4.4.1 S t a t ic Stress Drop
The estimated static stress drops for ML 2.5 to 4.0 aftershocks of the Northridge earthquake, ranging from 0.04 bar to 70 bars, are comparable to stress drops found for some other events of similar magnitude. For example, ML 2.3-4.0 earthquakes in New England were found to have ~a=2.6-20.1 bar [Feng and Ebel, 1996]; ML 2.0- 3.5 aftershocks of the Coalinga earthquake, ~a=0.5-80 bar [Lindley and Archuleta, 1992]; ML 2.0-4.9 earthquakes in the Seattle area, ~a=0.4-25 bar [Frankel et al., 1999]; JMA magnitude 3.5-4.9 events in Hokkaido, ~a=0.03-30 bar [Fujita et al., 1995]; Mn 1.4-3.9 earthquakes near Parkfield, ~a=2-30 bar [ 0 'Neill, 1984]; and ML events near San Juan Bautista, ~a=1-10 bar [Bakun and McLaren, 1984].
However, these stress drops average at least an order of magnitude lower than those found in some other studies of similar-sized earthquakes. For instance, Frankel and Kanamori [1983], who use a method similar to that used here, find an average stress drop for small Southern California earthquakes of 170 bars, greater than any stress drops observed in this study. Abercrombie and Leary [1993] and Abercrombie [1995] compile stress drops for events over a large range of magnitudes, and those with Mw of about 2.5 to 4.0 have stress drops ranging from about 5 bars to 1000 bars. Aftershocks of the Lorna Prieta earthquake with ML ~ 1.5-4.5 are found to have stress drops of 1-800 bars [Guo et al., 1997] or, similarly, 6-266 bars [Hough et al., 1991]. Events of ML 2.8-4.2 in Round Valley are found to have ~a=10-200
[Smith and Priestley, 1993]; ML 1.8-4.5 events in the vicinity of Bordertown, Nevada,
~a :;;::: 60 bars [Ichinose et al., 1997]; and ML 1.8-4.5 events near Oroville, California,
~a= 14-170 bar [Fletcher et al., 1984].
It is currently unclear whether these variations in stress drop estimates reflect true orders of magnitude spatial and temporal variability in typical earthquake stress
drop, or are artifacts of varying data quality or differences in methodology. Increased use of high-quality data from borehole seismometers [Abercrombie and Leary, 1993]
and comparison of various time- and frequency-domain techniques are necessary to resolve this question.
4.4.2 Stress Drop Variations with Magnitude
I observe an increase in static stress drop with magnitude for ML 2.5 to 4.0 Northridge aftershocks. The same trend has also been reported forM >4 Northridge aftershocks [Mori et al., 1996]. Other studies, however, have determined that static stress drop does not vary with magnitude over large ranges of magnitude [Abercrombie and Leary, 1993; Abercrombie, 1995). There are several proposed explanations for an observed trend in stress drop with magnitude. Mori et al. [1996) suggest that it indicates that more energetic earthquakes tend to grow to be larger magnitude events. It has also been suggested that there is a minimum nucleation size of earthquakes, causing small-magnitude events to have low stress drops since they cannot rupture a smaller area. The observations of Archuleta et al. [1982), that stress drop increases with magnitude only for M <3 events, is consistent with this model. This theory does not explain, however, why the trend of increasing stress drop with magnitude would continue for larger events, as it does for M >4 Northridge aftershocks [Mori et al., 1996). Abercrombie and Leary [1993) and Abercrombie [1995) suggest that the apparent lower stress drops and minimum source areas for small events are artifacts of attenuation of high frequency seismic waves. It could be that an increase in stress drop with magnitude is not universal, but occurs in some circumstances, such as the Northridge sequence, or it may be that the observations presented here have been affected by the attenuation of high frequencies.
4.4.3 Stress Drop Variations with Depth
The simple model summarized in Equation 4.2 predicts that stress drop should scale with effective normal stress. One would more realistically expect the maximum stress
drop to scale with effective normal stress. While fault heterogeneity could present barriers to slip which stop the rupture early, the total stress on the fault would provide an upper limit to stress drop.
An increase in maximum stress drop with depth is found for shallow events, ~5
km depth, consistent with this model. However, for earthquakes deeper than 5 km, no correlation between maximum stress drop and depth was found. This indicates that one of the assumptions of Section 4.1 must not hold at depth. One possibility is that effective normal stress does not substantially increase with depth below '"'"'5 km due to elevated pore fluid pressure following a lithostatic gradient. This interpretation is consistent with the results of Chapter 2, which indicate that the deviatoric stress magnitude at depth is low. High pore pressure, and the resulting low effective normal stress, would lead to weak faults and low deviatoric stress.
Alternatively, the fault friction model may be incorrect and earthquake stress drop may not scale with the magnitude of the effective normal stress on the fault. A lack of scaling between stress drop and mainshock-induced stress change also suggests that stress drop is not strongly controlled by the magnitude of stress on the fault. This would be possible if the slip and stress drop were primarily controlled by the dynamic stress pulse or by a pulse of extreme fault weakening [Heaton, 1990; Andrews and Ben-Zion, 1997]. In this case, the slip and the stress drop would be controlled more by the duration and magnitude of the dynamic stress or fault weakening pulse than by the static effective normal stress on the fault. Dynamic faulting weakening is also consistent with the low deviatoric stress magnitudes observed in Chapter 2.
I observe higher average stress drops for deeper aftershocks due to an increase in minimum stress drop at 15 km depth. It appears that smaller stress drop events are inhibited at depth, which is unexpected. The lack of low stress-drop events may be due to a material property change. The Northridge aftershocks below about 15 km depth appear to occur within a high-seismic-velocity ridge [Hauksson and Haase, 1997], indicating that material properties may play an important role. One possible scenario is that only more energetic events are capable of growing to M >2.5 in stronger materials.