STATION CORRECTION ANALYSIS FOR SURFACE-WAVE MAGNITUDES OF NEW ZEALAND EARTHQUAKES

Station terms and standard errors are presented for 345 world-wide stations used in the determination of surface-wave magnitudes of 190 selected New Zealand earthquakes over the period 1901-1993 [I]. These will facilitate the estimation of surface-wave magnitudes of other earthquakes in the New Zealand region. The station terms and the residuals from the linear model used to estimate them are both found to be weakly related to the mean distance from the earthquakes recorded by each station. The horizontal and vertical components at a given site are treated as separate stations. The station term for the horizontal component tends to exceed that for the vertical component at mean distances in the 20°-40° range.


INTRODUCTION
This paper describes the station correction analysis for surfacewave magnitudes of a selection of 190 of the larger New Zealand earthquakes over the period 1901 to 1993 [I].It follows a similar study [2,3] carried out on a smaller selection of earthquakes with data from fewer stations.The methodology of the previous study has been followed in the main.An exception, discussed below, is in the treatment of the horizontal and vertical components at a single station.
The larger data set analysed in the present study allows station terms to be estimated for many more stations.It also offers the prospect of improved estimates of the station terms for the 96 stations included in the previous study.
Estimates of Ms are normally made only from data recorded at distances less than 160°, e.g., as practised in the ISC Bulletin.This would exclude data from many stations in Europe, as seen in Figure 1, reducing our data set for New Zealand earthquakes from 2040 station observations of Ms to 1577.However, as found previously [2], data at distances > 160° is made admissible by correcting for bias by calculating station corrections using analysis of variance.

METHOD
The data set used for this study has been described elsewhere [I], together with the computation of surface-wave magnitudes at each station from the seismograph records.
The estimation of station terms has been carried out simultaneously with the estimation of the surface-wave

Institute of Geological & Nuclear Sciences, Lower Hutt Member Fellow
magnitudes, by fitting an analysis-of-variance model incorporating both earthquake terms and station terms.The model used is as follows [2]: (1) where MiJ is the magnitude of the ith earthquake computed from the seismographic record at the jth station, m; is the "true" average magnitude of the ith earthquake, cj is the fixed effect of the jth station, and the eiJ are independent normally distributed random errors with a common variance cr 2 that combines both observational inaccuracy and modelling deficiency.
The modelling deficiency includes differences in the average attenuation along the paths to the stations, but as we are concerned solely with New Zealand events the paths to any given station will not vary greatly and the differences in average attenuation are therefore not expected to be large [2].The above model is readily fitted by the method of ordinary least squares, although solving for such a large number of parameters (535) as are in the present study is demanding of computer memory.The size of the problem was substantially reduced by omitting from the data set, for model-fitting purposes, those stations which have only one observation.These stations contribute nothing to the estimation of magnitude, but their station terms can be estimated separately by

RESULTS
The station terms, C , and standard errors, S( c), are listed in given bys = 0.200.
The three or four letter station codes are those used by the ISC [4,5].In some cases a single letter code ("M" or "Z") follows the station code.Some earlier events were recorded on undamped Milne seismographs at certain stations.These observations have been treated as belonging to a different station from later recordings made at the same sites with damped seismographs, with an "M" added after the station code to distinguish the Milne instrument.Likewise horizontal and vertical components at the same site have been treated as separate stations in all cases, and a "Z" following the station code distinguishes the vertical component, where available.A somewhat different practice was adopted in the previous study [2], in which horizontal and vertical components were regarded as coming from the same station, and therefore averaged, except where they were found to differ significantly.
The linear model (l) does not allow independent estimation of all parameters; one parameter, or linear combination of parameters, must be fixed arbitrarily.As in the previous study [2], the station "UPP" (Uppsala) was chosen as a reference station and its station term arbitrarily set to zero, with a consequential systematic effect on all estimated magnitudes.Since the mean of the station terms turned out to be 0.001, the results are essentially the same as if the mean of the station terms had been set to zero.
The station terms and standard errors may be used to streamline the computation of surface-wave magnitudes of New Zealand earthquakes in future studies, by correcting each station observation and averaging all corrected observations to produce -0.2 l::,. l::,.l::,.
-0.6 0 50 Clearly, the greater the number of stations used, the smaller the standard error S( m ) will tend to be.The data in Table 1 allow an examination of possible relations between station effects and distance.In Figure 2 the station term is plotted against the mean distance of the station from earthquakes it recorded.Also plotted is a robust smooth trend line computed using the Splus function "lowess" [6].It can be seen that the station term varies systematically with distance, being most negative (-0.07) at about 90° and most positive (+0.18) at about 173° (the greatest mean distance in the data set).

Figure 2 Plot of station terms against mean distance, in degrees, of New Zealand earthquakes from the station, distinguishing horiwntal and vertical components (damped seismographs) and undamped Milne seismographs. A robust smooth trend, computed using the Splus "lowess "function {6/, has been fitted through all the data.
The trend in Figure 2 is consistent with the expected secondorder effects of the geometry of the world's surface on surfacewave attenuation.Surface-wave trains diverge out to distances of 90° and then converge between 90° and 180°.Hence the attenuation of surface waves will tend to be greater out to 90° and less between 90° and 180°, relative to the mean attenuation relation used for estimates of surface-wave magnitude at individual stations [I].It should be no surprise, then, to see the decreasing trend in station terms out to 90° and the increasing trend from 90° to 180°.
The relatively small spread of station terms at mean distances greater than 150° suggests less variability in this range.This is confirmed by a plot of the absolute value of the residuals from model (1) against distance (Figure 3), again with an accompanying trend line.Here, the residual r;i of the ith earthquake at the jth station is defined by • 0.8 a. • ,. Figure 3 shows that the size of the residuals, although quite variable, decreases, on average, from about 0.13 to about 0.1, as the distance increases from about 90° to 173°.Thus, it is the stations at distances greater than 160° which contribute data of highest precision to the estimation of New Zealand surfacewave magnitudes, provided that station corrections are made.This is a significant result, since it is common practice to use only stations at distances in the range 20° s D s 160° to estimate surface-wave magnitudes (e.g. the ISC Bulletin).The data at distances greater than 160° are particularly important for New Zealand earthquakes because they comprise about a quarter of the total available data.Their relatively high precision makes them even more important.0.6 • 50 100 150

Mean distance {degrees)
Figure 4 Difference of station terms estimated from the horizontal and vertical components recorded at a single site plotted against mean distance, in degrees, of New Zealand earthquakes from the site.A robust smooth trend, computed using the Sp/us "lowess" function [6/, has been fitted through the data.
Although we have no data from stations at, or close to, a distance of 180°, it is noted that near the antipode the maximum phases of surface wave trains can arrive simultaneously from different directions.For large earthquakes, this effect may occur within about 4° of the antipode, i.e. at distances;: 176°.
Enhancements of peak amplitudes by superposition are clearly possible in this situation, and focusing with strong amplifications of up to an order of magnitude, within 2° of the antipode, have been demonstrated [7] for body waves from the 1968 Inangahua, New Zealand, earthquake recorded in Spain.
A surface-wave amplitude amplification by a factor of ten implies an overestimate of Ms by an increment of 1.0.Such data might be rejected as outliers [3 ], or data from distances;: 178° could be systematically excluded.
The results include separate estimates of the station effects for both the horizontal and vertical components at 105 sites.This is a sufficiently large data-base to analyse for systematic differences between these two components.Overall, the station terms of the two components differ significantly at only five sites at the 1 % level, and a further four sites at the 5% level.The former sites are "AFI" (Afiamalu, Samoa), "DBN" (De Bilt, The Netherlands), "RAR" (Rarotonga), "RIV" (Sydney) and "TAS" (Tashkent); the latter are "SBA" (Scott Base, Antarctica), "SHE" (Shanghai), "TFO" (Tonto Forest, Arizona), and "TUC" (Tucson, Arizona).For all of these sites except "SHE", the station term for the horizontal component exceeds that for the vertical component.It is notable that the nine sites listed include four with mean distances less than 40°, out of a total of only seven such sites in the data set.The differences at these four sites are supported by a high number of station observations and in three cases they are significant at the I% level.In Figure 4, the difference between the horizontal and vertical station terms is plotted against mean distance from the earthquake sources.It can be seen that the difference tends to be positive at short distances, being about 0.2 at 20° and decreasing to be about zero, on average, at distances greater than 90°, as shown by the robust smooth trend line.The positive tendency at distances less than 40° is well supported by the data, as indicated above, but there are few stations to determine if there is any real difference in the 40° -80° range.A physical explanation for this tendency is lacking at present.

CONCLUSION
The station correction analysis presented here will facilitate the estimation of surface-wave magnitudes of future New Zealand earthquakes, as well as past events not included in the present data set [1].The wide range of values found for the station terms underlines the importance of applying station corrections, especially when only a small number of observations is available for a given earthquake.The station terms cover a larger set of stations than have been included in a previous study, and generally have lower standard errors than previous estimates.The use of more stations will tend to increase the precision of magnitude estimates in future studies.
The relations between station term and distance and between absolute residual and distance have clarified the important role of stations at distances greater than 160° in the estimation of surface-wave magnitudes of New Zealand earthquakes.

Figure 1
Figure 1 Histogram of mean distances from New Zealand earthquake sources of the stations outside of New Zealand used to determine surface-wave magnitudes.

Figure 3
Figure 3 (a) Plot of absolute value of residuals from model (1) of station observations against distance, in degrees, from earthquakes to station.Also shown is a robust smooth trend computed using Sp/us "lowess" function /6].(b) Trend from (a) on enlarged scale.

Table 1 ,
together with the mean earthquake-station distance, D (in degrees), and the number of observations, N, at each station.For stations included in the the previous study [2], the station terms do not differ greatly in most cases from the values given previously, but many of the standard errors are smaller because of the larger number of observations contributing to the estimates.The residual standard deviation from model (I) is