Significance of statistical relations derived from geophysical data

Most geophysical phenomena have typical interrelations in time and space. But these restrictions are frequently forgotten by investigators processing data in order to verify, or to detect, the laws of nature. For example, the claimed relations between geophysical events and eosmical data are numerous, but rather few such relationships survive the next decade. One main reason for this is certainly the use of random sampling techniques when investigating geophysical data, in spite of the fact that statistics of related terms were studied by Markov half a century ago.

If long series of records are available, the sampling complications due to serial correlation can be removed by selecting dates separated by a proper interval of time. But in most cases we have data only for relatively short intervals, and we are therefore forced to use all data to get optimum determination of the statistical parameters. The significance of these parameters then depend very much on the serial correlations involved.

The purpose of this paper is to derive tests of significance, which may be applicable to a variety of such investigations when serial correlations are present in the data.