61. Bird, P., C. Kreemer, and W. E. Holt [2010] A long-term forecast of shallow seismicity based on the
Global Strain Rate Map, *Seismol**. Res.
Lett., 81*(2), 184-194, doi:
10.1785/gssrl.81.2.184.

**Introduction**. The
Global Strain Rate Map (GSRM) of Kreemer *et al.* (2003) was the main
result of Project II-8 of the International Lithosphere Program. The GSRM
is a numerical velocity gradient tensor field model for the entire Earth’s
surface that describes the spatial variations of horizontal strain rate tensor components,
rotation rates and velocities. The model consists of 25 rigid spherical
plates and ~25,000 0.6° by 0.5°
deformable grid areas within the diffuse plate boundary zones (*e.g.*,
western North America, central Asia, Alpine-Himalaya belt). The model provides
an estimate of the horizontal strain rates in diffuse plate boundary zones as
well as the motions of the spherical caps . This is
one of the first successful models of its kind that includes the kinematics of
plate boundary zones in the description of global plate kinematics.

The vast majority of the data used
to obtain the GSRM comes from horizontal velocity measurements obtained using
Global Positioning System (GPS) measurements. The latest model version of
May 2004 (*i.e.*, GSRM v.1.2) includes 5170 velocities for 4214 sites
world-wide (Holt *et al.*, 2005). Most geodetic velocities are
measured within plate boundary zones. The observed velocities are obtained from
86 different (mostly published) studies. The model includes additional
constraints on the style (not magnitude) of the strain rate tensor inferred
from moment tensors of shallow earthquakes. In addition, geologic strain rates
in central Asia inferred from Quaternary faulting data are fit simultaneously
with the geodetic velocities to improve the model there. See Kreemer *et al.*
(2000; 2003) for more details.

It was always a goal of the GSRM
Project to support long-term forecasts of seismicity based on tectonic
deformation. Two recent developments make this especially timely.
First, the Collaboratory for the Study of Earthquake Predictability (CSEP;
Jordan *et al.* 2007) is accepting global models for prospective
testing. To date, they have only registered global models that are based
on smoothing of instrumental seismicity (*e.g.*, Kagan and Jackson 2010?),
so it would be valuable to compare results with a model based on
tectonics. Second, the Global
Earthquake Model project will soon create an update to the Global Seismic
Hazard Map of Giardini *et al.* (1999), which
was based primarily on instrumental and historical catalogs. The new map
is likely to be based primarily on traces and slip rates of faults, so
comparisons to seismicity models incorporating geodesy and plate tectonics
should be illuminating and helpful.

To convert the GSRM to a forecast
of long-term shallow seismicity, we apply the hypotheses, assumptions, and
equations of Bird
and Liu (2007), who referred to them as the Seismic Hazard Inferred From
Tectonics (SHIFT) hypotheses: (1) The long-term seismic moment rate of any
tectonic fault, or any large volume of permanently-deforming lithosphere, is
approximately that computed using the coupled seismogenic thickness (*i.e.*,
the seismic coupling coefficient times the seismogenic thickness) of the most
comparable type of plate boundary; and (2) The long-term rate of earthquakes
generated along any tectonic fault, or within any large volume of
permanently-deforming lithosphere, is approximately that computed from its
moment rate (of the previous step) by using the frequency/magnitude
distribution of the most comparable type of plate boundary.

In this conversion, we faced four conceptual and/or practical difficulties:

First, the strain-rates available are not always the kinds of strain-rates that would be preferred. The strain-rates in GSRM were largely determined by GPS geodetic velocities, assumed plate and boundary geometry, and some local geologic and strain-direction constraints. Except where faults are creeping (or where they have many small earthquakes during the measurement period), the strain-rates inferred from differentiation of GPS velocities are dominantly elastic strain-rates associated with rising deviatoric stresses. However, the strain-rates input to SHIFT calculations should ideally be long-term permanent strain-rates with no elastic components. Geodetic strain-rates typically have smoother map patterns than long-term permanent strain-rates which include singularities along fault traces. However, in a 2-D Earth-surface model based on plate-tectonic concepts, cross-boundary line integrals of these two kinds of strain-rate across a given plate boundary are the same, because both are equal to the relative plate velocity, regardless of timescale. The use of available GSRM strain-rates, which include some elastic components, should not greatly affect the total long-term seismicity computed in a SHIFT model, but only smooth its spatial distribution. On the scale of global maps and forecasts this smoothing is relatively insignificant compared to grid aliasing, digitization error, and other local error sources. Thus we disregard this distinction.

Second, GSRM treats plate interiors as perfectly rigid and predicts zero strain-rates in these regions. Yet a global seismicity forecast with zero rates in plate interiors would be both unrealistic and irresponsible. Our solution is to forecast a uniform low seismicity rate in all plate interiors, which is based on the collective frequency/magnitude distribution of these regions in the years covered by a reliable catalog. This makes our model formally a hybrid of two methods (SHIFT- and catalog-based), but as the two parts are spatially distinct there is little chance that these components will be confused.

Third, the basic SHIFT hypotheses
do not specify how to decide which is the “most comparable type of plate
boundary” for a given spatial grid point. This must be determined by
subsidiary rules or hypotheses appropriate to the data and/or models
available. We cannot use all of the decision rules suggested in Table 2
of Bird and Liu
(2007) because they assumed that all subduction zones and spreading ridges
were represented by discrete fault traces, which is not the case in GSRM.
Fortunately, Kreemer *et al.* (2002) published a global map separating the
deforming regions of GSRM into four deformation regimes: subduction,
ridge/transform, diffuse oceanic, and continental (**Figure 1**). We
use their map as the basis for assignments, and in some cases also use the
tectonic style (*e.g.,* normal-faulting, strike-slip, thrust-faulting, or
mixed) of the local strain-rate tensor.

Finally, we
found that our raw (uncorrected) forecast was seriously underpredicting global
shallow seismicity (by a factor of 2) and that this was primarily due to
underpredictions of subduction seismicity (by a factor greater than 3).
We identified three quantifiable sources of underprediction
in subduction zones: (1) inappropriate geometric factors in the moment-rate
formula for many thrust faults whose dips are much less than 45°; (2)
velocity-dependence of coupled seismogenic thickness in subduction zones
inferred by Bird
*et al.* (2009); and (3) time-dependence of global seismicity, which
has increased since the calibration period of 1977-2002 studied by Bird and Kagan (2004).
Compounding the corrections for these effects requires scaling-up the forecast seismicities of all grid points in the subduction-zone
deformation regime by about a factor of 3. We apply smaller empirical
correction factors to each of the other three deformation regimes. This
yields an adjusted forecast that is reasonably consistent with the map-pattern
and frequency/magnitude graph of the 33-year-old Global Centroid Moment Tensor
catalog.

** P.S.** In December 2011, this model was installed in
the Global testing region of the Collaboratory for the Study of Earthquake
Predictability (CSEP). Specifically,
it was placed in the high-resolution category (cell size 0.1 x 0.1 degree x 70
km) because our cell size of 0.6 x 0.5 degree x 70 km was not a good match for
the low-resolution category (cell size 1 x 1 degree x 30 km). As of 2014.01,
this testing had not yet started, and the test duration is undefined. Since our
model does not include aftershocks or other time-dependent processes, we expect
the model to do relatively better over longer time-windows (

** P.P.S.** This tectonic forecast was updated in 2015 by
using version 2.1 of the Global Strain Rate Map; please refer to Bird & Kreemer [2015a,b].

**Figure 1.
Deformation r**egimes as defined by Kreemer *et al.*
(2002): Subduction (S); diffuse Oceanic (O); Ridge-transform (R); Continental
(C). Also shown are 189 shallow earthquakes above =
5.66 from the CMT catalog, 1977-2009.03, which did not fall into any of these
regimes. These are considered intraplate (I) earthquakes.

**Figure 2**.
Frequency/magnitude plot of the 189 shallow intraplate earthquakes from Figure
1. Also shown are 3 tapered Gutenberg-Richter model curves (Jackson and
Kagan, 1999; Kagan and Jackson, 2000). All models have the same asymptotic
spectral slope of *β* = 0.63, but differ in the choice of corner
magnitude *m*_{c}. While the match to the curve with corner
magnitude of 9 appears best, it must be noted that this depends on the size of
the single largest earthquake.

**Figure 3**. SHIFT/GSRM
global long-term forecast of the rates of shallow earthquakes above *m*_{T} = 5.66. This model has been
adjusted to match global shallow earthquake rates from CMT in 1977-2009.03 by
using one free parameter for each of four deformation regimes, and one for the
intraplate area. Rates are expressed as earthquakes per square meter per
second, including aftershocks. Coloring of the map employs a logarithmic
scale to express variations across almost 4 orders of magnitude from peak
subduction-zone rates to intraplate rates. Mercator projection.

**Figure 4**. SHIFT/GSRM
global long-term forecast of the rates of shallow earthquakes above *m*_{T} = 8.00. Conventions as in Figure
3. In this model, mid-ocean spreading ridges and ideal oceanic transforms
do not contribute to seismicity at magnitudes above 8, while the contributions
of continental rifts and transpressive oceanic transforms are generally small.

**Figure 5**.
Frequency/magnitude curve of the SHIFT/GSRM long-term shallow earthquake
forecast, retrospectively compared to the CMT catalog of 1977-2009.03. No
single tapered Gutenberg-Richter model is expected to fit this global composite
of different tectonic regimes. Therefore a straight-line
Gutenberg-Richter model with spectral slope *β* = 0.63 is shown for
comparison. Error bars on CMT earthquake counts are two-sigma sampling
errors if and only if the distribution of earthquake counts follows the
binomial distribution; actual sampling errors are probably larger due to
earthquake clustering.

**Figure 6**. Cumulative
spatial distribution functions for both forecast and actual numbers of shallow
earthquakes above in a 32.25-year
period. The abscissa is cumulative dimensionless area of Earth surface,
relative to unity for the whole Earth. Grid cells with low forecast
earthquake rates contribute to the left end of each curve, and grid cells with
high forecast rates contribute to the right ends of each curve, as explained in
text.

**Figure 7**. Cumulative
spatial distribution function for actual numbers of shallow earthquakes above in
a 32.25-year period (vertical axis; ordinate) is plotted against cumulative
spatial distribution function of forecast numbers (horizontal axis;
abscissa). Grid cells with low forecast earthquake rates contribute to
the lower left end of the curve, and grid cells with high forecast rates
contribute to the upper right ends of the curve, as explained in text. An
ideal forecast would yield a straight line with slope of unity, as shown by the
dotted line (except for small variations caused by finite-catalog sampling
errors). See text for discussion of the discrepancy in the lower-left
portion of the curve. The Cramér/von Mises
error measure is the root-mean-square discrepancy between the curve and the
diagonal when both axes are nondimensionalized to range [0, 1].