New Zealand Journal of Geology & Geophysics abstracts
Quantifying the M8 algorithm: model, forecast, and evaluation
David Harte1
Dong-Feng Li2
Maaike Vreede3
David Vere-Jones1
Qiong Wang4
1Statistics Research Associates
PO Box 12649
Thorndon, Wellington 6144, New Zealand
2School of Mathematical Science
Peking University
Beijing 100871, China
3Department of Statistics
Massey University
Private Bag 11222
Palmerston North 4442, New Zealand
4Seismological Bureau of Xinjiang Uygur
42nd South Beijing Rd
Urumqi, Xinjiang 830011, China
Abstract We develop procedures for
evaluating the efficacy of the M8 algorithm and producing probability
forecasts in both time and space. Our modelling method uses the
Critical Series developed by Harte et al. in 2003 as a predictor
variable in a logistic regression. The M8 algorithm calculates seven
time series, and the Critical Series embodies the non-linear rules for
combining the behaviour of these seven time series. The M8 algorithm is
typically evaluated in (spatial) circles of quite large radius. Our
implementation of this has many large overlapping circles covering New
Zealand. This raises both practical and statistical problems. From a
practical perspective, we really want probability forecasts within
relatively small non-overlapping synoptic cells. Further, statistical
evaluation of the overlapping circles approach is complicated by the
lack of independence. In this paper, we develop both the overlapping
circle and synoptic forecasting methods and statistical tests for their
evaluation. We then compare results of the two approaches. Although the
results indicate a significant relationship between the M8 Critical
Series and numbers of large earthquake events, the forecasting success
may be largely due to their dependence on slow variations in deep
activity, which might be better examined directly as a possible source
of predictive information.
Keywords earthquake prediction; probability
forecasts; M8 algorithm; pattern recognition; logistic regression;
spatial temporal predictor
G06024; Online publication date 8 May 2007; Received 19 July 2006;
accepted 13 April 2007
New Zealand Journal of Geology & Geophysics, 2007, Vol. 50:
117—130
0028—8306/07/5002—0117 © The Royal Society of New Zealand 2007
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