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Long-term correlations in earth sciences

In this article we review the occurrence and consequences of long-term memory in geophysical records like climate and seismic records, and describe similarities with financial data sets. We review several methods to detect linear and nonlinear long-term correlations, also in the presence of external trends, and show how external trends can be detected in data with long-term memory. We show as well that long-term correlations lead to a natural clustering of extreme events and discuss the implications for several geophysical data sets.