An Instrumental Earthquake Magnitude Scale

^*

In the course of historical or statistical study of earthquakes in any given region it is frequently desirable to have a scale for rating these shocks in terms of their original energy, independently of the effects which may be produced at any particular point of observation. On the suggestion of Mr. H. O. Wood, it is here proposed to refer to such a scale as a "magnitude" scale. This terminology is offered in distinction from the name "intensity" scale, now in general use for such scales as the Rossi-Forel and Mercalli-Cancani scales, which refer primarily to the local intensity of shock manifestation.

The writer is not aware of any previous approach to this problem along the course taken in this paper, except for the work of Wadati cited below. Total original energies have been calculated for a number of shocks, using seismometric and other data; but such a procedure is practicable only for a limited number of cases, whereas it is desired to apply a magnitude scale to all or nearly all of the shocks occurring.

Mr. Maxwell W. Allen states that he has for some time employed an arbitrary scale for rating large earthquakes, based on the amplitudes of earth motion calculated from the reports of distant stations. This laborious procedure is not far removed in principle from that adopted in the following discussion. Doubtless it has also occurred to others, but has failed of general application because of its paucity of dependable results.

In the absence of any accepted magnitude scale, earthquakes have occasionally been compared in terms of the intensity on the Rossi-Forel or some similar scale, as manifested near the epicenter. Even when reliable information is obtainable, this method is obviously exposed to uncertainties arising from variations in the character of the ground, the depth of the focus, and other circumstances not easily allowed for. In a region such as Southern California, where a large proportion of the shocks occur in almost unpopulated districts, while still others are submarine in origin, any general procedure of this kind is out of the question.

Despite the evident difficulties, the requirements of research, as well as the public interest, call for some estimate of the magnitude, in the sense here used, of each important shock in the California region. This led to an attempt at constructing a magnitude scale based on instrumentally recorded amplitudes at the seven stations of the Southern California group.

Precision in this matter was neither expected nor required. What was looked for was a method of segregating large, moderate, and small shocks, which should be based directly on instrumental indications, and thus might be freed from the uncertainties of personal estimates or the accidental circumstances of reported effects. The method used proved to be much more selective than had been anticipated, assigning observed earthquakes to as many as fifteen well-defined scale numbers, with possibilities of further extension and finer subdivision.

The procedure used was suggested by a device of Wadati,¹ who plotted the calculated earth amplitudes in microns for various Japanese stations against their epicentral distances. He employed the resulting curves to distinguish between shallow and deep earthquakes, to calculate the coefficient of absorption for surface waves, and to make a rough comparison between the magnitudes of several strong shocks. . . .

In practice we have to compare shocks from different foci, and probably different also in the mechanism of occurrence. Comparison is thus rendered very inexact. However, useful results can be obtained by comparison of the records at several stations. It is necessary to establish empirically a relation between the maximum seismographic amplitudes of a given shock at various distances; this is done by assuming that the ratio of the maximum amplitudes of two given shocks, as registered by similar instruments at equal epicentral distances, is a constant. That is, if shock A is registered with maximum amplitude 5 millimeters at 75 kilometers and 2 millimeters at 200 kilometers, while shock B registers with maximum amplitude 15 millimeters at 75 kilometers, then shock B should register 6 millimeters at 200 kilometers.

The precision of magnitudes based on such an assumption is evidently impaired by a variety of conditions. The most obvious of these are the effects of inhomogeneity in the propagation of elastic waves, of varying depth of focus, of difference in mechanism of shock production, of the ground at the several stations, and of the instrumental constants.

The most serious of these difficulties is the first. In most cases energy appears to be radiated unequally in different azimuths from the point of origin. This may arise from the circumstances of origination of the shock (strike of the fault, nature of displacement on the fault) or from differences in geological structure along the various wave paths. When the records of a number of stations surrounding the epicenter are available, this effect can be allowed for to some extent; but it remains an obstacle in the way of any precise determination of earthquake magnitudes, which can only be overcome with the advent of a more detailed understanding of the dynamics of shock production, and more complete information as to the various local structures.

Variation in depth of focus is less important. The majority of shocks in this region appear to originate at depths not far different from 15 kilometers. The effect of even considerable departures from this level can be reduced, for all but the smallest shocks, by using the records at stations distant 100 kilometers or over.

It is nearly certain that in most, though not all, of the stronger shocks the distribution of energy among various frequencies is not the same as for weaker shocks. Especially when there is evidence of extended movement along a fault, a high proportion of energy appears to go into waves of long period. As the maximum phase on the seismograms usually exhibits longer periods than the beginning of the record, the effect is to exaggerate the maxima. Comparison with the recorded maxima of a smaller shock then leads to an overestimate of the difference in magnitude. Fortunately, this effect does not appear to be larger than the other sources of error; and with long experience, or with more precise theories of shock production, it should be possible to take it into account quantitatively.

In comparing records from different stations, conclusions are affected by differences in ground and in the instrumental constants. If the latter are known with precision, the periods of the seismographic maxima may be measured, and the actual amplitudes of earth displacement calculated and used for estimating magnitudes. The procedure is somewhat laborious; and, as will appear presently, it can be dispensed with if the constants of the various instruments are approximately the same. The short period torsion seismometers installed at the Southern California stations are designed to have identical constants; but, owing to unavoidable irregularities in manufacture, some differences exist. It is not convenient to determine the constants from time to time; however, it is known that the constants of any one instrument remain relatively fixed over periods of years.

Determination of constants would make it possible to separate the purely instrumental effects from those due to ground; but, because of the uncertain elements in the latter, no great access of precision in estimating magnitudes would follow. In practice it is considered that the effect of ground and that of the instrument combine in each case into a fairly uniform deviation from the mean registered amplitudes for all stations and instruments; so that statistical study of a group of shocks will lead to average corrections applicable to the amplitudes registered by each individual instrument. These corrections turn out to be small, and of the same order as fluctuations due to other causes.

For precise purposes, it would be desirable to identify the phases of each seismogram, and to compare amplitudes of the same wave or set of waves at the various distances. Such identification is difficult and questionable for many of the smaller shocks, and is too time-consuming for use in routine work where hundreds or thousands of shocks must be dealt with. Thus the scale has been set up on the basis of measurements of the maximum recorded amplitude. This maximum will of course not always correspond to the same wave-group or phase. It will change especially with distance, coinciding with

or Q for very near shocks, at intermediate distances with some member of the complicated S series of phases, and at the larger distances with a slow surface wave. However, if the magnitude scale is set up empirically for the measured maximum amplitudes, these considerations do not directly affect its precision. If it were strictly true that all seismograms written by identical instruments at any one distance were simply enlarged or reduced copies of one another, such an empirical scale would apply perfectly, and magnitudes derived from it would be exact.

The foregoing considerations are preliminary to the actual setting up of a workable empirical scale of magnitudes. To derive such a scale, a representative group of shocks (those of January 1932) was carefully studied, and the logarithm of the recorded amplitude in each case plotted against the epicentral distance. Curves were drawn through the several points referring to each shock and were seen to be roughly parallel, as the hypothesis of proportional amplitudes requires. These were then combined into a single curve, parallel to the individual shock curves, and passing through an arbitrarily selected point. . . .

. . . . .

The procedure may be interpreted to give a definition of the magnitude scale number being used, as follows: The magnitude of any shock is taken as the logarithm of the maximum trace amplitude, expressed in microns, with which the standard short-period torsion seismometer (

sec.,

) would register that shock at an epicentral distance of 100 kilometers.

This definition is in part arbitrary; an absolute scale, in which the numbers referred directly to shock energy or intensity measured in physical units, would be preferable. At present the data for correlating the arbitrary scale with an absolute scale are so inadequate that it appears better to preserve the arbitrary scale for its practical convenience. Since the scale is logarithmic, any future reduction to an absolute scale can be accomplished by adding a constant to the scale numbers. . . .

Until more instrumental data on larger shocks are available, it does not seem prudent to attempt an application of the magnitude scale to shocks which occurred in years when no instrumental data of the type here used were available. In the course of time it may become possible to assign magnitudes to the larger shocks on the basis of the extent of the area of perceptibility; but at present such estimates must necessarily be so tentative that it seems inadvisable to give figures which might readily lend themselves to misinterpretation. Something can be done in the way of comparing shocks occurring m the same general region; thus all the phenomena indicate that the major earthquake in Nevada on October 2, 1915, was of somewhat higher magnitude than the Nevada shock of December 20, 1932, studied above, which has been assigned a magnitude of 7.5 with some uncertainty. It would be unwise to go on to estimate by how much the magnitude of the two shocks differs. Opinion based partly on comparison of seismograms has classified the 1915 shock as of about the magnitude of the San Francisco earthquake of 1906; it appears safe to conclude that both of those shocks exceeded magnitude 7.0, and may have been of magnitude 8 or perhaps larger. In the case of the 1906 shock, the extended motion on the fault must have required a relatively long time for its completion; the seismograms in such a case would presumably not be representative of the total energy liberated.

Another case is that of the Imperial Valley earthquake of June 22, 1915, which very obviously exceeded the shock of February 25, 1930, in the same region, and therefore is known to have been of magnitude greater than 5.0. As shocks continue to occur, and our knowledge of the seismographic and other effects in the marginal areas of perceptibility increases, we may eventually be able to decide upon magnitudes for all the important earthquakes which have occurred in this region. . . .

Returning now to the discussion of the effects of various magnitudes, it appears that shocks of magnitude 1.5 (10⁹ ergs) are the smallest definitely reported as perceptible. Such reports usually refer to aftershocks of larger earthquakes, when persons are in a specially sensitive frame of mind, or they come from observers in possession of instruments or mechanical indicators which they can use to test their impressions. The smallest shocks which are likely to be noticed in the immediate vicinity of the epicenter are of about magnitude 2.5 (10¹¹ ergs). A few reports are usually received when such shocks occur in settled areas. Magnitude 3 is almost always reported; while magnitude 3.5 (10¹³ ergs) attracts general attention, is reported felt to distances of the order of 30 kilometers, and reaches intensity IV on average ground near the epicenter.

The lower limit of damaging shocks is about magnitude 4.5 (10¹⁵ ergs). The most serious results at this stage are broken chimneys and injured brick walls, when constructed poorly and situated on bad ground. Examples are: the Brawley earthquake (4.5) of March 1, 1930 (in this case damage was probably increased by the weakening of inferior structures in the shock of magnitude 5.0 four days earlier), and the Whittier-Norwalk shock of July 8, 1929 (4.7).

The discussion has supplied several instances of shocks of magnitude near 5.0. Their effects are closely similar, and conform to the following description: On good ground, apparent intensity, VII is manifested only within a few kilometers of the epicenter; but on soft ground it may occur at considerably larger distances, and some instances of apparent intensity VIII may be observed. The mean radius of the outer limit of IV is about 90 kilometers, and perceptibility extends to about 130 kilometers.

Two shocks of magnitude slightly exceeding 6 have been studied. In both cases, VII is manifested on good ground to about 25 kilometers from the epicenter. It is probable that the maximum intensity on good ground would be nearly VIII; in one case no data are available, and in the other the epicentral area lay in an alluvial basin, where VIII was manifested in many places, and possibly IX in a very few instances. The outer limit of IV is near 250 kilometers, and perceptibility extends to about 300 kilometers.

One shock has been assigned magnitude 6.5. Its effects definitely exceed those of the two shocks just mentioned. The Utah earthquake of magnitude 7.0 is the largest shock to which a magnitude can be assigned with the same precision as for smaller shocks. This and the Nevada shock of 1932 clearly manifested higher intensities at all epicentral distances than any of the other shocks here studied; and it is equally evident that the Nevada shock was much the larger of the two, which supports the magnitude 7.5 assigned to it.

In view of the foregoing facts, it seems assured that earthquakes destructive over even a moderately extended area are of magnitude 6

(10¹⁸ ergs) and over, except in cases where very bad ground and construction are involved. The lower margin of major earthquakes, in which phenomena of faulting, etc., are to be expected to a significant extent, appears to be about magnitude 7.5 (10²¹ ergs). How far above this the magnitudes of actual earthquakes may extend is a difficult, and in one sense an unanswerable, question. Judging by the relative amplitudes of distant recorded shocks, there must be cases of at least magnitude 9, and very probably 10.

^* From Seismological Society of America Bulletin 25 (1935), 1–32.

¹ K. Wadati, Geophys. Mag. (Tokyo) 4 (1931), 231.