No Apparent Accelerating Moment Release in Areas of High Stress

Aurélie Guilhem and Roland Bürgmann


The search for spatio-temporal interactions between earthquakes is fundamental in order to understand the stress evolution in the lithosphere as well as the earthquake mechanism. Many studies have been conducted to analyze the evolution of seismicity in relation to the stress field, with the idea that continuous plate motion needs to be accommodated on faults by the occurrence of earthquakes releasing the accumulated stress. This earthquake cycle theory, first developed by Reid in 1910, introduced the relation between elastic stress accumulated along the fault zone and occurrence of earthquakes. The Accelerating Moment Release (AMR) idea was developed by Bowman et al. (1998) and is based on the hypothesis that prior to a large earthquake the stress field in the vicinity of the next rupture increases in such a way that one can observe an acceleration of the background seismicity following a power-law function. The change in the seismicity rate produces a regional increase in the cumulative Benioff strain, which is a measure of the cumulative seismic energy of the seismic events considered prior to a mainshock. To quantify the AMR, one examines the ratio, called c-value, between the root-mean-square of a power-law time-to-failure function versus a linear fit to the cumulative energy of the events. A strong case for AMR would be for c less than 0.5. Previous works (Guilhem et al., 2007; Hardebeck et al., 2008) showed that AMR, observed for all M6.5+ earthquakes in Southern California of recent times (Bowman et al., 1998; Bowman and King, 2001), is very sensitive to three free parameters: magnitude range of the pre-seismicity, area surrounding the events (considering a circular search) and the time period prior to a large earthquake. Because of the large dependence on the choice of the free parameters, doubts about the validity of the analysis have emerged (Hardebeck et al., 2008).

AMR search in Parkfield region

Mignan et al. (2007) suggested that if AMR exists, one should in theory observe it over an entire earthquake cycle. The Parkfield region is an excellent example for studying AMR where M6.0 earthquakes, since 1857, repeat over a relatively short earthquake cycle (22 years on average). We studied the AMR during the last two earthquake cycles, from 1935 to 1966 and 1967 to 2004, using the ANSS seismicity catalog (2.0 $\leq$ M $\leq$ 7.0 in a 5-by-5 degree region centered on the nucleation zone). Computation of the AMR in the area was performed using various magnitude and distance ranges. The lowest c-values noticed during the first earthquake cycle (about 32 years, from 1934 to 1966) was 0.65 for a search area radius of 85 km, indicating that no AMR was objectively observed during the time period. The second earthquake cycle (1967 to 2004) did not show any case of AMR; the c-value is equal to  1 over all radii considered (0 to 200 km) (Figure 2.8). The AMR results appeared to be very sensitive to the occurrences of the 1983 M6.5 Coalinga and 2003 M6.5 San Simeon earthquakes and in particular to their aftershock sequences. Declustering the earthquake catalog to remove most of the aftershocks was performed, but still no change was detected in the AMR.

AMR appears to be biased by the occurrence of large earthquakes during the studied period (Figure 2.8). A large event in the beginning of a chosen observation period tends to dominate the analysis and to increase the c-value, compared to a mainshock at the end of the time period that would significantly decrease the c-value and support the case for AMR (small c-value).

Figure 2.8: AMR in the Parkfield region in a 60-km radius region. The c-value for the 1967-2004 period does not show any AMR, with a c-value equal to 1. The red dashed line shows the power-law function, and the blue line shows the best-fit linear trend of the cumulative Benioff strain. The occurrences of the 1983 M6.5 Coalinga and 2003 M6.5 San Simeon earthquakes, and their aftershock sequences, dominate the signal.
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AMR and Stress

In order to complete the analysis of AMR in Southern California, we evaluated AMR in apparent high stress regions. Maps of stress changes were computed by Andrew Freed at Purdue University considering the coseismic, postseismic and interseismic stress changes of all M7+ earthquakes in Southern California for the last 200 years (Freed et al., 2007). We tested for AMR in the areas of high stress (Figure 2.9), using the hypothesis that the high stress regions represent the places of eventual future events, compared to the regions of low stress, and where we would expect to detect significant AMR if the AMR idea is correct. We studied the AMR for the two high stress regions presented in Figure 2.9 over various time ranges, starting in 1950 to 2008. The test was performed for an eventual mainshock in the region on June 1st, 2008, about 6 months after the end of the analyzed earthquake catalog. We considered all seismic events occurring in the high stress regions ($\Delta$$\sigma$ $\geq$ 10 bars), excluding events in lower stress areas, and we computed the AMR in such way that we considered the entire high stress regions. No AMR was detected in those two regions (c-values remained between 0.8 and 1.0). We performed an AMR search in the area of low stress resulting from the occurrence of the great Fort Tejon earthquake, and we did not find evidence of AMR. No difference is observed in the AMR between high and low stress areas. Also, we performed an AMR study over the entire region, considering all events in regions where the stress exceeds 10 bars as well as all events with no condition on the stress field, and again no significant variation was observed.

Figure 2.9: AMR study in the northern high stress region. The circles materialize the distance every 50 km from a possible epicenter (black cross). The red dots are the M2.5+ earthquakes located in a high stress region (stress larger than 10 bars), and the black dots show other M2.5+ events in the study region. The background colors show the stress field computed by Andrew Freed for 2005.
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Recent AMR studies (Guilhem et al., 2007; Hardebeck et al., 2008) emphasize the high sensitivity to the choice of free parameters considered in the AMR idea, which becomes a data-fitting exercise with no real power in earthquake forecasting. No evidence of AMR was noticed in the Parkfield region where periodic M6.0 earthquakes occur. AMR, which should be related to high stress regions, is not observed in Southern California, even considering various time, magnitude and distance ranges. Finally we noticed the significant impact of the timing of large events during the pre-mainshock period on the AMR calculations. A large earthquake occurring in the early time period will cancel an eventual AMR case by adding a significant cumulative Benioff strain in a very short time. The contrary is observed when the large shock occurs at the end of the time analysis, forcing to an AMR case.


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Bowman, D.D. , and G.C.P. King (2001), Accelerating seismicity and stress accumulation before large earthquakes, Geophys. Res. Lett., 28, 4039-4042.

Freed, A.M., S.T. Ali, and R. Bürgmann (2007), Evolution of stress in Southern California for the past 200 years from coseismic, postseismic and interseismic stress changes, Geophys. Journ. Intern., 169, doi: 10.1111/j.1365-1246X.2007.03391.x.

Guilhem, A., R. Bürgmann, A.M. Freed, and T. Ali (2007), Accelerating Moment Release in Areas of High Stress? Preliminary Results, 2006-2007 Berkeley Seismological Laboratory Annual Reports.

Hardebeck, J.L., K.R. Felzer, and A.J. Michael (2008), Improved Tests Reveal that the Accelerating Moment Release Hypothesis is Statistically Insignificant,Journ. of Geophys. Res., in press.

Mignan, A., D.D. Bowman, and G.C.P. King (2007), A Mathematical Formulation of Accelerating Moment Release Based on the Stress Accumulation Model, Journ. of Geophys. Res., 111, B11304.

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