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.