JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 102, NO. Bll, PAGES 24,411-24,435, NOVEMBER 10, 1997

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1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 102, NO. Bll, PAGES 24,411-24,435, NOVEMBER 10, 1997 Stress evolution in southern California and triggering of moderate-, small-, and micro-size earthquakes Jishu Deng 1 and Lynn R. Sykes Lamont-Doherty Earth Observatory, Columbia University, Palisades, New York Department of Earth and Environmental Sciences, Columbia University, New York Abstract. We calculate the evolution of stresses in southern California, extending the study of Deng and Sykes [1997] by increasing from 6 to 36 the number of earthquakes for which coseismic changes in stress are computed and by expanding from M > 6 to M > 1.8 the range of magnitudes M of events whose focal mechanism solutions are examined in the context of the evolving stress field. The cumulative stress on a given date is calculated with respecto an arbitrary zero baseline just before the 1812 Wrightwood earthquake. By taking into accounthe long-term stress loading associated with 98 fault segments and coseismic stress changes for 36 significant earthquakes, our calculations indicate that more than 85% of M > 5 earthquakes from occurred in regions of positive change in Coulomb failure function (ACFF). Most of the remaining about 15% earthquakes that occurred in areas of negative ACFF fall very close to boundaries between positive and negative ACFF, some of which are sensitive to the less well controlled slip distributions of the earliest historic events. Calculations also show that from 1981 until just before the 1992 Landers earthquake more than 85% of small- (M > 3) and micro-size (M > 1.8) shocks in the Seeber and Armbruster [1995] catalog with mechanisms involving either NW trending fight-lateral or NE trending left-lateral strike-slip faulting occurred in regions of positive ACFF. The ratio of encouraged to all small- and micro-siz events reaches a high value of about 88% if an apparent coefficient of friction Ix between 0.0 and 0.6 is used. The highest percentage of earthquakes occurred in areas where stress is about 1 MPa above the 1812 baseline. Most (66%) events occurred in regions of ACFF between 0.0 and 2.0 MPa. The upper limit indicates that the approximate range of stress variation in the earthquake cycle is of the order of 2.0 MPa. The fact that the locations of most moderate-, small-, and micro-size earthquakes are still related to stress changes remaining from large historical events might be used to constrain slip distribution of some of those earthquakes and to constrain the locations of future significant events. 1. Introduction events occurred in areas where stress is about 1.0 MPa above the arbitrary zero baseline of Deng and Sykes [1997] found that about 95% of the well- Stress and its changes are two of the most important factors located earthquakes of magnitude M > 6 in southern California controlling the earthquake process. The direct measurement of occurred in regions that are calculated to have moved closer to stress in the Earth at hypocentral depths is very difficult. failure as quantified by changes in the Coulomb failure function, Changes in stress associated with seismic activity, however, can ACFF (equation(1), below), accumulated since In this be calculated using simple models. $teketee [1958] derived the paper we expand their work by studying the occurrence of large numbers of smaller events with known or inferred focal set of equations that can be used to compute deformation caused by a shear dislocation of a fault embedded in an elastic halfmechanisms. Our calculations show a magnitude-independent space. With additional contribution from other authors [e.g., correlation between the occurrence of earthquakes and ACFF. Okada, 1992] it is now possible to calculate changes in stress About 85% of strike-slip earthquakes of M > 1.8 occurred in associated with any style of earthquake faulting that can be areas where ACFF was positive as of the dates of theft modeled using dislocation displacements across patches of simple occurrence. The ratio of encouraged (+ACFF) to all events planar geometry. The calculated change in stress, when reaches a high value of about 88% if an apparent coefficient of friction between 0.0 and 0.6 is used. Most events occurred in combined with the principles of the Coulomb failure law [Hubbert and Rubey, 1959; Brace, 1960; Scholz, 1990], can regions of ACFF between 0 and 2.0 MPa. For both magnitude significantly improve our knowledge of how much a fault ranges 1.8 < M < 3.0 and 3.0 < M < 5.0, the highest percentage of segmenthat may rupture in a future earthquake is moved toward 1Now at Seismological Laboratory, California Institute of Technology, Pasadena. Copyright 1997 by the American Geophysical Union. Paper number 97JB /97/97JB ,411 failure (or "triggered") by previous shocks [e.g., Harris and Simpson, 1992; Jaum and Sykes, 1992; Stein et al., 1992; King et al., 1994; Simpson and Reasenberg, 1994; Deng and Sykes, 1996]. Interseismic tectonic loading during the cycle of large to great earthquakes is also fundamental to understanding the earthquake process and to earthquake prediction. Simpson and Reasenberg

2 24,412 DENG AND SYKES: STRESS TRIGGERING IN SOUTHIERN CALIFORNIA [1994] modeled the stress loading rate for major faults in the San Francisco Bay area by using dislocations with the appropriate long-term slip rate extending along vertical fault planes from 13 to 100 km in depth. The dislocations represent stable sliding beneath the locked part of the fault. They show that M > 5 earthquakes on the Calaveras fault occurred in regions where stress recovered soonest from the stress relaxation associated with the 1906 San Francisco earthquake of M w 7.8 [Simpson and Reasenberg, 1994]. Jaumd and Sykes [1996] adopted a similar stress loading model for major faults in northern California and concluded that moderate-size earthquakes in the greater San Francisco Bay region between 1850 and 1993 occurred outside of areas where cumulative changes in stress were negative at the time of their occurrence. Southern California (Figure 1) is a region of high population and complex infrastructure that are at risk from earthquakes. The region is now closely and extensively monitored by both geodetic and seismic instruments. Deng and Sykes [1997] used those data to correlate the occurrence of moderate-size earthquakes with calculated values of ACFF as a function of time. They found that about 95% of well-located earthquakes of M > 6 in southern California since 1812 occurred in areas of positive ACFF. Harris and Simpson [1996] concluded that the great Fort Tejon earthquake of 1857 affected the occurrence of subsequent moderate-sizevents for as long as 50 to 100 years. Other stress studies also demonstrated that earthquakes in southern California are related to stresses generated by previous events and tectonic loading [King et al., 1994; Stein et al., 1994; Harris et al., 1995; Deng and Sykes, 1996]. Those studies, however, were limited to stress calculations for either small numbers of earthquakes or small numbers of fault segments. The purpose of this paper is to expand the work of Deng and Sykes [1997] by systematically studying the correlation between calculated ACFF as it evolves with time and the occurrence of smaller earthquakes than those previously examined. The catalog of the Southern California Seismographic Network (SCSN) is complete for earthquakes of different magnitude ranges for different time periods: the larger magnitudes (M > 5) are complete between 1932 and 1995 and the smaller magnitudes (M > 1.8) are complete since The very detailed focal 36 ø, Parkfield elp SB SBC 34 ø Pacific Ocean I 100km I SD 32 ø 122øW 120ø 118 ø 116 ø 114 ø Figure 1. Major place names, active faults, and fault segments in southern California. Long-term slip rates of selected segments of San Andreas (SAF, bold line) and other major faults are shown in millimeters per year [Petersen and Wesnousky, 1994; Working Group on the Probabilities of Future Large Earthquakes in Southern California, 1995]. Segments of San Andreas fault: CS, Carrizo; CVS, Coachella Valley; MS, Mojave; SBS, San Bernardino. Other faults: CPF, Cerro Prieto; EF, Elsinore; IF, Imperial; LSF, Laguna Salada; NI, Newport- Inglewood; PF, Pisgah; PVF, Palos Vetdes; RCF, Rose Canyon; SCF, San Clemente; SJF, San Jacinto; WWF, White Wolf. B B, Bombay Beach; CP, Cajon Pass; ID, Indio; LA, Los Angeles; LP, Lompoc; MP, Mill Potrero; NR, Northridge; P, Pallet Creek; SB, Santa Barbara; SBC, Santa Barbara Channel; SBD, San Bernardino; SD, San Diego; SGP, San Gorgonio Pass; SS, Salton Sea; TR, Transverse Ranges, which represents a much broader region than actually shown; VT, Ventura; W, Wrightwood; WC, Wallace Creek. Arrows denote sense of long-term relative motion acros selected major faults.

3 ß DENG AND SYKES: STRESS TRIGGERING IN SOUTHERN CALIFORNIA 24,413 Critical CFF Positive ACFF Initial CFF Negative ACFF Plate 1. Simplified Coulomb failure law shown by Mohr diagram. Symbols ' and o are shear and normal components of stress on a potential fault. Hot (red) color represents highest value of Coulomb failure function (CFF), and cold (blue) color represents lowest value of CFF. Intersection of ' axis and line of critical CFF is cohesion, x 0. Positive changes in CFF associated with either previous earthquakes or tectonic buildup indicate movement toward failure and increased likelihood of slip in future earthquakes. Negative values indicate movement away from failure. mechanism solutions of thousands of small earthquakes provided by Seeber and Armbruster [1995] enable us to compare the evolving values of ACFF with "background" earthquakes down to a much smaller threshold of magnitude than was possible in previous studies. For the first time, our studies show that a high to the local fault orientation. The work of Tse and Rice [1986] and Gilbert et al. [1994] constrain the loading model for a strikeslip fault to the one that involvestick-slip along the upper locked part and steady sliding along the deep unlocked part of the fault. The long-term slip rate for both locked and unlocked parts of a percentage of "background" small- and micro-size earthquakes fault is identical. Thus the interseismic loading for the locked occur preferentially in areas that have been moved closer to failure, i.e., in regions of positive ACFF. part of a strike-slip fault comes mainly from the continuoustable sliding that extends in depth well below the seismogenic zone, The minority of events that occurred in regions of calculated which contains that portion of a fault capable of building up negative ACFF may also convey important information. If we assume that those misfits arise from miscalculations of ACFF (as contrasted to a true discrepancy), we may better constrain the stress and rupturing in earthquakes. Wide areas of significant horizontal detachment faulting immediately beneath the seismogenic zone in the crust of the Earth are not in accord with coseismic slip distributions of some older significant historical the observations of Gilbert et al. [ 1994]. earthquakes. The stress fields of some of those past great earthquakes still appear to control the occurrence of current For an infinite half-space, Matsuura et al. [1986] showed that the above tectonic loading mechanism for a reasonably long events. Hence the distribution of events of all sizes and their strike-slip fault is identical to the case in which "virtual relationship to calculated values of the Coulomb stress should be displacement" of opposite sign to that of deep aseismic slip is of great value in assessing future seismic hazards in southern accumulated continuously across the shallow seismogenic part of California. the fault. Both models give the same changes in stress. Savage [1983] developed a similar "virtual displacement loading" mechanism for dip-slip faults. That is, the interseismic loading for a long thrust fault is equivalento continuous accumulation of 2. Model of Stress Evolution as a Function "virtual normal displacement" at the long-term rate of fault slip. of Time Since 1812 In this study, interseismic loading is modeled by putting virtual negative displacements across the locked parts of 98 fault Unlike many other earthquake triggering studies, we segments in southern California with long-term slip rates > 3 mm/ incorporate interseismic tectonic loading into the stress yr. As Deng and Sykes [1997] demonstrated, these 98 fault evolutionary computations using a model constrained from both numerical calculations and geodetic measurements. Tse and Rice [1986] proposed that deformation of the deep unlocked part of a strike-slip fault is dominated by temperature-controlled stablesliding at the average long-term slip velocity. Gilbert et al. [1994] discovered that the observed direction of maximum shear strain close to several major faults in California is nearly parallel segments are responsible for most of the tectonic deformation in that region as measured by Global Positioning System (GPS) and other geodetic techniques. Coseismic changes in stress are inserted in the model whenever a significant earthquake occurs. Hence the cumulative effect is a combination of continuous interseismic stress loading and discontinuous coseismic releasing of stress. All calculations

4 24,414 DENG AND SYKES: STRESS TRIGGERING IN SOUTHERN CALIFORNIA I! II II

5 DENG AND SYKES: STRESS TRIGGERING IN SOUTHERN CALIFORNIA 24,415 are performed for dislocations in an elastic half-space [Okada, 1992]. We use changes in the Coulomb failure function (ACFF) to quantify how much a fault is encouraged (moved toward failure) or discouraged (moved away from failure) as modified from Scholz [1990] ACFF - A'c + I. o (1) where Ax and Ao are cumulative changes in shear stress (positive for increase in rake direction) and normal stress (positive for increased tension) respectively. The "apparent" coefficient of friction g represents the combined effect of the actual coefficient of fiction and the fluid pore pressure. These changes are calculated with respect to an arbitrary zero baseline in 1812 just prior to a large to great shock along the San Andreas fault [Deny and Sykes, 1997]. This approach is probably a good approximation for the elastic part of the s½ismogenic zone, where we perform our calculations in this paper. We are currently working on an advanced numerical model which can be used to handle viscoelastic relaxations at the base of the seismogenic zone. The new model will be the topic of another paper. Plate 1 illustrates ACFF on a Mohr diagram for the simplified case in which the apparent coefficient of friction g is fixed. Each constant value of the Coulomb failure function (CFF) represents a straight line parallel to the critical failure envelope. Hot (red) colors indicate higher values of CFF and cold (blue) colors represent lower values. Each value of ACPF is related to the changes in shear stress,xx and normal stress Ao. Positive changes in both shear stress and tensional normal stress will increase the value of CFF and move the fault closer to failure. On the other hand, negative changes in CFF will discourage a fault from failure in an earthquake. Our calculations are focused on calculating ACFF for the whole of southern California and attempting to correlate the occurrence of earthquakes with the calculated values of CFF. 3. Triggering of M > 5 Earthquakes Between 1933 and 1995 We use the same arbitrary baseline as Deng and Sykes [1997] and assign a starting value of ACFF = 0 at all observing points just before the Wrightwood earthquake of December 8, The shear modulus and Poisson's ratio were fixed throughout our study as 33 GPa and 0.25, respectively. All calculations for M > 5 earthquakes are for points at a depth of 8.0 km and an apparent coefficient of friction g = 0.6. Moderate-size earthquakes generally did not occur in areas where the sign of CFF changed as g was varied in our calculations. In section 4.3 we show the effect of g on triggering of small- and micro-siz earthquakes. The difference between our new calculations and those of Deng and Sykes [1997] is that we now incorporate coseismic stress changes associated with 30 additional earthquakes in our evolutionary calculations. The appendix describes the source parameters of the newly added events. We discuss in the next sectionsnapshots showing ACFF at various times since 1933 for both strike-slip and dip-slip faults and compare ACFF at the sites of many smaller earthquakes. We use the term "stresshadow" to describe regions of negative ACFF following the usage of Harris and Simpson [1993, 1996]. The areas of positive ACFF are called stress-enhanced zones. Emphasis will be given to the new features of the snapshots and newly added earthquakes. The major characteristics and events covered by Deny and Sykes [1997] are not reiterated.

6 24,416 DENG AND SYKES: STRESS TRIGGERING IN SOUTHERN CALIFORNIA

7 DENG AND SYKES: STRESS TRIGGERING IN SOUTHERN CALIFORNIA 24, Stress for Vertical NW Trending Strike-Slip Faults Stress in The evolutionary stress as of State of stress just before Long Beach earthquake of differs from that of 1933 in that moderate to large earthquakes in northern Baja California and the Imperial Valley (December 30, The catalog of M > 5 earthquakes is complete for southern 1934; December 31, 1934; May 19, 1940) changed ACFF California only after 1932 when the Southern California significantly. The March 11, 1933, Long Beach; June 8, 1934, Seismographic Network was established. In addition to the Parkfield; and March 25, 1937, Buck Ridge earthquakes created December 8, 1812; January 9, 1857 (surface rupture model by Sieh [ 1978]); and March 26, 1872, earthquakes used by Deng and changes also, but only in relatively local areas, since they were of M < 6.5. Plate 2b shows 16 strike-slip earthquakes of M > 5 Sykes [1997] in the stress model, we add coseismichanges in between 1942 and In terms of number of earthquakes per stress associated with seven more pre-1933 events of M > 6 that decade of that size, the time interval between 1942 and 1952 is occurred at Parkfield, along the San Jacinto fault zone, and in northern Baja California. Plate 2a shows the cumulative ACFF probably the most active period of the last 60 years. Of the 16 earthquakes, 13 were located in regions of positive ACFF, which for vertical right-lateral strike-slip faults trending 321 ø, i.e., those ranged from 0.03 (San Clemente Island earthquake of December of San An:lreas type, from 1812 until just before the M w 6.4 Long 26, 1951) to 4 MPa (Desert Hot Springs event of December 4, Beach earthquake of March 11, Focal mechanism 1948). The other three earthquakes occurred near the boundaries solutions for earthquakes that occurred along faults of San between stress-enhanced and stress shadow zones. The stresses Andreas type between 1933 and 1942 are superimposed on the at the hypocenters of the two events on August 29, 1943, and map of ACFF. March 15, 1946, are very sensitive to the assumed southeastern The newly included stress changes for those additional strong extent of the December 8, 1812, Wrightwood event and to the earthquakes did not change the fact that most moderate-size strike and dip of the Owens valley earthquake of March 26, 1872, earthquakes occurred in regions of positive ACFF. Among the 15 respectively. earthquakeshown in Plate 2a, 12 are located in stress-enhanced The Manix earthquake of April 10, 1947, may have occurred zones (Table 1). The ACFF at the locations of these 12 events is along a left-lateral strike-slip fault trending NE-SW in the between 0.07 (Twentynine Palms earthquake on March 3, 1942) Mojave desert [Doser, 1990a]. It is also located in a region of and 4 MPa (shock on December 24, 1934, north of Parkfield). negative ACFF but close to the zero contour. The geodetic The Parkfield earthquakes of June 1934 occurred in a very small measurements shown by Deng and Sykes [1997, Figure 5] area of negative ACFF, which was created by the March 3, 1901, suggesthat they underestimated tectonic loading in the Mojave and March 10, 1922, events. The small negative zone is hardly desert by about 5 mm/yr between the two geodetic stations visible on the stress map, but it is the direct result of the MOJA and PEAR. When more geodetic measurements using assumption that the 1901, 1922, and 1934 Parkfield earthquakes Global Positioning System (GPS) become available, we may be ruptured exactly the same segment of the San Andreas fault with able to localize the 5 mm/yr deformation to one or more faults in the same amount of slip. the Mojave desert and to improve our estimation of the stress at Compared to the diagrams of Deng and Sykes [1997], the the location of the Manix earthquake. stress pattern is significantly different in that a large shadow zone was created by the 1892 Laguna Salada earthquake in northern State of ACFF just after Kern County earthquake of Baja California, which still persists as of The coseismic Plate 2c shows the cumulative ACFF just after the great stress change of that event is modeled here but was not by Deng earthquake of July 21, Earthquakes that occurred along and Sykes [1997]. If that earthquake actually ruptured a segment NW trending right-lateral strike-slip faults between 1952 and 1968 are also shown in Plate 2c. All of the 12 events are located as long as 40 km with a maximum displacement of several meters in stress-enhanced zones. The ACFF at the location of these and a M w of 7.3 as discussed in the appendix, we calculate that it events is between 0.05 (Kelso earthquake on September 26, must have relaxed stresses associated with NW trending strike- slip faults in southernmost California including San Diego, as 1965) and 4 MPa (Arroyo Salada event on March 19, 1954). shown in Plate 2a. Rockwell [1989] suggested that the December Plate 2d shows the coseismic stress change associated with the 30, 1934, event occurred to the southeast of rupture zone of great 1952 earthquake itself. Although the 1952 event was a the 1892 earthquake, placing the 1934 shock in a stress-enhanced great shock, the stress change it produced at the sites of any of those 12 events that occurred thereafter is very small (less than zone. Only limited information is available for the 1892 event MPa). The main reason for that was that its mechanism Whether the San Diego area is located in a region of positive or was very different from that of the San Andreas type. negative ACFF depends critically on the value of M w used for the 1892 shock. Future detailed palcoseismological studies of the 1892 earthquake along the Laguna Salada fault could play a key Calculations of stress in Earthquakes that occurred between 1968 and 1980 are shown in Plate 2e on a map of ACFF calculated just before the Borrego Mountain event of role in constraining seismic hazards assessments for the Nine out of 11 of those shocks are located in stresssouthernmost part of California including San Diego and its neighboring counties. The stress shadow for events of San Andreas type created by the 1892 shock decreases asymmetrically with time. The Laguna enhanced zones, i.e., those of positive ACFF. The stress at the location of these nine events varied from 0.04 (offshore earthquake of October 24, 1969) to about 2 MPa (shock in Brawley zone of November 4, 1976). Two earthquakes are Salada fault itself is associated with fairly low long-term slip located in small shadow zones: one is the Superstition Hills event rates, about 4 mm/yr [Savage et al., 1994]. Stress buildup of September 30,!971; another is the Imperial Valley earthquake associated with the more active Imperial and Cerro Prieto faults of October 15, The focal mechanism of the 1971 lead to those regions emerging from the 1892 stresshadow fairly quickly. Its shadow persists much longer to the west and northwest where long-term rates of faulting are much smaller. Superstition Hills earthquake is poorly controlled. The nearby 1968 Borrego Mountain earthquake could also have moved it closer to failure. The stress at the location of the 1979 Imperial

8 24,418 DENG AND SYKES: STRESS TRIGGERING IN SOUTHERN CALIFORNIA Table 1. Summary of Triggering of M > 5 Strike-Slip Earthquakes Between 1933 and 1995 Positive ACFF Negative ACFF Period Number of Minimum, Maximum, Number of Minimum, Maximum, Events MPa MPa Events MPa MPa Valley event, however, is dependent on the rupture model for the was created by the 1892 Laguna Salada earthquake and several 1892 Laguna Salada and the 1940 Imperial Valley earthquakes, other nearby strong earthquakes. The stress shadow created by the former of which is uncertain as is its M w Stress in The state of stress just before the Victoria earthquake of June 9, 1980, in Baja California is shown the 1812 and 1857 events continues to shrink in size and area as tectonic stresses accumulate. The areas of high positive ACFF are potential sites of moderate to large earthquakes. in Plate 2f. Among the 11 earthquakes of M > 5 that occurred between 1980 and 1992, 10 are located in stress-enhanced zones. The ACFF for these 10 events is between 0.04 (the Oceanside earthquake of July 13, 1986) and 6 MPa (Victoria, Baja California, earthquake of June 9, 1980). Teleseismic waveform inversions [Pacheco and Nabelek, 1988] indicate that the 1986 Oceanside earthquake released a large part of its seismic moment along a NW striking dip-slip fault. A large number of firstmotion arrivals (see the appendix), however, indicate that the 3.2. Stress Evolution for Dip-Slip Faults In southern California, dip-slip earthquakes occur less frequently than strike-slip events and faults of that type have lower rates of long-term displacementhan several of the most active strike-slip faults. We present two snapshots to show the cumulative stress changes since 1812 on typical fault planes. Except for the strike, dip, and rake of the observing points, all initial rupture actually started with a predominance of right- other parameters used are the same as those for the series of lateral strike-slip motion. Plate 2f shows the focal mechanism calculations for strike-slip faults Stress evolution in Plate 3a shows the stress on solution of the 1986 Oceansid earthquake obtained from the firstmotion data set. Another event of interest is the 1988 Pasadena earthquake, which occurred very close to the sharp boundary fault planes with strike 270 ø, dip 30øN, and rake 60 ø. We choose this set of strike, dip, and rake to representhe fault plane and between the stress shadow and stress-enhanced zones. The sense of motion of several thrust earthquakes that occurred in location of that boundary, however, is again very sensitive to the southern California, for example, the Santa Barbara earthquake of uncertain rupture pattern for the 1812 Wrightwood earthquake on August 13, Focal mechanisms of five other M > 5 the San Andreas fault. Palcoseismic and other new data may help to better constrain the slip distributions of old larger events such earthquakes that either did or may have occurred on north dipping fault planes after 1968 are also plotted on Plate 3a. All as the 1812 Wrightwood earthquake. of these events were located in the central and western Stress just before the Landers sequence of Plate 2g shows ACFF as calculated just before the Joshua Tree earthquake of April 23, 1992, which began the Landers earthquake sequence. All three of the large events in 1992 occurred in areas of ACFF about +1 MPa. Coseismic changes associated with the Landers sequence are included in our model and are shown in Plate 2h. Transverse Ranges. The E-W trending bands of varying ACFF in and near the Santa Barbara Channel are caused by the tectonic loading associated with several of the blind thrust faults that we used in our model. It is more difficult to approximate the tectonic loading for blind thrust faults than for vertical strike-slip faults or surface-breaking thrust faults by using a simple elastic dislocation model. Thus we think that the narrow E-W trending Evolution of stress after the Landers sequence. bands in Plate 3 are more likely to represent artifacts than real Plate 2h shows calculations of stress evolution until 2025 states of stress. Most of the earthquakes plotted, however, assuming that no strong earthquakes occur between 1997 and then. Strike-slip earthquakes of M > 5 between the 1992 Big Bear event and the end of 1995 are superimposed on Plate 2h. Except for the Wheeler Ridge earthquake of May 28, 1993, which occurred in a shadow zone created by previous earthquakes, all of the others are located in areas of positive ACFF between 0.01 and about 1 MPa. The Wheeler Ridge earthquake of 1993 is located near the source region of the July occurred in regions of positive ACFF of a relatively long wavelength. Alternative models, for example, one incorporating a three-dimensional viscoelastic theology, could significantly improve the stress loading mechanism of blind-thrust faults State of ACFF in Stresses on fault planes of strike 135 ø, dip 30øS, and rake 110 ø until just before the Victoria, Baja California, earthquake of June 9, 1980, are shown in Plate 3b. The selected strike, dip, and rake are close to those of the 21, 1952, Kern County earthquake. Earthquakes of M > 5 that focal mechanisms of the events shown in Plate 3b. The 1994 are located well inside regions of negative ACFF, however, are very rare in our study. The stress pattern in Plate 2h is similar to Plate 2k of Deng Northridge earthquake and the sequence of earthquakes in central California off the San Andreas fault in the 1980s are plotted. The 1985 Kettleman Hills earthquake is located at the boundary and Sykes [1997]. The major difference is the shadow in between regions of positive and negative changes in stress. All southernmost California and northernmost Baja California, which others occurred in regions of positive ACFF.

9 DENG AND SYKES: STRESS TRIGGERING IN SOUTHERN CALIFORNIA 24, Summary of Triggering of M > 5 Strike-Slip Earthquakes than 10 SCSN stations reported first motion data. The events in the catalog were also relocated by Seebet and Armbruster In Plates 2 and 3 we show snapshots of stress for typical strike- [1995]. The catalog of Seebet and Armbruster [1995] provides slip faults and for dip-slip faults with a small component of strikethe best available and most reliable focal mechanisms for a large slip motion. Plates 2 and 3 also display focal mechanism number of earthquakes in southern California. We use their solutions for earthquakes of M > 5. Figure 2 is a histogram of the catalog and compare the location of events of M > 1.8 with ACFF frequency of occurrence of these strike-slip events as a function with 1812 again taken as the zero baseline. The lower threshold of ACFF. Since the number of moderate-size thrust events is so magnitude is chosen because the earthquake catalog of SCSN is small (about 10), we did not construct a histogram for those complete for M > 1.8 since events. About 85% of the 74 strike-slip earthquakestudied are located in areas of positive ACFF; that is, the distribution is very skewed toward positive values. The average ACFF is 0.9 MPa above the 1812 baseline of stress. The only event that is located 4.1. Earthquakes on Vertical Strike-Slip Faults Plates 4a and 4b show the stress evolution as of While in areas of large calculated negative ACFF (-3.4 MPa) in Figure 2 occurred on October 15, This event is related to the stress shadow generated by the poorly controlled slip distribution of the Laguna Salada earthquake of Among other shocks that occurred in regions of negative ACFF, most were located very the ACFF in Plates 4a and 4b is the same as that in Plate 2e, the focal mechanism solutions shown are for smaller earthquakes. Plates 4a and 4b are for events from 1981 to 1992 of 3.0 < M < 5.0 and 1.8 < M < 3.0, respectively. The earthquakes are selected from Seeber and Arrnbruster's [1995] catalog, by allowing the close to boundaries between positive and negative ACFF, which slip vector to vary up to 25 ø in strike, dip, and rake from that of are sensitive to uncertainties in the slip distributions of certain vertical right-lateral strike-slip fault trending 321 ø, i.e., typical large historical earthquakes. So, a high percentage of M > 5 San Andreas style of faulting. Only those events that occurred events can be explained in terms of evolution of the ACFF; that before the 1992 Landers earthquake are plotted. Notice that a is, they occurred in areas of positive ACFF as stresses recovered from shadows created by previous events, especially large to great shock since cutoff in mechanism occurs at about 35.5øN and at about 120øW in the Seeber and Arrnbruster [1995] catalog. Hence it does not include the northern or western parts of Plate 4. A dominant number of the earthquakes in Plates 4a and 4b are 4. Triggering of Small- and Micro-Size remarkably constrained to regions of high positive ACFF. The Earthquakes Between 1981 and 1992 locations of a number of earthquakes close to latitude 34øN The calculations we presented thus far indicate that the ACFF can be used to strongly constrain or predict the location of earthquakes of M > 5. This result encourages us to look at the define a sharp boundary that almost exactly coincides with the computed boundary between shadow and stress-enhanced zones. Only a small percentage of these events occurred in the middle of locations of smaller earthquakes with respecto ACFF. Seeber the shadow zones. This result suggests that the locations of and Arrnbruster [1995] used the phase reports from SCSN stations to compute focal mechanism solutions for over 10,000 events as small as magnitude 1.8 are still related to stress changes (such as remaining stress shadows) associated with historical earthquakes that occurred from 1981 to 1994 using a grid-search large and great earthquakes that occurred 100 to 200 years ago. procedure. Their catalog (now available through the SCEC data center) includes all good to high quality events for which more Long-term and continued monitoring of micro-siz earthquakes is important in the sense that they may contain information on the 40 ' ' I ' ' ' I ' ' ' I ' ' ' I ' ' ' I ' ' ' I ' ' ' I ' ' ' o Coulomb Stress (MPa) Figure 2. Histogram of frequency of occurrence of moderate-size earthquakes as a function of ACFF for events of M > 5 between 1933 and More than 85% of these moderate-siz earthquakes occurred at locations of positive changes in stress. A significant number of the remaining events occurred close to a boundary between regions of positive and negative ACFF.

10 ß 24,420 DENG AND SYKES: STRESS TRIGGERING IN SOUTHERN CALIFORNIA 0 ' '' I ' ' ' I ' ' ' I ' ' ' I ' ' ' I ' ' ' I ' ' ' I ' ' ' I Coulomb Stress (MPa) Figure 3. Histogram of frequency of occurrence of 330 small earthquakes of M > 3 from Plate 4a as a function of ACFF (IX--0.6). More than 85% of the shocks occurred in regions with ACFF > 0. Highest percentage of earthquakes occurred in areas where AC.FF since 1812 is about 1 MPa. temporal migration of the stress front. That migration maybe a 4.3. Summary of Triggering of Small- and Micro-Size useful intermediate- or long-term precursor to future large to Strike-Slip Earthquakes great earthquakes. The distribution of small- and micro-sizearthquakes in the 4.2. Earthquakes on Thrust Faults evolving stress field of southern California can also be illustrated by histograms. Figures 3 and 4 show earthquake frequency as a Plates 4c and 4d show the stress evolution on thrust faults of function of magnitude and the sign of evolutionary changes in strike 270 ø and dip 30 ø as of Two discouraging factors are stress for the event shown in Plates 4a and 4b, respectively, i.e., apparent in Plates 4c and 4d in terms of the relationship of events of San Andreas type of faulting. Both histograms indicate earthquakes to ACFF. One is the narrow E-W trending bands of that more than 85% of small- and micro-sizearthquakes of varying ACFF created by the blind thrust faults that we discussed strike-slip type occurred in stress-enhanced zones. earlier. The other is the relatively small number of earthquakes An apparent coefficient of friction IX-0.6 is used to obtain the that occurred on thrust faults. The small number of events, ACFF shown in Plate 4. The number of encouraged (ACFF > 0) however, does not weaken our argument that even micro-size small- and micro-sizearthquakes changeslightly if a different e.arthquakes, when classified by mechanism type, reflect stress!x is used. Figure 5 shows the ratio of encouraged events to all changes resulting from past seismic activity on a timescale of earthquakes shown in Figures 3 and 4 as a function of IX. The hundreds of years. dominant feature of the curve is that for 0 < IX < 0.6, the 25. ' I ' ' ' I ' ' ' I ' ' '! ' ' ' I ' ' ' I ' ' ' I ' ' ' I !:,..:.:.: > :::: ::... :.,q. 5.3 ) :.. > : k., ß,xx. :':x, :.: ': :.:: ::.[ ½:.[: :..:... :5:?.:.:.' Coulomb Sess (MPa) Figure 4. Same as Figure 3 except that histogram for 2167 earthquakes plotted in Plate 4b of 1.8 < M < 3.

11 DENG AND SYKES: STRESS TRIGGERING IN SOUTHERN CALIFORNIA 24, ø 34 ø d21, ,., o 0 -L,_o,,, ',. ', II=. ' M=7 32",, A 36 ø 82110/2. "' ' 85108/ / ø 9ad01/17 -. I=5 M=6 M=7 32" 122øW B 120 ø 118 ø 116 ø 114 ø MPa I0 20 Plate 3. Coulomb stress evolution at various times with respecto zero baseline in 1812 calculated at depth of 8 km for faults with a large thrust component. E-W trending zones around Santa Barbara are generated by the several blind thrusts listed by Deng and Sykes [1997, Table 1], (a) just before 1968 Borrego Mountain earthquake for faults of strike 270 ø, dip 30 ø to north, and rake 60 ø, and (b) just before 1980 Victoria, Baja California, earthquake for southerly dipping faults with strike 135 ø, dip 30 ø, and rake 110 ø.

12 24,422 DENG AND SYKES: STRESS TRIGGERING IN SOUTHERN CALIFORNIA i t e o * II II o O0 0 :..,e ß ß._../. : oo.0o.o øj e II II o o o o I: ij [] i. i

13 DENG AND SYKES: STRESS TRIGGERING IN SOUTHERN CALIFORNIA 24,423 percentage stays at about 88, with some weak peaks of short wavelength. The percentage systematically goes down from about 88 to about 84 if!x is increased from 0.6 to 1.0. Althougl we cannot resolve the exact value of Ix, we think the reasonable range is between 0.0 and 0.6 for the long-term effects that we examined. Our range for Ix does not conflict with the low!x values obtained by Seeher and Armbruster [1997] for tectonic loading in southern California. A closer examination of Plates 4a and 4b indicates that a large number of the events in shadow zones occurred to the north of Big Bear near 34øN, 117øW. So, in addition to possibly being affected by changes in IX, stresses in that region are very sensitive to the actual distribution of slip in the large to great Wrightwood earthquake of The current distribution of small- and microsize earthquakes in that area instead might be used in future work to constrain or invert for the extent of rupture in the 1812 Wrightwood earthquake. Figures 3 and 4 also show that the highest percentage of events occurred near 1 MPa for both groups of earthquakes. Assuming that the same pattern will continue in the future, that peak stress could be an important parameter that might be used to better constrain the location of future earthquakes. 5. Permissible CFF for Faults Figures 2, 3, and 4 show a strong correlation between the occurrence of earthquakes and cumulative ACFF; that is, most events occurred in areas of ACFF between 0 and 2 MPa above the 1812 baseline. This observation indicates that most of the active faults on which earthquakes occur are within 2 MPa of the critical failure stress. Figure 6 illustrates the approximate range of permissible CFF for active faults in southern California. The maximum relaxation of-2 MPa in Figure 6 is probably somewhat dependent on the timescale we use for our calculations, i.e., the use of an 1812 baseline. This number, however, is of the same order of magnitude as stress drops in many earthquakes [Scholz, 1990]. This is not too surprising since our calculations of stress evolution cover about 180 years, i.e., nearly one cycle of great earthquakes along the most active faults. Whenever the stress recovers by about this magnitude after a previous event, the fault is ready to rupture again in the next earthquake. In other words, the stress on a fault can vary for up to a maximum level that is of the order of 2 MPa with time in an earthquake cycle. 6. Conclusions We continued the study of Deng and Sykes [1997] by calculating the cumulative Coulomb failure function, ACFF, for southern California as a function of time with respect to an arbitrary zero baseline in We take into accountectonic stress loading associated with 98 fault segments as well as coseismic stress changes associated with 36 earthquakes of M > 6. We then examine the distribution of events of M > 1.8 in terms of their occurrence in space and time with respecto our calculations of the evolving stress field. Our calculations show that between 1933 and the present, more than 85% of the M > 5 earthquakes occurred in regions of positive ACFF. Most other M > 5 events occurred very close to the calculated boundaries between stress shadow and stressenhanced zones. The locations of several of those boundaries are very sensitive to the slip distributions of the older large to great

14 24,424 DENG AND SYKES' STRESS TRIGGERING IN SOUTHERN CALIFORNIA ,, I,,,I,,i I,, i, I... I... I... I... I... I S Apparent Coefficient of Friction Figure 5. Percentage of encouraged (ACFF > 0) small- and micro-siz earthquakes as a function of Ix. earthquakes in the 19th century. Only one event of M > 5, the 1993 Wheeler Ridge earthquake, occurred in the middle of what we calculate to be a large shadow zone, in that case the one created by the 1952 Kern County earthquake. The locations of small- (3.0 < M < 5) and micro-size (M < 3) earthquakes are also well-constrained by the stress model. Our result indicates that the stress on a fault can vary up to a maximum of about 2 MPa during an earthquake cycle. The above calculations indicate that current moderate-, small-, and micro-size earthquakes, even shocks as small as magnitude 1.8, are related to coseismic stress changes in large to great historic events, even those that occurred 100 to 200 years ago. result shows that from 1981 until just before Landers earthquake The stress shadows from those major earthquakes have not been sequence of 1992 more than 85% of the examined 2497 right- completely restored in all areas by tectonic stress lateral strike-slip earthquakes of M > 1.8 occurred in stress- reaccumulation. The distributions and mechanisms of more enhanced zones. The ratio of encouraged to all small events reachs a high value of about 88% if the apparent coefficient of friction Ix is between 0.0 and 0.6. A significant number of the other small- and micro-size shocks occurred close to the stress boundary, which again is sensitive to the length of rupture and modern earthquakes might be combined with paleoseismological techniques to better constrain or to invert for the slip distribution of significant older earthquakes. The fact that so many of the earthquakes that we studied occurred in regions of calculated positive values of ACFF displacements in the 1812 Wrightwood earthquake. The highest indicates that many future moderate, large, and great earthquakes percentage of events occurred at locations where stress is about 1 will occur in stress-enhanced zones. In the future, detailed MPa above the 1812 baseline. While the size of the peak stress, 1 MPa, may be related to the timescale of almost 200 years we used for our calculations, it is comparable to many of the stress drops calculated from the spectra of seismic waveforms. Our calculations also show that most events occurred in areas of ACFF between 0.0 and 2.0 MPa, independent of magnitude. This studies focused on those regions where stress is above or close to 1 MPa might help to better constrain the locations of future earthquakes. It is also surprising that a simple half-space model is so successful in predicting regions of earthquake occurrence in a tensoffal sense. Clearly, viscoelastic effects do occur on timescales of years to centuries and need to be modeled in future work. 0 MPa, Minimum Relaxation -2 MPa, Maximum Relaxation Figure 6. Approximate range of permissible Cl for fault shown by modified Mohr diagram.

15 DENG AND SYKES: STRESS TRIGGERING IN SOUTHERN CALIFORNIA 24,425 Appendix: Data Used in Calculations of Stress Evolution We use the results of Doser [ 1994] and Silver and Masuda [ 1985] to model the slip distributions for the 1915, 1934, and 1980 A1. Slip Distribution of Moderate to Large Earthquakes earthquakes in northern Baja California. Events that occurred south of 32øN are not considered in this study. Deng and Sykes [1997] included rupture models for six A1.2. Parkfield earthquakes of 1901, 1922, 1934, and onshore earthquakes of M > 7 in their calculations of the stress Bakun and McEvilly [1979, 1984] suggested that the field. In addition to those events, we have now added coseismic Parkfield segment of the San Andreas fault has been ruptured slip distributions for 30 additional moderate- to large-size periodically by similar earthquakes in 1901, 1922, 1934, and earthquakes (Tables A1 and A2) in our new stress evolutionary Based on intensity maps and an empirical relationship model. Each of these 30 events is approximated by a shear between area of modified Mercalli intensity VI and seismic dislocation of a given size across one or more rectangular fault moment [Hanks et al., 1975], Bakun and McEvilly [1984] patches (large rupture zones are modeled by more than one planar obtained similar moments for each of these events. Near-field patch.) About 70% of the newly added slip models are for geodetic measurements indicate that the Parkfield earthquakes on earthquakes that occurred along the Parkfield segment of the San June 8, 1934, and June 28, 1966, released nearly the same amount Andreas fault, the San Jacinto fault zone, the Imperial fault, and of seismic moment [Segall and Du, 1993], although the actual major faults of northern Baja California. Rupture models for these events are listed in Table A2 and will be described below slip distribution for these two events is not as indistinguishable as Bakun and McEvilly [1984] proposed using surface waves. on a region-by-region basis. The detailed rupture models for the Segall and Du [1993] suggesthat the 1934 event stopped at a original six earthquakes of M > 7 are not repeated since they are fault stepover, whereas the 1966 earthquake ruptured an described by Deng and Sykes [1997]. In this paper, we use M w additional segment to the south of that stepover along the San for moment magnitude. If a moment magnitude is not available Andreas fault. We use two simple fault patches to match the for an earthquake, M, the local magnitude, is used. inferred rapture results for the 1966 Parkfield earthquake by AI.1. Seismicity in northern Baja California. Several Segall and Du [1993]. Only the northern patch of the two that earthquakes in Table A2 occurred south of the United Statesbroke in the 1966 earthquake is used for the 1934 event, but with Mexico border. Because the occurrence of some of the largest of a larger amount of slip. The slip models for the events of March those events also significantly modified the stress field in 3, 1901, and March 10, 1922, while they are arbitrarily assumed southern California, we include them in our new stress to be the same as that of the 1934 earthquake (Table A2), are calculations. Mueller and Rockwell [ 1995] mapped 4 m of lateral uncertain and very poorly constrained. and 3.5 m of normal dip slip that occurred in an earthquake along a 22 km segment of the Laguna Salada fault, which dips about A1.3. Earthquakes along the San Jacinto fault zone and the Imperial fault. The San Jacinto fault zone and the Imperial ø southwest. That fault is part of the southernmost Valley fault have been very active since the great Fort Tejon extension of the Elsinore fault system. They infer that that earthquake of January 9, The slip patterns of the more displacement occurred in the large to great earthquake of recent events are mainly constrained from strong-motion studies February 24, They state that the mapped rupture length of (Imperial Valley earthquake of October 15, 1979 [Archuleta, 22 km probably represents a minimum length for this widely felt 1984]), waveform inversions and aftershock distributions event. Mueller and Rockwell [1995] and others give the (Superstition Hills earthquake of November 24, 1987 [Magistrale magnitude of the 1892 event as 7.1 to 7.5. Based on the et al., 1989; Sipkin, 1989]), and mapping of surface raptures empirical relationship between scalar seismic moment and the (earthquake of November 24, 1987, on the Elmore Ranch fault areal distribution of modified Mercalli intensity VI of Hanks et al. [Sharp et al., 1989]). For some relatively older events, such as [1975], we obtain a magnitude M w 7.1 for the 1892 earthquake those of April 21, 1918; July 23, 1923; March 25, 1937; October from the very limited felt reports [Toppozada et al., 1981]. In 21, 1942; March 19, 1954; and April 9, 1968, the slip is deduced any case, this is likely the largest event whose coseismichanges from the rapture length, depth of small shocks in the region, and in stress are included in this study but not in the study by Deng the scalar seismic moment as calculated from waveforms and Sykes [1997]. We assume that the same amount and sense recorded at teleseismic distances [Doser, 1990b, 1992; Bent and of slip as mapped by Mueller and Rockwell [1995] extended over Helmberger, I991; Petersen al., 1991 ]. One older earthquake a 40 km long segment of the Laguna Salada fault. With an that occurred close to the towns of San Jacinto and Hemet on assumedepth of rupture of 14 km, this yields M w 7.3 for the 1892 event. Since the uncertainties in slip and rupture length associated with this event are large [Rockwell, 1989], future December 25, 1899, was assigned the same rapture geometry and displacement as that of the 1918 event. Since the reported effects of this event and the 1918 earthquake are very similar [Hanks et detailed investigation of the 1892 Laguna Salada earthquake al., 1975; Toppozada et al., 1981], both probably occurred along could improve our model of stresses in southern California. As stated earlier, whether its M w is 7.1 or 7.5 does influence the present value of ACFF for strike-slip faults of NW trend in the San Diego area. Doser [1994] collected teleseismic waveforms for the November 21, 1915, Volcano Lake; December 30, 1934, Laguna the San Jacinto fault zone, and we assume that in our stress calculations. Some workers, however, have placed the two events on two nearby but distinct fault segments that make up the San Jacinto zone. Felt reports for earthquakes that occurred on or near the San Jacinto fault zone were very limited before significant settlement Salada; and December 31, 1934, Colorado River Delta of that region starting about 1900 [Agnew, 1991]. No earthquakes and inverted the data for rupture length and seismic earthquakes that occurred along the San Jacinto fault zone before moment for each event. The more recent Victoria earthquake of June 9, 1980, along the Cerro Prieto fault was recorded by a relatively larger number of global seismic stations. Silver and Masuda [1985] computed its rupture length and seismic moment 1899 are used in our calculations of the cumulative stress changes, although several older earthquakes may well have occurred before Our limited knowledge of them does not allow us to include them in our calculations.

16 24,426 DENG AND SYKES: STRESS TRIGGERING IN SOUTHF_ RN CALIFORNIA I I I I I Iq I I I I IIIII I I I I I I I I I I I I IIIIIIIIIIIIIII IIIII1 IIIIIIII I I I I I Iø I I I I IIIIIIIIIIII IIIIIIIIIIII

17 DENG AND SYKES: STRESS TRIGGERING IN SOUTHERN CALIFORNIA 24,427 IIIII _ II!1111 IIIIII I I I I I I Iø I I I I I I I I I I I I I I I I I I I I I I I I I I I I I Illllllllllllllllllll Illl Illllllllllllll

18 24,428 DENG AND SYKES: STRESS TRIGGERING IN SOUTHERN CALIFORNIA Z '" z m ZZZZ < < < < < < < < < < < < < <m< < < < < < < I I I I I I I I I I I I IIIII1 IIIIIIIIII I I, I I I I I I I I I I I I I I I I I I I I I I I I I I I IIIIIIII1 IIIIIII I I I I I I I I I I I I I I I

19 DENG AND SYKES: STRESS TRIGGERING IN SOUTHERN CALIFORNIA 24,429 z z z zz zzz zz mmmmm<mmm m i i z <.

20 24,430 DENG AND SYKES: STRESS TRIGGERING IN SOUTH] RN CALIFORNIA

21 DENG AND SYKES: STRESS TRIGGERING IN SOUTHERN CALIFORNIA 24, : :03* M M : :45* M M : :45 M M :45' :16 M M : : : :27 M M M M :27* : : :28 M f 5.5 M M 5.3 M :28' : : :25 M M 5.7 M M :25* : :12' :12' M M M M o o Figure A1. Focal mechanism solutions tor moderate-sizearthquakes between 1940 and 1995 calculated using computer program FPFIT by Reasenberg and Oppenheimer [1985]. Station locations are plotted on lower hemispherequal-area projection. Dark dots and shaded quadrants represent compressional first motion, while open dots and white quadrants indicate dilatational first motion. Velocity model for southern California is from Hauksson and Jones [1989]. A star next to the origin time indicates that there are two or more possible focal mechanism solutions for that earthquake. A1.4 Slip models for other significant earthquakes. In addition to events in the above three regions where strike-slip earthquakes dominate, many other significant earthquakes with a variety of focal mechanisms occurred at widely distributed locations. Most of the larger events since 1932 have received individual study using a combination of seismic and geodetic data. We use simple fault patches (Table A2) to approximate the rupture in the following earthquakes: March 11, 1933, Long Beach; March 15, 1946, Walker Pass; April 10, 1947, Manix; December 4, 1948, Desert Hot Springs; February 9, 1971 San Fernando; May 2, 1983, Coalinga; August 4, 1985, Kettleman Hills; April 23, 1992, Joshua Tree; June 28, 1992, Big Bear, ana January 17, 1994 Northridge. We did not model the coseismic stress change in the large M 7.1 offshore earthquake of December 21, 1812, near Santa Barbara because its mechanism is uncertain. Likewise, we did

22 24,432 DENG AND SYKES: STRESS TRIGGERING IN SOUTHERN CALIFORNIA : : : :42* M M M M : :41' : :00 M M M M :00* : : :41 M M M M : :03' :47 M M M :10 M : :47' :45 M-5.4 M-5.4 M :06 M : : : :00' M M M M Figure A1. (continued) not model the stress drop in the M w 6.6 November 4, 1927, shock shorter time interval, 1933 to The new catalog is based on off the coast of westernmost southern California since its location a list of M > 5 earthquakes we obtained from the data center of is poorly known. Both of these offshore events were located on the periphery of our study area and their inclusion would probably only affect dip-slip faults in nearby onshore areas. the Southern California Earthquake Center (SCEC). We removed obvious aftershocks, which are close both in time and space to their mainshocks, from the catalog. Fortunately, special studies have been done for a large number of these earthquakes. In Table A2. Focal Mechanism Solutions of Moderate-Size Earthquakes A1 the mechanisms for them are taken from published references. For the events whose mechanisms are not available in the literature, we used the furst-motion data from both the SCEC Deng and Sykes [1997] cataloged all available source data center and from the Seismological Laboratory bulletin information for M > 6 earthquakes in southern California (Pasadena and auxiliary stations) and used the grid-search between 1812 and For this study we collected source program of Reasenberg and Oppenheimer [1985] to obtain focal parameters for 138 earthquakes down to magnitude 5 but for a mechanism solutions (see section A3). For some of the older

23 DENG AND SYKES' STRESS TRIGGERING IN SOIYI'HERN CALIFORNIA 24, : : : :24' M M M M : :39 M M :27 M :27 M Figure A1. (continued) earthquakes with less than five reported first motion observations Earthquake Center grant number USCPO scope D. SCEC (compression or dilatation) it was not possible to calculate a publication 364. Lamont-Doherty Earth Observatory comfibution reasonable mechanism. In this case, if the general tectonic setting in the neighborhood of the hypocenter is simple, we References inferred or assigned a solution based on well-determined source parameters of more recent events. We assigned a lower quality to Agnew, D.C., How complete is the pre-instrumental reco of 56 focal mechanism solutions either inferred from other earthquakes in southem Catifomia, in Enviromemal Perils San Diego earthquakes or calculated from a small number of first motion Region, edited by P. L. Abbott and W. J. Elliott, pp , San Diego Assoc. of Geol., San Diego, Calif., reports. We did not use 25 events that either were reported by an Anderson, J. G., The 4 September 1981 Santa Barbara Island, California, insufficient number of seismic stations or occurred in very earthquake: Interpretation of strong motion data, Bull. Seis.mol. & c. complicated tectonic settings. The new catalog should not be Am., 74, , confused with that of Deng and Sykes [1997], which spans a Anderson, J. G., and P. Bodin, Earthquake recurrence models aad historical seismicity in the Mexicali-!mperial valley, Bull. Seisrnol. longer time interval ( ) but only for events of M > 6. Soc. Am., 77, , Archuleta, R. J., A faulting model for the 1979 Imperial Valley A3. Focal Mechanism Solutions Based on First Motion Data earthquake, J. Geophys. Res., 89, , Bakun, W., and T. McEvilly, Earthquakes near Parkfield, California: Figure A1 shows lower hemispherequal-area projections of Comparing the 1934 and 1966 sequences, Science, 205, , the focal mechanism solutions obtained from first-motion data. Bakun, W. H., and T. V. McEvilly, Recurrence models and Parkfield, Velocity model for southern California is taken frdm Hauksson California, earthquakes, J. Geophys. Res., 89, , and Jones [1989]. The first-motion data are from SCSN. For the Bitth, M., and C. F. Richter, Mechanisms of the aftershocks of.the Kern pre-1959 events, we checked the preliminary first-motion reports County, Califomia, earthquake of 1952, Bull. Seismol. Soc. Am., 48, , posted in SCSN with the Seismological Laboratory bulletin. The computer program HYPOINVERSE [Klein, 1985] is combined Bent, A. L., and D. V. Helmberger, Source complexity of the October 1, 1987, Whittier Narrows eaxthquake, J. Geophys. Res., 94, , with FPFIT [Reasenberg and Oppenheimer, 1985] to compute the focal mechanism solutions. Multiple solutions are indicated by a Bent, A. L., and D. V. Helmberger, A re-exarn tion of historic star to the fight of origin time. For multiple solutions, we prefer earthquakes in the San Jacinto fault zone, California, Bull. Seismol. Soc. Am., 81, , the one which is more consistent with that of recent earthquakes. Boore, D. M., and D. J. Stiem'an, Source parameters of Pt. Muga, Our preferred focal mechanisms for these events are list in Table California earthquake of 21 February, 1973, Bull. Seismol. Sot:. Am., A1 and plotted on the colored plates. 66, , Brabb, E. E., Chittenden, California, ea.,- quake of Seg 14, 1963, Spec. Rep. Calif Div. Mines Geol., 91, 45-53, Acknowledgments. We thank D. Davis, C. Kisslinger, W. Menke, C. Scholz, B. Shaw, R. Simpson, and an anonymous reader for critical reviews of the manuscript. This study benefitted from our use of the catalog of focal mechanisms and locations for more than 10,000 Brace, W. F., An extension of the Griffith theory of fracta to rocks, J. Geophys. Res., 65, , Burdick, L. J., and G. R. M½llman, Inversion of the body WaVeS from the Borrego mountain earthquake to.the source mechanism, Bu!l. Seismol. earthquakes in southern California as compiled by Seeber and Armbruster Soc. Am., 66, , [1995]. We thank R. Simpson, who provided his dislocation program Chakrabarty, S. K., and C. F. Richter, The Walker Pass arat DLCI.1 using Okada's [1992] expressions. P. Reasenberg and D. Oppenheimer gave us copies of their computer programs FPFIT, structure of the southern Sierra Nevada, Bull. Seisrnol. Soc; Am., 39, , FPPLOT, and FPPAGE. The stress tensors were calculated using DIS3D Choy, G. L., Source parameters of the Coalinga, California earthquake of and checked with DLCI.1. The DIS3D code was written and improved May 2, 1983 inferred from broadband body waves, U.S. Geol. Surv. by S. Dunbar and Erikson [1986] using the expressions of G. Converse. We thank K. Hafner for giving us access to the SCSN data center. The GMT system [Wessel and Smith, 1991] was used to produce our figures. We thank J. Armbruster, J. Beavan, C. Scholz, L. Seeber, B. Shaw, X. Song, and M. Spiegelman for discussion and comments. This study was supported by NSF Cooperative Agreement EAR , USGS Cooperative Agreement A0899, and Southern California Open File Rep., 85-44, , Corbett, E. J., and C. E. Johnson, The Santa Barbara, Catdomia, earthquake of 13 August 1978, Bull. Seismol. Soc. Am., 72, , Corbett, E. J., and K. A. Piper, Santa Barbara Island, Caldornia earthquake, September 4, 1981 (abstract), Eos Trans, AGU, 62, 958, e arthquakes

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