We study the spatial clustering of shallow aftershock hypocenters with respect to focal mechanisms of mainshocks. Several earthquake catalogs are used: the Harvard CMT global catalog, the PDE earthquake list, the CIT/USGS catalog of earthquakes in Southern California, and a catalog of focal mechanisms for all earthquakes in Southern California with magnitude larger than 6, since 1850. In these calculations we need to account for possible systematic bias in hypocenter distribution due to the geometry of seismogenic zones, especially the geometry of subduction zones. We also select only the strike-slip earthquakes from the catalogs to investigate the aftershock clustering in circumstances more favorable for direct observation. Fig. 2 displays all of the 28 strike-slip earthquakes from the Ellsworth catalog and M >= 3.5 events from the CIT/USGS catalog during 1932-1997. We consider any earthquake which is rotated (in 3-D) -- no more than 20 from a pure strike-slip focal mechanism -- as a strike-slip event. We compare the spatial distribution of hypocenters before each strong earthquake (Mw >= 5.8 or Mw >= 6.0) with the distribution during the first 250 days after the earthquake and the distribution for the time interval extending beyond 250 days. If the friction coefficient in the Coulomb criterion is non-zero, one should expect that after a strong earthquake, aftershocks and other earthquakes would concentrate in the direction of the P-axis (dilatational quadrant) rather than in the direction of the T-axis (compression quadrant). Such a correlation for selected earthquake sequences has been pointed out previously for individual earthquakes; however, it has not been established whether such correlation is a general feature of earthquake occurrence. We study spatial earthquake distributions for several choices of focal sphere partition, cutoff magnitude, focal mechanisms of large events, time periods, distance from a mainshock, etc. Although some earthquake distributions are in agreement with a non-zero friction coefficient, other similar distributions produce an opposite pattern, suggesting that the concentration of events along the P- and T-axes is due to random effects. Thus, our results indicate that aftershock sequences do not exhibit a systematic migration of hypocenters: the difference between pre-earthquake and post-earthquake distributions is either positive or negative in the direction of both axes. This result implies that the friction coefficient in the Coulomb law is close to zero.
We compute the incremental stress tensor in the upper crust of southern California as a function of time since 1850, and compare observed seismicity with the estimated stress increment at the time of each earthquake. We model crustal deformation using updated geodetic, especially GPS data and geologically determined fault slip rates. We subdivide the crust into elastic blocks, delineated by faults. Between earthquakes, a fault moves freely below a locking depth with a rate determined by the relative block motion. We compute normal and shear stress on nodal planes for each earthquake in the catalog. We compare the locations of earthquakes with the resolved shear, resolved compression, and resolved Coulomb stress before the earthquakes. We consider the stress increments from previous earthquakes, and the aseismic tectonic stress, both separately and in combination.
We compiled a catalog of southern California 256 earthquakes with magnitudes greater than 5. We use the catalog's time window 1850-1996, the space window 32.0-36.0N, 114.0-122.0W. The beginning date depends on magnitude as follows:
| Mag | Year |
| 5 | 1925 |
| 5.25 | 1910 |
| 5.5 | 1910 |
| 5.75 | 1910 |
| 6 | 1890 |
| 6.25 | 1890 |
| 6.5 | 1880 |
| 6.75 | 1870 |
| 7 | 1850 |
| 7.25 | 1850 |
| 7.5 | 1850 |
| 7.75 | 1850 |
| 8 | 1850 |
Many of the source mechanisms for 5 <= M <= 6 were arbitrarily set to strike 320, dip 90, and rake 180 as a default.
We also use the Ellsworth (1990) historical/instrumental earthquake catalog (M >= 6) which we supplied with focal mechanisms. We use the catalog's time window 1850-1996, the space window 32.0-37.0N, 114.0-122.0W. Several other catalogs of fault-plane solutions are used in the study: Harris et al. (Nature, 1995) list of southern California earthquakes 1968-1993 (M >= 5), L. Jones' (1993, personal communication) catalog of earthquakes 1986-1993 (M >= 5), and the list of 1990-1995 moment-tensor inversions of Terrascope records by Thio and Kanamori (BSSA, 1995; 1996; M >= 3). The catalogs have several tens or a few hundreds of events.
The locations and mechanisms of earthquakes are best correlated with the aseismic shear stress, which grows at a constant rate in our model. Inclusion of the cumulative coseismic effects from past earthquakes does not significantly improve the correlation. The variations in normal stress, either from the seismic or aseismic sources, do not correlate well with earthquake locations and mechanisms. In general, correlations between normal stress and earthquakes often change sign if there is a slight modification of the initial parameters of our computations, for example the starting date of the catalog, exclusion of earthquakes with closely spaced epicenters, use of point vs distributed sources. The results are unstable because there are so few earthquakes in the catalog.
We investigated the influence of the catalog selection, catalog time and space limits, temporal delay between earthquakes, and of the tectonic stress on the correlation values. We also tried to exclude from the calculations the pairs of earthquakes within a close distance in space and the earthquakes with a stress value below a threshold of 0.01 or 0.1 bar (Harris et al., Nature, 1995). The correlation between the incremental stress and seismic moment is low and it strongly depends on the choice of the catalog and on the calculations parameters. In general, the selection of earthquake pairs with a temporal separation less than 500 days increases the correlation level, whereas the influence of the epicentral distance and stress level is not obvious.
We analyzed the influence of the Ft. Tejon 1857 earthquake on subsequent activity (Harris and Simpson, GRL, 1996). Our calculations are slightly different than those by Harris and Simpson (1996): we use a larger spatial window (32.0-37.0N, 114.0-122.0W) and the Ellsworth (1990) catalog. In Figure 1a,b we display two patterns of earthquake focal mechanisms colored according to the correlation between the stress caused by the 1857 earthquake and the seismic moment. The results suggest that there is no obvious `stress shadow' in the early years after the 1857 earthquake. The correlation values do not exhibit a clear pattern. We repeated the computations using different versions of the catalog, and adding the tectonic stress to the static stress due to the 1857 event. Again no obvious pattern emerges.
Publications and reports resulting from resulting from this project:
Jackson, D. D., Y. Y. Kagan, X. B. Ge, Z. K. Shen, and D. Potter, 1997. Stress Propagation and Earthquake Probabilities, paper presented at the SCEC workshop "Earthquake Stress Triggers, Stress Shadows, and their Impact on Seismic Hazard", on March 21-22, 1997 at the USGS in Menlo Park, CA.
Kagan, Y. Y., and D. D. Jackson, 1997. Spatial aftershock distribution, J. Geophys. Res., submitted.
Kagan, Y. Y., and D. D. Jackson, 1997. Stress in southern California, 1850-1996, manuscript, in preparation.
Kagan, Y. Y., and D. D. Jackson, 1997. Earthquake slip distribution, manuscript, in preparation.
List of captions
Fig. 1. Maximum horizontal shear stress rates in southern California (in 10^10 Pa/yr, derived from geodetic velocity map solution v2.0. Gray squares and thick gray curve represent epicenters and surface rupture traces of past earthquakes over magnitude 6. The degree of grayness reflects the time elapsed since that earthquake.
Fig. 2. Focal mechanisms of strike-slip earthquakes in southern California from Ellsworth [1990] catalog and epicenters of M >= 3.5 events during 1932-1997. Symbol size is proportional to earthquake magnitude. Stripes in `beach-balls' are concentrated toward the earthquake fault plane projection to indicate the presumed fault plane.
