Aftershocks: Earthquakes or Afterthoughts?

(EOS, weekly transactions American Geophysical Union 11/11/97)
S. E. Hough and L. M. Jones
United States Geological Survey, 525 S. Wilson Ave, Pasadena CA, 91106
We tend to view aftershocks as afterthoughts, in both their scientific and societal impact and importance. Seismologists who communicate with the media are often asked, 'was it just an aftershock?', with the 'just' implying, even if unsaid, 'if you say yes, then we don't have to worry about it'. Seismologists themselves tend to dismiss events subsequent to a large mainshock as very much secondary in importance. Even when appreciable in their own right, they typically generate only a fraction of the scientific interest and investigation as the mainshock. However, a consideration of recent earthquake sequences suggests that aftershocks may have important consequences. Were a future San Andreas event to produce an aftershock comparable in magnitude and relative location as the M6.5 Big Bear aftershock to the M7.3 Landers earthquake of 1992, the result could be a M6.5+ event at the northern edge the Los Angeles basin.

By every criteria ever used, an individual aftershock does not differ from an individual earthquake. In particular, the rupture processes and ground motions are indistinguishable. Aftershocks differ from other earthquakes only in that we expect them. Unlike most earthquakes, aftershocks occur within predictable bounds of space, time, and magnitude. They are most common immediately after the mainshock and decay in time with approximately the reciprocal of time since the mainshock [Omori's law, (Utsu, 1961)]. The magnitudes follow a Gutenberg-Richter relation, with the number of aftershocks proportional to ten to the power of the magnitude times a negative constant b. b is close to one so each unit decrease in magnitude leads to an order of magnitude decrease in number [Gutenberg and Richter, 1954]. This leads to a distribution of the largest aftershock that peaks at approximately one unit of magnitude below the mainshock (sometimes referred to as Bath's law [Richter, 1958]).

The above properties of aftershock sequences allow for time-dependent prediction of aftershock probabilities [Reasenberg and Jones, 1989]. The standard calculation of probabilities distinguishes aftershocks from mainshocks in that probabilities of future aftershocks are not affected by an earthquake that is already itself an aftershock. However, aftershock sequences clearly do have subsequences that sometimes stand out as distinct clusters: in reality, even aftershocks can have aftershocks.

Spatially, aftershocks cluster around the mainshock rupture surface but can occur at significant distance. The 1992 M7.3 Landers, California, earthquake triggered events hundreds of kilometers away [Hill et al., 1993]. A rule of thumb has been suggested to use the term aftershock only when the event occurs within one fault length (i.e., the length of the fault that ruptured in the mainshock; 80 km in the case of the Landers earthquake) of the mainshock rupture.

Aftershocks on faults other than the one that produced the mainshock are the norm. Hauksson et al. (1994) estimated that at least 20 faults were involved in the aftershock sequence of the Landers earthquake. The most distant was the M6.5 Big Bear aftershock at a distance of roughly 36 km from the mainshock epicenter [Figure 1; Jones and Hough, 1995]. Large aftershocks (close to M6) have occurred on faults distinct from the mainshock rupture after the 1994 M6.7 Northridge earthquake (11 hours later), the 1952 M7.5 Kern County earthquake (37 hours later), and the 1979 M6.5 Imperial Valley earthquake (8 hours later).


Figure 1. Figure 1. Southern California region including regional faults (light lines) and topography (grey scale). Large symbols indicate the 1952 Kern County (circle), 1992 Landers (star), and 1994 Northridge (square) mainshocks; smaller respective symbols indicate the largest and most distant M>5.5 aftershock. The symbol for the largest Kern County aftershock overlaps with that of the mainshock; for Landers, the Big Bear aftershock was both the largest and the most distant M>5.5 aftershock. A hypothetical San Andreas rupture is shown as a thick black line; hypothetical aftershock is indicated by the white star.

The general public often believes that both the number and magnitude of aftershocks decrease with time, but it appears that only the number decreases. Thus, large late aftershocks are not uncommon. The largest or second largest aftershock to the 1933 M6.4 Long Beach, 1947 M6.5 Manix, 1968 M6.5 Borrego Mountain, 1983 M6.5 Coalinga, and 1989 M6.9 Loma Prieta earthquakes all occurred at least three months after the mainshock. More recently, the greater Los Angeles region was startled awake in the early hours of two successive mornings, with two late M~5 aftershocks of the 1994 Northridge earthquake. These ghosts of earthquakes past generated open skepticism in the media, that aftershocks so large could occur so late.

At the other extreme, very large aftershocks may be overlooked completely because they occur so close in time to the mainshock. In addition to the aftershocks discussed above, the largest aftershock to the Northridge earthquake was a M6 event just one minute after the mainshock. This event has not been investigated in detail, but is located approximately 8 km NE of the mainshock. The 1992 Landers earthquake is interpreted as having generated two M5.6 aftershocks to the south of the epicenter, in a region not thought to have ruptured during the mainshock [Hough, 1994]. These two events occurred approximately 30 seconds and 3 minutes after the mainshock. They have been associated with 11 km of mapped surface rupture on the Eureka Peak fault, and thus represent two of the three earthquakes that produced surface rupture in Southern California during 1992. The first of these events would not likely ever have been identified, were it not for the fortuitous existence of a portable seismometer array.

Aftershocks comprise many of the largest events in our catalogs. A search of the Southern California Seismic Network catalog reveals 74 M5.5 and larger events since 1932; of these, 25 are clear aftershocks to 11 mainshocks. In three other cases, a doublet of M>5.5 event occurs in which the larger of the events occurs second. Only 32 events do not occur as part of a sequence with at least one other M5.5 event. Considering those M>5.5 events that do occur in a sequence with at least one other M>5.5 event, the majority (8 of 13) of mainshocks produce their largest aftershock within an hour of the mainshock. A region close to a large aftershock may thus experience even higher ground motions than during the mainshock, while it is still in the early aftermath of the first shaking.


Figure 2. Figure 2. The distance to the largest aftershock in each sequence (bottom left); the time delay of the largest aftershock from its mainshock (top left); the distance to the most distant M>5.5 aftershock (bottom right); and the time delay to the most distant M>5.5 aftershock. In all cases, histograms show generalized bins centered on values shown, not exact averages. Includes the three cases for which the 'aftershock' is larger than the 'mainshock' (i.e., first event). Distances shown are relative to mainshock epicenter; although distance to mainshock rupture plane would provide a more clear sense of aftershocks that distinct from their mainshock, this quantity is unknown for some of the events in the data set.

Figure 2 presents four panels: binned distance separations between mainshock and largest aftershock (or foreshock and mainshock) for 13 sequences from the catalog and the delay between these events and their mainshocks are shown at left; the right panels show similar results for the M>5.5 aftershock that is most distant from its mainshock. (This figure does not include the 1968 Borrego Mountain earthquake and its largest aftershock, which are the only events in the data set to be separated by over a year). Figure 2 illustrates that, while the largest aftershocks do tend to occur within 10 km of the mainshock epicenter, it is not uncommon for the largest aftershock to be 30 km or more away. Moreover, over half of the first events in the sequence generated at least one M>5.5 secondary event that was over 10 km from the epicenter. Although the Big Bear event was relatively distant from its mainshock, it is clearly not unique in this regard.

It should be noted that considerable uncertainty exists regarding locations associated with some of the earlier sequences; also whether or not all of the very early aftershocks would be documented at all. It is therefore possible, if not likely, that the numbers presented here underestimate both the numbers of large aftershocks produced and their average distances from their mainshocks.

It should also be noted that, given the long fault ruptures associated with large earthquakes, an aftershock could be close to the mainshock rupture plane but quite distant from the epicenter. However, Figure 1 suggests that large aftershocks completely off the mainshock rupture plane might not be uncommon.

Figure 1 includes a hypothetical San Andreas rupture that would be similar in overall length to that of the Landers event. Also shown is a hypothetical aftershock that is comparable in distance to the other aftershocks shown. The implications of this comparison are clear: while there is no reason to believe that a large aftershock to a San Andreas event will occur near the population centers of the great Los Angeles region, there is no reason to think that it won't, either.

In recent years, researchers have looked at complex earthquakes worldwide and raised the possibility that one of the major fault systems in the Los Angeles basin, such as the Sierra Madre thrust fault, could rupture essentially simultaneously with the San Andreas, adding a M~7.5 rupture to the M~7.8 San Andreas event and making for something of a 'doomsday' scenario for the greater Los Angeles region [Bayarsanan, 1996]. A consideration of the relative repeat times of major San Andreas events (on the order of 200 yrs) compared to events on the Sierra Madre fault (on the order of a thousand years) implies that concurrent rupture of these fault systems is not likely to be a common occurrence among SAF events. However, many other faults are also adjacent to the San Andreas and a garden-variety M7.8 event will have a largest aftershock in the neighborhood of M6.8, so a large aftershock in the Los Angeles region is a real possibility.

Two arguments can be made against the likelihood of this scenario. The first is simply that the largest aftershock to a SAF event could occur to the north, in an area even less populated than the mainshock region itself. The second is something akin to scientific conventional wisdom, that SAF events do not produce energetic aftershock sequences. This latter argument derives some support from the lack of felt reports revealing large aftershocks to the 1857 Fort Tejon earthquake (although Agnew, 1978 discusses felt reports consistent with two M~6 aftershocks), and from the relatively limited aftershock sequence that occurred following the 1989 Loma Prieta earthquake. The argument also derives some support from a recent study that concludes that the overall energy release in aftershock sequences is lower for ruptures on faults that are longer and better developed [Jones, 1997].

However, by no stretch of the imagination is our history of SAF sequences extensive (and there remains debate on whether or not Loma Prieta should even be counted as a SAF event). Moreover, even a relatively light aftershock sequence to a M7.5-M7.8 SAF event could still easily produce one or more M6 aftershocks; roughly the size of the Whittier earthquake of October 1, 1987, which damaged 10,000 buildings [Jones, 1990].

We have presented some of the common characteristics (and, in some cases, commonly misconstrued characteristics) of aftershock sequences. What are the consequences of these facts?

First, aftershocks to large earthquakes can be very damaging earthquakes in their own right and should be addressed in planning scenarios. Aftershocks will obviously affect smaller regions than the mainshock, but, because of variations in location and radiation pattern and the cumulative nature of building damage, aftershocks can potentially be more damaging in some locations than their mainshock. For example, a relatively small (M5.8) aftershock to the 1952 M7.5 Kern County earthquake was located directly under the city of Bakersfield, damaging many additional buildings and killing two workmen who were repairing damage from the mainshock [Steinbrugge and Moran, 1955] In some cases, a large aftershock may expand the extent of the region that require emergency services, such as the case of Landers-Big Bear.

Individuals involved with modern post-earthquake activities generally are aware of aftershock risk. In fact, one of the first-ever US early-warning systems was installed by researchers at the U.S. Geological Survey in Menlo Park at the failed Nimitz Freeway in Oakland following the 1989 Loma Prieta earthquake: emergency workers at the freeway received advance notice of any strong aftershock ground motions recorded in the epicentral region, approximately 80 km to the south, via an electromagnetic signal sent in advance of the strong S waves from the event. However, the experience of researchers in the seismically active state of California is that public awareness of potential damage from aftershocks, including large events both very early and very late in the sequence, could be enhanced.

Second, off-fault aftershocks are common. An off-fault aftershock to a southern San Andreas earthquake could potentially occur within the Los Angeles basin and should be included in planning scenarios.

Third, aftershocks are a substantial percentage of the large earthquakes in our catalog. Seismologists often lament the lack of adequate data because of the slow pace of geologic time relative to a typical research career. However, many strong motion instruments in use even today require substantial processing before data is made available; it is not uncommon for networks that run such instruments to be under budget constraints that preclude processing of subsequent 'lesser' events. By providing the necessary support to processing and make available the strong motion records of all large aftershocks in our databases, we could significantly increase the number of available records. Aftershocks are earthquakes and sometimes they are big earthquakes.

Fourth, aftershocks are the only earthquakes we know will occur within specified temporal and spatial bounds. Planning before the mainshocks for quick, portable seismometer deployments will greatly improve the quality of data we can record. Because of the strong temporal clustering of aftershocks, a deployment that is not underway within a few hours will record significantly fewer earthquakes, providing a strong impetus for local maintenance of portable instrumentation as opposed to central storage. Although coordination of multi-institutional response is also desirable, the productive first few hours after a mainshock should not be sacrificed to this goal.

Bibliography

Agnew, D.C. and K.E. Sieh, A documentary study of the felt effects of the great California earthquake of 1857, Bull. Seismol. Soc. Am., 68, 1717-1729, 1978

Bayarsayhen, C., A. Bayasgalan, B. Enhtuvshin, K.W. Hudnut, R.A. Kurushin, P. Molnar, and M. Olziybat, 1957 Goby-Altai, Mongolia earthquake as a prototype for Southern California's most devastating earthquake, Geology, 24, 579-582, 1996.

Hough, S.E., Southern surface rupture associated with the 1992 Landers earthquake, Bull. Seismol. Soc. Am., 84, 817-825, 1994

Jones, B.G, and C.N. Nicolaides, The Whittier Narrows, California earthquake of October 1, 1987: buildings at risk, Earthq. Spectra, 4, 35-42, 1990.

Jones, L.M., Aftershock productivity as a function of cumulative fault offset (abstract), Seismol. Res. Lett., 1997.

Jones, L.E. and S.E. Hough, Analysis of broadband recordings of the 6/28/92 Big Bear Earthquake: Evidence for a multiple-event source, Bull. Seismol. Soc. Am., 85, 688-704, 1995.

Reasenberg, P.A. and L.M. Jones, Earthquake hazard after a mainshock in California, Science, 243, 1173-1176, 1989.

Steinbrugge, K.V., and D.F. Moran, Structural damage to buildings, in Caliif. Div. Mines, 171, G.B. Oakeshott, ed., 259-270, 1955.

Utsu, H., A statistical study on the occurrence of aftershocks, Geophys. Mag., 30, 521-605, 1961.

Richter, C.F., Elementary Seismology, W.H. Freeman and Co., San Francisco, 1958.