Data coverage and completeness

Fortunately, the great bulk of deep earthquakes in the region studied occur under land areas, mainly the center of the North Island and the North-East of the South Island. Relatively speaking, therefore, the deeper events are well situated for good coverage with dry land based seismometers. However, this is offset by two key fea- tures. First, the three-dimensional distances between source and recording stations are commonly of the order of several hundred kilometers, which severely limits the detectability of smaller events, particularly in the early periods when the network was sparse and the instruments less sensitive. The second feature relates to the difficulty of establishing a reliable velocity model for seismic waves which traverse the regions beneath the volcanic zone. The result is that hypocentres and depths for the deeper events may be significantly in error. This problem is particularly acute for events in the region North-East of the North Island, where further complications arise from changing network coverage and instruments over the decades.

For the 1940s and 1960s an appraisal of the network coverage for deep earthquakes is given in Vere-Jones, et al. (1964). From that study it would appear that the coverage at depth 50km would be incomplete for magnitude below 5. For the period 1970s and late 1980s a reasonable lower threshold might be 4.5, and for the later periods a threshold of 4 or even 3.5.

Then we turn to the internal statistical evidence for the catalogue completeness. Here we use the technique of reverse cusum analysis. In essence, this means setting a reference level x for either occurrence frequencies or mean magnitudes from the recent period when the data is assumed to be complete, and comparing the results from earlier periods with this. The cusum (cumulative sum) defined by P

i

(xi− x)

compares the slopes of the cumulative curves. Where a change of slope occurs, there should be some underlying change in the mean frequency or mean magnitude. Thus it is not the levels which are important, but the change in slope.

Unfortunately, one characteristic of the deep earthquakes over the last few decades is that there have been gross fluctuations in occurrence frequencies which can hardly be attributed to network effects. The fluctuations are not restricted to one geograph- ical region or to one magnitude class, but appear to affect occurrence rates across the whole region. This means that recent occurrence rates are no guide to occur- rence rates in earlier periods, and therefore cannot be made a meaningful reference point for cusum analysis.

The mean magnitude P

i

(mi − m), however, has been much more stable, and it

is reasonable to assume that an increase in mean magnitude as we go backwards in time is mainly to be attributed to incomplete coverage of the smaller events. By carrying out such studies for different magnitude classes, we can obtain a reasonable impression of the threshold magnitude level for reliable event detection in earlier periods.

ure 8.1, the increasing trend of yearly counts displayed in the left top of Figure 8.1 indicates uncertainties of probable contributing factors for the seismicity esca- lation, a real change or simply catalogue incompleteness. The most probable factor of contributing this is a combination of both factors at different degrees in different periods. The right top plot gives the magnitude-frequency relationship. The cumu- lative plots in the bottom should be read in a reverse direction since the specified training period, from where an average seismicity either monthly mean frequency or magnitude in high quality data set is taken as a reference value x and the cumulative deviation P(xi− x) is drawn from recent to the past. In the bottom of Figure 8.1,

the dropping slope of cumulative frequency and the ascending cumulative magnitude strongly suggest the incompleteness of the catalogue at this magnitude threshold. Only after 1970, does the catalogue completeness look convincing. Note that the right bottom plot is based on event by event scale, hence the dash lines delimiting the calendar years are separated apart in different degrees due to fluctuations in occurrence frequencies.

When the magnitude cutoff comes to 4.5, the evidence of catalogue completeness is indicated through yearly occurrence number, magnitude frequency and the cu- mulative plots of Figure 8.2 which suggests a relatively quiet period in historical seismicity in New Zealand from 1960s to late 1980s (Reyners, 1989). However, the abruptly ascending slope appearing in the cusum magnitude in the earliest period, approximately from 1945 to 1950, suggests that the catalogue may be still incom- plete at some seismic active zones in this early postwar period. Similar analysis in Figure 8.3 shows that after 1988, probably 1989, the catalogue is relatively homo-

geneous at magnitude threshold level m0 = 3.5. These figures are easily produced

by using SSLib package in R, see Statistical Research Associates Limited referred in the reference list. This is an optimistic viewpoint, and it is likely that some events are missing even within the periods indicated. However, such omissions are unlikely to be on a large enough scale to affect the broad conclusions made in the present study.