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compelling evidence for characteristic earthquakes. One of these is from the Superstition Hills fault, a strike-slip fault in southern California. The other is from the Lost River Range fault, a normal fault in Idaho.

Along the Superstition Hills fault, Lindvall and others (6) documented many small offset landforms (predominantly rivulets), including offsets that accrued during and immediately following the Mw6.6 Superstition Hills earthquake of 1987. One of their topographic maps shows a small sand dune offset of ≈70 cm, the amount associated with the 1987 earthquake and afterslip (Fig. 1). An older dune exhibits an offset of ≈140 cm, twice the 1987 earthquake offset. Half of this offset accrued during the 1987 earthquake and aftercreep; and half probably occurred during an earlier earthquake, the age of which has been constrained to the period between about AD 1700 and AD 1915 (7).

Fig. 2 displays all of the measurements of small offsets and a graph of slip along the fault in 1987. For reference, the fainter lines represent multiples of the local 1987 values. Seventeen of the offsets fit the double multiple of the 1987 curve, eight fit the triple multiple, two fit the quadruple multiple, and two fit the quintuple multiple, within the errors of the measurements. About 20% of the measurements cannot be explained as a multiple of the local 1987 offset, and most of these are only marginally misfit.

A reasonable conclusion from these data is that the 1987 event nearly duplicated at least two previous slip events, with respect to rupture length, slip magnitude, and distribution. The Superstition Hills fault thus exemplifies characteristic behavior.

Lost River Range Fault. Investigations of the Lost River Range fault, a normal fault, which produced a MS 7.3 earthquake in 1983, also revealed evidence for characteristic slip (8). The earthquake resulted principally from dip slip of up to ≈2.6 m and minor left-lateral slip along the 22-km-long Thousand Springs segment of the fault (Fig. 3). Degraded scarps along most of this rupture present clear evidence for previous rupture.

Salyards (9) was able to reconstruct the slip associated with these ancient scarps by analysis of many scarp profiles measured after the earthquake. Fig. 4 displays his comparison of the pattern of offset in 1983 and earlier events, the youngest of which occurred ≈7000 yr ago (10). Vertical offsets of 1983 appear as solid dots at each of 33 sites. Vertical offsets of the previous event appear as open circles. These were calculated from surveyed scarp profiles, using the height of the first bevel above the 1983 scarp. The graph shows that slip during the penultimate event roughly mimicks the 1983 rupture. At only 9 of the 33 sites do the 1983 and older offsets differ by more than a factor of two. Where previous offsets were a half meter or less, the 1983 values were also low. Where prior offsets were more than a meter, the 1983 values usually were also more than a meter. These data show that

FIG. 1. Evidence for characteristic slip along the Superstition Hills fault. One sand dune exhibits an offset of ≈70 cm, which accrued during the 1987 Mw 6.6 earthquake and afterslip. The older sand dune displays an offset that is twice as large. This is the cumulative product of the 1987 event and a previous event that occurred within the past 300 years. This map was redrafted from Lindvall et al. (6).

FIG. 2. Small offsets along the Superstition Hills fault show that repeated small offsets characterize ruptures of the fault. For simplicity, the slip function of the 1987 earthquake appears without the hundreds of data points from which it was constructed. Multiples of the 1987 slip function provide a reference for interpreting the older offsets. The fact that most of the older offsets fall on one of the 1987 multiples supports a characteristic-slip model for the Superstition Hills fault. Graph was redrafted from Lindvall et al. (6).

the fault exhibits nearly characteristic slip for the past two and perhaps three events.

Along both the Lost River Range fault and Superstition Hills fault, the basic slip functions have been repeating. Interevent deviations at any one site are almost always less than an order of magnitude and most commonly less than a factor of two. Actual variation from event to event may be even smaller, because some of the differences in the data may be due to uncertainties in reconstruction of penultimate scarp height from the profiles.

From this high degree of similarity in surficial patterns and fault geometry, it is reasonable to conclude that the Superstition Hills fault and the Thousand Springs segment produce characteristic earthquakes. In the case of the Superstition Hills fault, the 1987 and previous rupture appear to span the entire length of the fault. The small offsets of individual earthquakes taper to zero at the end of the fault, as does the cumulative geological offset. In the case of the Lost River Range fault, the northern and southern terminations of the principal 1983 earthquake rupture are at major geometrical and geological breaks in the fault zone. Total geological offset across the northern segment boundary is much less than along the Thousand Springs segment. Furthermore, scarp morphology along segments to the north and south indicate that their previous events occurred well after the previous event on the 1983 segment (8, 11, 12). And so, for at least the past two events, the Thousand Springs segment has been a characteristic, repeated source. Late Pleistocene fault scarps within the gap in Holocene faulting between the Warm Springs and Thousand Springs segments, however, suggest that a still-earlier event involved rupture through the segment boundary. Complexities of this sort are the topic of the next section.

Interaction of Slip Patches

Imperial Fault. The Imperial Valley earthquakes of 1979 and 1940 provide a uniquely well-documented case of repeated historical rupture of the same fault. Unlike the two examples discussed above, though, this case does not support a characteristic-slip model. It does suggest that individual parts of a fault have slip functions that do not vary greatly through several earthquake cycles.

In the case of these Imperial Valley earthquakes, adjacent patches have ruptured historically in two different modes: singly and in tandem. The M7.1 1940 earthquake resulted from faulting along the entire 60-km length of the Imperial fault, the

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