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Ubiquity of, and geostatistics for, nonstationary increment random fields
Author(s) -
O'Malley Daniel,
Cushman John H.
Publication year - 2013
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1002/wrcr.20328
Subject(s) - variogram , fractional brownian motion , geostatistics , kriging , random field , mathematics , statistical physics , brownian motion , discretization , geology , mathematical analysis , statistics , spatial variability , physics
Nonstationary random fields such as fractional Brownian motion and fractional Lévy motion have been studied extensively in the hydrology literature. On the other hand, random fields that have nonstationary increments have seen little study. A mathematical argument is presented that demonstrates processes with stationary increments are the exception and processes with nonstationary increments are far more abundant. The abundance of nonstationary increment processes has important implications, e.g., in kriging where a translation‐invariant variogram implicitly assumes stationarity of the increments. An approach to kriging for processes with nonstationary increments is presented and accompanied by some numerical results.