Notes on "long-term continuum strain-rates" by Peter Bird, 2013.01:
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These notes explain the long-term continuum strainrates that I
reported to UCERF3 and to the Western-US National Seismic Hazard
Map 2014 team, based on my NeoKinema fault-based deformation models.

"Continuum" refers to the parts of the lithosphere lying between
the modeled faults.  These volumes may well have additional faults 
(not named, digitized, or explicitly modeled), and they may well be
seismogenic.  This is the motivation for including long-term 
continuum strain-rates in a deformation model.

"Long-term" refers to many "earthquake cycles" or thousands of years,
not to the brief "interseismic" period which is typically sampled by GPS.
Over a long timescale, the elastic contribution to continuum strain-rates
is expected to average to almost zero.  Therefore, the long-term continuum
strain-rates quoted here represent (model rates of) permanent straining,
which could potentially be seismogenic (e.g., in one logic-tree branch).

Strain-rates are provided on a standard grid with 0.1 degree
resolution, provided by the hazard mapping team.  For UCERF3,
the template grid points were specified as (latitude, longitude);
but for NSHM2014 the template points were (longitude, latitude).
Some template grid points are outside the regions I modeled with
finite-elements, and zero strain-rate tensors are reported for 
these points.

At each surface point, the 3 components quoted are: 
    e-dot_EW, e-dot_NS, and e-dot_NE.
All are in SI units of per-second.
Extensional strain components are considered positive,
as is elongation of a square into a SW-&-NE-pointing parallelogram.
For e-dot_NE, I use the "tensor" formula:
    e-dot_NE = (1/2) * ((dV_E/d_N) + (dV_N/d_E)),
{rather than the "engineering" formula which lacks the factor of (1/2)},
where V is the long-term horizontal velocity vector at the surface, 
and "N" and "E" are shorthand for locally North-pointing and 
East-pointing coordinate axes with distances in units of meters.

Strain-rates are quoted only for the horizontal Earth-surface "plane."
Since these strain-rates are (by definition) not elastic, they probably
obey conservation-of-volume, and the vertical principal strain-rate
can be easily estimated as:
      e-dot_rr = -(e-dot_EW + e-dot_NS).

To convert these strain-rates to equivalent rates of faulting and seismicity:
(1) Compute the vertical (principal) strain-rate using the formula above.
(2) Find the 2 other principal strain-rates in the horizontal plane.
(3) In general, 2 of the 3 principal strain-rates will have the same sign;
    NO faulting could be generated by the difference between these two; however,
    2 sets of conjugate faults could be generated by the differences
    between each of these 2 axes and the axis of the principal strain-rate of unique sign.
(4) Choose the dip angles you prefer for each type of fault (strike-slip, thrust, & normal).
(5) Choose the coupled seismogenic thickness ["c z" of Bird & Kagan, 2004, BSSA]
    that you prefer; based on Table 5 in that paper, something like 8000 to 18000 
    (expressed in SI units of meters) seems appropriate.
(6) Choose the elastic shear modulus that you think appropriate, in SI units of Pa.
(7) Convert all this information into seismic moment rates per unit area.
(8) Choose the frequency/magnitude or frequency/moment relation that you prefer.
(9) Convert seismic moment rates to earthquake rates at the desired threshold moment/magnitude.

For further reading on this topic, see
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.