Some long-run properties of geophysical records
Article first published online: 9 JUL 2010
Copyright 1969 by the American Geophysical Union.
Water Resources Research
Volume 5, Issue 2, pages 321–340, April 1969
How to Cite
1969), Some long-run properties of geophysical records, Water Resour. Res., 5(2), 321–340, doi:10.1029/WR005i002p00321., and (
- Issue published online: 9 JUL 2010
- Article first published online: 9 JUL 2010
- Manuscript Received: 14 OCT 1968
A variety of geophysical records are examined to determine the dependence upon the lag s of a quantity called ‘rescaled range,’ denoted by R(t, s)/S(t, s). If there had been no appreciable dependence between two values of the record at very distant points in time, the ratio R/S would have been proportional to s0.5. But, in fact, as first noted by Edwin Hurst, the R/S ratio of hydrological and other geophysical records is proportional to sH with H ≠ 0.5. Hurst's original claims must be tightened and hedged, and his estimates of H must be discarded, but his general idea will be shown to be correct. We have shown elsewhere that this behavior of R/S means that the strength of long-range statistical dependence in geophysical records is considerable.