Download Teleseismic imaging of subaxial flow at midocean ridges: traveltime

Geophys. J. Int. (1996) 127,415-426
Teleseismic imaging of subaxial flow at mid-ocean ridges:
traveltime effects of anisotropic mineral texture in the mantle
Donna K. Blackman,' J.-Michael Kendall,2y* Paul R. D a ~ s o n , ~
H.-Rudolgh Wenk,4 Donald Boyce3 and Jason Phipps Morgan'
IGPP, Scripps Institution of Oceanography, La Jolla, CA 92093-0225, USA
Department of Physics, Unioersity of Toronto, Toronto, Ontario, Canada
Sibley School of Mechanical & Aerospace Engineering, Cornell University, Ithaca, NY 14853-7501, USA
Department of Geology & Geophysics, Unioersity of California, Berkeley, CA 94720, USA
Accepted 1996 July 5. Received 1996 June 24; in original form 1995 October 5
SUMMARY
Deformation of peridotite caused by mantle flow beneath an oceanic spreading centre
can result in the development of seismic anisotropy. Traveltime anomalies and shearwave splitting will develop as seismic energy propagates through such an anisotropic
region, thus providing a signature of the deformation field at depth. In this study we
investigate the nature of deformation associated with mantle upwelling for two models
of flow in the upper 100 km of the mantle. The finite-strain fields of the passive
upwelling model versus the buoyancy-enhanced upwelling model are quite different.
This suggests that mineral aggregates deform differently in the two models, thus
developing seismic signatures that are distinguishable. Numerical estimates of the
corresponding mineral textures are made using polycrystal theory for olivine with four
operative slip systems. The activation of a slip system is determined for each grain on
the basis of the local critical resolved shear stress. The computed grain deformation
reflects a balance between stress equilibrium, for the aggregate as a whole, and strain
continuity between neighbouring grains within the aggregate. This approach enables a
direct link to be made between the model flow fields and the resulting texture
development. Given these mineral orientation distributions, elastic parameters are
calculated and wavefronts are propagated through the anisotropic structure. Traveltimes
for teleseismic body waves are computed using ray theory, and amplitudes are estimated
for an across-axis profile extending 100 km from the ridge axis. Relative P-wave
residuals of up to 1 s are predicted for the buoyant model with on-axis arrivals being
earliest, since near-vertical velocities are fastest beneath the axis. On-axis P-wave
arrivals for the passive model are half a second earlier than arrivals 60 km off-axis,
and relative delays continue to increase slowly as distance from the ridge increases.
S-wave splitting of almost a second is predicted for the buoyant model, whereas less
than a half-second of splitting is determined for the passive model.
Key words: anisotropy, body waves, mid-ocean ridge, ray tracing, upper mantle.
1 INTRODUCTION
The evidence available for determining the nature of mantle
flow beneath oceanic spreading centres is indirect: surface
volcanism occurs only in a narrow axial zone; the deep median
valley at slow-spreading ridges is dynamically maintained,
whereas at fast-spreading ridges an axial volcanic high occurs;
*Now at: Department of Earth Sciences, University of Leeds, Leeds,
LS2 9JT, UK.
01996 RAS
ophiolite sequences commonly show significant alignment of
minerals along the palaeo shear direction in their mantle
sections; and seismic anisotropy in the upper mantle beneath
old ocean crust exhibits a fast propagation direction aligned
with palaeo plate motion. The narrow axial zone of surface
volcanism (Macdonald 1982) indicates that although mantle
upwelling probably occurs over a broad region at depths of
1W200 km beneath a spreading centre (e.g. Sleep 1975), the
magma, and perhaps the residual matrix flow as well, must
become more focused at shallow depths. The dynamic support
415
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D.K . Blackman et al.
of a deep median valley indicates rapid across-axis changes in
mantle structure, either in the form of an axial asthenospheric
suction due to the separation of thick plates (Lachenbruch
1973) or necking of a rigid lithosphere that thickens rapidly
off-axis (Tapponnier & Francheteau 1978). The lack of a deep
valley at fast-spreading ridges suggests that mantle structure
varies less rapidly across the axis than at slow-spreading ridges.
The alignment of mantle minerals in ophiolite sections (e.g.
Nicolas & Christensen 1987) provides a means for mapping
the deformation field that may exist beneath oceanic crust.
The fact that these minerals have highly anisotropic seismic
properties allows us to relate measurements of seismic anisotropy in the oceans (Raitt et al. 1969; Shimamura 1984;
Nishimura & Forsyth 1989) to current and past mantle-flow
geometries. Only now is the geophysical community beginning
to undertake long-term teleseismic experiments at mid-ocean
ridges that image the in situ deep structure at a resolution that
can improve our understanding of processes on the scale of
ten to a few hundred kilometres (e.g. Forsyth & Chave 1994).
To assess the sensitivity of teleseismic body-wave observations to changes in the physical parameters that may control
mantle upwelling at mid-ocean ridges, we present an integrated
numerical study: first we perform geodynamical modelling of
subaxial flow fields; this is followed by calculation of the
mineral texture development in the corresponding mantle rock;
elastic coefficients of the mantle are then determined from this
polycrystal orientation distribution using single-crystal properties and appropriate averaging; finally wavefront propagation
through the resulting anisotropic structure is analysed.
There are two components of mantle flow beneath an
oceanic spreading centre, passive and buoyancy driven, and
the different relative strengths of the two can lead to a
significantly different subaxial structure (Turcotte & Phipps
Morgan 1992; Scott 1992). The passive component is induced
by the spreading of the lithospheric plates with a simple pattern
of upwelling beneath the axis and overturn to follow the
spreading direction off-axis (Sleep & Rosendahl 1979; Reid &
Jackson 1981). As the subaxial asthenosphere rises during
passive upwelling, melting occurs due to decompression. This
basaltic melt separates from the peridotite matrix and eventually rises to form oceanic crust at the ridge axis. Localized
buoyancy forces develop in the upwelling mantle due to the
presence of the interstitial melt (Rabinowicz, Nicolas &
Vigneresse 1984; Scott & Stevenson 1989). In addition, compositional buoyancy of mantle that has experienced melt
extraction (Oxburgh & Parmentier 1977) and thermal buoyancy will also enhance vertical flow rates beneath a spreading
centre. The strength of the buoyancy-driven flow relative to
ongoing passive upwelling is not well known, so we investigate
two end-member flow models to estimate the possible differences in seismic structure that could occur, and to assess our
ability to recognize them in teleseismic body-wave arrivals at
the seafloor.
The upper mantle beneath a spreading ridge is composed of
peridotite and the main mineral component is olivine. Olivine
single crystals are highly anisotropic for elastic-wave propagation, with P-waves travelling along the a-axis 25 per cent
faster than along the b-axis (Verma 1960). Based on observations of peridotite xenoliths in basalts, it is likely that olivine
deforms at upper-mantle conditions largely by intracrystalline
slip accompanied by dynamic recrystallization. With such
mechanisms, preferred orientation (texture) develops, as has
been observed experimentally (Raleigh 1968; Carter &
Ave’Lallemant 1970) and is predicted by polycrystal plasticity
models (e.g. Wenk et al. 1991). Elastic-wave anisotropy has
been observed in experimental and natural peridotite samples
(Christensen 1984). Recently Boudier & Nicolas (1995)
described high fabric anisotropies in Oman peridotites. Using
petrofabric analysis and modelling elastic properties, Mainprice
(1995) reported effective P-wave anisotropies,
T)/
V r , up to 20 per cent from these sub-Moho peridotites.
Crystalline alignment in a polycrystal during deformation is
a complicated non-linear process. In the case of deformation
by slip, polycrystal plasticity theories, developed to predict the
deformation of metals, have been successfully applied to many
minerals. If dynamic recrystallization occurs by subgrain
rotation, similar mechanisms apply. In fact, in the case of
olivine, recrystallization and deformation produce similar textures in experiments (Raleigh 1968; Carter & Ave’Lallemant
1970). For simple monotonic strain histories the strength of
preferred orientation increases (though non-linearly) with overall strain. Such deformation regimes have been recently incorporated in heterogeneous, large-scale models to predict texture
and anisotropy development during mantle convection
(Chaste1 et al. 1993). This model was able to plausibly predict
the general azimuthal variation in P-wave velocities associated
with horizontal flow due to plate motion as observed by Raitt
et al. (1969). It also showed that preferred orientation along
a streamline is highly variable, increasing or decreasing,
depending on the local incremental strain. Clearly preferred
orientation cannot be predicted if only the finite-strain ellipsoid
is known.
In this paper we apply a similar approach to a more local
feature and demonstrate that the elastic structure can vary
significantly on the scale of 10 km in regions of high flow or
thermal gradients, both of which occur in the vicinity of a
spreading centre. Surface-wave studies of anisotropy in the
oceanic mantle have necessarily assumed that large layers of
constant elastic properties (e.g. hexagonal anisotropy or transverse isotropy) can approximate the actual seismic structure
(Forsyth 1975; Tanimoto & Anderson 1984; Nishimura &
Forsyth 1989). Our detailed investigation of mantle deformation via polycrystal plasticity, which is linked directly to
velocity structure, allows us to construct a continuous, spatially
varying anisotropic seismic model. Since we can accommodate
all symmetries, no assumption about the symmetry class of
the effective sample anisotropy is required and we are not
restricted to a layered geometry, which would be a poor
representation of the subaxial structure.
(v-
2 L I N K E D MODELS O F FLOW, TEXTURE
DEVELOPMENT A N D SEISMIC VELOCITY
STRUCTURE
2.1 Flow models
A finite-element flow model developed by Phipps Morgan and
co-workers (Cordery & Phipps Morgan 1992; Jha, Parmentier
& Phipps Morgan 1994) is used to predict deformation in the
vicinity of a spreading ridge. Boundary conditions imposed at
the surface require that the temperature is 0 “C and the velocity
equals the spreading rate. The centre of spreading, the ridge
axis at the surface, defines a symmetry plane for both temperature and velocity. Far off-axis (250 km in these runs), velocities
0 1996 RAS, GJI 127, 415-426
Subaxial $ow at mid-ocean ridges
are set to match the predictions of a corner-flow model (e.g.
Reid & Jackson 1981), except that the monotonic decrease
from the spreading velocity begins at the base of the lithosphere
rather than at the seafloor. Horizontal temperature gradients
vanish at the right boundary. At the base (250 km depth),
velocities are constrained to match the predictions of a simple
corner-flow model and the temperature is held at 1325"C. The
melting curve is defined to be T, = 1100"C + 3.25 ("C k m - ' ) ~ ,
so melting begins at about 70 km depth. The degree of melting
affects the density of the residual, which is tracked, and the
amount of melt retained in the interstices of the residual is
controlled by the specified porosity (4). The viscosity of the
mantle has a simple temperature dependence such that the
asthenosphere has constant viscosity and there is an increase
of two orders of magnitude for the viscosity of the lithosphere,
whose base is marked by an isotherm (either 700 "C or 1000"C).
Physical parameters that affect the pattern of mantle flow
beneath a spreading centre include asthenosphere viscosity,
the amount of melt retained in the mantle matrix, the degree
of depletion of the residual mantle (how much melt has been
removed), the temperature at which mantle becomes more
rigid in the lithosphere, and the plate-spreading rate. A series
of simulations in which these parameters were varied individually shows that viscosity plays the major role in controlling
whether buoyancy effects dominate the flow structure. Fig. 1
shows that for an asthenosphere viscosity (p) of 10'' Pa s the
flow is essentially a passive response to plate spreading. In
417
contrast, for p = 5 x 10" Pa s vertical flow rates are enhanced
by a factor of three and the flow is focused beneath the axis
in response to buoyant forces. About 20km off axis, the
competing effects of depletion buoyancy, melt buoyancy and
lithospheric thickening combine to force material to sink. Thus,
a rather tight circulation pocket forms at depths of 40-70 km
and distances of 20-50 km off-axis (Sotin 8~Parmentier 1989;
Scott 1992). The finite strain that develops is quite different
for these two models (Fig. 1, lower panels). There is notable
vertical stretching beneath the axis for the buoyant case and
high strains develop in the tight circulation region. The highly
strained material is then rafted off-axis to create a layer of
subhorizontally oriented strain ellipses at depths of 4-80 km.
The orientations of the strain ellipses in the lithosphere are
inclined counterclockwise to the horizontal in the passive-flow
case, indicating that deformation continues to some extent
within the plate. In the passive upwelling zone and below the
base of the plate, the finite strain basically matches that
predicted by McKenzie (1979) for a constant-viscosity cornerflow model. In the buoyant case the ellipses rotate clockwise
towards the vertical near the base of the plate due to the
relative motion between the lithosphere and the asthenosphere.
The basic nature of the buoyant-flow regimes remains the
same for a range of parameter choices, but the details vary
with assumed melt retention factor (4, porosity), rigidus temperature of the lithosphere ( T )and spreading rate (SR). The
flows depicted in Fig. 1 have 4=O.ll, ?;=700°C and SR=
Figure 1. Models of flow and deformation fields for the buoyant case (right) and the passive case (left). Viscosity j1=5 x 10" Pa s for the buoyant
case and p = 10'' Pa s for the passive case; melt retention Q =0.11; spreading rate = 18 mm yr-'; rigidus temperature T = 700 "C.Top: flow vectors
overlying greyshade of the temperature field; solid lines show melt content increasing from 1 per cent (outermost contour) at intervals of 1 per
cent; dashed lines show the fraction of mantle depletion increasing upwards from 0.04 at that interval. Bottom: finite strain ellipses for the flow
models above. Strain begins to accumulate along flow lines (dotted lines) at 100 km depth in these cases.
0 1996 RAS, G J I 127,415-426
D.K . Blackman et al.
418
SR
=
75 mm/yr
60
km
80
#
*s-"
I00
1
0
40
80
-
1
0
120
Tlith = 1000°C
d
e
P
t
h
km
1
0
40
ao
120
distance from axis (km)
Figure 2. The dependence of finite strain on the physical parameters
assumed in flow modelling. Values are as is Fig. 1 except where
otherwise specified (viscosity p = 5 x 10" Pas; melt retention d=O.ll;
spreading rate= 18 mm yr-'; rigidus temperature T = 700 "C). Top:
SR=75 mm yr-l. A similar pattern of strain ellipses results for p =
10'' Pa s or $=0.06. Bottom: 7;=1000°C.
18 mm yr-' half-rate (the rate with respect to the ridge axis;
relative motion between the two plates would be twice the
half-rate). Relative to this reference, the strength of focusing
and subaxial flow enhancement decreases similarly for either
p = 10'' Pa s, 4=0.06 or S R = 7 5 mm yr-'. Fig. 2 (top) illustrates how the tight circulation region is muted for these
parameter values and the lobe extending toward the ridge axis
on the right in Fig. 1 is absent. The vertical stretching beneath
the axis is reduced and the high-strain region at depth occurs
only beyond 40 km off-axis. A value of 1000°C for 'I; results
in a reduction in the magnitude of finite strain 10-30 km deep
in the asthenosphere (Fig. 2, bottom), but the predicted orientations remain essentially the same as for 'I;= 700 "C (compare
Fig. 2 and Fig. 1, left). Within the shallow lithosphere, the
finite strain is greater for T = 1000 "C due to the higher velocity
gradients within the wedge formed by the steeper isotherms
directly beneath the ridge axis.
2.2 Development of mineral texture
Texture simulations assumed a 'lower-bound' approach, which
was described in some detail by Chaste1 et at. (1993). Initially
aggregates having a random orientation distribution of 1000
grains are assumed to reside at each nodal point at the base
of the texture model (100 km). The responses of these aggregates to the flow gradient are evaluated numerically using
local incremental velocity gradients. Deformation is assumed
to occur by slip on the four different slip systems documented
for olivine (Bai, Mackwell & Kohlstedt 1991). Their activity
is specified with the critical resolved shear stress (Table 1). A
viscoplastic lower-bound model that favours stress equilibrium
over strain compatibility has been chosen on the basis of the
limited number of independent slip systems in olivine crystals.
Earlier work found that the self-consistent theory (Wenk et al.
1991) and even a relaxed Taylor model (Takeshita et al. 1990)
yield similar results in the case of olivine. Using the lowerbound approach, the stresses in all crystals of an aggregate are
identical, trivially satisfying equilibrium. The deformation may
vary from crystal to crystal, but the stress is constrained to
ensure that the average of the crystal deformations equals the
macroscopic deformation. By allowing the crystals within an
aggregate to deform independently, it is possible to accommodate an arbitrary deformation while having only four slip
systems in each crystal, provided that all crystals do not have
equivalent orientations. Straining in general is non-uniform
and variations in the deformation rate as great as a factor of
two arise.
This numerical approach does not incorporate possible
effects of recrystallization (see Section 4), and, as is the case
for nearly all polycrystal models, the lower-bound approach
tends to overemphasize the role of texturing in polycrystal
deformation. The predicted orientation distributions are qualitatively similar, although the strength of the determined fabrics
may differ somewhat in intensity from those that would occur
in actual peridotite.
The calculated textures for the buoyant and passive flow
models are quite different, as shown by pole figures of the
[ 1001 and [OlO] axes of the olivine aggregates throughout the
models (Fig. 3). Particularly important is the [ 1001 pole figure,
which displays the distribution of fast seismic axes. Textures
in the passive case develop below the base of the lithosphere
so the thickness and depth extent of the layer with strong
preferred orientation increases steadily off-axis. The buoyantcase textures can be broken into three regions, each with rather
different characteristics: ( 1 ) a subaxial zone within 15-20 km
of the ridge axis; (2) an intermediate zone about 15-40 km
from the ridge axis; (3) an off-axis zone at distances greater
than 40-50 km.
During buoyant flow, the initially random distribution of aaxes quickly evolves to a distribution restricted to the x2-x3
plane directly below the ridge axis (x, is the horizontal, acrossaxis direction, x2 points into the page and x3 is vertical). At
depths of 20-60 km and within 15 km of the axis, a high
percentage of a-axes are oriented vertically. This high degree
of alignment is reduced near the surface as the stagnation
point in the flow is reached and material is incorporated into
the lithosphere. This weakening of the fabric is expected as the
Table 1. Active slip systems of olivine used in texture calculations.
Slip-plane normal
Slip direction
Critical shear stress at 1400°C
(0 10)
(001)
(0 1 0)
(100)
ClOOl
ClOOl
15 MPa
16 MPa
40 MPa
35 MPa
coo11
coo 11
0 1996 RAS, GJI 127, 415-426
Figure 3. Pole figures showing the calculated orientation distributions of 1000 olivine grains within the aggregate at each node point in the buoyant (right) and passive (left) models. The aggregates
are undeformed at 100 km depth. Deformation of the grains within the aggregate is tracked as it moves along a streamline and is subjected to the gradients in flow velocity corresponding to the
models shown in Fig. 1. The pole figures are equal-area projections in the x1-x3 plane. Top panels show [lo01 (a-axis) orientations (fast P direction); bottom panels show [OlO] (b-axis) orientations
(slow P direction). The missing pole figures in the centre of the tight circulation region of the buoyant model indicate that the texture calculation was not used here (see text). The thick grey line
shows the 700°C isotherm.
Subaxial $ow at mid-ocean ridges
0 1996 RAS, GJI 127, 415-426
419
420
D.K . Blackman
et
al.
orientation of the shear changes with respect to the axis of the
texture orientation when the aggregate transits the near-axis
region at shallow depths (Chaste1 et al. 1993). 15-30 km offaxis the a-axis girdle is inclined about 45" from the vertical at
depths of 60-80 km. As the aggregates enter the tight circulation region, most a-axes migrate to the edge of the girdle,
but some remain in the very centre (pointing out of the page).
Flow gradients below the base of the lithosphere act to diffuse
the olivine alignment. Thus, the a-axis concentrations are not
as high in any single plane or direction at depths of 20-30 km
in this intermediate region as they are directly beneath the
axis. Further off-axis, the lithosphere is characterized by a
shallow section with a diffuse a-axis girdle inclined 15-20"
clockwise from horizontal. With depth in and below the
lithosphere, this girdle is replaced by a better-defined one that
is about 30" counterclockwise from horizontal, although many
poles stay at the apex of a slightly rotated vestige of the
shallow girdle. The b- and c-axis distributions are more diffuse
in this region, although there is a tendency for the b-axes to
congregate perpendicular to the a-axis girdles. A layer of
strong preferred orientation occurs at depths of 65-85 km with
[lo01 horizontal. At the top of this off-axis layer there is a
strong maximum with [ 1001 pointing to the right but most of
the layer shows varying a-axis directions throughout an x1-x2
plane. The b-axes tend to be vertical in the lower part of
the layer.
The tight circulation region presented difficulties in tracking
several streamlines of the flow. The interpolation of flow rates
between nodes implies the existence of a point of zero velocity
within this region and a small zone of recirculation about that
point. The textures for particles that experienced recirculation
were not used in the computation of node-point stiffnesses
since their relevance is questionable. The seismic model requires
a continuous distribution of elastic parameters, so the values
from the horizontally adjacent node points (3 km to the side
rather than the 6 km spacing used in Fig. 3 for illustrative
purposes) were assigned to the nodes at the centre of the
recirculation zone.
During passive flow, the most significant crystal alignment
develops in the high-shear region below the base of the rigid
lithosphere. A girdle of [loo] poles essentially parallels the
base of the plate with subhorizontal orientations off-axis. Close
to the axis, the girdles incline about 45", corresponding to the
steep dip of the axial wedge formed by the plate; although it
is difficult to discern in Fig. 3, there is a concentration in the
plate-spreading direction within the horizontal projection of
the girdle of a-axis directions. The definition of the preferredorientation plane is clearest about 20 km below the rigidus
and slowly becomes more diffuse with depth. Above the base
of the lithosphere, textures are diffuse, reflecting the competing
effects of basal shear and the stress-free surface. [OlO] tends
to align perpendicular to the [ 1001 girdle so that off-axis poles
align 15-20' clockwise from vertical within the layer of preferred orientations. Below this layer, textures remain random
for this model.
The a-axes are only roughly aligned parallel to the flow
directions: there are asymmetric deviations and large scatter.
These deviations are due to simple shear, which has been
discussed in detail by Wenk & Christie (1991) and for olivine
by Wenk et a!. (1991). In summary, polycrystal plasticity
simulations predict neither that slip directions align with flow
lines (Francis 1969) nor that they align with the long strain-
ellipsoid axes. This lack of clearly discernible behaviour was
also observed experimentally in the field of dislocation slip
(Zhang & Karato 1995), where deformed crystal alignment
generally plotted between curves defined by the finite-strain
orientation and the flow-parallel direction.
2.3 Velocity structure
The texture predictions for each 1000-grain aggregate are
expressed by the orientations of the constituent olivine crystals.
The effective elasticity for each aggregate is calculated using a
simple Voigt average of the stiffnesses (expressed as the fourthorder tensor cijkl) over all crystal orientations. Therefore, Cijkl
for each olivine crystal must be rotated into a global coordinate
system. In general, this results in 21 independent elastic constants from which the P- and S-wave velocities for a given
nodal point and wavefront normal (or slowness) can then be
calculated (Fig. 4; see Appendix of Kendall & Thomson 1989).
Although monoclinic symmetry is expected due to the 2-D
nature of the flow field, averaging the elastic constants for
each crystal aggregate yields non-monoclinic terms that arise
from the initially random crystal orientations. In practice these
terms have little effect on the wave velocities as they are
generally two orders of magnitude, or more, smaller than the
13 monoclinic elastic constants.
To isolate the effects of the flow-induced anisotropy we have
used very simple velocity models. The effects of heterogeneity
due to the presence of melt and lithospheric thickening are
not included here (we return to the subject of possible melt
effects in the Discussion). The elastic models are 3-D, symmetric
about the ridge axis and uniform along this axis. Although the
flow and texture predictions of the previous section are for
2-D flow, the elastic model must be 3-D as wave propagation
in anisotropic media is not necessarily confined to the sourcereceiver plane.
Variations in the direction of maximum S-wave splitting
generally do not coincide with the direction of maximum Pwave velocity, as is shown by the vectors in Fig.4. For the
buoyant case, the only region where the two directions coincide
is at the base of the off-axis layer 60-80 km deep. Throughout
the rest of this model, maximum S-wave splitting tends to
occur 35-45' from the direction of maximum P-wave velocity.
In the passive case, the two directions do coincide more
frequently, particularly in the layer beneath the lithosphere
where the greatest preferred orientation develops. The degree
of S-wave anisotropy is a few per cent lower than the degree
of P-wave anisotropy at most of these locations. Differences
in the direction of maximum P-wave velocity versus maximum
S-wave splitting are typically 30-50" in the region below the
wedge formed by the steep lithosphere within 30 km of the axis.
The degree of anisotropy in the horizontal plane is generally
somewhat lower than the maximum at a given location within
the models due to the fact that preferred crystal orientation
tends to be at an angle to the horizontal. In the passive case,
there are somewhat greater a-axis concentrations in the spreading direction than in the other horizontal directions. This
results in horizontal P-wave anisotropies of 2-8 per cent in
the region near and below the base of the plate, fastest in the
plate-spreading direction and at the higher values in the older
part of the plate. In the buoyant model, horizontal P-wave
anisotropies are low (1-4 per cent) in the upper 50 km, but
0 1996 RAS, GJI 127, 415-426
Subaxial $ow at mid-ocean ridges
Passive Model
421
Buoyant Model
O T
T
0
100 km
distance from axis
100 km
0
distance from axis
Figure 4. Wave surfaces for the effective elastic parameters, cijkl,computed at each node point from the polycrystal distributions shown in Fig. 3.
The outermost surface (heavy line) is the P wave and the inner surfaces (thin lines) are the S waves. The thick vector shows the direction of fastest
P-wave propagation, and its length is proportional to the degree of anisotropy. The largest vectors correspond to 18 per cent anisotropy. The
thin vector shows the direction/degree of maximum S-wave splitting, (Sfaat
-Sslow)/Saverage,
in the wavefront-normal direction. The scale for the
degree of splitting is the same as for the P-wave anisotropy.
-
the high-strain layer at 60-80km depth has higher values
(6-12 per cent).
3 BODY-WAVE PROPAGATION BENEATH A
SPREADING CENTRE
Wave propagation is simulated using a program designed to
trace seismic rays through multilayered 3-D inhomogeneous
anisotropic media with curved interfaces (Guest & Kendall
1993). The program is based on asymptotic ray theory for
anisotropic media (cervenf 1972; Kendall & Thomson 1989).
Density and 21 independent elastic constants are specified on
a rectangular grid of knot points. A four-point 3-D cubic
spline is used to interpolate between knot points, returning
the required parameter and its first and second derivatives.
These derivatives are required to solve the ray and geometricalspreading equations that track the ray and its amplitude
through a given seismic velocity model (cerveni 1972). The
ray angle of incidence on the bottom of the model is varied to
simulate lower-mantle and core phases.
Fig. 5 shows nearly vertically travelling P rays (PKP, corresponding to a compressional wave that travels through the
Earth's core as well as the mantle) and the resulting traveltimes
through the buoyant and passive models. In the buoyant
model, traveltimes at the ridge axis are about a second earlier
than arrivals further than 50km off-axis. This is due to the
high-velocity subaxial region for vertically travelling P waves.
The transition in this model from the axial region, which has
high velocities compared to the surrounding lower-verticalvelocity regions, is sharp enough to cause wavefront folding
and caustics. This produces traveltime triplications and
increased amplitudes at about 40 km distance from the axis.
In the passive-flow case, P-wave traveltimes are again predicted
0 1996 RAS, GJI 127, 415-426
to be earlier at the axis than off-axis but the magnitude of the
relative delay at 100 km distance is about 0.5 s. Unlike the
buoyant case, for which off-axis traveltimes are essentially
constant beyond 50 km distance, the passive case is characterized by slowly but steadily increasing P-wave traveltimes
off-axis. For both models, ray paths and traveltimes for P
waves with an incident-ray angle of 25" (i.e. lower-mantle
turning phase) are similar to the P K P results, but, relative to
the axis, they are asymmetrical and the traveltime anomaly is
somewhat larger.
Because the model is anisotropic, at least two shear waves
will arrive at the surface. Fig. 6 shows the predicted traveltimes
for these quasi-orthogonally polarized shear waves. In the
buoyant case, the shear wave polarized in the (quasi-) radial
direction (particle motion in the x1-x3 plane) arrives at the
ridge axis 0.8 s ahead of the shear wave that is polarized in
the (quasi-) transverse direction (particle motion parallel to
xz). Conversely, the off-axis region beyond 25 km in the
buoyant model shows the opposite effect, with the transversely
polarized shear wave leading the radially polarized shear wave.
At the axis in the passive model, the radially polarized shear
wave leads the transversely polarized wave by only a couple
of tenths of a second. Off-axis the sense of polarization of the
first- versus the second-arriving shear wave switches, similar
to the buoyant case, but the time separation is about half that
of the former model. For the buoyant model it is difficult to
trace S waves of a single polarization vertically through the
region 15-20km off-axis, since the two S wavesheets have
similar velocities and energy is coupled between the polarization directions. Ray theory for anisotropic media is not
strictly valid in regions where the S wavesheets cross, but these
cases are easily monitored and the handful of S rays along
which this occurred do not have traveltimes plotted in Fig. 6.
422
D.K . Blackman et al.
Passive Model
B u o y a n t Model
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40
80
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-40
0
40
80
distance from a x i s ( k m )
Figure 5. Ray paths and traveltimes for near-vertical P waves that propagate through the anisotropic velocity models shown in Fig. 4. Buoyant
model at right, passive at left. The complex shallow (10-40 km depth) velocity structure within 15-40 km of the axis acts to defocus energy in the
buoyant model and to slightly focus it in the passive model. Traveltime triplication occurs 35-45 km off-axis in the buoyant case as the defocused
rays cross other straighter rays.
All rays arrive at the surface within 400 m of the cross-axis
profile along which they started at 100 km depth, the base of
the seismic model, and most are within 200m of the surface
trace of the starting profile. Deviations from the starting profile
are greater for the S waves near the axis than off-axis, or for
the P waves in general.
The amplitudes of body-wave arrivals contain diagnostic
information about the underlying velocity structure. For
example, comparison of P-wave amplitudes with S-wave amplitudes across the axis can suggest different types of structural
complexity. In our models, high amplitudes for P waves are
predicted at off-axis distances of 35-40 km in the buoyant
case, as opposed to predictions of high S-wave amplitudes at
distances of 10 km (radially polarized shear wave), or 0 and
42 km (transversely polarized). Amplitudes in the passive case
display less variation across the profile, with only a small Pwave increase at the axis and small S-wave amplitude peaks
at about 40 km off-axis.
4 DISCUSSION
4.1 Recognizing subaxial structure in teleseismic data
The difference in teleseismic P-wave traveltimes predicted for
the two models of mantle anisotropy at a spreading centre is
substantial, suggesting that it should be possible to distinguish
between passive and buoyancy-enhanced upwelling. The Pwave anomaly increases slowly with off-axis distance to a
fraction of a second for the passive case. In contrast, for the
buoyant case the U-shaped traveltime delay is predicted to
increase away from the axis to about 40 km where it levels off
at about 1 s relative to arrivals at the axis. This pattern could
be resolved for teleseismic P waves whose angle of incidence
is up to 30" from the vertical.
Observing an axis-centred traveltime P-wave anomaly such
as we predict would require an array of receivers deployed on
the seafloor. The resolution of Global Seismic Network teleseismic data with surface bounce-points near the ridge will not,
in general, be sufficient to image structures on the scale of a
few tens of kilometres. P-wave traveltime anomalies across an
array of ocean-bottom seismometers can be determined to
within about 0.3 s accuracy in typical conditions (Blackman,
Orcutt & Forsyth 1995), so a 1 s anomaly would be well above
the uncertainty level.
The nature of the traveltime anomaly predicted for anisotropy developed during mantle upwelling is similar to the
pattern observed on the east flank of the southern mid-Atlantic
ridge. A relative P-wave delay of about 0.5 s was observed
between an ocean-bottom seismometer 25 km east of the axis
and those 55-75 km off-axis on the same ridge flank (Blackman
et al. 1993a; Blackman et al. 1995). This traveltime anomaly
includes corrections for topographic effects, and contributions
due to crustal structure are probably less than about 0.2 s
(Tolstoy, Harding & Orcutt 1993). Although they do not
conclusively show an axis-centred fast anomaly pattern, the
sparse high-quality data from this experiment suggest that
anisotropy may be a major contributor to the observed
traveltimes. Seafloor experiments conducted to date have not
been designed to image this type of structure so we must look
to future data sets for constraints on whether the buoyant or
passive models best explain the observations.
Because of the 10s-100km lateral scale of the subaxial
structure, it is unlikely that surface waves of 15-100 s periods
can be used to examine the near-ridge anisotropy. Beyond
0 1996 RAS, GJI 127,415-426
Subaxial $ow at mid-ocean ridges
Buoyant Model
18.0
17.5
(r,
17.0
-8
5
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16.5
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16.0
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Passive Model
75.51
15.0‘
I
-80
I
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I
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-40
0
40
80
distance f r o m axis ( k m )
Figure 6 . Traveltimes for near-vertical, quasi-orthogonal S waves
traced through the anisotropic velocity models illustrated in Fig. 4.
The traveltime of the quasi-radially polarized shear wave is indicated
by dots; that of the quasi-transversely polarized shear wave is shown
by asterisks. For both models, the polarization of the first-arriving
shear wave at the axis is opposite to that of the first-arriving shear
wave more than 40km off axis. The off-axis splitting should be
resolvable in both cases, although the prediction for the buoyant
model is twice that for the passive model. In practice, resolving the
predicted axial splitting may be possible in the buoyant case but is
unlikely for the passive case.
about 70 km off-axis, on the other hand, surface waves could
provide constraints on whether a layer of subhorizontal fastaxis alignment occurs, as is predicted for all models of buoyancy-enhanced flow. Given a sufficiently small resolution kernel
[30-40 km depth extent, such as could be expected at the
upper end of observable frequencies (15-25 s periods) in oceanic data (Blackman et aE. 1995)] in the appropriate depth
range (at the base of the lithosphere in the passive case or
60-80 km depth in the buoyant case), one might discern a
layer whose properties differ significantly from those of the
surrounding media.
We find that fairly thin ‘layers’ with high degrees of anisotropy are expected to result from mantle deformation at a
spreading centre rather than thicker layers with low degrees
of anisotropy. In the buoyant case, the layer that is rafted offaxis after material transits the tight circulation region has Pand S-wave anisotropies up to 18 per cent and 14 per cent
respectively. Values directly beneath the axis in this model also
reach 12-18 per cent for P waves travelling at depths of
30-60 km. The highest degree of P-wave anisotropy in the
0 1996 RAS, GJI 127, 415-426
423
passive case is about 12 per cent and occurs in a layer about
30 km thick beneath the base of the lithosphere. This is
important since many studies determine fairly low degrees of
anisotropy but the region in which the interpreted anisotropy
occurs is limited or not well constrained. Raitt et al. (1969)
and Shearer & Orcutt (1985) determined P-wave anisotropies
of 6-8 per cent in the uppermost several kilometres of the
oceanic mantle. Nishimura & Forsyth (1989) determined Swave anisotropies of about 2 per cent for upper-mantle regions
10s to 100 km thick. On land, S K S studies (e.g. Silver & Chan
1991) assumed a value of 4 per cent anisotropy to interpret
SKS data in terms of subcontinental mantle anisotropy. Our
results suggest that the actual degree of anisotropy may be
substantial but that it occurs over a smaller region.
Interpreting P-wave traveltimes alone to determine anisotropic velocity structure does not provide a unique answer;
only through a combined analysis of P- and S-wave traveltimes,
and of the variations in their amplitude, do we stand a chance
of narrowing the field of candidate models. The predicted offaxis shear-wave splitting is twice as large for the buoyant
model as it is for the passive model. The deep U-shaped
traveltime anomaly pattern and its levelling off beyond
40-50 km is characteristic of the P waves in the buoyant case.
This type of signal would be expected for a range of flow
models where buoyant flow rates are of the order of, or larger
than, passive flow rates.
4.2 Limitations of modelling approach
Our numerically linked calculations of flow, mineral texture
and its seismic velocity signature, and anisotropic ray tracing
produce a consistent picture of the structure of the upper
mantle beneath a spreading centre. We can have confidence in
our predictions of the velocity structure to the extent that we
believe we have captured the essential physics of the systems
abstracted in our computer codes. One important aspect that
we cannot directly quantify is that of the recrystallization of
deforming minerals and the influence it may have on mantle
textures. The effect of recrystallization on olivine preferred
orientation has been the subject of study for some time
(Ave’Lallement & Carter 1970; Karato 1994). A definitive
explanation of olivine behaviour during shear flow is not yet
available but recent work by Zhang & Karato (1995) indicates
that subgrain rotation may be the dominant mechanism for
dynamic recrystallization at the temperatures and pressures
expected in the upper mantle beneath spreading centres. If this
is indeed the case, our texture estimates should be reasonable
representations since the deformation mechanism we have
employed will remain the operative mechanism during
subgrain rotation.
If olivine grains recrystallize with a texture that reflects the
local stress field (Karato 1988), the regions of our model that
would be most affected are the very high-strain areas just
below the lithosphere and the tight circulation region for
buoyant flow. In the case of the latter, material that transits
the circulation lobe will experience a continuously changing
stress field so it is unlikely that any strong preferred orientation
of recrystallized grains would result. Note that even under the
assumption of shear-induced deformation, the rather high
degree of alignment that forms on the upgoing limb of the
lobe is diffused as the aggregates follow the streamlines around
and back down off-axis (Fig. 3).
424
D. K . Blackman et al.
Our assumption of a simple stepwise temperature dependence of mantle viscosity influences the details of the strain
field within which texture develops, but the nature of our
predictions would not change drastically if a more realistic
viscosity field was used. The 3-D spreading-centre flow field
calculated using a stepwise temperature-dependent viscosity
(Blackman & Forsyth 1992) is quite similar to the flow
predicted for fully temperature- and depth-dependent viscosity
(Shen & Forsyth 1992). Schubert, Froidevaux & Yuen (1976)
showed that with a self-consistent thermo-mechanical flow
model, the region of high strain near the base of the lithosphere
is fairly narrow for plate ages of 10 Myr (120 km off-axis in
our models), but that the transition in mantle strength broadens
significantly with age. This suggests that the basic pattern of
texture that we predict for the region within 100 km of the
axis is robust; a more complete model would likely predict
further textural evolution off-axis.
Incorporation of the effects of melt in the mantle could
significantly modify our seismic predictions in the axial region,
particularly for the S waves. We chose to examine the effects
of anisotropy alone for two reasons: (1) the possible contribution of this aspect of the seismic structure is more easily
understood in isolation; (2) the effect that melt may have on
wave propagation depends very strongly on the nature of melt
distribution, which is not well known (e.g. Schmeling 1985;
Forsyth 1992). In the passive-flow model, the melt fractions
are low, exceeding 0.02, melt/(melt+matrix), only in a small
region just below the axis (Fig. 1). Kendall (1994) estimated
that such small melt contents, uniformly distributed in pennyshaped pores within the melt zone, would produce a P-wave
traveltime delay with an axial maximum of less than 0.2 s and
a monotonic decrease in delay away from the axis as the
thickness of the melt region decreases. The corresponding
passive-case S-wave delays reached 0.4 s at the axis (Kendall
1994). In our buoyant model, melt fractions reach 0.06 in the
shallowest part of the melt zone, increasing steadily from 0.01
at 70 km depth where melting begins. For this model, melt is
restricted to a region within about 20 km of the axis, much
narrower than in the passive case. If the melt is uniformly
distributed in grain intersections, a narrow axial P-wave delay
of about half a second could result. Kendall (1994) showed
that if melt is distributed in thin, vertically aligned cracks, the
introduced anisotropy can result in S-wave splitting of up to
2 s near the axis. A more complete series of ray-tracing
experiments, with a range of assumed melt geometries and
distributions (Blackman & Kendall 1996), suggests that even
in the higher-melt-fraction buoyant case the textural anisotropy
signal dominates the P-wave traveltime anomaly pattern. The
presence of melt complicates the shear-wave signal but the
effect is to accentuate the shape of the traveltime anomaly
predicted for the texture-only models.
We have assumed that the peridotite arrives at the 100 km
deep base of the texture model with a random orientation, a
simplification that allows us to investigate the structure associated only with the upwelling and melting beneath the spreading
centre. If material encounters significant flow gradients elsewhere in its journey through the mantle, our predicted texturing
would act to modify pre-existing fabrics. As discussed by
Chaste1 et al. (1993), mantle textures are likely to be reset at
the olivine-to-spinel phase transition. These authors show that
broad convective cells develop preferred orientation planes
about 30" off-vertical in the upwelling zone. Imposing the
texturing that we calculate for the local region around the
spreading centre on such pre-existing structure should not
produce major differences in the end result since the sense of
texturing is the same as we determine. If, on the other hand,
there is significant lateral flow in the upper mantle as it is fed
to a spreading centre (e.g. Phipps Morgan & Smith 1992). the
pre-existing textures may be quite different. The orientation of
pre-existing texture does affect the evolution of subsequent
alignments since the activation of a usually easy slip system
may not be possible if most grains are not favourably aligned
(note the way textures evolve near the axial stagnation point
in our models-the nature of the textures that develop off-axis
reflect, to some extent, the fact that a fairly strong texture
already exists due to deformation in the upwelling zone). The
flow gradients in the buoyant model beneath the axis and in
the tight circulation regions are most likely much higher than
gradients that would occur due to larger-scale mantle flow.
Thus, we would expect that deformation associated with the
very localized buoyancy forces would dominate the texture
development near the axis as soon as material enters the
melting region (about 70 km depth).
There is clearly no direct relationship between the olivine
orientation distributions that we determine from the texture
calculations and the distribution that would be inferred from
the finite strain (compare the lower panels in Fig. 1 and the Pwave anisotropy vectors in Fig. 4). It has previously been
suggested that the preferred orientation of olivine a-axes will
follow the finite-strain ellipse (e.g. McKenzie 1979; Ribe 1989;
Ribe & Yu 1989), and computing the finite strain associated
with a given flow field is much less computationally demanding
than the texture calculation. Using such models may be
applicable for a certain material in a limited range of conditions
but this cannot be generalized. By choosing an ad hoc linear
relationship between finite-strain magnitude and degree of
anisotropy, we can produce P-wave traveltime anomalies that
are similar in shape to those determined from the full analysis
(Blackman et al. 1993b) but we are unable to match simultaneously the magnitude of the predicted delays for buoyant
and passive models.
5 CONCLUSIONS
Deformation by intracrystalline slip in olivine during viscous
mantle flow beneath an oceanic spreading centre results in a
strong preferred orientation in peridotites and significant seismic anisotropy in the upper 100 km of the mantle. Our linked
numerical models of flow, texture development and anisotropic
wave propagation provide quantitative insight into how thin
layers of high anisotropy can characterize regions of rapid
variation in the flow field of the upper mantle.
Very different distributions of shear-induced olivine alignment are determined for passive upwelling versus buoyancyenhanced upwelling. In the passive case, the strongest preferred
orientation develops at and below the base of the lithosphere,
the fast P-wave axis of olivine grains tending to parallel the
plate base. In the buoyant case, strong vertical alignment
occurs directly beneath the ridge axis due to focusing of the
flow and a tight circulation lobe forms in response to the
focusing. The associated texture development produces a
60-80 km deep layer of subhorizontally aligned fast seismic
axes that is rafted away off-axis.
Ray tracing through these generally anisotropic structures
0 1996 RAS, GJI 127, 415-426
Subaxial flow at mid-ocean ridges
indicates that sufficient across-axis variation would exist to
produce observable signals on an array of seafloor instruments
with apertures of about 100 km. Relative traveltime anomalies
of 0.5-1 s, shear-wave splitting of a similar magnitude and
amplitude variations due to the development of caustics all
provide diagnostics for differentiating between subaxial structure associated with the different flow models.
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