The knowledge of the quantitative relationships between various magnitude determinations is vital to the reliability of seismic risk assessment. The diversity of these determinations in the Arctic, as well as elsewhere, is related to the use of various wave types, differences in the instrumental design of the worldwide and regional networks, and specific features of local magnitude scales.

I analyzed the unification possibilities of various magnitude characteristics on the basis of the Arctic seismological databank (ASD) [1].

Although the relationship between the magnitude determinations from body and surface waves was shown to be generally nonlinear [e.g., 2], its linear approximation, implemented in the regression formulas published in tens of publications and employed in this work, was acknowledged to be practically acceptable.

The main ASD components are the General, Arctic Canada, Northern Yakutia, and Fennoscandia catalogs. The desired samples of earthquake parameters are provided by a database management system (DBMS). One of the DBMS functions is the calculation of the sought for relations and estimation of their statistical reliability. Assuming that the determination accuracy is magnitude-independent, these relations were calculated by the method of orthogonal regression [3].

Beginning from 1964, the General catalog is based solely on the catalog of the International Seismological Center (ISC), and most of its information has been recovered from three sources: the ISC; the National Earthquake Information Center (NEIC), United States; and the Monitoring Observation Station (MOS), Joil1t Institute of Physics of the Earth, Russian Academy of Sciences, Obninsk. These data allow the magnitude determination from the body and surface waves, namely, mb (ISC), Ms (ISC), mb (NEIC), Ms (NEIC), mb (MOS), and Ms (MOS) (see Note to Table 1). Note that the surface wave magnitude determinations in our country have used both the vertical component (MLV) and full vector of the horizontal component (MLH), and the bulletins list both values. However, as is shown in [4], the equation of regression between these determinations has the form MLV = 0.98 MLH + 0.07, which implies their nearly absolute coincidence.

To make the solution more correct, restrictions were imposed on the earthquakes to be analyzed.

The region under consideration was bounded by 65°N to exclude the earthquakes of the Pacific seismic belt, which differ, by their tectonic origin, from the Central Arctic earthquakes.

The study time period began in 1970, the year by which the domestic network was nearly completely equipped with the short-period SKM instruments, whose free periods (1.2-1.5 s) are close to those of the Benioff instruments (0.8-1.0 s) used by the ISC and NEIC networks. Before 1970, mb (MOS) was mainly determined by the medium-period SK instruments with free periods of 5-8 s.

Finally, the hypocenters considered were bounded by a depth of 35 km because of a pronounced amplitude attenuation of surface waves from the deeper events [5].

The calculation results for the actual range of mag­nitudes (3.5-6.5) of Arctic earthquakes are presented in Table I and figure, which show that the linear approximation is fairly reliable and the correlation coefficient does not drop below 0.73 in all cases considered.

As expected, the best statistical properties and the slope nearly equal to 1 are characteristic of the ISC and NEIC determinations based actually on the same original data.

The situation is different for the similar pairs of the ISC and MOS determinations: with the correlation coefficients being rather high, the slope is markedly different from 1, particularly for the determinations from surface waves. The comparison with similar calculations for the earthquakes of 1970-1971 in various regions [6] shows nearly absolute coincidence for the body waves and obvious discrepancy between the surface wave determinations. Similar differences in the relations between Ms3 and Msl (Ms2) are reported in [7].

Since the early (until the 1960s) instrumental observations of magnitudes in the Arctic were based on the  surface waves, whereas the role of the longitudinal waves sharply increased in the subsequent years, the formulas relating mb and Ms are most interesting for the magnitude unification. Presently, a great number of such formulas obtained for various regions and from diverse data are known, including explosions and theoretical calculations [e.g., 4-6, 8]. To the best of my knowledge, the slopes of the curves mb (Ms) range within wide limits between 0.33 and 1.10, but the values between 0.47 and 0.65 dominate. The free term varies mainly from 1.3-1.4 to 2.8-2.9. Its individual values may reach -0.3 and 4.0-4.5, and the predominant range is 2.2-2.8. The regression equation parameters obtained here fall within the latter. Unlike [6], our data do not yield any evidence of the dependence of the magnitude relation parameters on the range of compared magnitudes. Moreover, as is seen from the figure and confirmed by calculations, the narrowing of the magnitude range, even down to 3.5-5.0, makes the solution unstable (R < 0.4-0.5).

To assess the influence of the tectonic factor on the regression parameters, similar calculations made separately for the earthquakes of the mid-Arctic seismic belt gave the relations close to the trans-Arctic ones. The most reasonable explanation of this similarity is that the mid-Arctic earthquakes dominate among the Arctic events: the number of determinations from the earthquakes outside the mid-Arctic belt is commonly one order of magnitude smaller.

Since the use of a maximally long interval of instrumental observations is vital to the seismic prediction studies, we tried to find the magnitude relation formulas for the time period before 1970. The regular information about the mb determinations from the Arctic earthquakes became available only from 1964. The calculation results for the period 1964-1969 are listed in Table 2. Only the data on the mbl-mb2 pair proved to be representative. Its regression formula is somewhat different from that obtained for the later years; however, it yields evidence of the obvious closeness between the ISC and NEIC determinations. Thus, the discrepancy between these formulas does not exceed 0.1 for the most representative magnitude range 3.5­5.5. It is noteworthy that the relation between mbl and mb3, though obtained only from 20 determinations, obviously diverges from that obtained for the later years, which is undoubtedly related to the aforementioned differences in the free periods of the Benioff and SKM instruments. Unfortunately, the constraints on the relation between mb and Ms are very scarce (12 determinations).

The situation is even more discouraging for the period before 1964. The magnitudes of the Arctic earthquakes at that time were determined by different authors mainly from the surface waves. The mb dependence derived from the few determinations by Sykes [9] and presented in Table 3 is close to the dependence mb (Ms3) established for the interval 1964-1969, their systematic divergence not exceeding 0.2.

The majority of the Arctic Canada earthquake magnitudes (not less than 95%) are determined with the help of the local magnitude scales ML [10, 11] and MN [12], only one of these values being available for each determination.

Table 1. Trans-Arctic equations of regression from data

of the General catalog for the period 1970-1991

Note: The notation used in the text and tables is as follows. D is the rms deviation of the function from the regression line and R is the correlation coefficient. Institutions: I, ISC; 2, NEIC; 3, MOS; 4, OTT (Ottawa); 5, BER (Bergen); 6, UPP (Uppsala); 7, PMR (Palmer); 8, APA (Apatity). Magnitudes: mb, body waves; Ms, surface waves; ML, local scale; MN, Nuttli scale [12]; Md5, record length; Md8, recording distance.

The determinations from the local scales are usually not cited whenever mb (ISC) or mb (NEIC) is available.

The earthquake data from the Canadian land and sea areas are processed at the Ottawa (OTT) Seismological Center and, recently, the Alaska Earthquake Information Center (AEIC). The Alaska earthquakes are dealt with at the Palmer (PMR) Center.

The above makes it clear that the prospects for deriving the relations between various magnitude determinations in Arctic Canada are not promising. This is corroborated by the data of Table 4 demonstrating the poor statistical background of the empirical formulas, namely, the small number of determinations (1­1.5 orders of magnitude smaller as compared with the General catalog), low correlation coefficients, and considerable rms errors. Overall, only the dependences mb2 (MN4) and, to a lesser degree, mbl (MN4) may be considered as the most reliable. High correlation coefficients for Ms2 (MN4) and ML4 (ML7) are based on a small number of determinations, whose increase may change the magnitude relation parameters.

In Northern Yakutia, it is interesting to calculate the relationship between various ISC and MOS determinations, on the one hand, and values of the energy class K, on the other hand. The intensity of all local earthquakes is traditionally estimated in terms of the energy class with the use of the Rautian master curve [13]. Table 5 presents the relationships derived here for the magnitude range from 3-3.5 to 6-6.5 (K ~ 9) on the basis of all evidence available from the ASD. As is expected, the amount of information is small, although the correlation coefficients are fairly high. The comparison with the dependences K (Ms) known from other regions [14] indicates close similarity with the Crimean relationship K = 1.75 Ms + 4.2 and rather high deviation from the Chukot one K = 1.5 Ms + 6.5.

Table 2. Regression equations from

the General catalog da­ta for 1964-1969

Table 3. Regression equation from

the General catalog data for the time before 1964

Table 4. Regression equations from the Arctic Canada cat­alog data

Table 5. Regression equations from the Northern Yakutia catalog data

Table 6. Regression equations from the Fennoscandia cata­log data

For the Fennoscandia earthquakes, the problem of the magnitude unification is most critical. This is related to both the differences in the determination approaches and a large number of the seismological centers involved in the magnitude determinations. These are the Bergen Observatory (BER), the institute in Uppsala (UPP) , the data processing center of the NORSAR network (NAO), the institute in Helsinki (HEL), and the Apatity station, Kola Section of the Russian Academy of Sciences (APA). These institutions employ three main methods: magnitude determinations from a local scale (ML) [15], record length (Md), and recording distance (Md). The magnitude types dominating in the ASD determinations are the surface wave magnitudes ML (BER) and ML (UPP), record length magnitudes Md (BER), and recording distance magnitudes Md (APA).

Presently, there are no means for providing the statistically meaningful constraints on the relation between local and worldwide magnitude deterrninations. Sufficiently reliable formulas exist only between some of the local determinations (Table 6).

The final conclusions may be stated as follows.

For the Arctic as a whole and the earthquakes in the magnitude range 3.5-6.5, there are reliable formulas for the relation between the mb and Ms determinations from the ISC, NEIC, and MOS data obtained since 1970. The number of previous determinations does not exceed 20-30.

The relation parameters for the mid-Arctic belt earthquakes are close to the whole-Arctic parameters, which may be explained by the fact that the former prevail among the Arctic earthquakes. The problem of the influence of the tectonic factor on the regression equation parameters remains open as yet.

The experimental background of the relations between the magnitude determinations from local scales of separate regions and ISC determinations is also inadequate, and the minimum magnitude threshold generally is not lower than 3.0. For some local magnitudes, the relation formulas cannot be derived at all due to the absence of any data.

The problem of deriving the relationships between local magnitude determinations is region-dependent. In Arctic Canada, the relationship MN (ML) cannot a priori be derived, because only one of the determinations is admissible in each case. Reliable regression formulas are obtained for certain local determinations in Fennoscandia.

Additional experimental data are required to refine the parameters of the relationships already obtained and derive new formulas. Thus, the problem of deriving the relations for the ML (NAO) and mb (NAO) determinations is rather relevant in Fennoscandia, where the NORSAR network plays the leading role in the recording of local earthquakes.

The lower magnitude threshold of the validity of the regression formulas derived above is mb = 3-3.5. This value appears to be a limiting one for the present network of the Arctic stations.

REFERENCES

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5.Prozorov, A.G. and Hudson, D., Regional and Local Factors Affecting the Relation between the MLH and mPV Magnitudes, in Magnituda i energeticheskaya klassifikatsiya zemletryasenii (Magnitude and Energy Classifi­cation of Earthquakes), Moscow: Nauka, 1974, vol. 1, pp. 208-216.

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