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as long as they are not superseded by later studies.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).