 |
| Titel |
Extended power-law scaling of heavy-tailed random air-permeability fields in fractured and sedimentary rocks |
| VerfasserIn |
A. Guadagnini, M. Riva, S. P. Neuman |
| Medientyp |
Artikel
|
| Sprache |
Englisch
|
| ISSN |
1027-5606
|
| Digitales Dokument |
URL |
| Erschienen |
In: Hydrology and Earth System Sciences ; 16, no. 9 ; Nr. 16, no. 9 (2012-09-10), S.3249-3260 |
| Datensatznummer |
250013466
|
| Publikation (Nr.) |
 copernicus.org/hess-16-3249-2012.pdf |
|
|
|
|
|
| Zusammenfassung |
| We analyze the scaling behaviors of two field-scale log permeability data
sets showing heavy-tailed frequency distributions in three and two spatial
dimensions, respectively. One set consists of 1-m scale pneumatic packer
test data from six vertical and inclined boreholes spanning a decameters
scale block of unsaturated fractured tuffs near Superior, Arizona, the other
of pneumatic minipermeameter data measured at a spacing of 15 cm along three
horizontal transects on a 21 m long and 6 m high outcrop of the Upper
Cretaceous Straight Cliffs Formation, including lower-shoreface bioturbated
and cross-bedded sandstone near Escalante, Utah. Order q sample structure
functions of each data set scale as a power ξ(q) of
separation scale or lag, s, over limited ranges of s. A procedure known as
extended self-similarity (ESS) extends this range to all lags and yields a
nonlinear (concave) functional relationship between ξ(q)
and q. Whereas the literature tends to associate extended and nonlinear
power-law scaling with multifractals or fractional Laplace motions, we have
shown elsewhere that (a) ESS of data having a normal frequency distribution
is theoretically consistent with (Gaussian) truncated (additive,
self-affine, monofractal) fractional Brownian motion (tfBm), the latter
being unique in predicting a breakdown in power-law scaling at small and
large lags, and (b) nonlinear power-law scaling of data having either normal
or heavy-tailed frequency distributions is consistent with samples from
sub-Gaussian random fields or processes subordinated to tfBm or truncated
fractional Gaussian noise (tfGn), stemming from lack of ergodicity which
causes sample moments to scale differently than do their ensemble
counterparts. Here we (i) demonstrate that the above two data sets are
consistent with sub-Gaussian random fields subordinated to tfBm or tfGn and
(ii) provide maximum likelihood estimates of parameters characterizing the
corresponding Lévy stable subordinators and tfBm or tfGn functions. |
| |
|
| Teil von |
|
|
|
|
|
|
|
|