Exponential decline of aftershocks of the M7.9 1868 great Kau earthquake, Hawaii, through the 20th century

Abstract

The remarkable catalog of Hawaiian earthquakes going back to the 1820s is based on missionary diaries, newspaper accounts, and instrumental records and spans the great M 7.9 Kau earthquake of April 1868 and its aftershock sequence. The earthquake record since 1868 defines a smooth curve complete to M 5.2 of the declining rate into the 21st century, after five short volcanic swarms are removed. A single aftershock curve fits the earthquake record, even with numerous M 6 and 7 main shocks and eruptions. The timing of some moderate earthquakes may be controlled by magmatic stresses, but their overall long‐term rate reflects one of aftershocks of the Kau earthquake. The 1868 earthquake is, therefore, the largest and most controlling stress event in the 19th and 20th centuries. We fit both the modified Omori (power law) and stretched exponential (SE) functions to the earthquakes. We found that the modified Omori law is a good fit to the M ≥ 5.2 earthquake rate for the first 10 years or so and the more rapidly declining SE function fits better thereafter, as supported by three statistical tests. The switch to exponential decay suggests that a possible change in aftershock physics may occur from rate and state fault friction, with no change in the stress rate, to viscoelastic stress relaxation. The 61‐year exponential decay constant is at the upper end of the range of geodetic relaxation times seen after other global earthquakes. Modeling deformation in Hawaii is beyond the scope of this paper, but a simple interpretation of the decay suggests an effective viscosity of 10 19 to 10 20 Pa s pertains in the volcanic spreading of Hawaii's flanks. The rapid decline in earthquake rate poses questions for seismic hazard estimates in an area that is cited as one of the most hazardous in the United States.