Model with deeper rupture (M2)
5.4 Inferring the geodetic locking depths on major faults
located near the top of the LC transition, whileDgeoddepends on the depth distribution of fault slip rates. Dlock either stays near VW/VS boundary when the earthquake is confined in SZ, or becomes shallower after deeper penetration of coseismic slip into the VS region, whileDgeodtends to deepen in all four models, as the slip deficit region expands in the late interseismic period. Therefore, Dlock and Dgeod reflect different aspects of fault behavior and could diverge, especially in the presence of deeper penetration of coseismic slip and significant afterslip.
Let us compare the results for cases with the same deeperDruptas M4 but three (a−b) values in the VS regions, 0.01, 0.02 and 0.04, respectively (Fig. 5.9D-F). For the case with the smallest (a−b) (Fig. 5.9F), rapid postseismic fault slip reaches a broader region surrounding the SZ, and decays in amplitude quickly afterwards, leading to a larger slip deficit zone even in the earlier interseismic period (50 yrs after the earthquake), and differences in the inferred Dgeod and its time evolution. This further demonstrates that the slip deficit zone is predominantly affected by postseismic slip in our models.
We note that the empirical estimate D0.5C tracks Dgeod closely, in particular for the case with a broader LC transition (Fig. 5.9D-F). As we also show in Fig. 5.6, the equivalent Dgeod (black dashed lines) is located close to the 0.5 contour lines of ISC below the SZ.
Therefore, the Dgeod could be empirically interpreted as the depth where fault slip rate reaches approximately half the plate loading rate.
Cases with SZ-confined rupture
Cases with deeper rupture
Dgeod DDlockrupt D0.5C
(A) M1 (B) M2 (C) M3
(D) lower (a-b)VS (E) M4 (F) lower (a-b)VS
Depth below the VW region (km)Depth below the VW region (km)
Figure 5.9: Time dependence of Dlock, Dgeod and D0.5C in the interseismic period. Dlock, the true locking depth, defined at the depth where fault slip rate reaches 0.1Vmax, is shown in red for several time windows in the interseismic period. Dgeod, inferred from surface geodetic measurements, is shown in blue with error bars for the marginal uncertainties.
D0.5C represent the depth at which ISC equals 0.5, i.e., V = 0.5Vpl. Drupt is indicated by the black solid line and the VW/VS boundary as the black dashed line. All depths are considered as the distance below the VW region. The three models on the top row have earthquake ruptures confined in the SZ, while the three on the bottom have deeper earthquake ruptures and different VS properties at deeper fault extensions.
uncertainty of and correlation between Dgeod and Vcr. Among these factors, a major and common source of uncertainty comes from the elastic structure. In Fig. 5.10, we explore whether the inversion based on the elastic dislocation model would bias the estimate of Dgeod when a more realistic LC transition and a typical layered structure (e.g., Kanamori and Hadley, 1975, a 1D reference model for Southern California) are present. We consider two slip rate profiles along depth, one from the more realistic LC transition (LCT) in our models and the other from the dislocation model (DSL), with the latter chosen so that both have nearly identical surface expressions. We find that the dislocation-model-based inver- sions of the synthetic surface profiles generated from the DSL and LCT in layered structure significantly underestimate Dlock by about 5 km. This is because more compliant shallow layer tend to produce more localized surface deformation that would be mapped into shal- lower locking depth in a homogeneous half-space. Geodetic studies on the San Andreas and San Jacinto faults indeed find that elastic heterogeneity, as well as fault geometry, has a large effect on the inference of fault locking depth and slip rate (Lindsey and Fialko, 2013;
Lindsey et al., 2013). However, the difference between results of DSL and LCT is smaller (about 1 km) in comparison, suggesting that geodetic inversions will not underestimate the apparent locking depth significantly simply because a more realistic transitional region is present (Savage, 2006). Considering that elastic heterogeneity, such as layered structure and damaged fault zone, especially in the shallow layers, (e.g.,Allam and Ben-Zion, 2012), are characteristic of tectonic faults, the geodetic inversions based on the dislocation model in a homogeneous half-space are likely to provide an underestimate ofDgeod.
The along-depth slip partition within a seismic cycle, as seen in our models, is illustrated in Fig. 5.11. Earthquake rupture can potentially penetrate deeper below the SZ, with Dlock migrating updip or otherwise stay in depth in the post- and inter-seismic periods.
(A) (B)
(C)
Figure 5.10: The effect of layered elastic structure on the inference of Dgeod and Vcr. (A) depth distribution of fault slip rates in the dislocation model (DSL) and the model with more realistic locked-creeping transition (LCT) and a representative layered structure (LS) withVpandVsshown (Kanamori and Hadley, 1975). The DSL and LCT have the equivalent surface expression in the half space (HS). (B) surface expression for different combination of fault slip rate profiles and elastic structure. (C) Inferred 1σ (68%) credible region in the parameter space ofDgeodorVcr. Given a certainVcr, inversion based on LCT and LS would underestimate Dgeod.
Regardless of the depth of coseismic slip, postseismic slip occurs in the creeping VS region below, expanding in space and yet decaying in amplitude, eventually leading to a slip deficit zone that slips below the plate rate. As a result, the divergence of the shallower Dlock and the deeper Dgeod is anticipated and indeed observed in all our models. Since Dgeod correlates strongly with Vcr in the inversion (Fig. 5.8A), a priori assumptions that Dgeodshould be the same as seismicity depth, which is more relevant toDlock, could lead to underestimation ofVcr, which could contribute to the discrepancy between the geodetic and geological estimates of the fault slip rate, among other factors (e.g., Chuang and Johnson,
2011). From the other perspective, the difference between Dlock and Dgeod, if accurately determined, would be indicative of the extent of deeper penetration of coseismic slip and/or the amplitude and spatial extent of postseismic slip. With the Carrizo segment of the SAF as an example (Fig. 5.1), the current discrepancy of the seismicity-based estimates (13.9, 14.4 and 16.0 km for 90%, 95%, and 99% cut-off depths, predominantly controlled by a local cluster,Lin et al., 2007) andDlock (18.7±2,Smith-Konter et al., 2011) could be even larger, if taking into account the potential bias in the inversions due to ignoring elastic heterogeneity, as illustrated in Fig. 5.10, suggesting that significant postseismic slip should have occurred, in addition to the coseismic deeper penetration as inferred from the paucity of microseismicity (Chapter 4).
Another important issue is the relation between the depths of coseismic rupture Drupt and interseismic fault locking Dgeod. In all our models,Dgeod is always deeper thanDrupt, because the slip deficit zone expands to counter-balance the contribution from the co- and post-seismic periods. In the limit where the postseismic slip is negligible,Dgeodcould coin- cide withDrupt, but this limit is probably unrealistic given that postseismic slip is commonly documented for large earthquakes (Marone et al., 1991; Hearn et al., 2002; Perfettini and Avouac, 2007). However, this reasoning for the maximumDruptbeing constrained byDgeod is based on the assumption of the quasi-periodic recurrence of large earthquakes, as is the case in our models. In reality, the relation betweenDruptandDgeodon the segment may be complicated by the variability of earthquake rupture, resulting in along-strike variations in slip and arresting depths, which might be assessed through paleoseismic trenching studies at different sites on the fault.
coseismic
(potential deep slip) postseismic interseismic
slip budget
Dgeod Drupt Dlock
Fault depth
SL
Dseis
Figure 5.11: Illustration of slip partition andDgeod,DseisDlock, andDruptin a seismic cycle.
The slip budget is split between the co-, post- and inter-seismic periods of fault. The gray profile indicates the depth distribution of stressing rates, which determinesDlock(horizontal red line) and corresponds to Drupt (horizontal black line) right after the earthquake. The red, orange and blue lines represent fault slip during the co-, post- and inter-seismic periods, with the red and blue dashed lines corresponding to the depth of dislocation model with the near-equivalent surface expression. The red and blue band indicate the approximate depth range forDseis and possible range forDgeod.