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STATIC STRESS CHANGES AND THE TRIGGERING OF EARTHQUAKES

Profile image of Geoffrey KingGeoffrey KingProfile image of Roger BilhamRoger Bilham
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Abstract

To understand whether the 1992 M = 7.4 Landers earthquake changed the proximity to failure on the San Andreas fault system, we examine the general problem of how one earthquake might trigger another. The tendency of rocks to fail in a brittle manner is thought to be a function of both shear and confining stresses, commonly formulated as the Coulomb failure criterion. Here we explore how changes in Coulomb conditions associated with one or more earthquakes may trigger subsequent events. We first consider a Coulomb criterion appropriate for the production of aftershocks, where faults most likely to slip are those optimally orientated for failure as a result of the prevailing regional stress field and the stress change caused by the mainshock. We find that the distribution of aftershocks for the Landers earthquake, as well as for several other moderate events in its vicinity, can be explained by the Coulomb criterion as follows: aftershocks are abundant where the Coulomb stress on optimally orientated faults rose by more than one-half bar, and aftershocks are sparse where the Coulomb stress dropped by a similar amount. Further, we find that several moderate shocks raised the stress at the future Landers epicenter and along much of the Landers rupture zone by about a bar, advancing the Landers shock by 1 to 3 centuries. The Landers rupture, in turn, raised the stress at site of the future M = 6.5 Big Bear aftershock site by 3 bars. The Coulomb stress change on a specified fault is independent of regional stress but depends on the fault geometry, sense of slip, and the coefficient of friction. We use this method to resolve stress changes on the San Andreas and San Jacinto faults imposed by the Landers sequence. Together the Landers and Big Bear earthquakes raised the stress along the San Bernardino segment of the southern San Andreas fault by 2 to 6 bars, hastening the next great earthquake there by about a decade.

Figures (15)
where o, is the greatest principal stress and 9; is the least principal stress. Equation (1) then becomes we can express the stress components applied to it in terms of the principal stresses
where o, is the greatest principal stress and 9; is the least principal stress. Equation (1) then becomes we can express the stress components applied to it in terms of the principal stresses
Figure 1. The axis system used for calcula- tions of Coulomb stresses on optimum failure planes. Compression and right-lateral shear stress on the failure plane are taken as positive. The sign of tg is reversed for calculations of right-lateral Coulomb failure on specified failure planes. Equation (9) is illustrated in Figure 2a. An elliptical slip distribution is imposed on a master fault in a uni- form, stress-free, elastic half-space. The contributions of the shear and normal components to the failure condi- tion, and the resulting Coulomb stresses, for infinitesi- mal faults parallel to the master fault, are shown in sep- arate panels. Such a calculation represents the change of Coulomb stress on these planes resulting only from slip on the master fault. The calculation is appropriate to de- termine, for example, the effect of Landers on a nearby segment of the San Andreas fault. One need only know the relative location of the San Andreas and Landers faults,
Figure 1. The axis system used for calcula- tions of Coulomb stresses on optimum failure planes. Compression and right-lateral shear stress on the failure plane are taken as positive. The sign of tg is reversed for calculations of right-lateral Coulomb failure on specified failure planes. Equation (9) is illustrated in Figure 2a. An elliptical slip distribution is imposed on a master fault in a uni- form, stress-free, elastic half-space. The contributions of the shear and normal components to the failure condi- tion, and the resulting Coulomb stresses, for infinitesi- mal faults parallel to the master fault, are shown in sep- arate panels. Such a calculation represents the change of Coulomb stress on these planes resulting only from slip on the master fault. The calculation is appropriate to de- termine, for example, the effect of Landers on a nearby segment of the San Andreas fault. One need only know the relative location of the San Andreas and Landers faults,
axis as shown in Figure 1 and the other is at @ + 90° From these two directions, the angle of greates compression 6, must be chosen. Thus the optimum fail. ure angle w, is given by @, + 8. Whereas the optimun planes are determined froma}, the normal and shear stress changes on these planes are determined only by the earthquake stress changes a}. Thus the changes ir
axis as shown in Figure 1 and the other is at @ + 90° From these two directions, the angle of greates compression 6, must be chosen. Thus the optimum fail. ure angle w, is given by @, + 8. Whereas the optimun planes are determined froma}, the normal and shear stress changes on these planes are determined only by the earthquake stress changes a}. Thus the changes ir
Figure 4. The effect of changing the regional stress o’ orientation (compare right and left panels) and the effective coefficient of friction x’ (compare top and bottom panels). The example is for a simplified Landers rupture (5 m of tapered slip on a 70-km-long, 12.5-km-deep fault). Regional stress magnitude is 100 bars. Friction controls the internal angle between right- and left-lateral slip planes, and the influence of the normal stress change on failure. The regional stress orientation controls the size of off-fault to fault-end lobes. Both Figures 5 and 6 show the four characteristic lobes of increased Coulomb stress rise and four lobes of Coulomb stress drop. The lobes at the ends of the fault extend into the fault zone, while the off-fault lobes are separated from the fault over most of its length by a zone where the Coulomb stress is reduced. The distributions of aftershocks are consistent with these patterns. In- creases of Coulomb stress of less than 1 bar appear to be sufficient to trigger events, while reductions of the same amount effectively suppress them. Relatively few events fall in the regions of lowered Coulomb stress, and the clusters of off-fault aftershocks are separated from the fault itself by a region of diminished activity. The distributions of Coulomb stresses can be modified as de- scribed earlier by adjusting the regional stress direction and changing 4’. However, any improvements in the correlation between stress changes and aftershock oc- currence are modest. Consequently, we have chosen to show examples with an average py’ of 0.4. Whatever val- ues we adopt, we find that the best correlations of Cou- lomb stress change to aftershock distribution are at dis- tances greater than a few kilometers from the fault. Closer to the fault, unknown details of fault geometry and slip distribution influence stress changes. At distances larger than about three fault lengths, the correlations are less clear because there are fewer aftershocks.
Figure 4. The effect of changing the regional stress o’ orientation (compare right and left panels) and the effective coefficient of friction x’ (compare top and bottom panels). The example is for a simplified Landers rupture (5 m of tapered slip on a 70-km-long, 12.5-km-deep fault). Regional stress magnitude is 100 bars. Friction controls the internal angle between right- and left-lateral slip planes, and the influence of the normal stress change on failure. The regional stress orientation controls the size of off-fault to fault-end lobes. Both Figures 5 and 6 show the four characteristic lobes of increased Coulomb stress rise and four lobes of Coulomb stress drop. The lobes at the ends of the fault extend into the fault zone, while the off-fault lobes are separated from the fault over most of its length by a zone where the Coulomb stress is reduced. The distributions of aftershocks are consistent with these patterns. In- creases of Coulomb stress of less than 1 bar appear to be sufficient to trigger events, while reductions of the same amount effectively suppress them. Relatively few events fall in the regions of lowered Coulomb stress, and the clusters of off-fault aftershocks are separated from the fault itself by a region of diminished activity. The distributions of Coulomb stresses can be modified as de- scribed earlier by adjusting the regional stress direction and changing 4’. However, any improvements in the correlation between stress changes and aftershock oc- currence are modest. Consequently, we have chosen to show examples with an average py’ of 0.4. Whatever val- ues we adopt, we find that the best correlations of Cou- lomb stress change to aftershock distribution are at dis- tances greater than a few kilometers from the fault. Closer to the fault, unknown details of fault geometry and slip distribution influence stress changes. At distances larger than about three fault lengths, the correlations are less clear because there are fewer aftershocks.
Figure 6. Coulomb stress changes calculated for the 23 April 1992 M, = 6.1 Joshua Tree earth- quake. The mainshock is indicated by the star. The model fault is 8-km long and 12.5-km deep with 0. 5. m of right-lateral slip, for a moment of 2 X 10° dyne-cm, following Savage et al. (1993) and Ammon et al. (1993). Stress is sampled halfway down the fault.
Figure 6. Coulomb stress changes calculated for the 23 April 1992 M, = 6.1 Joshua Tree earth- quake. The mainshock is indicated by the star. The model fault is 8-km long and 12.5-km deep with 0. 5. m of right-lateral slip, for a moment of 2 X 10° dyne-cm, following Savage et al. (1993) and Ammon et al. (1993). Stress is sampled halfway down the fault.
Figure 5. Coulomb stress changes associated with the 15 March 1979 Homestead Valley earth- quake sequence (M, = 4.9, 5.2, 4.5, and 4.8). The fault (enclosed white line) is 5.5-km long by 6-km deep, with 0.5 m of tapered slip and a mo- ment of 4.2 x 10” dyne-cm, following Stein and Lisowski (1983) and King et al. (1988). Stress is sampled halfway down the fault.
Figure 5. Coulomb stress changes associated with the 15 March 1979 Homestead Valley earth- quake sequence (M, = 4.9, 5.2, 4.5, and 4.8). The fault (enclosed white line) is 5.5-km long by 6-km deep, with 0.5 m of tapered slip and a mo- ment of 4.2 x 10” dyne-cm, following Stein and Lisowski (1983) and King et al. (1988). Stress is sampled halfway down the fault.
Figure 7. A depth cross section of Coulomb stress changes for the 1979 Homestead Valley fault (essentially the L/W = 1 fault in Fig. 8 made along the distance = 0 km line), with aftershocks from Hutton et al. (1980). Because the section does not pass through the centers of the off-fault lobes, the lobes appear shallower and smaller than at their maxima. The stress concentration at base of fault is exaggerated because fault slip is not tapered with depth.
Figure 7. A depth cross section of Coulomb stress changes for the 1979 Homestead Valley fault (essentially the L/W = 1 fault in Fig. 8 made along the distance = 0 km line), with aftershocks from Hutton et al. (1980). Because the section does not pass through the centers of the off-fault lobes, the lobes appear shallower and smaller than at their maxima. The stress concentration at base of fault is exaggerated because fault slip is not tapered with depth.
Figure 8. Coulomb stress changes as a function of fault length, L. Off-faul stress lobes diminish as the fault lengthens relative to its down-dip dimension, W. Both faults are 12.5-km deep with a stress drop of ~45 bars. Stress is sampled halfway down the fault.
Figure 8. Coulomb stress changes as a function of fault length, L. Off-faul stress lobes diminish as the fault lengthens relative to its down-dip dimension, W. Both faults are 12.5-km deep with a stress drop of ~45 bars. Stress is sampled halfway down the fault.
Figure 11. Coulomb stress change caused by the Landers rupture. The left- lateral M; = 6.5 Big Bear rupture occurred along dotted line 3 hr 26 min after the Landers mainshock. The Coulomb stress increase at the future Big Bear ep- icenter is 2.2 to 2.9 bars. Figure 10. Distribution of modeled fault slip for the Landers earthquake from Wald and Heaton (1994), derived from joint inversion of strong motion, telese- ismic, geodetic, and surface slip data. Three planar fault segments are used, which correspond approximately to the mapped fault trace. Although the surface rupture is 70-km long, the fault slip is concentrated over a strike length of just 40 km.
Figure 11. Coulomb stress change caused by the Landers rupture. The left- lateral M; = 6.5 Big Bear rupture occurred along dotted line 3 hr 26 min after the Landers mainshock. The Coulomb stress increase at the future Big Bear ep- icenter is 2.2 to 2.9 bars. Figure 10. Distribution of modeled fault slip for the Landers earthquake from Wald and Heaton (1994), derived from joint inversion of strong motion, telese- ismic, geodetic, and surface slip data. Three planar fault segments are used, which correspond approximately to the mapped fault trace. Although the surface rupture is 70-km long, the fault slip is concentrated over a strike length of just 40 km.
Figure 12. Coulomb stress changes at a depth of 6.25 km caused by the Lan- ders, Big Bear, and Joshua Tree earthquakes. The Big Bear earthquake, which lacked surface rupture, is modeled as an 18-km-long by 12.5-km-deep vertical fault with 0.83 m of left-lateral slip, for a moment of 5.5 x 10” dyne-cm, fol- lowing limited seismic (Hauksson et al., 1993) and geodetic (Murray et al., 1993, Massonnet et al., 1993) evidence. Most M, > 1 aftershocks occur in regions where the failure stress is calculated to have increased by = 0.1 bar, and few events are found where the stress is pre- dicted to have dropped (Fig. 12). Even when all seis- micity within 5 km of the Landers, Big Bear, and Joshua Tree faults is excluded, more than 75% of the after- shocks occur where the stress is predicted to have risen by >0.3 bar. In contrast, less than 25% of the after- shocks occur where the stress dropped by >0.3 bar. The same correspondence can be found among M, = 4 earth- quakes that took place during the 9-month period April through December 1992 from Hauksson et al. (1993). The largest shock to fall on or near the San Andreas, the 29 June 1992 M, = 4.7 Yucaipa event (due east of San Bernardino in Fig. 13), occurred where the failure stress change on the San Andreas is calculated to have risen by 5 bars. Aftershocks to Landers also occurred as far as 1250 km north of the mainshock, largely in geother- mal areas (Hill et al., 1993). At these distances, the static Coulomb stress changes are much smaller than the tidal
Figure 12. Coulomb stress changes at a depth of 6.25 km caused by the Lan- ders, Big Bear, and Joshua Tree earthquakes. The Big Bear earthquake, which lacked surface rupture, is modeled as an 18-km-long by 12.5-km-deep vertical fault with 0.83 m of left-lateral slip, for a moment of 5.5 x 10” dyne-cm, fol- lowing limited seismic (Hauksson et al., 1993) and geodetic (Murray et al., 1993, Massonnet et al., 1993) evidence. Most M, > 1 aftershocks occur in regions where the failure stress is calculated to have increased by = 0.1 bar, and few events are found where the stress is pre- dicted to have dropped (Fig. 12). Even when all seis- micity within 5 km of the Landers, Big Bear, and Joshua Tree faults is excluded, more than 75% of the after- shocks occur where the stress is predicted to have risen by >0.3 bar. In contrast, less than 25% of the after- shocks occur where the stress dropped by >0.3 bar. The same correspondence can be found among M, = 4 earth- quakes that took place during the 9-month period April through December 1992 from Hauksson et al. (1993). The largest shock to fall on or near the San Andreas, the 29 June 1992 M, = 4.7 Yucaipa event (due east of San Bernardino in Fig. 13), occurred where the failure stress change on the San Andreas is calculated to have risen by 5 bars. Aftershocks to Landers also occurred as far as 1250 km north of the mainshock, largely in geother- mal areas (Hill et al., 1993). At these distances, the static Coulomb stress changes are much smaller than the tidal
Figure 13. The largest Coulomb stress changes at depths between 0 and 12.5 km caused by the Landers, Big Bear, and Joshua Tree earthquakes, shown with the first 25 days of seismicity from Hauksson ef al. (1993). Also shown are the largest two aftershocks to occur during the following 8 months, the 17 November 1992 M, = 5.3 and 4 December 1992 M, = 5.1 shocks. Few aftershocks are seen near Indio in the Coachella Valley where the San Andreas was loaded by the Lan- ders earthquake and, to a lesser extent, by the Imperial Valley (Hanks and Allen, 1989), Elmore Ranch, and Su- perstition Hills (Hudnut et al., 1989) events [the effect of these earthquakes is shown in Stein et al. (1992)]. The lack of earthquakes near Indio appears to be an ex- ception to the observation that Coulomb stress rises are accompanied by at least some activity, although trig- gered surface slip was seen at several points between Indio and the southeastern end of the San Andreas (D. Ponti, personal comm., 1992). Landers aftershocks could be absent in the Coachella Valley because the total stress there is lower, because the fault is locally tougher, or because modulus contrasts modify the Coulomb stresses. We examined the effect of a low-modulus Mojave tec-
Figure 13. The largest Coulomb stress changes at depths between 0 and 12.5 km caused by the Landers, Big Bear, and Joshua Tree earthquakes, shown with the first 25 days of seismicity from Hauksson ef al. (1993). Also shown are the largest two aftershocks to occur during the following 8 months, the 17 November 1992 M, = 5.3 and 4 December 1992 M, = 5.1 shocks. Few aftershocks are seen near Indio in the Coachella Valley where the San Andreas was loaded by the Lan- ders earthquake and, to a lesser extent, by the Imperial Valley (Hanks and Allen, 1989), Elmore Ranch, and Su- perstition Hills (Hudnut et al., 1989) events [the effect of these earthquakes is shown in Stein et al. (1992)]. The lack of earthquakes near Indio appears to be an ex- ception to the observation that Coulomb stress rises are accompanied by at least some activity, although trig- gered surface slip was seen at several points between Indio and the southeastern end of the San Andreas (D. Ponti, personal comm., 1992). Landers aftershocks could be absent in the Coachella Valley because the total stress there is lower, because the fault is locally tougher, or because modulus contrasts modify the Coulomb stresses. We examined the effect of a low-modulus Mojave tec-
Group on California Earthquake Probabilities, 1988). The San Bernardino Mountain segment last ruptured in 1812 (Fumal et al., 1993); given its 24 + 3 mm/yr slip rate (Weldon and Sieh, 1985), a =4.3-m slip deficit has since accumulated, which could yield an M = 7.5 event. The Coachella Valley segment last ruptured in 1680, has a Because the southern San Andreas fault is late in the earthquake cycle, the long-term probability of a great earthquake on any of its three southern segments was high before the Landers earthquake took place (Working
Group on California Earthquake Probabilities, 1988). The San Bernardino Mountain segment last ruptured in 1812 (Fumal et al., 1993); given its 24 + 3 mm/yr slip rate (Weldon and Sieh, 1985), a =4.3-m slip deficit has since accumulated, which could yield an M = 7.5 event. The Coachella Valley segment last ruptured in 1680, has a Because the southern San Andreas fault is late in the earthquake cycle, the long-term probability of a great earthquake on any of its three southern segments was high before the Landers earthquake took place (Working
Figure 15. Coulomb’ stress change caused by the Landers, Big Bear, and Joshua Tree earth- quakes resolved on the San Jacinto fault. The San Jacinto is assumed to be vertical, right-lateral, and 12.5-km deep; stress is sampled every 5 km along the fault at a depth of 6.25 km. The lower panel depicts the slip required to relieve the imposed stress increase. depths shown in our figures, the stress change on the San Andreas and surrounding faults roughly doubles (Fig. 14, middle panel, and Fig. 15, upper panel) and the slip required to relieve the stresses likewise grows (Fig. 14, lower panel, and Fig. 15, lower panel). The time needed for substantial relaxation depends on the viscosity of the lower crust, or on the rate at which creep propagates down the fault, which is perhaps in the range of 30 to 100 yr. Thus, the stress changes caused by major events such as Landers do not diminish with time; rather they grow and diffuse outward from the source. If one were also to include the secular rate of stressing caused by the
Figure 15. Coulomb’ stress change caused by the Landers, Big Bear, and Joshua Tree earth- quakes resolved on the San Jacinto fault. The San Jacinto is assumed to be vertical, right-lateral, and 12.5-km deep; stress is sampled every 5 km along the fault at a depth of 6.25 km. The lower panel depicts the slip required to relieve the imposed stress increase. depths shown in our figures, the stress change on the San Andreas and surrounding faults roughly doubles (Fig. 14, middle panel, and Fig. 15, upper panel) and the slip required to relieve the stresses likewise grows (Fig. 14, lower panel, and Fig. 15, lower panel). The time needed for substantial relaxation depends on the viscosity of the lower crust, or on the rate at which creep propagates down the fault, which is perhaps in the range of 30 to 100 yr. Thus, the stress changes caused by major events such as Landers do not diminish with time; rather they grow and diffuse outward from the source. If one were also to include the secular rate of stressing caused by the

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Geophysical Research Letters, 1996

Stress-drops for small to moderately sized earthquakes in Southern Califomia are found to vary systematically with sourcedepth and location (tectonic environment). We determine highquality fault-plane solutions, plus depth and source duration, for 17 significant (M > 3.9) aftershocks associated with the June 28, 1992 Big Bear sequence, including the more recent April 4, 1994 19:04 GMT Mw 4.6 Lake Arrowhead aftershock, and a Mw 4.2 Banning Pass event which occurred on May 31, 1993 at 08:55 GMT Given source durations and moments obtained from long-period source estimations, and assuming a circular fault model, we estimate stress-drop for each event. Big Bear aftershocks are moderate to high (> 100 bars) stress-drop. Events deeper than 12 km are generally high stress-drop (> 100 bars), while shallower events exhibit moderate to high stress-drops. These results are compared with a similar analysis of Landers aftershocks in the Mojave block. For the Big Bear region, stress drops appear to correlate with depth, with the deepest events yielding the highest stress-drops. In general, events in this region yield higher stress-drops than events occuring in the Mojave block and those associated with the Landers and Joshua Tree sequences. Comparisons of ML to Mo are consistent with the stress-drop results: deep, high stress-drop events show elevated ML to Mo ratios.

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In the shadow of 1857‐the effect of the Great Ft. Tejon Earthquake on subsequent earthquakes in southern California
Aneli FT

Geophysical Research Letters, 1996

The great 1857 Fort Tejon earthquake is the largest earthquake to have hit southern California during the historic period. We investigated if seismicity patterns following 1857 could be due to static stress changes generated by the 1857 earthquake. When post-1857 earthquakes with unknown focal mechanisms were assigned strike-slip mechanisms with strike and rake determined by the nearest active fault, 13 of the 13 southern California M>5.5 earthquakes between 1857 and 1907 were encouraged by the 1857 rupture. When post-1857 earthquakes in the Transverse Ranges with unknown focal mechanisms were assigned reverse mechanisms and all other events were assumed strike-slip, 11 of the 13 earthquakes were encouraged by the 1857 earthquake. These results show significant correlations between static stress changes and seismicity patterns. The correlation disappears around 1907, suggesting that tectonic loading began to overwhelm the effect of the 1857 earthquake early in the 20th century.

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The Relationship of Small Earthquakes to Strain Accumulation Along Major Faults in Southern California
Richard Strelitz

1983

Fault-plane solutions for recent small (ML ≤ 4.6) earthquakes in the central Transverse Ranges, California, were determined using an azimuthally-varying crustal model. The dominant type of faulting observed is reverse faulting on east-striking planes, which suggests a regional stress field characterized by north-south compression. Some strike-slip faulting also occurs. There is some indication that strike-slip earthquakes may be more common than reverse-slip earthquakes during episodes of crustal dilatation (Sauber et al., 1983). The rate of north-south crustal shortening attributable to small earthquake deformation during 1974-1976 is two orders of magnitude smaller than the 0.3 parts per million per year north-south contraction measured at the surface by Savage et al. (1978). The scatter in earthquake hypocenters and general inconsistency of focal mechanisms with geologically determined motions on nearby major faults indicate that the small earthquakes in this region are not assoc...

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Seismicity in the Western Great Basin Apparently Triggered by the Landers, California, Earthquake, 28 June 1992
Yuehua Zeng

Within 24 hr after the Landers earthquake, there were three magnitude 3.4+ events in western Nevada and an unexpected, widespread increase in the rate of small events. Based on combined catalogs for northern Nevada, southern Nevada, and southern California, and a model that assumes statistical independence of events in these regions, the probability of this happening in a 24-hr period by random chance is less than ~10 -~2 per day. Therefore, there is high statistical confidence that the increased seismicity was triggered by the Landers event. Based on the statistical model, we develop a list of 227 earthquakes in the first 83 days following the Landers earthquake, each of which has no more than 10% probability of occurring by random chance. The suspect events are broadly distributed in regions that correlate with historical activity in the Great Basin. The events are not uniquely associated with known volcanic activity, or with zones that were previously active with microearthquakes or aftershock sequences. The magnitudes of the largest triggered events appear to decrease with distance. With time, the number of suspect events decreases at a rate comparable to the rate of decrease of aftershocks of the Landers and Big Bear earthquakes.

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