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| JOURNAL HOME | HELP | CONTACT PUBLISHER | SUBSCRIBE | ARCHIVE | SEARCH | TABLE OF CONTENTS |
Department of Geological Sciences, Michigan State University, East
Lansing, Michigan
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INTRODUCTION |
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 TOP INTRODUCTION HISTORICAL BACKGROUNDTHEORETICAL BACKGROUND FOR THE...AMPLITUDE-ONLY APPROACH AND...ACCURACY OF THE K-CLASS...NATIONAL APPLICATION OF THE...REGRESSIONS BETWEEN MAGNITUDE...DISCUSSIONCONCLUSIONSACKNOWLEDGMENTSREFERENCES |
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K = log10 E (in joules).
The nature, origin, and methodology of this system are poorly known to Western seismologists studying Soviet and Russian seismological data, and yet are of great interest and importance to those conducting detailed research on the seismicity of the former USSR. Since its inception, K-class has been the primary means of quantifying the size of small events in the former USSR and continues to be used for that purpose today. In most of this region, scientists employed the method of Rautian (1960), using the maximum horizontal (for the S wave) and vertical (for the P wave) amplitudes, which became the standard for local and regional networks in the early 1960s. In this paper, we describe the origins and basic principles of the energy class system, as well as the methodology generally used today by the regional networks (figure 1) of the states of the former USSR.
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HISTORICAL BACKGROUND |
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TOPINTRODUCTIONHISTORICAL BACKGROUNDTHEORETICAL BACKGROUND FOR THE...AMPLITUDE-ONLY APPROACH AND...ACCURACY OF THE K-CLASS...NATIONAL APPLICATION OF THE...REGRESSIONS BETWEEN MAGNITUDE...DISCUSSIONCONCLUSIONSACKNOWLEDGMENTSREFERENCES |
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The study of regional seismicity was not well-developed at that time, so there were no specifications for seismic stations and proper instrumentation had not yet been developed. Even the goals of the study of local seismicity were still being discussed. Procedures for measurements, data processing standards, and documentation did not exist in any formal manner. At the beginning, the members of the expedition considered themselves pioneers as they tried to understand what earthquakes were, how to describe them, and how to determine the regional seismicity. At that time, Western scientific publications were seldom available in the USSR, even at the Geophysical Institute in Moscow. This did not worry the members of the expedition; they had a good education in physics and fresh views. They did not become followers, but proposed their own ideas and fields of study and developed new methods based on the data they obtained.
Seismic activity in the Garm region remained high, even several years after the Khait earthquake. During 1955, 5,000 earthquakes were recorded by seismic stations in an area of 1 x 1.5 degrees. The members of the expedition had to process all of these earthquakes by hand; thus relatively simple, usually graphical, methods were required. The first goal was to find an accurate, but simple, way to determine the hypocenters and origin times at a time when the computer era had not yet begun. Because of the strong lateral velocity heterogeneities, methods like that of Wadati (e.g., Wadati 1927, 1933) were unsatisfactory. Thus Riznichenko (1958) proposed a graphical method valid for a constant velocity or horizontally layered medium. Rautian further developed this method, which calculated graphical templates based on given velocities and station locations, for the case of any 3-D velocity variations (Nersesov and Rautian 1960). This was applied to a simple, but realistic, velocity model of the Garm region resulting in graphics that did not require any separate calculations. As a result, four technicians could process 3,000-5,000 earthquake hypocenters per year with an error of no more than 2-3 km.
The next step was to quantify earthquake size. At the time, most members of the expedition did not know about the Gutenberg and Richter (1942) concept of magnitude. Initially, V. I. Bune, who was then director of the Tajik Seismological Institute, developed a scale in which energy was estimated by noting the maximum distance to which earthquakes were recorded and the displacements and phases observed at regional and teleseismic distances (Bune 1955, 1957; Solov'ev 1961). This method was time-consuming and required information from outside the expedition. At the same time he also proposed his version of calculating energy from surface waves (Bune 1956) in instrumental records following the method of Golitsyn (1919). This method missed the main part of energy in short-period arrivals, which underestimated the energy, and the assumption of spherical spreading in the calibration overestimated the energy. These two factors tended to cancel each other out yielding results that were reasonable. Bune (1956) also erroneously assumed that attenuation close to the source (< 100 km) was the same as at greater distances (100-400 km). Because of this assumption, the results at close distances tended to underestimate the energy by 1-2 orders of magnitude (Katok 1964). So, these early proposals had problems.
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THEORETICAL BACKGROUND FOR THE K-CLASS |
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TOPINTRODUCTIONHISTORICAL BACKGROUNDTHEORETICAL BACKGROUND FOR THE...AMPLITUDE-ONLY APPROACH AND...ACCURACY OF THE K-CLASS...NATIONAL APPLICATION OF THE...REGRESSIONS BETWEEN MAGNITUDE...DISCUSSIONCONCLUSIONSACKNOWLEDGMENTSREFERENCES |
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Ideally, if energy spreads out uniformly in all directions, E =
4
r2k
; where is the total energy
density that crosses normal to a unit area on a surface of radius r
following an earthquake and k is a coefficient that accounts for the
effects of the Earth's surface, the incidence angle, the relationship between
measured maximum amplitude on a single component and total vector, etc.
This condition is valid only near the hypocenter, at distances of no more than 10-20 km. At these distances, the source signal has not yet been modified by scattering processes and can be assumed to be a short pulse moving away from the source and perpendicular to the wave front. Anelasticity does not strongly affect the amplitudes of the direct wave at these small distances; thus it was assumed that it could be neglected. Since the earthquake source process is short, later arrivals are scattered waves with random directions that do not come from the origin and, in a strict calculation of energy flux, the vector sum should be zero and can be ignored. Thus 10 km was chosen as the reference distance to which the energy density was normalized. At greater distances, the waveform becomes more complex due to scattering and multiple phases.
The 100-km distance used by Richter (1935) for the definition of the ML scale is not proper because the waveform at that distance is complex and strongly dependent on the local structure of the Earth's crust and its thickness. The direct wave is superimposed by scattered phases and cannot be distinguished from them. In addition, waves from the Moho arrive at distances depending on the crustal thickness; at about 80 km in the Caucasus and 150 km near Garm.
The instrumentation at Garm recorded displacement; thus to get energy density both amplitude and frequency needed to be measured. After looking at thousands and thousands of seismograms, Rautian visualized the wave as the superposition of two or more pulses of different frequencies and realized that seismic energy came in a wide frequency band. The first version of what became the energy class tried to separate different frequencies visually and measure each of them separately to calculate total energy. However, visual "spectral analysis" of a seismogram by different members of the expedition showed that measuring frequency content by eye was too complicated; each person calculated different frequencies and the results were very scattered.
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AMPLITUDE-ONLY APPROACH AND CALIBRATION |
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TOPINTRODUCTIONHISTORICAL BACKGROUNDTHEORETICAL BACKGROUND FOR THE...AMPLITUDE-ONLY APPROACH AND...ACCURACY OF THE K-CLASS...NATIONAL APPLICATION OF THE...REGRESSIONS BETWEEN MAGNITUDE...DISCUSSIONCONCLUSIONSACKNOWLEDGMENTSREFERENCES |
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To calibrate the amplitude-only estimate to energy, Rautian personally
measured the energy of a large number of earthquakes by using visually
estimated spectra. Because of the technology of the time, she made many
simplifying assumptions. The details are presented in Rautian
(1960), but in brief, to
calculate E, the pulse duration (
), amplitude (A), and
frequency (f) of the arrivals were measured. The energy density,
, was then determined by = (Af)2 ; a
series of corrections (k) for magnification, total vector, surface
effects, units, etc., were then applied. The dependence of k on
distance, r, was determined by examining the variation at stations at
different distances for a given earthquake. The resultant curve was used to
normalize to a distance of 10 km. Then, log E (normalized to
10 km) = log 4 k.
The amplitude measurements, [AP(r) + AS(r)], were also normalized to r = 10 km using the amplitude-distance relationship (see below). The resulting relationship was log E (at 10 km in joules) = 1.8 log [AP(10 km) + AS(10 km)] + 6.4. Thus, it turned out that an amplitude of 100 microns at a distance of 10 km corresponded to log E of 10. The correlation was done with events over a wide range of log E values, from 5 to 13.
Why the coefficient 1.8? If the spectral content did not change with energy, it should have a value of 2.0. If the corner frequency, f0, separating the spectrum into its flat part (f < f0) and its steep, high-frequency part (f > f0), changes as (log f0/log E) = -1/3 (see Kanamori and Anderson 1975), the coefficient should be 1.5. In 1956, however, the expedition chose to believe the empirical data and not to follow a simple assumed model with, at the time, unknown validity. Zapol'skii and Khalturin (1960) found that the dominant frequency of small earthquakes decreased much more slowly with magnitude; this was later confirmed with more data (Rautian et al. 1978)
Many years later, while studying the source spectra of earthquakes, Rautian and Khalturin realized the reason. Almost all earthquakes have a broad velocity spectrum with two corner frequencies, f1 and f2. The velocity spectra are, on average, flat between f1 and f2, and the ratio f2/f1 is on average about 10. Thus the spectral content does not change as fast as a spectrum with a single corner frequency implies. The coefficient of 1.8 reflects such kinds of spectra and events and is thus intermediate between 2.0 and 1.5.
Rautian wanted to call this new scale "energy." However,
Nersesov said, "No, do not be so hasty, let us call it simply energy
class." Since the Russian spelling of class is kacc, the scale was
defined as K = log E, in joules. The first outline of the
energy class scale was presented in Rautian
(1958) and then combined with
the expedition's 1957 report on procedures for analyzing earthquakes and
published as Methods for the Detailed Study of Seismicity
(Riznichenko 1960). It was not
perfect, but it was useful and appeared at the right time. The use of
K-class to represent log E was widespread in the former USSR
by 1961.
The shape of the calibration curve with distance is, in general, similar to that of Richter's (1935) for ML and is approximately r-2 up to 60-100 km, where waves coming from the Moho create a "hump." Beyond 100-200 km, the shape of the amplitude-distance curve is not simple because of the changing spectral content of the waves with distance, due both to attenuation and the appearance of larger, lower frequency waves at the larger distances. For simplicity in use in calculating the K-class, the log-distance scale was adjusted to make the amplitude-distance curve a straight line (figure 2). Thus while the distance axis appears to be logarithmic, examination of it in detail will show that the horizontal scale was altered to incorporate the "hump" (compare with figure 6).
The first version of the K-class scale was calibrated for the VEGIK short-period seismometer (T0 = 0.1-0.8 sec), which was in common use in the 1950s. Later these were replaced at many stations by the SKM seismometer (T0 = 0.2-1.5 sec) and more recently by SM3 seismometers. The amplitude-distance calibration curves differ on these two instruments. Some early calibration curves also delineated a band within which an integer K-class value was assigned. Later, the lines were drawn to represent a specific K-class value. Figure 2 shows the nomogram for SKM instrumentation.
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ACCURACY OF THE K-CLASS DETERMINATION |
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TOPINTRODUCTIONHISTORICAL BACKGROUNDTHEORETICAL BACKGROUND FOR THE...AMPLITUDE-ONLY APPROACH AND...ACCURACY OF THE K-CLASS...NATIONAL APPLICATION OF THE...REGRESSIONS BETWEEN MAGNITUDE...DISCUSSIONCONCLUSIONSACKNOWLEDGMENTSREFERENCES |
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Second, a systematic error exists because the method ignores the spectral content. The effects of this differ randomly among earthquakes within the same area and systematically between events in different tectonic settings. As a result, K, as estimated from displacement, differs from the energy, as calculated from spectrum. This difference is a function of the earthquake source "rigidity." For individual events, this source component of the deviation of K is the same among all the seismic stations. For example, in the Garm region, the source deviation is about zero for earthquakes in the northern part of the region (Paleozoic granites and thrusting) but is 0.2-0.4 in the southern part of the region (Meso-Cenozoic rocks with some normal faults). The largest difference between K and log E, as calculated from event spectra, was found in the Kopetdag area, where most earthquakes occur in soft and strongly fractured rock and where strike-slip faulting predominates. In this region, the earthquakes typically have low-frequency source spectra and the K values are overestimated by 0.7-1.0 compared to energy calculated from their spectra.
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NATIONAL APPLICATION OF THE K-CLASS |
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TOPINTRODUCTIONHISTORICAL BACKGROUNDTHEORETICAL BACKGROUND FOR THE...AMPLITUDE-ONLY APPROACH AND...ACCURACY OF THE K-CLASS...NATIONAL APPLICATION OF THE...REGRESSIONS BETWEEN MAGNITUDE...DISCUSSIONCONCLUSIONSACKNOWLEDGMENTSREFERENCES |
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The Kamchatka and Sakhalin regional networks did not follow the Garm method. They created their own K-scales, which were different from the national ("continental") standard, because they presumed that the differences in tectonic setting (subduction zone), velocity structure, and attenuation would be important.
In fact, the attenuation in these Pacific regions was found to be stronger than on the continent. The first local K-class scale developed in the Russian Far East was based on the southern Kurile network deployed on Iturup, Kunashir, and Shikotan islands in 1957. Energies were calibrated using a similar approach to Rautian (1960) incorporating amplitude, frequency, and duration (Fedotov et al. 1961; Fedotov 1963). Two variant nomograms were produced, one that separated intermediate from normal focus earthquakes (figure 3), and a second that was an average for all events down to a depth of 160 km (figure 4). For simplicity of calculation, only the maximum amplitude of the S wave in microns was used; however, unlike the Rautian (1958, 1960) system, it was normalized by period, T, and the curves were in terms of the S - P time. The distance calibrations in terms of both amplitude and energy were performed using events of energy class 11 at different focal depths; because of the similarity of the curves for depths greater than 50 km, they were averaged in the first variant as an intermediate depth nomogram. The authors noted that in using the second nomogram, variations of greater than 0.5 K units could occur at S - P distances greater than 20 sec because of the uncertainty in depth. These nomograms were used in Sakhalin and the Kuriles from 1961 to 1965.
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Subsequently, the southern Kurile nomogram was revised by Solov'ev and Solov'eva (1967), primarily because of differences in attenuation observed as the network was enlarged and additional data were acquired; the methodology of using ASmax/T remained the same (figure 5). This nomogram was used in both the Kuriles and Sakhalin Island starting in 1965 (Kondorskaya and Shebalin 1977). The current Kamchatka nomogram is shown in figure 6.
There is a significant difference between the "continental"
(Rautian 1958,
1960) and Far Eastern
relationships (figure 7). The
energy class calculated using the first Kurile and Kamchatka nomogram is lower
than the Rautian (1960) value
by 
0.5-0.7 log units and by 1.5-1.7 log units using the Sakhalin
nomogram of Solov'ev and Solov'eva
(1967). In the compilation by
Kondorskaya and Shebalin
(1977), the Fedotov
(KF) and Solov'ev
(KS) determinations were reduced to the Rautian
standard by: K = KF + 0.6 and K =
KS + 1.7.
The difference in shape can be ascribed to variations in attenuation and
propagation of Lg phases between the continent and subduction zones
(Rautian et al.
1981). However, the difference in intercept, which is controlled
by energy at short distances, is more difficult to explain. Rautian
(1960) uses units of
amplitude, A, on the vertical axis of the nomogram, while the Far
Eastern nomograms use A/T. Since for K = 10, the
general frequency of earthquakes in central Asia is about 3 Hz, an amplitude
of 100 microns at 10 km for a K = 10 event corresponds to
A/T = 300 micron/sec. On the Far Eastern variants, the
corresponding value (S - P 1.2 sec) is about 2,000.
Thus, the discrepancy is likely a result of an error in the method of
calculating energy and/or calculation of the coefficient.
Outside the USSR, Mongolia was the only country to use the K-class extensively; this resulted from the fact that the initial Mongolian seismic network was deployed by the USSR and many of its seismologists were trained there.
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REGRESSIONS BETWEEN MAGNITUDE AND K-CLASS |
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TOPINTRODUCTIONHISTORICAL BACKGROUNDTHEORETICAL BACKGROUND FOR THE...AMPLITUDE-ONLY APPROACH AND...ACCURACY OF THE K-CLASS...NATIONAL APPLICATION OF THE...REGRESSIONS BETWEEN MAGNITUDE...DISCUSSIONCONCLUSIONSACKNOWLEDGMENTSREFERENCES |
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Since energy is proportional to amplitude squared, in an ideal situation
the relationship should be of the form magnitude = c + 0.5K,
where c is some constant (Richter
1958). Early empirical studies using independent data suggested
that the relationship between magnitude and K-class was M =
(K - 4)/1.8 (Rautian
1960) for the range 4 
K 13. Similarly, Solov'ev
and Solov'eva (1967)
empirically obtained the relationship M = (KS -
2)/1.8 for Sakhalin.
Theoretically, both mb and
MS are tied to specific frequencies, while
K is (ideally) obtained from a wide range of frequencies. In practice
K is linked to the period of short-period sensors, which varies over
an interval from 0.1-0.2 to 1.5-2 sec. In addition, there will be regional
variations in attenuation, Q(
), resulting from tectonic
variations; in some cases these may affect very small areas. Although the
major differences should be due to variations in source depth and the tectonic
setting, local variations in Q and the variability of tectonic
regimes in some areas result in the scattering of K-class values even
within a specific seismic region.
These difficulties notwithstanding, the relationship between K-class and magnitude has been of great interest to seismologists working with data from the former USSR. In order to examine the empirical relationship between magnitude and K-class, we tabulated magnitude and K-class values reported for each of the seismic regions used in Earthquakes in the USSR and its successor publication, Earthquakes of Northern Eurasia (Zemletryaseniya Severnoi Evrazii), for 1970-1997. Because K-class and magnitude are both independent variables with their own uncertainties, one can not simply calculate a regression holding one as the dependent variable. We thus calculated an orthogonal regression (see figure 8 for an example) that minimizes the sum of the squares of the distance to the regression line. It should be noted that K-class is calculated, and calibrated, for events generally smaller than K = 10-11, while teleseismic magnitudes are calculated for larger events. For smaller events of mb (or MS) around 4, magnitude is often calculated with very few stations or using stations with potentially weak arrivals, thus increasing the uncertainty and scatter. The Kurile K-class data were only available as integers, hence, each integer bin was averaged and the regression calculated based on the bin averages; K-class 14 bin was omitted for both mb and MS as they were defined by only a few points and K = 9 (for both mb and MS) and K = 9.5 (for MS) were omitted because small-magnitude events were not reported.
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Magnitude = c + s (K - 14).
This formulation eliminates having sign variations on c and makes
comparisons clearer in the range for which K-class and magnitude are
both calculated (9 K 14).
The mb regressions
(table 1) are generally
similar, close to 5.41 + 0.43 (K - 14), in the K-class range
of interest (9 K 14) except for Crimea, Sakhalin, Kurile,
and Kamchatka (figure 9A).
Crimea, Sakhalin, and Kamchatka have higher c and s values
than the other regions, while Kurile has a similar slope, but higher
c. As noted above, the three Far Eastern regions use a different
formulation for K and are therefore expected to be different from the
rest of the former USSR; the difference for the Crimea may reflect a small
number of data points. It is interesting that the Kurile regression differs
from both Sakhalin (which administers the Kurile network) and Kamchatka (which
is tectonically similar).
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The MS regressions are more variable
(table 1 and
figure 9B), reflecting the fact
that the methodology and frequencies for calculating mb
and K are much closer than those for determining
MS. Slopes for the MS values vary from
0.5 to 0.8, and the mean regression is 5.52 + 0.702 (K - 14),
excluding the Carpathians, which are based on very limited data, and the
Russian Far East, which have c values > 6.4. In general, however,
most of the curves are fairly close to each other in the 10 K
14 range (figure 9B).
Again, the Far Eastern regions are expected to be somewhat different because
of the different methodologies used for K.
We note, however, that both c and s can vary considerably (0.5 in c and 0.1 in s) depending on the regression methodology and algorithm, data set used, cut-off magnitudes and K-classes, and to what degree the data are cleaned.
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DISCUSSION |
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TOPINTRODUCTIONHISTORICAL BACKGROUNDTHEORETICAL BACKGROUND FOR THE...AMPLITUDE-ONLY APPROACH AND...ACCURACY OF THE K-CLASS...NATIONAL APPLICATION OF THE...REGRESSIONS BETWEEN MAGNITUDE...DISCUSSIONCONCLUSIONSACKNOWLEDGMENTSREFERENCES |
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16-17.
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CONCLUSIONS |
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TOPINTRODUCTIONHISTORICAL BACKGROUNDTHEORETICAL BACKGROUND FOR THE...AMPLITUDE-ONLY APPROACH AND...ACCURACY OF THE K-CLASS...NATIONAL APPLICATION OF THE...REGRESSIONS BETWEEN MAGNITUDE...DISCUSSIONCONCLUSIONSACKNOWLEDGMENTSREFERENCES |
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Although digital methods have been developed to calculate energy from teleseismic data (e.g., Choy and Boatwright 1995; Newman and Okal 1998) and regional data (e.g., Boatwright et al. 2002), they still require an understanding of, or correction for, the focal mechanism, site amplification, scattering, and/or other regional geologic factors that preclude their use on a massive scale. Especially in the former USSR, where some networks still operate with analog systems and depend on technicians to read arrivals, the K-class method remains a useful and (relatively) standardized tool that can be rapidly applied. The methodology for the K-class was appropriate for the time, although the calculation by hand using only amplitude was tedious and not entirely accurate for estimating the true energy because frequency is not used; low-frequency earthquakes have overestimated values of K, with errors reaching 0.5-1.0 units.
The senior authors hope that with digital recording and advances in processing capability, the calculation of the energy class can return to its original intent, calculated directly and routinely from the energy density. They believe that using the later part of the coda for source spectra estimation (Rautian and Khalturin 1978) is the most appropriate way to get seismic energy along with seismic moment, apparent stress, etc. This method was developed for analog records with band-pass filters and can be easily adapted for digital instrumentation use. The size of earthquakes for which the method can be applied depends on the density of the seismic network. For small events, energy class could still be used.
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ACKNOWLEDGMENTS |
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TOPINTRODUCTIONHISTORICAL BACKGROUNDTHEORETICAL BACKGROUND FOR THE...AMPLITUDE-ONLY APPROACH AND...ACCURACY OF THE K-CLASS...NATIONAL APPLICATION OF THE...REGRESSIONS BETWEEN MAGNITUDE...DISCUSSIONCONCLUSIONSACKNOWLEDGMENTSREFERENCES |
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REFERENCES |
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TOPINTRODUCTIONHISTORICAL BACKGROUNDTHEORETICAL BACKGROUND FOR THE...AMPLITUDE-ONLY APPROACH AND...ACCURACY OF THE K-CLASS...NATIONAL APPLICATION OF THE...REGRESSIONS BETWEEN MAGNITUDE...DISCUSSIONCONCLUSIONSACKNOWLEDGMENTSREFERENCES |
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the coda for determination of the earthquake source spectrum.
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Savarensky, E. F., S. L. Solov'ev, and D. A. Kharin, eds. (1962). Atlas of Earthquakes in the USSR. Moscow: Izdatel'stvo Akademii Nauk SSSR, 337 pps. (in Russian).
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Department of Geological Sciences
Michigan State
University
East Lansing, Michigan 48824
USA
fujita{at}msu.edu
(K.F.)
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