Estimating Second-Order Parameters of Volcanicity from Historical Data
Peter Guttorp, Mary Lou Thompson
Journal of the American Statistical Association
In order to study patterns of volcanicity it is important to use historical data. However, these data are frequently incomplete. We develop a nonparametric procedure for estimating second order parameters of the point process of eruption starts from a catalog. This method requires an assumption of underlying stationarity, and of smoothness of the probability of recording an eruption as a function of time. We illustrate the procedure on the Smithsonian catalog, using global data from the last
... years or less, and also specializing to data from Japan and Iceland from the last 200 years. The global and the Japanese data sets show little structure, while the Icelandic data exhibits a tendency towards periodic behavior, with a period of about 40 years. We do not see any regularity corresponding to tidal cycles. Simkin et al. (1981) . in their list of recorded volcanic eruptions from 8300 Be to 1980 AD. discuss the possibility of finding trends or cycles in the historical data. In a plot of 3-year running average number of active volcanos reported the last 120 years. they note that, although an increasing trend due to reporting is dominating. some dips in the series correspond to events such as the World Wars and the Depression. whereas some peaks follow particularly spectacular eruptions. such as.Krakatua and Pelee. At any point in time. we assume that there is a corresponding probability that. should an eruption have occurred. it would have been recorded. The available catalog hence represents only a partial listing of the eruptions thathave occurred. There are. of course. many factors which lead to there being fewer and fewer recorded eruptions as the record goes back' into the past. There has been a continuing increase in the number of known volcanos throughout the history of the catalog. although the rate of increase appears to have diminished in this century. About 30% of the known volcanos are erupting at anyone . time. In this paper we have elected to look only at the yearly numbers of starts of volcanic eruptions from 1500 through 1980. As the earlier data are very uncertain. we win mostly concentrate on the last 200 years. The analysis presented here adapts and extends the methodology developed by Brillinger (1979. cf. also Lee and Brillinger, 1979) in order to study Chinese earthquake data. to the volcanic data. We win be estimating the (conditional) probability (or Conditional intensity) of an eruption k: years after a given eruption. and assess the standard error of this estimate. with an aim at detecting cyclic behavior in the historic records. We will look at worldwide data. in order to be able to make comparisons with Hamilton (1973). who found evidence of a relation with tidal cycles. In addition. we will study the eruptions in the Japanese region and on Iceland separately. section 2 we present the general methodological problem and introduce an estimator for the recoramg probabilities are J\.lUJWlll. recording prebabilities is section 3. section 4 we metaods to Simkin et al.