Maximum‐Likelihood Recurrence Parameters and Conditional Probability of a Ground‐Rupturing Earthquake on the Southern Alpine Fault, South Island, New Zealand

Abstract

Abstract The Alpine fault in south Westland, New Zealand, releases strains of Pacific–Australian relative plate motion in large earthquakes with an average interevent spacing of ∼330 years. A new record of earthquake recurrence has been developed at Hokuri Creek, with evidence for 22 events. The youngest Hokuri Creek earthquake overlaps in time and is believed to be the same as the oldest of another site about 100 km to the northwest near Haast. The combined record spans the last 7900 years and includes 24 events. We study the recurrence rate and conditional probability of ground ruptures from this record using a new likelihood‐based approach for estimation of recurrence model parameters. Paleoseismic parameter estimation includes both dating and natural recurrence uncertainties. Lognormal and Brownian passage time (BPT) models are considered. The likelihood surface has distribution location and width parameters as axes, the mean and standard deviation of the log recurrence for the lognormal, and the mean and coefficient of variation for the BPT. The maximum‐likelihood (ML) point gives the parameters most likely to have given rise to the data. The ML point, 50‐year conditional probabilities of a ground‐rupturing earthquake are 26.8% and 26.1% for the lognormal and BPT models, respectively. Contours of equal likelihood track the parameter pairs that are equally probable to have given rise to the observed data. Conditional probabilities on the lognormal 95% boundary around the ML point range from 18.2% to 35.8%. An empirical distribution model completely based on past recurrence times gives a similar conditional probability of 27.1% (9.6%–50.2%). In contrast, the time‐independent conditional probability estimate of 13.6% (8.8%–19.1%) is about half that of the time‐dependent models. A nonparametric test of earthquake recurrence at Hokuri Creek indicates that time‐dependent recurrence models best represent the southern Alpine fault of the South Island, New Zealand.