Earthquake Relocation and Fault Mechanics

Earthquake catalogs are always dominated by the smallest recorded events, e.g. magnitude 1–2 earthquakes for well-instrumented regions such as can be found in California.  Routine catalog location errors for such events are of order 1 km, much larger than some interesting fault-zone structures and the earthquakes themselves (several tens of meters).  This severely limits their usefulness in studies of earthquake mechanics.  However, earthquakes that have similar locations and focal mechanisms generate seismograms at a given station that appear similar (Figure 1).   By cross-correlating these seismograms one can measure extremely accurate relative arrival times (in the best cases with errors as small as 1/40th of the sampling rate), and from these one can obtain relative locations that are factor of 10 to more than 100 times better than in the catalog (Figure 2).  These improved locations have allowed us to image fault-zone structures that are invisible in the original catalogs (Figure 3).

Figure 1

Figure  1.  Sixteen earthquakes with dimensions of tens  of meters, spanning  several years and hundreds of meters along the San Andreas  fault in  central California,  recorded at the station JCB.

Figure 2

Figure 2.  Several hundred earthquakes spanning over 1 km of the Calaveras fault in central California.  After correcting for time-dependent station delays, the 1-km-long  shallower streak (as viewed down its plunge) consists of earthquakes whose centroids span only a few tens of meters vertically and less than 10 m perpendicular to strike.

Figure 3

Figure 3.  The upper panel below shows, in black, the Northern California Seismic Network (NCSN) catalog locations of 2500 microearthquakes in a vertical cross-section along the San Andreas fault near San Juan Bautista.  Circles give an indication of size, assuming circular ruptures with a 3 MPa stress drop.  The lower panel shows the same earthquakes following our relocation.  Note the near-horizontal "streaks" of microearthquakes that in the NCSN catalog are hidden by location error.  The red circles in the upper panel show earthquakes that were not relocated because of poor signal-to-noise ratio (they were too small) or clipping (they were too large).


The origin of the seismically-defined lineations in Figures 2 and 3 is currently a subject of great interest.  Because we see similar slip-parallel lineations on normal and thrust faults in Kilauea Volcano (basically a pile of basaltic rubble), we conclude that they result from a structural organization of the fault surface, and not (for example) an inherited sedimentary layering.  We first observed such streaks in the East Rift Zone of Kilauea Volcano, Hawaii (Figure 4), where from geodetic data we inferred that they represented the edge of a locked, shallow region that was being slowly eroded by steady creep at greater depth (Figure 5).  This scenario is consistent with the vertical extent of the lineation (~100 m) and the increase in earthquake rate and moment rate since the previous dike intrusion in 1982.  A similar explanation has been proposed for the streaks in central California, but the evidence there is more equivocal.

Figure 4 and 5

Figure 4 (left).  (a) and (b), Map view and vertical cross-section (looking NE) of earthquakes occurring in 1991 in the Upper East Rift Zone of Kilauea.  (c) and (d), The same earthquakes following relocation by waveform cross-correlation.  The roughly 3 km depth is consistent with geodetic estimates of the transition from a locked fault at shallow depth to steady creep of the deep rift zone at greater depth.

Figure 5 (right).  (a), Diagram of the numerical model of the Upper East Rift, showing the creeping deeper rift zone and the shallow locked strike-slip fault.  (b) Active height and cumulative moment along the shallow fault, computed assuming the stress field was “reset” by the last dike intrusion in 1982, as a function of motion of the deep rift.  Approximately 2.5 m of strike-slip motion accumulated between 1982 and 1991.  (c) Number and cumulative moment of earthquakes through the beginning of 1992, when a new intrusion again reduced the seismicity rate.  Compare to panel (b).

Earthquake Mechanics From Precise Relative Locations

Because the relative location errors between the nearest events in our relocated catalogs (meters) are now much smaller than the rupture dimensions (tens of meters), these catalogs contain a wealth of information concerning earthquake interaction.  One of our most surprising observations is that within about 1 day of a microearthquake on the central San Andreas fault, aftershocks are more likely to occur immediately to the NW than to the SE by a factor of nearly 3:1 (Figure 6).  On a vertical strike-slip fault in a homogeneous body there is no mechanism for producing such asymmetry.  However, the San Andreas fault in this region juxtaposes two very different rock types, with higher seismic wavespeeds  on the Pacific plate, and this breaks the symmetry.  We have used analytical and numerical models of elastodynamic ruptures to explain the aftershock asymmetry in terms of how the material contrast across the fault affects the dynamics of the mainshock (Figure 7).  Understanding earthquake behavior on a fault separating different rock types has implications for seismic hazards because such material contrasts can also give rise to rupture directivity, which has a significant impact on ground shaking.

Figure 6

Figure 6.  Left panel:  The stacked aftershock sequences of 5500 microearthquakes along 60 km of the San Andreas fault near San Juan Bautista, occurring from 1984-1998.  Each mainshock is placed at the origin, and the relative locations of all events within the next 10 hours are projected onto the fault surface after normalizing distances by the estimated mainshock size (assuming circular ruptures with a stress drop of 10 MPa).  Right panel:  A greyscale image of aftershock density on the left, emphasizing the elongate “hole” left by the mainshock and the much higher aftershock density to the NW.  The ellipse, symmetric about the origin, is drawn to guide the eye and represents a stress drop of 4.5 MPa. The asymmetry disappears more than a few days after the mainshock and farther away than about 2 mainshock radii.

Figure 7

Figure 7.  Numerical simulation of an elastodynamic rupture on a bimaterial interface.  In the context of the San Andreas fault, right is to the SE and left is to the NW.  The bottom panel shows a space-time plot of the rupture with the outermost lines indicating the rupture front and the greyscale image indicating slip speed.  Stress barriers are placed at +/- 160 m.  When the SE-propagating front encounters the barrier, the tensile stress pulse behind the front (produced by the material contrast) continues down the fault and carries a dying slip pulse with it (inset).  This slip pulse smooths the displacement gradient and reduces the stress perturbation at the SE margin of the mainshock relative to that at the NW margin (blue curve, top panel).  In addition, because the tensile stress pulse that carried the slip pulse far into the barrier is a transient (dynamic) phenomenon, once slip ceases the SE margin of the mainshock is left far below the failure threshold, unlike the NW margin (red curve, top panel).  Both mechanisms could contribute to the observed aftershock asymmetry.