An explanation for the change in b-value preceding large earthquakes

Earthquakes were one of the first natural systems recognized to have power law scaling. Don Turcotte has contributed to and inspired others in the study of earthquakes, as well as many other topics in earth and planetary geophysics. Earthquake cumulative frequency-magnitude (CFM) distributions are described by the Gutenberg-Richter power law where the scaling exponent is the b-value. CFM distributions for time intervals leading up to, but not including, a large event in a region are typically found to have steeper slopes (larger b-value) than distributions that include the large event. The often reported "change in b-value" preceding large earthquakes is shown to be a consequence of temporal truncation of the data sets analyzed. We find that an upper-truncated power law applied to earthquake CFM distributions yields a time-independent scaling parameter, herein called the α-value. The α-value obtained by applying an upper-truncated power law to distributions both leading up to and including the large event is shown to be constant and equal to the long-term b-value. We analyze earthquakes associated with subduction of the Nazca plate beneath South America, and find a region of isolated seismic activity at depths >500 km between 20° S and 30° S. For the entire record, 1973-2000, the earthquake CFM distribution in this isolated region is well described by a Gutenberg-Richter power law with b = 0.58. The data set includes several large seismic events with m_b > 6.8. A power law applied to the CFM distributions for short time intervals between the large events yields b-values greater than the 0.58 b-value for the entire record. CFM distributions for the short time intervals are better described by an upper-truncated power law than by a power law. The α-value determined by applying an upper-truncated power law to the short time intervals is equal to the b-value obtained by applying the Gutenberg-Richter power law to the entire record. Temporal changes in b-value are due to temporal fluctuations in maximum magnitude. Analysis of four Flinn-Engdahl regions, two in subduction zones and two along spreading ridge axes, demonstrates wider applicability of the results. The α-value is an unchanging characteristic of the system that may be determined from a short-term record.