Ubiquity of, and geostatistics for, nonstationary increment random fields

Authors

  • Daniel O'Malley,

    Corresponding author
    1. Department of Earth, Atmospheric and Planetary Sciences, Purdue University, West Lafayette, Indiana, USA
    • Corresponding author: D. O'Malley, Department of Earth, Atmospheric and Planetary Sciences, Purdue University, West Lafayette, IN 47907, USA. (omalled@gmail.com)

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  • John H. Cushman

    1. Department of Earth, Atmospheric and Planetary Sciences, Purdue University, West Lafayette, Indiana, USA
    2. Department of Mathematics, Purdue University, West Lafayette, Indiana, USA
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Abstract

[1] 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.

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