (2012-01-04), S.29-42 |
| Datensatznummer |
250013110
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| Publikation (Nr.) |
 copernicus.org/hess-16-29-2012.pdf |
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| Zusammenfassung |
| We use three methods to identify power-law scaling of multi-scale log air
permeability data collected by Tidwell and Wilson on the faces of a
laboratory-scale block of Topopah Spring tuff: method of moments (M),
Extended Self-Similarity (ESS) and a generalized version thereof (G-ESS).
All three methods focus on q-th-order sample structure functions of
absolute increments. Most such functions exhibit power-law scaling at best
over a limited midrange of experimental separation scales, or lags, which
are sometimes difficult to identify unambiguously by means of M. ESS and
G-ESS extend this range in a way that renders power-law scaling easier to
characterize. Our analysis confirms the superiority of ESS and G-ESS over M
in identifying the scaling exponents, ξ(q), of corresponding structure
functions of orders q, suggesting further that ESS is more reliable than
G-ESS. The exponents vary in a nonlinear fashion with q as is typical of real
or apparent multifractals. Our estimates of the Hurst scaling coefficient
increase with support scale, implying a reduction in roughness
(anti-persistence) of the log permeability field with measurement volume.
The finding by Tidwell and Wilson that log permeabilities associated with
all tip sizes can be characterized by stationary variogram models, coupled
with our findings that log permeability increments associated with the
smallest tip size are approximately Gaussian and those associated with all
tip sizes scale show nonlinear variations in ξ(q) with q, are consistent with a
view of these data as a sample from a truncated version (tfBm) of
self-affine fractional Brownian motion (fBm). Since in theory the scaling
exponents, ξ(q), of tfBm vary linearly with q we conclude that nonlinear
scaling in our case is not an indication of multifractality but an artifact
of sampling from tfBm. This allows us to explain theoretically how power-law
scaling of our data, as well as of non-Gaussian heavy-tailed signals
subordinated to tfBm, are extended by ESS. It further allows us to identify
the functional form and estimate all parameters of the corresponding tfBm
based on sample structure functions of first and second orders. |
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