SURFACE WAVE MAGNITUDES OF SOME NEW ZEALAND EARTHQUAKES 1901-1988

This paper gives a list of magnitudes on the surface wave scale for a selection of larger New Zealand earthquakes that occurred in the period 1901-1988. Most of the events considered were of shallow origin h < 45 km, and the magnitudes ranged from about 5 to 7.8. The Analysis of Variance method of statistical analysis was used to correct the large set of station observations so as to provide consistent mean magnitudes for each event. The resulting station terms and standard errors are given. Comparisons made between the results of this study and the relatively few previous M determinations show little change except for one or two important events~ In particular the magnitude of the 1968 Inangahua earthquake was found to be 7.4 (±0.07), which is somewhat greater than previous estimates. INTRODUCTION The need to redetermine the magnitudes of New Zealand's larger earthquakes on a consistent basis has been apparent for some time. Previously published catalogues containing New Zealand earthquakes [1-4) give magnitudes determined on a variety of bases (ML, in,,, Ms), and those bases were not always specified. Sometimes there are significant discrepancies between the magnitudes quoted by different authors for the same event, and sometimes a reasonably determined magnitude has never been published. For example, the 1922 December 25 and 1932 May 5 events were both listed by Gutenberg and Richter [1] as being of magnitude 6-7.5. Clearly the above situation was unsatisfactory and it was decided to determine, on a consistent basis, the magnitudes of a selection of local earthquakes, using the surface wave scale. The overall study was conducted by the senior author of this paper, as described in full elsewhere ( 5] . In the present paper we describe the data that were gathered, the basic Ms determination, the statistical analysis used to resolve the individual station Ms values into robust corrected mean values, and the associated standard errors. We also make comparisons with selected previous Ms determinations, and briefly discuss some of the more significant findings. 1. Physics and Engineering Laboratory, DSIR 2. Geophysics Division, DSIR THE DATA The starting point for selecting a list of earthquakes to be studied was the list compiled by Smith [3) having a selection of events of magnitude c. 5. 0 and greater during the period 1921 to 1974. This list was supplemented with further events from Smith and Berryman [ 4] and elsewhere so as to include a range of larger events that have occurred since instrumental surface wave recording got under way around the turn of the century. The list is thought to be at best complete only for magnitudes of Ms ::i!' 6. 9, but for magnitudes below this level a primary motivation for selection was to at least include all those events for which felt intensity isoseismal maps were available, together with some others of particular seismological interest. As described in the next section, M8 is determined from the amplitude, A, and period, T, of the surface waves as recorded by seismographs located at stations all around the world. Data collection consisted of finding as many (A/T) pairs of the chosen events at as many st~tions as could be cost-effectively searched. Data were obtained from many stations, of which 81 stations proved useable in our statistical analysis. Data were obtained mainly from station bulletins, plus international bulletins, or readings were made directly from the original seismograms. The number of observations found for individual events varied enormously. The number per event that were usable in our statistical analysis, ranged from 2 to 22, depending on the magnitude, depth and year of the event. BULLETIN OF THE NEW ZEALAND NATIONAL SOCIETY FOR EARTHQUAKE ENGINEERING, Vol. 23, No. 3, September 1990 SURFACE WAVE MAGNITUDE CALCULATION The values of M5 determined from surface waves recorded at any given station were calculated by two formulae, depending on the type of seismograph that had made the recording. Firstly, for certain of the earlier events on the list, valuable data were recorded on undamped Milne seismographs at various stations. For these M6 was calculated for each observation using the expression found by Ambraseys [6], Ms log(2,\) + 1. 25 log(D) + 4. 06 (1) in which (2A) is the double trace amplitude (peak-to-peak) in millimetres, D is the epicentral distance (event to station) in degrees. Secondly, for data recorded by post-Milne damped seismographs, ~s was calculated ~or each observation using the expression commonly known as the "Prague formula" [7], Ms ~ log(A/Tlmax + 1.66 log(D) + 3.3 (2) in which (A/Tlmax is the maximum ratio of t~e ground amplitude, A, of the surface waves in micrometres, and T, the associated period in seconds. Dis the epicentral distance in degrees. This formula is now used by the US National Earthquake Information Service and the International Seismological Centre in the routine reporting of global seismicity. For horizontal motions the amplitude and period were taken as,


INTRODUCTION
The need to redetermine the magnitudes of New Zealand's larger earthquakes on a consistent basis has been apparent for some time.

Sometimes
there are significant discrepancies between the magnitudes quoted by different authors for the same event, and sometimes a reasonably determined magnitude has never been published.For example, the 1922 December 25 and 1932 May 5 events were both listed by Gutenberg and Richter [1] as being of magnitude 6-7.5.

Clearly
the above situation was unsatisfactory and it was decided to determine, on a consistent basis, the magnitudes of a selection of local earthquakes, using the surface wave scale.The overall study was conducted by the senior author of this paper, as described in full elsewhere ( 5] .In the present paper we describe the data that were gathered, the basic Ms determination, the statistical analysis used to resolve the individual station Ms values into robust corrected mean values, and the associated standard errors.We also make comparisons with selected previous Ms determinations, and briefly discuss some of the more significant findings.

THE DATA
The starting point for selecting a list of earthquakes to be studied was the list compiled by Smith [3) having a selection of events of magnitude c. 5. 0 and greater during the period 1921 to 1974.This list was supplemented with further events from Smith and Berryman [ 4] and elsewhere so as to include a range of larger events that have occurred since instrumental surface wave recording got under way around the turn of the century.
The list is thought to be at best complete only for magnitudes of Ms ::i!' 6. 9, but for magnitudes below this level a primary motivation for selection was to at least include all those events for which felt intensity isoseismal maps were available, together with some others of particular seismological interest.
As described in the next section, M 8 is determined from the amplitude, A, and period, T, of the surface waves as recorded by seismographs located at stations all around the world.Data collection consisted of finding as many (A/T) pairs of the chosen events at as many st~tions as could be cost-effectively searched.
Data were obtained from many stations, of which 81 stations proved useable in our statistical analysis.
Data were obtained mainly from station bulletins, plus international bulletins, or readings were made directly from the original seismograms.The number of observations found for individual events varied enormously.
The number per event that were usable in our statistical analysis, ranged from 2 to 22, depending on the magnitude, depth and year of the event.

SURFACE WAVE MAGNITUDE CALCULATION
The values of M 5 determined from surface waves recorded at any given station were calculated by two formulae, depending on the type of seismograph that had made the recording.
Firstly, for certain of the earlier events on the list, valuable data were recorded on undamped Milne seismographs at various stations.
For these M 6 was calculated for each observation using the expression found by Ambraseys [6], in which (2A) is the double trace amplitude (peak-to-peak) in millimetres, D is the epicentral distance (event to station) in degrees.
Secondly, for data recorded by post-Milne damped seismographs, ~s was calculated ~or each observation using the expression commonly known as the "Prague formula" [7], in which (A/Tlmax is the maximum ratio of t~e ground amplitude, A, of the surface waves in micrometres, and T, the associated period in seconds.
Dis the epicentral distance in degrees.This formula is now used by the US National Earthquake Information Service and the International Seismological Centre in the routine reporting of global seismicity.
For horizontal motions the amplitude and period were taken as, where N and E refer to the two orthogonal components (generally north-south and.eastwest.If only one horizontal component was available, an increment of 0.1 was added to that magnitude to allow for the likely contribution of the missing component.The raw magnitude observation M .. at station j from earthquake i is written: 11 M;j (4) 199 where M. is the "true" average magnitude, c. is the ~orrection for station j, and eii iJ a random error that combines observational inaccuracy and modelling deficiency.

JOINT CALCULATION OF MAGNITUDES
The presence of the station term c. means that the estimated magnitudes are boupled together.
The coupling between two events can be thought of as the number of stations contributing to both, but this is only approximate, as two events will be coupled if they have no station in common but individually have stations in common with a third event.
In the data considered here, all events are coupled, but the strength of the coupling varies greatly between events.
There may be complications.As written, the "station" term in equation ( 4) also includes differences in the average attenuation along the paths to the stations.
For a station recording earthquakes in different regions of the world this could be expected to be different for each region.
As we are concerned solely with New Zealand events, we can neglect this effect, recognising that it will, however, have a small impact on our estimates.
Seismographs at different magnifications and distances will record and report different subsets of the data: low magnification, distant stations will only report the larger events, while high magnification, near stations may be overloaded by these and so only report smaller ones.
The number of stations reporting an event generally increases with increasing magnitude.
These effects cause two problems.First, there may be an uneven coupling of magnitudes, in that the link between large and small magnitudes is afforded only by stations that record both.The coupling problem is much exacerbated here by changes to the seismograph network with time.We will examine this later, but an example will illustrate the problem.
The earliest two events we considered were largely recorded on Milne seismographs which, except at Melbourne (MEL), recorded no other events (Table 1) .
Coupling of these events to the rest is thus relatively poor.
The second is one of biased sampling.
smaller events are only reported from stations with a high signalto-noise ratio, the sample is biased in favour of higher magnitudes.Conversely, if larger events overload some stations, then the largest amplitudes may tend to be omitted from the sample, leading to a bias towards lower magnitudes.
The first problem is overcome to the extent possible by our method, which reflects the coupling, or lack of it, in the standard error of the estimated Thus the inherent uncertainty of a poorly coupled event is reflected in a higher standard error for that event.
The second problem we ignore.
There are complex procedures for dealing with it that we believe to be unjustified in the data considered here.
There is certainly no evidence for significant biasing downwards of the larger events, which only reach Ms 7. 8.
Possible upward biasing of the The problem is made more complex by being compounded with the first and second problems: the number of European data depends on the size of the event.
If one were concerned about assessing the relative sizes of New Zealand events in a global catalogue, this would be a major concern, and some sort of weighting scheme would be necessary to diminish the effect of the concentration of European data.
However, our goal is to produce a consistent, quantitative ranking of New Zealand events only, and so no such steps have been taken.
In equation ( 4) the errors e .. are assumed to be independently distribut'Ja with common variance a 2 , i.e. there is assumed to be no variation in the precision of the readings between stations.
Examination of some magnitude residuals r;j (5) (where the circumflex A denotes an estimated quantity) at individual stations indicated that this was a satisfactory assumption.It follows that a conventional least-squares solution of the set of equations ( 4) yields estimates of the standard errors of both the average magnitudes and the station terms.
There is a trivial complication.It can be seen that adding any constant to all the average magnitudes and subtracting the same constant from all the station terms will leave equation ( 4) unaltered.
In other words the "baseline" of magnitudes and station terms are inseparable.It is usual to resolve this problem either by having a reference station for which the station term is fixed at zero (eg Haines, Ref. 8) or by requiring that the sum of all the station terms be zero.
We have adopted the first method, choosing as the reference station Uppsala (UPP), which reported 29 of the 69 events for which M was determined.
As it turned out, adopttng the second criterion would have made negligible difference to the average magnitudes, as the average of the station terms was -o.03.Requiring that the average station term be zero would have subtracted an insignificant 0.03 from every magnitude.
A final point.
In the collected data a number of stations had reported only a single event.This single reading in effect defines (rather poorly) their station term and the station in fact makes no contribution to the average magnitude of the event.
Thus "useful" information is contributed only by stations that have reported at least two events, and there were 81 such stations (but see discussion below).

ANALYSIS OF THE DATA
Because of the problems attended to in the previous section and in the interests of showing that the final magnitudes were as consistent as possible, a number of experiments were conducted.
First, it was not clear that the station term would be the same for the horizontal and vertical components at a station where examined to ascertain whether the vertical and horizontal data could be combined.
At most stations this appeared to be the case, and, at those stations, the horizontal and vertical raw magnitudes were arithmetically 201 averaged and the data re-processed.
The effect on the calculated average magnitudes was (gratifyingly) negligible.
At six stations, the difference between the vertical and horizontal station term was <' .0. 2.
Only at TAS (Tashkent) and RIV (Riverview, New South Wales) were the differences statistically significant.However, the distinction between the vertical and horizontal components was retained for these six stations.This increased the effective number of "stations" in the analysis from 81 to 87.
A second, allied problem arose with the Milne data.
At some stations, a Milne was replaced by some other instrument.Because of the very different nature of the Milne seismograph and the different formula used to calculate Milne magnitudes (equation 1), the distinction between Milnes and other seismographs was retained.
A third concern was allied to the second: other instrumental changes would have taken place during the 87 year period considered that might have had the result of causing the station terms to change with time.One important change known to have had a major effect on the networl<:: was the establishment during the 1960's of the World Wide Standard Seismograph Network (WWSSN) , featuring 100 s period Press-Ewing seismometers with 15 s period galvanometers.
In fact, the only station at which a change of instrumentation to Press-Ewings is noted in the International Seismological Centre catalogues and which reported data from both the pre-and post-WWSSN era was RIV.Therefore RIV was experimentally treated as two separate "stations" for the pre-and post-WWSSN era.The station terms for the two "stations" were found to be almost identical, and so the distinction between pre-and post-WWSSN was dropped.
In the calculation of surface wave magnitudes, it is customary not to include data from stations very close (within 20° angular distance) or very remote (beyond 160° angular distance) .This is done to avoid near-source complications, and amplification due to focussing at 180°.Since many European stations are 160° -170° away from New Zealand, a significant amount of data would be lost by enforcing the 160° rule.At the same time, as the variation in distance to any station is small, any amplification effect will tend to be amalgamated into the station term.Examination of the magnitude residuals (observed magnitude minus estimated average magnitude) at stations beyond 160° shows no more scatter than the others supporting the view that the variation in amplification with distance is not great.
Accordingly, these data have been incorporated into the analysis.
We conclude that the final results are stable to small changes in the estimation process and represent as consistent a set of magnitudes as one can expect to get from such data.The results of the above calculations are given in Tables 2 and 3.In the right-hand column of these tables, together with the magnitude (M 5 ) , we give the standard error (dM) and the number of station magnitudes used for each event (n).
For completeness we also include the station terms and standard errors ( within each distance range (0°).Eighty seven stations with 2 or more recordings, plus 9 Milnes with only one recording are shown at the median distance of their observations.

COMPARISON WITH MAGNITUDES FROM OTHER STUDIES
The magnitudes estimated here represent no great change from the previously adopted   that were hitherto without an instrumentally assessed magnitude, and one or two events with small but important differences.

IMPORTANT EARTHQUAKES
It is beyond the scope of this paper to discuss every event for which our magnitude is different from that previously adopted.However, because of their importance, a few events are worthy of mention.Its reassessment at 6.7 must have significant impact on the assessment of seismic hazard in this region.
The magnitude of the 1904 event is largely determined from Milne seismographs and that of the 1901 one is wholly so (Table 1) .Their poor coupling to the rest of the data is reflected in relatively large standard errors for these events.Moreover, there is a possibility of systematic error due to a different magnitude formula being used for Milne data (equation 1), although equations (1) and (2) seem to give consistent Ms values over the full range of distances [5].However, as the variation of distances between the earthquakes and any station is very small, any error in the distance correction term will be incorporated into   Similarly, a base-line error between the two formulae will also be largely absorbed into the station terms.We conclude that the magnitudes calculated for these events are acceptably consistent with the rest of the set.
Of the earthquakes with magnitudes greater than were previously assessed, the 1968 Inangahua event, estimated at M = 7. 4, is the most important.Abe [13,14)  Revision of the Inangahua magnitude upward to 7.4 could have a similar effect on the magnitude assessment of the 1848 event.

ACKNOWLEDGEMENTS
Much of the data set was not available in New Zealand and this necessitated visits by the senior author to Australia and England in order to obtain sufficient data.Acknowledgement is made of the financial support of the DSIR which made this possible, and the authors wish to express their gratitude to friendly co-operation during this trip of the following people and organisations: M Leiba and K Mccue (Australian Seismological Centre, Canberra); N Ambraseys (Imperial College, London); R Adams and A Hughes (International Seismological Centre, Thatcham, England).
We also wish to thank DSIR colleagues for helpful reviews of this paper, namely J Haines, G McVerry and D Rhoades.
In addition we thank our colleagues H Anderson, B Ferris, M Reyners and T Webb for kindly helping by providing some of the information used in this study.

TABLE 1 : STATION MAGNITUDE DATA SETS FOR THE 1901, 1904 AND 1968 EVENTS
A third problem arises from New Zealand's geographical isolation.Stations reporting

Table 4
). Stations are shown in alphabetical order

TABLE 2 (continued)
* No surface waves observed

TABLE 4 :
and Smith