Constraining mantle rheology by observations of seismic anisotropy beneath transform
boundaries
Bradford H. Hager, Massachusetts Institute of Technology; John A. Collins, Woods Hole
Oceanographic Institute; Anne Sheehan and Peter Molnar, University of Colorado; and
Kimon Ioannides, Concord Academy
Seismic anisotropy results from the lattice preferred orientation of crystals arising
from deformation by power law creep. If the pattern of finite strain in the mantle could
be inferred, the presence or absence of seismic anisotropy would be diagnostic of whether
the in situ rheology is linear or nonlinear. Since laboratory experiments investigating
deformation of silicates typically are carried out at strain rates millions to billions times
higher than those in the mantle, it is important to test extrapolations of experimental
results using observations of anisotropy generated (or not, if deformation occurs via
diffusion creep) by flow in the mantle. Probably no other place in the mantle is flow
better characterized than beneath transform faults in oceanic lithosphere.
In the uppermost mantle, where we expect the greatest seismic anisotropy, flow
beneath oceanic transforms will be dominated by the shearing generated by relative plate
motion. We compute flow for a simple model that assumes that mantle flow is driven by
strike-slip motion at velocity  vp on an infinitely long transform fault, imposed as a
surface boundary condition. An analytic solution for the flow field can be obtained by
assuming that the mantle is a (possibly non-Newtonian) halfspace with an effective
viscosity = o(o/)(n-1) = o(o/)(n-1)/n, where o is a reference viscosity at reference
deviatoric stress, oor reference strain rate, o and n is the stress exponent. The velocity
field is purely toroidal; taking the y axis parallel to the transform, the x axis perpendicular
to the transform, and the z axis down, the only non-zero component of velocity is vy=
vp(1-2/where  = sin-1(x/r) and r= (x2+z2)1/2. The deviatoric strain rate and stress are
given by edev = v/r and dev= o(ro/r)1/n, where ro is the distance from the origin where
the stress reaches reference value o. The deformation occurs by simple shear on planes
fanning out from the origin. The strain rate, which falls off as 1/r, does not depend upon
n, but the stress, which decays as (ro/r)1/n, dies out less quickly for dislocation (n=3) than
for diffusion creep (n = 1). If flow is nonlinear (e.g., n=3), deformation results in
preferred orientation of olivine in a characteristic pattern.
Seismic anisotropy is often attributed to motion of tectonic plates over the mantle
below. Such movement would induce another component of strain and (for n=3)
anisotropy beneath the transform fault, requiring a numerical 3-D flow calculation. Near
the surface, the deformation geometry and dev are dominated by the transform shear,
while at depth they are dominated by the shear due to absolute plate motion. The
transition from transform-dominated shear to absolute plate motion-dominated shear
depends on the relative magnitude of the two contributions. The dev falls off rapidly
away from the transform, reaching a fairly constant value through most of the model.
Thus, determining whether seismic anisotropy is confined to the region near a transform
or extends more widely should place strong constraints on the strain rate at which the
transition between linear and nonlinear rheology occurs in the mantle.