CHAPTER 3

An estimation of possibilities for the unification of arctic earthquake magnitudes

In regard of arctic earthquakes, the problem of revealing qualitative relations between different determinations of magnitudes, which if not solved, drastically decreases the substantiation of the assessed seismic hazard, is as challenging as in any other region. The diversity of these determinations in the Arctic, is related, like elsewhere, to the application of different types of waves, specific hardware of the global and some regional networks, and peculiar features of local magnitude scales.

This section is aimed at analyzing the possibility for unification of magnitude characteristics on the basis of the Arctic Seismological Data Bank (ARS) (Avetisov and Vinnik,1995) created by VNIIOkeangeologia, such as estimating the statistic background for the problem solution, exhibiting the amount of information on different ratios, correlation coefficients, and standard deviations. Noteworthy is a comparison of the newly obtained relations with previous ones.

The scheme of this work is controlled by the ARS¸s structure the main components of which, as aforesaid, are the following catalogues: The General Catalogue, Arctic Canada, Northern Yakutia, and Fennoscandia. The Data Bank Control System (DBCS) allows necessary samplings to be made using all earthquake parameters. One of DBCS¸s functions is calculation of correlation equations in question assessing their statistic credibility. In consideration of the assumption that every magnitude is determined with the same error, the relations were computed through the method of orthogonal regression (Antonova and others,1968).

In the General Catalogue which since 1964, as aforesaid, has been based almost solely on the catalogue of the International Seismological Center (ISC), the most comprehensive information on earthquake magnitudes has been collected from three agencies: ISC, NEIC (National Earthquake Information Center of the USA), and MOS (Experimental Expedition of the RAS Institute of the Earth Physics, Obninsk). Each of them provides an opportunity to make determinations from body and surface waves, that is mb (ISC), Ms (ISC), mb (NEIC), Ms (NEIC), mb (MOS) and Ms (MOS). In symbols adopted by ARS these are correlative with mbl, Msl, mb2, Ms2, mb3, and Ms3. It is noteworthy that in the practice of this country magnitude values have been determined from surface waves using the vertical component (MLV) and full vector of the horizontal component (MLH) with reference to both values contained in the bulletins. However, according to (Gorbunova and others,1974), the regression equation between these two determinations looks as follows: MLV=0.98 MLH +0.07, which practically means their complete coincidence.

Seeking a more correct solution, a number of limitations were set forth for the selection of earthquakes subject to analyses.

The geographic scope of the region was restricted to 65° N in order to avoid inclusion in the sampling of earthquakes from the Pacific seismic belt which are different in tectonic nature from Central Arctic earthquakes.

The year 1970 was taken as a starting point, because by that period the national station network had been almost fully equipped with SKM short-period seismographs with reference periods of 1.2-1.5 s which are the closest to those of Benioff (0.8-1.0 s) used in the ISC and NEIC networks. Prior to 1970 mb (MOS) determinations were mainly performed by medium-period seismographs with reference periods of 5 to 8 s.

The third condition of sampling was the depth of hypocenters limited down to 35 km, which is due to an essential decrease in magnitude of surface waves at deeper events (Prozorov and Hudson,1974). The results obtained through the method of orthogonal regression for actual arctic earthquakes magnitude range 3.5-6.5 are summarized in Table 4 and Fig.5.

Table 4

Transarctic equation of regression
from data of the General Catalogue
for the period 1970-1994

N-quantity of definitions; D - RMS deviation of the function from the regression line; R-correlation coefficient.

Fig. 5 Diagrams of relationships between different determinations of magnitudes based on the General Catalogue data.

It is seen that in all instances within the available range of magnitudes the cluster shows a fairly confident approximation by a linear relation, and the correlation coefficient R is never lower than 0.73.

Expectedly, the best statistic indices (R=0.90 and 0.92) and the slope which is practically equal to 1, come under the ISC and NEIC types of determinations of the same name, which are actually based on the same reference data.

In ISC and MOS determinations the situation is different for similar pairs: at rather high correlation coefficients (0.82 and 0.83) a considerable deviation of the slope from 1 is observed, and especially for the values determined from surface waves. A comparison with similar calculations performed by V.I.Khalturin (1974) using earthquakes of 1970 to 1971 from various regions, shows a nearly full coincidence in body and clear discrepancy in surface waves. In the first instance, V.I.Khalturin had for 576 earthquakes within the range of magnitudes 4.9 to 6.2 the regression equation as follows: mb (USA) =0.94 mb (MOS) + 0.05 at R=0.71, while in the second instance, yet for stronger 687 earthquakes with magnitudes 5.0 to 7.3 , Ms (USA) = 1.0 MLH -0.15. It is noteworthy that similar differences in the ratios Ms3 and Ms1 ( and Ms2, as now admissible) have been also determined by others. Thus for example, Jordan and Hunter (1972) basing on world-wide events present two equations one of which Ms (USA) =1.02 Ms (MOS) - 0.21, is nearly the same as that obtained by V.I. Khalturin, while the other Ms (MOS) =0.82 Ms (USA) + 1.19 is definitely close to ours.

In consideration of the fact that at the first stages of instrumental observations in the Arctic ( approximately until 1960s) magnitudes were basically determined from surface waves, while subsequently the role of determinations performed from compressional waves drastically increased. For the unification of the data, formulas linking the values of mb and Ms are of most practical interest. At present, a large number of these are known for various regions from various authors using different materials, including both data on explosions and theoretical computations. (Gorbunova and others,1974; Prozorov and Hudson,1974; Khalturin,1974; Bath,1981, etc.). In the function mb (Ms) the complete set of angular coefficient values known to the author falls within a fairly wide range of 0.33 to 1.1 with predominant values ranging between 0.47 and 0.65. The values of the free member are ranging mainly between 1.3-1.4 and 2.8-2.9 with single offsets down to minus 3 or 4-4.5 with the predominance of 2.2-2.8. As we see, our parameters of the regression equations definitely fall within the predominant ranges. In contrast to V.I.Khalturin, our data set no dependence of relation formula parameters versus the range of compared magnitudes. Moreover, the figures give a quality picture, and the calculations confirm that with the range of magnitudes narrowing at least to 3.5-5 the solution becomes fairly unstable. (R< 0.4-0.5).

In order to establish a possible relation of the regression equation parameters versus peculiar features of the tectonic nature of seismicity, similar calculations were performed separately for the earthquakes of the Mid-Arctic Belt (Table 5). The comparison shows that the relations obtained are very similar to almost completely identical to transarctic ones. However, the same comparison suggests the most realistic explanation of the aforesaid similarity: Mid-arctic earthquakes are presented as a vast majority in the overall mass of arctic earthquakes. This is supported by the data of Table 6 showing that the number of determinations made from earthquakes outside the Mid-Arctic Belt are considerably lower, and equation parameters,, are remarkably different from both Mid-Arctic and transarctic. Therefore, the question of the impact of the arctic earthquakes tectonic nature on the quantitative characteristics of the regression equation may be kept open for further data acquisition.

Table 5

Equations of regression
of the earthquakes in the Mid-Arctic Belt
for the period 1970-1994

Table 6

Equations of regression
of the earthquakes in Arctic Canada
and North Alaska from data of the General Catalogue
for the period 1970-1991

In view of extreme importance of application of maximum long interval of instrumental observations for the purpose of seismic forecast, an attempt has been made to determine relation formulas up to the temporal period of 1970. In practice, information on mb determinations of arctic earthquakes has been regularly contributed since 1964, i.e. from the advent of the ISC catalogues. The calculating results of 1964 to 1969 are summarized in Table 7. The only sampling on the pair of mb1 and mb2 has turned out to be representative. Its regression formula somewhat differs from that obtained over the later years, yet, it shows a definite similarity between ISC and NEIS determinations. Thus, for the most representative range of magnitudes 3.5-5.5, the difference in calculations from these formulas does not exceed 0.1. Remarkable is the relation of mb1 vs. mb3 though being obtained from 20 determinations only shows a clear difference from that obtained later. This is undoubtedly related to the aforesaid difference of the own periods of the Benioff and SKM seismographs. Unfortunately, there is no sufficient information for establishing correlation between mb and Ms determinations . The relation mb1(Ms3) computed from 12 points only shows a coincidence of the angular coefficient and the value of the free member which is by 0.6 lower as compared with the Gutenberg equation for the world-wide determinations.

Table 7

Equations of regression
from data of the General Catalogue
for the period 1964-1969

The situation with the period prior to 1964 is even more complicated. Magnitudes of arctic earthquakes for this period of time were determined by various scientists mainly from surface waves. The relation obtained through the use of few mb determinations published by L. R. Sykes (1965) is summarized in Table 8. This is essentially close to mb1(Ms3) relation established for the period of 1964-1969 (Table 7). There is a systematic deviation between them which does not exceed 0.2.

Table 8

Equations of regression
from data of the General Catalogue
before 1964

In conclusion, over the period of 1970-1991, for earthquakes in the range of magnitudes 3.5-6.5, the unification of mb and Ms determinations performed by various agencies may be confidently made from the relation formulas summarized in Table 4. For the complete previous period of instrumental observations only formulas with poor statistical background as presented in Tables 7 and 8 may be offered for review.

Magnitudes of the overwhelming majority of earthquakes in Arctic Canada (95% min.) are determined using the local magnitude scale. Prior to 1968 the Richter scale was used in all determinations. This was originally intended for earthquakes with epicentral distances of up to 600 km (Gutenberg and Richter,1942) and later extrapolated for more distantly spaced events (Gutenberg and Richter,1956). In the first and second instances, the maximum Lg phase of shear and surface waves was used, respectively. For the reason of poorer attenuation of surface waves the values obtained from them turned out to be overestimated, with overestimations sometimes reaching 1 to 1.5 units according to A. Stevens et al. (1973).

Since 1968, apart form Richter¸s, the Nuttli scale has become applicable (1973). This is based on measurements of the amplitude and Lg maximum phase period on short-period Benioff seismographs and intended for the range of epicentral distances of 400 to 3000 km (MN). Therefore at present, the situation with determinations of earthquake magnitudes in Arctic Canada is as follows:

- MN determinations are performed under three conditions: epicentral distance is over 400 km, Lg period is shorter than 1.3 s, travel paths do not cover a significant part of the oceanic crust where Lg phase is either highly attenuated or absent whatsoever;

- with lack of data beyond the the distance of 400 km, periods shorter than 2 s and the absence on the travel path of significant parts of the oceanic crust, the determinations are made through the Richter scale (ML) using surface waves (Lg phase);

- in oceanic areas, the Beaufort Sea, Baffin Bay and elsewhere with Lg phase missing, the determinations are made through the Richter scale (ML) using shear waves (Sn phase). As soon as the nature of shear waves attenuation is poorly known, these should be regarded as preliminary determinations. If there are mb(ISC) or mb(NEIC) for such earthquakes, then ML is not to be determined.

It is also noteworthy that earthquakes of the Canadian onshore and offshore areas are processed by the Seismological Center in Ottawa, ML (OTT) and MN (OTT) (according to ARS legend, they correspond to ML4 and MN4). Recently they have been supplemented by AEIC (Alaska Earthquake Information Center). Earthquakes of Alaska are processed by the center in Palmer: ML (PMR) (according to ARS, ML7).

The results of the relation formula computation within the magnitude range between 3-3.5 and 6-6.5 are summarized in Table 9.

Table 9

Equations of regression
from data of the
Arctic Canada Catalogue

It is evident that in general, regardless of statistics which is several times worse than in the General Catalogue, that all determination of local magnitudes of the Arctic Canada are sufficiently reliable for correlation with mb1 and mb2 values. This removes the problem of impossibility to obtain the relation MN versus ML. The relation between for the local determinations and Ms2 though having fairly high correlation coefficients (over 0.8) are based, in our view, on insufficient determinations.

In the Northern Yakutia an interest has aroused towards the computation of regression formulas for different determinations of ISC and MOS magnitudes and values of K energy class which has been conventionally used for the assessment of all local earthquakes through the Rautian¸s palette (1964). Our formulas obtained on the basis of all material available form ARS and characterizing the magnitude range of 3-3.5 to 6-6.5 (K=9 and greater) are presented in Table 10. As it should have been expected, the amount of information is small, though correlation coefficients are sufficiently high. A comparison with K(Ms) relations known for other regions (New catalogue..,1977) shows that this value is close enough to that obtained for Crimean earthquakes: K=1.75 Ms + 4.2 and notably different from those of Chukchi Peninsula: K =1.5 Ms +6.5.

Table 10

Equations of regression
from data of
the Northern Yakutia Catalogue

In our view, the problem of unification of magnitudes for Fennoscandian earthquakes in the most challenging. This is attributed to both the difference in the methods of determination and great number of seismic centers making such determinations and publishing the results. Among the latter the Seismological Laboratory of Bergen (BER), Norway, and Seismological Institute of Uppsala (UPP), Sweden, should be distinguished . Over the last 10 to 15 years a large amount of information has been contributed by NORSAR Seismic Network Processing Center (NAO), Norway, HAGFORS (HFS) seismic system, Sweden, and Seismological Institute of Helsinki (HEL). Among national centers, the Kola Subsidiary of the Russian Academy of Sciences is a regular contributor of data on earthquakes in Fennoscandia based on the data provided by the Apatity Station (APA). These agencies apply three major methods of magnitude determination: from the local scale developed by M.Bath et al. (1976) and based on measurements of the amplitude and surface waves maximum phase period (ML); from the duration of records (Md) and recording distance (Md). As it was mentioned above, in ARS the main magnitude windows have taken the most frequently used types from the abundance of magnitude determinations: from surface waves ML (BER) and ML (UPP) (in ARS ML5 and ML6, respectively), from the duration of records Md (BER) (in ARS Md5) and from the recording distance md (APA) (in ARS Md8). An attempt has been made to obtain a relations between the above types of magnitudes and also between them and mb and Ms defined by ISC. The results of this attempt are shown in Table 11. It is seen that the direct link with mb1 allowing the unification of Fennoscandian earthquakes magnitudes to be made with those of other arctic regions is established only for the determinations of Md5 and Md8, however also basing on a small amount of data. This fact has appeared to be unexpected because the author is aware of at least of two mb (ML) relations for Fennoscandian earthquakes published by other scientists. It is the formula by M.Bath et al. (1976), obtained in early 1970s from though unknown to us but sufficient number of determinations, and formula by B.A. Assinovsakya (1994) obtained from 45 determinations. To explain where the above authors took such a number of determinations one should suggest that they used cumulative data on mb from various agencies, particularly many mb (NAO) and mb (HFS) determinations have been known, and their own determinations could be also possible. This approach does not seem to us quite correct. This may be the cause why the above relations are so drastically different from each other: mb=0.49 ML + 2.93 according to M.Bath et al., and mb =1.28 ML -0.95 according to B.A. Assinovskaya. For ML=4 and ML=3 the differences in mb reach 0.5 and 1.5, respectively.

Table 11

Equations of regression
from data of
the Fennoscandia Catalogue

The factual base of relations between local determinations is essentially better, which allows the mb correlation formula to be produced for all available determinations. Yet, it should be noted that relations between local determinations and mb1 span magnitudes 3-3.5 and greater while interior Fennoscandian values cover the range between 1.-1.5 and 4-4.5. Consequently, the use of the obtained relations seeking to tie the local determinations to mb1 for weak earthquakes is only possible given the parameters of these relations are preserved within the domain of minor magnitudes.

Summing up the aforesaid, the following conclusions may be drawn regarding the possibilities available for the unification of different magnitude determinations of the arctic earthquakes:

- for the Arctic Region in general, with respect to earthquakes of magnitudes ranging between 3.5 and 6.5 there are reliable relations between mb and Ms which have been determined by ISC, NEIC and MOS since 1970. For the earlier period, the number of employed values does not basically exceed two to three dozens;

- parameters of relation formulas for the earthquakes of the Mid-Arctic Belt are close to those of the Arctic in general, however, this is rather attributed to their great part in the total number of earthquakes. The impact of the tectonic factor on the regression formula parameters remains to be further discussed;

- for the Arctic Canada, statistically dependable relation formulas have been obtained providing possible correlation between the local and common arctic determinations. Some additional information on the northern Yakutia and Fennoscandia would be required.

- the lower limit of magnitudes for which the produced relation formulas are true is the mb value of 3-3.5. This appears to be the limit for the contemporary network of arctic stations.