Geoscience Reference
In-Depth Information
The inconsistency between Love- and Rayleigh-
wave data, first noted for global data, has now
been found in regional data sets and it appears
that anisotropy is an intrinsic and widespread
property of the uppermost mantle. The crust and
exposed sections of the upper mantle exhibit lay-
ering on scales ranging from meters to kilome-
ters. Such layering in the deeper mantle would
be beyond the resolution of seismic waves and
would show up as an apparent anisotropy. This,
plus the preponderance of aligned olivine in
mantle samples, means that at least five elastic
constants are probablyrequired to properly
describe the elastic response of the upper man-
tle. It is clear that inversion of P-wave data,
for example, or even of P and SV data can-
not provide all of these constants. Even more
serious, inversion of a limited data set, with
the assumption of isotropy, does not necessar-
ily yield the proper structure. The variation of
velocities with angle of incidence, or ray param-
eter, will be interpreted as a variation of velocity
with depth. In principle, simultaneous inversion
of Love-wave and Rayleigh-wave data along with
shear-wave splitting data can help resolve the
ambiguity.
Because seismic waves have such long
wavelengths, a mantle composed of oriented
subducted slabs with partially molten basaltic
crusts could be misinterpreted as a partially
molten aggregate with grain boundary films
and oriented crystals. Global tomography can
only resolve large-scale features. Anisotropy and
anelasticity, however, contain information about
the smaller scale fabric of the mantle. Both
anisotropy and anelasticity may be the result of
kilometer, or tens of kilometer, scale features or
the result of grain-scale phenomena.
solid. For example, in layered media, the veloc-
ities parallel to the layers are greater than in
the perpendicular direction. This is not gener-
ally true for all materials exhibiting transverse or
hexagonal symmetry. Backus (1962) derived other
inequalities which must be satisfied among the
five
elastic
constants
characterizing
long-wave
anisotropy of layered media.
The effect of oriented cracks on
seismic velocities
The velocities in a solid containing flat-oriented
cracks, or magma-filled sills, depend on the elas-
tic properties of the matrix, porosity or melt
content, aspect ratio of the cracks, the bulk mod-
ulus of the pore fluid, and the direction of propa-
gation. Substantial velocity reductions, compared
with those of the uncracked solid, occur in the
direction
normal
to
the
plane
of
the
cracks.
Shear-wave
birefringence
also
occurs
in
rocks
with oriented cracks.
Figure 20.5 gives the intersection of the veloc-
ity surface with a plane containing the unique
axis for a rock with ellipsoidal cracks. The short-
dashed curves are the velocity surfaces, spheres,
in the crack-free matrix. The long-dashed curves
are for a solid containing 1% by volume of aligned
spheroids with
5 and a pore--fluid bulk
modulus of 100 kbar. The solid curves are for
the same parameters as above but for a rela-
tively compressible fluid in the pores with mod-
ulus of 0.1 kbar. The shear-velocity surfaces do
not depend on the pore-fluid bulk modulus. Note
the large compressional-wave anisotropy for the
solid containing the more compressible fluid. The
ratio of compressional velocity to shear velocity is
strongly dependent on direction and the nature
of the fluid phase.
There is always the question in seismic inter-
pretations whether a measured anisotropy is due
to intrinsic anisotropy or to heterogeneity, such
as layers, sills or dikes. The magnitude of the
anisotropy often can be used to rule out an
apparent anisotropy due to layers if the required
velocity contrast between layers is unrealistically
large.
α
=
0
.
Transverse isotropy of layered media
A material composed of isotropic layers appears
to be transversely isotropic for waves that are
long compared to the layer thicknesses. The
symmetry axis is obviously perpendicular to the
layers. All transversely isotropic material, how-
ever, cannot be approximated by a laminated
The
velocities
along
the
layers,
in
the
