59. Bird, P., Y. Y. Kagan, D. D.
Jackson, F. P. Shoenberg, & M. J. Werner [2009] Linear and nonlinear
relations between relative plate velocity and seismicity, *Bull. Seismol.
Soc. Am., 99*(6), 3097-3113, doi:10.1785/0120090082, with electronic
supplements.

**Abstract**. Relationships between relative plate velocity and
seismicity differ by plate boundary class. We test the null hypothesis of linearity
of earthquake rates with velocity in each of 7 classes. A linear relationship
is expected if earthquake rate is proportional to seismic moment rate, which is
proportional to relative plate velocity. To reduce bias by aftershocks and
swarms, we estimate independence probabilities of earthquakes and use them as
weights. We assign shallow earthquakes to boundary steps and classes, then
sort boundary steps within each class by velocity, and plot cumulative
earthquakes against cumulative model moment rate. We use 2 measures of
nonlinearity, and 10^{4} stochastic simulations to assess significance. In
subduction zones the relationship between seismicity and velocity is nonlinear
with 99.9% confidence. Slower subduction at <66 mm/a (producing 35% of tectonic
moment under the null hypothesis) produces only 20% of subduction earthquakes.
Continental convergent boundaries display similar nonlinearity (*P* <
0.001 for the null hypothesis). Ocean spreading ridges show seismicity
decreasing with velocity. Oceanic transform faults and oceanic convergent
boundaries show marginal nonlinearity (*P* < 0.01; *P* <
0.05). Continental rifts and continental transform faults follow the null
hypothesis. Three effects may contribute to velocity-dependence in subduction:
(1) The brittle/ductile transition at a critical temperature is advected deeper
by faster underthrusting; (2) subducted sediment is viscous, so lower stresses
in slower boundaries discourage earthquakes; (3) pore pressures increase with
velocity, encouraging frictional failure. Mechanism (1) has only minor effects
on earthquake productivity, but mechanisms (2) and (3) could be important.

complete final manuscript with figures

**FIGURES**

**Figure 1**. Cumulative independent earthquake count (diamonds) and
cumulative independent seismic moment (crosses) of Continental Transform Fault
plate-boundary steps, ordered by relative plate velocity from slow on left to
fast on right. Abscissa is cumulative model tectonic moment rate, assuming
constant coupled seismogenic thickness, constant spectral slope, and constant
corner magnitude. Diagonal reference line represents the null hypothesis of
linearity.

**Figure 2**. Cumulative independent earthquake count (diamonds) and
cumulative independent seismic moment (crosses) of Continental Rift Boundary
plate-boundary steps, ordered by relative plate velocity. Conventions as in
Figure 1.

**Figure 3**. Cumulative independent earthquake count (diamonds) and
cumulative independent seismic moment (crosses) of Oceanic Transform Fault
plate-boundary steps, ordered by relative plate velocity. Conventions as in
Figure 1.

**Figure 4**. Cumulative independent earthquake count (diamonds) and
cumulative independent seismic moment (crosses) of Oceanic Convergent Boundary
plate-boundary steps, ordered by relative plate velocity. Conventions as in
Figure 1.

**Figure 5**. Cumulative independent earthquake count (diamonds) and
cumulative independent seismic moment (crosses) of Oceanic Spreading Ridge
plate-boundary steps, ordered by relative plate velocity.

**Figure 6**. Cumulative independent earthquake count (diamonds) and
cumulative independent seismic moment (crosses) of Subduction-zone
plate-boundary steps, ordered by relative plate velocity.

**Figure 7**. Cumulative independent earthquake count (diamonds) and
cumulative independent seismic moment (crosses) of Continental Convergence Zone
plate-boundary steps, ordered by relative plate velocity.

**Figure 8**. “Slow” subduction zones (*v* < 67 mm/a; heavy
green lines) outside orogens (shading) from the PB2002 model of *Bird [2003]*,
who defined them as convergent boundaries with associated volcano(es)
(triangles) and/or Wadati-Benioff zones of intermediate-depth seismicity
(circles). Large asterisks indicate slow subduction zones that were not
included in the “Subduction zone deformation regime” of *Kreemer et al.*
[2002]. Earthquakes deeper than 70 km are from CMT and volcanoes are from *Simkin
& Siebert* [1995].

**Figure 9**. Thermal structure of a vertical cross-section of a model
subduction zone, after 100 m.y. of subduction at 60 mm/a. The F-D grid has
been rotated for greater realism, as explained in text. Geotherms of the
subducting oceanic plate (right) and the volcanic arc (left) were fixed as
boundary conditions. Diagonal line indicates the interplate shear zone.
Contour interval 50 C.

**Figure 10**. Depths (below seafloor) to various temperatures in the
interplate shear zone, from F-D thermal models like that shown in Figure 9.
The 150 C isotherm is suggested as an estimate of the lower limit of the
(potentially) frictional and seismogenic portion of the shear zone.

**Figure 11**. Potentially seismogenic lithosphere thicknesses, expressed
as depth extents of the (potentially) seismogenic portion of the interplate
subduction shear zone. Obtained from Figure 10 by subtraction of a constant
12.4 km depth to the beginning of the seismogenic zone.

**Figure 12**. Estimated variations in corner magnitude of shallow subduction
zone earthquakes due solely to velocity-dependent variations in thermal
structure, as shown in Figures 10-11. Fixed point is the global average value
of *Bird &
Kagan [2004]*, plotted at the
relative plate velocity of the 1960 Chilean earthquake. In very slow
subduction, plate-bending earthquakes may dominate the corner magnitude.

**Figure 13**. Global-average histograms of shallow earthquake counts, by
focal mechanism, in subduction zones of the PB2002 model (outside designated
orogens). Width of all bins is 10 km. Thrusting earthquakes located to the
right of the trench probably did not occur on the interplate shear zone, but
were due to plate bending. Some thrusting earthquakes to the left of the
trench were also due to plate bending. By estimating that plate-bending
produces equal numbers of normal and thrusting earthquakes, we compute the
fraction of earthquakes taking place on the interplate shear zone to be 100% -
9.4% - 2 x 14.5% = 62%.

**Figure 14**. Normalized earthquake productivity (defined in text)
variations predicted from the F-D thermal models of Figures 9-12, and the
observed earthquake partitioning in subduction zones from Figure 13. Greater
seismogenic lithosphere thickness at higher velocity is offset by the effect of
higher corner magnitude, predicting roughly uniform productivity.

**Figure 15**. Potential extent of subducted evaporite sediments (white
honeycomb pattern) based on present plate velocities from PB2002 [*Bird*, 2003] and an assumption
that some evaporites travel at the velocity of the subducting plate (AF or
EU). Evaporites under the Italian peninsula are hypothetical, and depend on
both the past motion of the peninsula with respect to Adria [here based on
Figure 6 of *Rosenbaum et al.*, 2008], and whether a suitably deep basin existed
for Messinian evaporite formation off the former southwestern continental
margin of the Adria microcontinent, prior to its collision with Italy.

**Figure 16**. Schematic diagram of possible conditions at intermediate
depth (*e.g.*, 27 km below sea level) in an interplate subduction shear
zone. The shear stress necessary to accommodate relative plate motion by
viscous flow (solid lines) might increase linearly or according to a
power-law. The shear stress necessary for frictional sliding (dashed curves) is
controlled by pore pressure, whose sensitivity to plate velocity is unknown.
Their intersection (at one of the 4 circled points) would divide low-velocity
aseismic behavior from high-velocity seismic behavior at this particular point
in the shear zone.