2.4 Geodetic recurrence values
Geodetic estimates of the slip deficit distribution along the AASZ have used a wide variety of modeling approaches, producing estimates of varying complexity. Some studies (e.g., Fournier & Freymueller (2007); Cross & Freymueller (2008)) used a sparse parameterization, with one or a few planes of uniform slip deficit defined and a coupling coefficient estimated to represent the slip deficit rate. Our own approach is closest to this end member approach, and we have adopted those results as long as they are not superseded by later studies. Other studies (e.g., Suito & Freymueller (2009)) estimated slip deficit on an array of small sub-faults, requiring substantial spatial smoothing in the inverse model. In these cases, we need to interpret the location of candidate section boundaries based on the spatial variations estimated in the model, define an average downdip width of the coupled patch and then average the slip deficit rate over our interpreted section. Additional studies use approaches that are intermediate between these two end members (e.g., Elliott & Freymueller, 2020; Drooff & Freymueller, 2021).
To generate geodetic recurrence values summarized in Table 2, we first generalize coupling values and map areas from previously published geodetic studies for each of the sections we define (Figure 2). In all cases, geodetic data is from onshore surveys. In some cases, such as for the Attu section, previously reported coupling values and the lateral extent of coupled polygons (Cross & Freymueller, 2008) nearly exactly match our representation. In other cases, we simplify and generalize the results of previous studies. For example, for the Prince William Sound section the results of Li et al., (2016) are represented here as a rectangular polygon with uniform coupling, while in reality the area is a complex mix of interseismic strain accumulation, slow slip events, and permanent deformation of the overriding plate, and the whole region is affected by 1964 postseismic movements. We based our estimate on the Li et al. (2016) model rather than the earlier Suito and Freymueller (2009) model because the more recent paper identified and modeled the changes in slip associated with the large multi-year slow slip events in Cook Inlet. The Elliott and Freymueller (2020) model shows similar boundaries for the Prince William Sound segment, but it uses several smaller fault segments to estimate a more spatially detailed slip deficit distribution. However, given that the 1964 earthquake appears to have ruptured the entire section as we have defined it, we opted to use the spatially simpler model and estimate the average slip deficit rate considering the estimates of all of the published studies.
We represent coupling polygons (Briggs, 2023) for each section with a buried, simplified, planar geometry for each section. This step is meant to convert from a plan-view representation of the coupled area to a three-dimensional polygon (dipping plane) for which we can calculate the area. These simple polygons are constructed to be consistent with geometries used in the ongoing USGS NSHM update for Alaska where the upper and lower depths are tied to the Slab2 model (Hayes et al., 2018). More complex approaches would use a curved interface, but we consider this simplification appropriate because the coupling patches are along the shallowest portion of the interface with generally little curvature, or restricted to narrow portions of the deeper interface. The plate interface or fault geometry is usually assumed rather than estimated in most studies of both interseismic slip deficit and coseismic slip, and where different studies do not use a model like Slab2, they often make different assumptions.
We next consider the appropriate plate convergence velocity to multiply by coupling to obtain the slip deficit rate. We start with relative Pacific-North America plate convergence velocities, and for sections west of Prince William Sound we correct these to relative Pacific-Bering velocities (Cross & Freymueller, 2008) centered along each fault section at the deformation front. This correction is small, and for most sections the Bering-North America motion is mostly trench-parallel. For sites in the Aleutians, there is an additional observed trench-parallel motion of the arc, which increases to the west (Cross & Freymueller, 2008). We removed the estimated trench-parallel arc velocity to derive the trench-perpendicular convergence (Pac-Arc OBS in Table 2). The Pac-Arc OBS values are identical to Pacific-Bering velocities (Figure 2) in the eastern portion of the AASZ (Yakataga to Sanak sections) but diminish to become only approximately half of the Pacific-Bering values in the far western portion of the AASZ, reflecting increasing obliquity of subduction in the west. Our assumption is that a substantial trench-parallel component of motion is accommodated by upper plate strike-slip faulting, such as the 2017 Mw 7.8 Komandorski Islands earthquake (Kogan et al., 2017; Lay et al., 2017), but about half of the oblique relative plate motion is accommodated on the subduction interface based on Cross and Freymueller (2008).
The procedure described in the previous paragraph gives us the plate convergence rate that is most consistent with that actually modeled in most geodetic studies in the region (e.g., Cross & Freymueller, 2008). Some recent studies have made slightly different assumptions (or made slightly different estimates) about the motion of blocks on the overriding plate (e.g., Li & Freymueller, 2018; Elliott & Freymueller, 2020; Drooff & Freymueller, 2021), for example dividing the Bering Plate into a series of smaller blocks. However, most of the differences in block motions between the models are in the trench-parallel direction and no larger than a few mm/yr, which means they have only a very small effect on the estimated plate convergence rate. When comparing multiple studies for the same section, we compared estimated slip deficit rates rather than simply coupling coefficients, as the latter depends on the assumed plate convergence rate, but we express all results as coupling coefficients given the plate convergence rates in Table 2.
Once areas are calculated for each coupling polygon and trench-normal convergence is estimated for each fault section, we use scaling relations derived from Shaw (2023) to estimate a range of magnitudes, implied slip per magnitude, and recurrence values (Table 2). Our use of the Shaw (2023) model is intended to align with the NSHM update and also to illustrate the general approach of using scaling relations to estimate moment accumulation rates. The LogA scaling of Shaw (2023) reproduces the approach of (WGCEP, 2003) and is
M = log10 A + C
where
M is magnitude, A is area, and C is a constant for circular ruptures with constant stress drop.
Magnitudes M are obtained from area using three values of C recommended by (Shaw, 2023) for LogA scaling (4.1, 4.0, 3.9). In turn, the three magnitudes are converted to moment magnitudes Mo and implied slip per event (S) from (Shaw, 2023) calculated as
S = Mo/(Aμ) = 101.5M +9.05/(Aμ)
where
μ = shear modulus = 3 · 1010 Pa
Finally, recurrence is estimated by dividing implied slip per event by convergence rate multiplied by the coupling (Table 2).
In summary, we use plate convergence rates and a generalized depiction of geodetic coupling to characterize moment accumulation for each fault section and scaling relations to derive recurrence rates assuming area-magnitude scaling and implied slip per event. We do not propose that the coupled areas are exact proxies for rupture areas. Instead, our goal is to approximate the recurrence rates of reasonable ruptures per fault section generalized from the available geodetic data. In the 2023 update to the NSHM for Alaska, we anticipate that rupture areas will be relaxed and that the coupled polygons will not be the only ruptures considered in the model.
Below, we discuss each fault section from east to west. Because observations are relatively sparse in the context of the ~3,500-km-long subduction zone, section boundaries are not proposed as hard and persistent rupture boundaries, nor are the sections meant to imply only characteristic rupture behavior. In fact, the largest historical ruptures have typically involved two or more sections defined here, and lesser earthquakes have resulted from partial ruptures within or across fault sections (Fig. 2). It is expected that future approaches to modeling subduction zone seismic hazard in the AASZ will not rely on defining ad hoc rupture sections, but will vary ruptures to satisfy multiple constraints along strike (Field et al., 2020).