5.4 Spatiotemporal variability of stress drop and the effects of
the 2004 M6 Earthquake
Figure 9 shows the stress drop spatial variations in 3 time periods: 1)
Mar 2001 – Sep 2004, 2) Sep 2004 – Sep 2005, and 3) Sep 2005 – Aug
2016, projected onto the San Andreas Fault. We smooth the distribution
by dividing the study area into 4 km (along strike) by 2 km (along
depth) grids, and obtain the median stress drop for grids with more than
5 earthquakes. Here we use the results for Strategy 6 (including
corrections for both spatial and temporal attenuation, and
depth-dependent velocity) and use earthquakes with M>1.1.
The relatively small number of earthquakes in time period 1 (before the
2004 M6 earthquake) limits the spatial resolution in that time period.
We also calculate a comparable figure using the results of Strategy 6,
without temporal variation (Figure S11) and observe very similar
patterns, suggesting that the results are not significantly affected by
uncertainties in the temporal corrections.
From Figure 9, we observe considerable small-scale heterogeneity, but
general stability and consistency over the entire time period. AS2007
also observed no significant change in the spatial distribution before
and after the 2004 M6 earthquake. We infer this to indicate that the
spatial variability in fault conditions is significantly larger than any
temporal effects caused by the coseismic or postseismic slip. Similar
spatial stability was reported by Ruhl et al. (2017) for the well
recorded Mogul earthquake sequence in Nevada, as well as Uchide et al.
(2014) for M3.0-4.5 earthquakes in the 2011 Tohoku earthquake area,
suggesting structural or material heterogeneity is the dominant factor
of stress drop variability. This is also consistent with the constant
rupture directivity of sequences at Parkfield analyzed by Abercrombie et
al. (2020), but contrasts with similar sized spatial and temporal
variation associated a M6 earthquake on the Gofar transform fault,
reported by Moyer et al. (2018).
Also in Figure 9, we observe no clear difference between the stress drop
distribution in the locked and creeping parts of the fault. Inversions
by Murray & Langbein (2006) indicate that above about 15 km depth, NW
of the 1966 hypocenter, the fault is essentially creeping throughout
this time period, and to the SE it is primarily locked, slipping
seismically and post-seismically in 2004 to 2005. This division is not
visible in Figure 9, suggesting that the stress drops of small
earthquakes are not primarily affected by the nature of slip on the
surrounding fault at large scale. These results contrast with the
reported along-strike variation in stress drop of earthquakes on the
Gofar oceanic transform associated with different levels of inferred
seismic and aseismic slip (Moyer et al., 2018). With only two examples,
we cannot draw any reliable conclusions as to why the faults may behave
(or only appear to behave) differently.
We compare our observations of spatially varying stress drop to the
various finite-fault inversions of the 2004 M6 earthquake (Dreger et al.
2005, Custódio et al., 2005) , but again see no clear correlation. This
is partly because of variability in the different inversions which do
not have resolution on the scale of the spatial heterogeneity we
observe, but we see strong variation in stress drop even in regions with
high slip in most models (e.g., between the 1966 hypocenter and SAFOD).
Combining GPS data and seismicity, Jiang et al. (2021) observed complex
multistage slip patterns, suggesting afterslip rate and local structure
controls fine-scale seismicity behaviors.
At smaller scale, we observe considerable variability, that shows some
consistency and some variation from the earlier results of AS2007. Their
study included more earthquakes before the 2004 M6, but also is likely
to have larger uncertainties because of the lower quality of their data.
The high level of small-scale heterogeneity is consistent with the
observations of the behavior of repeating sequences by Lengline and
Marsan (2009). It does not show any clear dependence on other known
characteristics of the fault zone. For example, we observe regions of
high and low stress drop around the hypocenters of both the 1966 and the
2004 earthquakes.
The temporal variations we observe in both attenuation and stress drop
are relatively small compared to the spatial variations. Figure S8 shows
the differences in attenuation in different depth and time periods.
Figure 10 compares our observed temporal variation in stress drop, in
the different time periods, to that reported by AS2007. Because of the
shorter time span of AS2007 after the 2004 earthquake, we only compare
the temporal changes between period 2 and period 1. For each grid used
in Figure 9, we calculate the difference in average stress drop values
between successive time periods (i.e., Period 2 - Period 1, and Period 3
- Period 2). Again, we use all earthquakes M>1.1; we obtain
consistent results with a magnitude cut off of 1.1 or larger (Figure
S10). Like AS2007, we observe regions of increase and decrease in stress
drop following the 2004 M6 earthquake. The region of high slip in the M6
earthquake (according to Dreger et al., 2005) encompasses stable patches
of high and low stress drop.
The increase in absolute values of attenuation at shallow depths
(< 4 km), obtained here following the 2004 M6 earthquake, are
almost a factor of ten smaller than those calculated from repeating
earthquakes in the same depth range by Kelly et al. (2013). This may
represent a combination of temporal averaging, and smoothing of
small-scale heterogeneous behavior in our larger-scale analysis, or
result from the uncertainties in either or both studies. Unlike Kelly et
al. (2013), we observe larger temporal variation in attenuation at
greater depths (5-8 km). This also contrasts with the conclusion that
the larger velocity changes (~0.25%) are limited to the
upper 1-2 km (Sheng et al., 2021; Wu et al., 2016). We observe a
decrease in attenuation from 2005 to 2016, that is about 1/2 to 2/3
times that of the increase following the 2004 M6 earthquake. This
asymmetry may indicate incomplete recovery, or simply reflect the
uncertainties. Malagnini et al. (2019) investigated temporal and spatial
changes in attenuation at Parkfield using coda waves, and reported
variation on a range of time scales. They found that the 2004 M6
earthquake affected the attenuation variation on the NE and SW sides of
the San Andreas Fault very differently. Our analysis averages the
behavior of both sides of the fault.
Clearly, fully separating temporal variation in stress drop and
attenuation remains a challenge, and we take this into account as we
attempt to interpret out results. To discuss the complex patterns, we
observe and their resolution, we focus on four regions indicated on
Figures 9 and 10. Ideally, we would use smaller regions, guided by the
spatial variation, but they contain insufficient earthquakes to make
reliable conclusions. We therefore choose regions thought to represent
different conditions and behaviors, and explore the stress drop
variations within.
Region I: SAFOD Region. We start by discussing the
shallow region surrounding SAFOD as it includes repeating sequences of
well-studied earthquakes that we can use to assist in assessing the
reliability of our results. It is a region of fairly average stress drop
values in our analysis (Figure 9). Abercrombie (2014) used an
individual-event based spectral-ratio approach to obtain corner
frequencies, and for earthquakes in the three sequences of earthquakes
targeted by SAFOD. For the largest magnitude sequence (T1,
M~2.1), the simple circular source model was a good
approximation, and Abercrombie (2014) found good agreement with the
results of AS2007 for the same events; both studies found that the
immediately after the 2004 M6 earthquake had significantly lower stress
drops than the other events. Time domain source modeling, also using
empirical Green’s functions, by Dreger et al. (2005), and Kim et al.
(2016) also revealed a similar relative temporal behavior for the same
earthquake sequence. Sequence T2 involved complex sources and was not
well modeled by Abercrombie (2014). Sequence T3 is too small to be
resolved in the study of AS2007, but Abercrombie (2014) observed similar
decrease in stress drop for events in this sequence immediately
following the 2004 M6 event, albeit with larger uncertainties. In Figure
11, we compare our results to those of Abercrombie (2014) for the same
earthquakes. We see better agreement for the lower frequency
measurements, but at higher corner frequencies the results of
Abercrombie (2014) are systematically higher. This could be due to
Abercrombie (2014) using a higher upper frequency limit for these
well-recorded earthquakes (~90 Hz) or else may be method
dependent (see Shearer et al., 2019; Abercrombie, 2021). Pennington et
al. (2021) performed a comprehensive comparison of methods to estimate
stress drop for earthquakes in the Prague, OK, 2011 sequence, and found
that although the absolute values varied considerably, there was good
agreement between the relatively low and high stress drop populations
among the different methods and independent studies. For the
better-quality results of Abercrombie (2014) in Sequences T1 and T3, we
observe that both studies have relatively low corner frequencies for the
events immediately after the 2004 M6, compared to the other events. This
comparison gives us some confidence that we are observing real temporal
variation. It is still possible that very localized, short term
variation in attenuation is causing similar apparent variation in source
parameters in all the studies. Certainly, the earthquake seismograms
recorded shortly after the M6 event have relatively low high-frequency
energy. The fact that in our work, and that of Abercrombie (2014) and
Abercrombie et al. (2020), some temporal stress drop variation remains
regardless of the various attenuation corrections tried, suggests that
at least some of the variation in source parameters is real.
Figure 10 shows on average a small increase in stress drop in the region
around SAFOD, in the year after the M6 earthquake, followed by a small
decrease. Figure 10, B1 shows the high level of variability and the
changes within the one-year period we average for our Time 2. The
variability implies that to identify more significant variations would
require smaller scale spatial and temporal resolution than is available.
Region II: Aseismic Creep Region. This region is of
interest as it is in the part of the fault thought to be almost entirely
slipping aseismically (e.g., Murray & Langbein, 2006). In our analysis,
it is characterized by relatively high values, but they are no higher
than those around the 2004 hypocenter, and the creeping region nearer to
SAFOD has lower values, negating a simple relation between high stress
drop and creep (Figure 9). AS2007 observed an apparent increase in
stress drop in this region, following the M6 but did not have sufficient
earthquakes to resolve it. The region is just outside the HRSN network,
but we observe a decrease in stress drop following the M6, and an
increase afterwards. Again, these are very small trends amidst much
variability (Figure 10, B2).
Region III: 1966 Hypocentral Region . This region, also
known as the Middle Mountain asperity, also shows variable behavior with
patches of relatively high and low stress drop. Unfortunately, the lack
of events in these individual smaller regions in all time periods means
that we cannot resolve time variation on this scale. The region is
dominated by a decrease in stress drop (Figure 10, B3) immediately
following the 2004 M6 earthquake, and then returns to normal within the
year. The immediate decrease of stress drop is consistent with
observations from other large earthquakes, for example, the M5.7 Prague
earthquake (Yenier et al., 2017). In fact, some high stress drop events
in the region near the end of time period 2 increase the average and
lead to an apparent decrease in stress drop in the following time period
(compare Figure 10, B3 with Figures 10, A2 and A3). In this region,
Abercrombie et al. (2020) and McLaskey et al. (2012) observed one
relatively well-recorded sequence to exhibit a possible decrease then
gradual increase in stress drop. South of the 1966 hypocenter in this
region, Jiang et al. (2021) observed significant coseismic slip and
afterslip about 8 hours following the 2004 earthquake, which coincide
with an area of stress drop increase (Figure 10, A2), suggesting
possible influence of fault slip on stress drop changes.
Region IV: 2004 Hypocentral Region . Like the hypocentral
region of the 1966 earthquake, this region shows some strong spatial
variation and less clear temporal variation, with opposite changes to
AS2007 (Figures 10, A1 and A2). This is largely because of the lack of
events prior to the M6 earthquake. Figures 10, A2, A3 and B4 suggest
that the region is dominated by a decrease in stress drop immediately
following the M6, and then gradual recovery. This region experienced
complex slip history with coseismic slip and afterslip featuring slip
reversals and slip pulses (area R1 in Jiang et al., 2021). These complex
stress changes complicate the interpretation of stress drop variations
in this region.
Overall, in regions I, which is located at the shallow portion of
cosesimic slip zone, we observe less coherent temporal changes in
relation with the 2004 M6 earthquakes, however, individual repeating
sequences exhibit robust stress drop decrease after the 2004 event. In
region II, where no significant coseismic and post-seismic slip has been
reported, we observe small trend with large variability. In region III,
where both significant seismic and postseismic slip are observed, clear
temporal variation of stress drop is observed. Temporal variation of
region IV is less resolved due to limited number of earthquakes prior to
the 2004 earthquake. Observations in regions I and III suggest that
fault slip influence spatiotemporal distributions of stress drop.
However, amplitudes of temporal stress drop changes are relatively small
compared to background stress drop spatial distributions, indicating
that local fault structure is likely the major cause of spatial
heterogeneity.