Tests of seismic hazard models
Authors: D A Rhoades, W D Smith, M W Stirling, Institute of Geological & Nuclear Sciences
Paper number: 3620 (EQC 01/460)
Abstract
Assessment of seismic hazard in New Zealand relies on the national seismic hazard model (NSHM). This model embodies a catalogue of active faults and a so-called background seismicity model. The former is derived mostly from geological studies of active faults throughout New Zealand, and estimates the likely magnitude and frequency of occurrence of earthquakes on each fault. The latter describes the very large number of mostly smaller earthquakes that occur without any apparent relation to known faults. Assessing earthquake hazard at any given location involves examining the likely ground motion that can occur there, caused by nearby earthquakes (a) on faults, and (b) in the background.
The report examines the accuracy with which the NSHM represents the occurrence of earthquakes in New Zealand: where, how often and how large. Some significant discrepancies are found from what has occurred historically. In particular, the NHSM predicts that in a period of 160 years there should be more than 50 earthquakes that are accompanied by surface rupture of faults; only 10 have been observed between 1840 and 2000.
The report also checks the rate at which seismic energy is released throughout New Zealand, as estimated by geodetic data and as predicted b the NHSM. It seems that the NHSM prediction is too low, although there are some complicating factors that are not yet well understood so this apparent discrepancy may not be significant.
A widely accepted model for earthquakes predicts that for every event of magnitude 7 there will be about 10 of magnitude 6, 100 of magnitude 5, and so on. The multiplier of 10 varies a little from place to place, but the rule seems ubiquitous. The report finds that the NHSM does not follow this model as closely as would be expected.
Each of these tests is done by careful attention to statistical procedure. Significant discrepancies have been found, which suggest that further development work is needed to refine the model so that it represents more accurately the earthquakes that are likely to occur in New Zealand.
Technical Abstract
Tests are described for checking the adequacy of a seismic hazard model against independent data. They have been applied to the national seismic hazard model (NSHM) for New Zealand. Significant discrepancies revealed by these tests direct attention towards the most unsatisfactory aspects of the NSHM, including data and assumptions.
The Poisson process assumption provides a basis for statistical tests comparing the frequency of surface fault rupture in the seismic hazard model with the historical record of surface fault rupture. Application of such tests to the NSHM has revealed a statistically significant discrepancy between the model and the historical record. The NSHM predicts a frequency of surface fault rupture in New Zealand earthquakes more than five times the historical rate, with more than 50 fault ruptures expected since 1840 and only 10 observed. The discrepancy is most marked in the Taupo Volcanic Zone, but is also appreciable in northern Canterbury and southern Fiordland. It is likely to be due to multiple causes, including underestimation of the mean recurrence interval between ruptures of some fault sources in the NSHM, a possible tendency for fault ruptures to occur in clusters, and probable incompleteness in the record of historical surface fault ruptures.
Under the stationary Poisson model, the elapsed time since the last rupture on any fault has an exponential distribution. If the recurrence interval is known, this allows the construction of a statistic, from the elapsed time, which has a common uniform distribution for all faults. Using the data from all faults together, goodness of fit tests can be used to check the overall consistency of the elapsed time and recurrence interval data. Application of such tests to the NSHM has not revealed any significant discrepancies. The statistical power of the test is weak because of the small proportion of fault sources for which any information on the time of last rupture is available. Future paleoseismic studies should aim to increase the available information constraining the time of last rupture of faults.
Geodetic data provide estimates of strain accumulation in any area of the crust and these can be converted into estimates of moment accumulation rate. Similarly seismic hazard models provide estimates of rates of occurrence of earthquakes of any given magnitude in any area, and these can be converted into estimates of the rate of moment release. If most of the moment rate is released in earthquakes, the ratio of the seismic moment rate to the geodetic moment rate should be not much less than one. A comparison of the seismic moment rate in the crustal seismotectonic zones of the NSHM with that expected from geodetic data has shown that overall the strain released under the model accounts for 0.6-0.8 of the geodetic moment rate. Within the individual seismotectonic zones, the ratio of NSHM moment to geodetic moment varies between 0.05 and 2. Further research is needed to understand these discrepancies.
Catalogues of earthquakes covering long time intervals and large areas are found nearly always to conform to the Gutenberg-Richter magnitude-frequency relation with modifications to accommodate the limit on the maximum size of an earthquake in the Earth’s crust. Seismic hazard models of a region should therefore conform both with this relation and with the magnitude-frequency distribution in the historical record. Comparison of the NSHM magnitude-frequency distribution with the historical record and with a plate motion-balanced frequency-magnitude distribution has revealed some discrepancies between the model and the data, and between the model and the Gutenberg-Richter relation. While the magnitude-frequency relation in the NSHM shows wide scatter above M7.0, there is a surplus of earthquakes in the range M7.0-M7.3 in the NSHM when compared with either historical data or the Gutenberg-Richter relation. Within the same magnitude range there is a deficit of distributed-source earthquakes and a more-than-compensating surplus of fault-source earthquakes under the NSHM. Modifications to the NSHM should be considered in order to rectify these discrepancies. The characteristic magnitude and/or mean recurrence interval probably needs to be adjusted for some fault sources. The upper magnitude limit of distributed earthquakes may need to be increased for some seismotectonic zones and a roll-off rather than a sharp magnitude cut-off adopted. Also, variability in the magnitude of earthquakes on a given fault source should be allowed for.
Order a research paper
Many of these research papers have PDF downloads available on the site.
If you'd like to access a paper that doesn't have a download, get in touch to ask for a copy.