-
Evolution of Earth Structure and Future Directions of 3D
Modeling
Asphericity, Anisotropy, and Anelasticity of the Mantle
Don L. Anderson
Summary It is no longer adequate to treat the Earth as a nearly
spherically sym-
metric body wi.th simple recei.ver, source and attenuation
corrections tacked on. The aspherical velocity structure is now
being determined by surface wave and body wave tomographic
techniques and it has been found that heterogeneities are present
at all levels. In the upper mantle the lateral varitJ-tions in
velocity are as large as the variations across the radial
discontinuities. There is good correlation of velocity wi.th
surface tectonic features in the upper 250 km but the correlation
rapidly dimishes below this depth. The focusing and defocusing
effect of these lateral varititions can cause large amplitude
anomalies and these effects can be more important than
attenuation.
Velocity varititions in the mantle can be caused by temperature,
mineralogy and anisotropy, or crystal orientation. The largest
varititions are caused by anisotropy and relaxation phenomena such
as partial melting and dislocation relaxation. There is increasing
evidence for anisotropy in the upper mantle and this must be taken
into account in Earth structure modeling. Both azimuthal and
polarization effects are important. Layer-ing or fabric having a
scale length less than a wavelength wi.ll show the statistical
properties of the small scale sttw:ture. Global maps of
heterogeneity and anisotropy show that if anisotropy is ignored the
data wi.ll be mapped into a false heterogeneity. Azimuthal
anisotropy compounds the off-great-circle problem.
The absorption band concept predicts that Q should be higher at
short periods than at long periods and that there should be large
lateral and radial varititions in Q. The t• controversy is probably
related to shifts in the ab-sorption band. If velocity is
anisotropic then Q should be as well. Evidence is starting to
suggest that there is a Love wave, Rayleigh wave discrepancy in Q,
suggestive of Q an~otropy.
The VELA Program, Twenty Five Year Review of Basic Research,
DARPA, Arlington, VA, p. 399-418.
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400 Erolvti1m of Earlil Stnldtln and Futun Dirrdimu in ...
Introduction Rapid progress has been made in the past few years
in understand-
ing departures of the Earth from an idealized spherically
symmetric, isotropic and perfectly elastic body. Although much can
be learned about the Earth, and the propagation of seismic waves,
by intensive study of energy in a few narrow spectral bands some
phenomena in these bands cannot be understood without information
from a broader band of fre-quencies. Understanding the amplitudes
of seismic waves, for example, requires knowledge of focusing,
scattering, anelastic dispersion and mode coupling and these in
turn require information about the Earth that can-not be obtained
by narrow band studies of single wave types.
There is increasing evidence that the Earth is laterally
heterogenous on all scales and at all depths. This heterogeneity
cannot be described with a standard set of travel time curves and
station and source residuals. Station residuals are demonstrably
affected by lower mantle as well as upper mantle heterogeneity.
Station residuals, in fact, form the basis of recent tomographic
studies of heterogeneity of the lower mantle and the upper mantle
near sources and receivers. Surface waves provide a more uniform
coverage of upper mantle heterogeneity, or asphericity, but with
the present limited number of broad-band digital stations the
lateral resolu-tion is poor.
Evidence for upper mantle anisotropy is also increasing.
Anisotropy introduces extra parameters into Earth structure studies
and a large data base is required. It now appears, however, that
some apparent struc-tural complexity may be the result of
attempting to satisfy data from the real Earth with isotropic
models. Small scale structure, such as lamina-tions, may also give
rise to an apparent anisotropy, giving hope that even
sub-wavelength complexities can be modeled.
The lateral heterogeneity of the upper mantle is such that
signifi-cant off-great-circle propagation is expected. The
resulting focusing and defocusing causes large amplitude
anomalies.
The physics of anelasticity and the associated anelastic
dispersion, i.e., frequency dependence of velocity, is now fairly
well understood. The shift of the absorption band with pressure,
temperature and tec-tonic stress explains the large lateral and
radial variations of Q and t•. The anisotropy of anelasticity is
one of the important problems to be resolved in understanding t•
and the amplitudes of seismic waves.
Asphericity of the Mantle The large variation in P- and
S-residuals, or station corrections,
and surface wave velocities are the most obvious manifestations
of lateral heterogeneity. P-wave station residuals are now
available for about 1000
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D.L. ANlerson 401
global sites, and many more if local and regional arrays are
considered. Travel-time anomalies were the basis of the early study
by Dziewonski, Hager and 0' Connell of the long wavelength
heterogeneity of the lower mantle. Dziewonski and Anderson
published new average travel times and station residuals for about
1000 stations using ISC data. For many stations they were also able
to derive the cos(29) and cos(48) azimuthal terms (see Figs. 1, 2
and 3). Dziewonski has recently published a spherical harmonic
description of asphericity of the lower mantle. His results show
that a significant portion of the static and azimuthal station
effect is due to structure in the lower mantle. This result
indicates that the use of average travel time curves with source
and receiver corrections is no longer adequate and that travel time
anomalies are not entirely due to upper mantle effects. The next
quantum jump is epicenter location ac-curacy which will involve a
three-dimensional description of velocity · throughout the Earth
combined with ray-tracing from source to receiver.
A variety of tomographic body-wave techniques has been developed
by Robert Clayton and his colleagues at Caltech. They have
successfully inverted 1. 7 x 106 body wave arrival times to define
the velocity in 5° x 5° x 200 km cells in the mantle. The lower
mantle results have been used by Brad Hager and his colleagues to
explain the long wavelength part of the geoid. The Clayton group
has also used the large, dense southern California array (SCARLET)
to obtain a detailed three-dimensional structure under this region
down to about 600 km. Global and regional body-wave tomography is
making it possible to model and understand heterogeneity on both a
global and regional scale. The body wave tomographic results to
date show that the regions between 670 and 800 km depth and D " are
the most heterogeneous parts of the lower mantle. Velocity
variations are of the order of several percent. The discovery of
small scale velocity anomalies in the lower mantle explains the
rapid lateral and directional dependence of station residuals and
shows that detailed three-dimensional modeling of the mantle is
required in order to improve epicentral locations. These small
scale velocity anomalies may also help explain the variation of
body wave amplitudes.
Surface Wave Tomography Several groups have recently analyzed
large numbers of long-period
digital seismograms with the aim of mapping the large scale
heterogeneity and anisotropy of the upper mantle. Nakanishi,
Tanimoto and Anderson have derived phase and group velocities over
many hundreds of paths, for both Rayleigh waves and Love waves.
Tanimoto is currently in-vestigating the resolving power and
uniqueness of this type of data. Nataf, Nakanishi and Anderson have
inverted this data for heterogeneity and.
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402 E110ltdion of Earlli Stnubm and Fllturr Dirrclilms ;,,
•••
polarization anisotropy of the upper mantle. Their model, NNAG,
is shown in a series of figures at the end of this report. Present
data is adequate to expand the heterogeneity to t = m = 6 for all
of the Earth, and t = m = 10 for some regions. The average
half-wavelength of resolvable features is about 2500 km. With a
greatly expanded global digital net-work it should be possible to
map heterogeneities as small as 500-1000 km. Portable digital
arrays can be used to map even smaller structures using body wave
and surface wave tomography.
Woodhouse and Dziewonski have used waveform matching techniques
to study the dispersion of surface waves, including higher modes,
over about 800 paths. They have inverted this infonnation to obtain
average shear wave velocities to depths of 670 km. In most regions
their results are similar to the Nataf, Nakanishi, Anderson model.
The differences are primarily due to different treatments of the
crustal correction, the neglect of anisotropy, different choice of
parameterizations, and different data sets. These differences
should be understood in the next year but higher resolution must
await the expanded global digital network.
Tanimoto and Anderson have recently determined the azimuthal
varia-tion of Love and Rayleigh waves on a global basis. The fast
directions of Rayleigh waves appears to correlate with flow
directions in the man-tle. The azimuthal dependence of surface wave
velocity will considerably complicate the ray tracing problem,
including focusing and defocusing. There is no reason to expect
that body wave propagation is immune from these anisotropic
effects.
Lay and Kanamori have ray traced through model NNA6, showing the
effects of focusing and defocusing. The amplitude anomalies due to
geometric effects are much greater than expected from Q effects.
Even relatively mild, long wavelength asphericity gives appreciable
amplitude and off great circle effects.
Anisotropy The most studied effects of anisotropy include
azimuthal variation
of P.i and surface wave velocities, shear wave birefringence and
polariza-tion anisotropy. The minerals of the mantle are strongly
anisotropic and are easily oriented by stress and flow. Variations
in crystal orientation are more important than differences in
temperature and composition in causing variation in velocity.
Global data requires upper mantle anisotropy in order to explain
Love and Rayleigh wave data and the cos(48) terms in station
residuals. In a few areas differences in arrival times of SH and SV
have been documented. In general SH > SV but this is reversed in
regions of ascending and descending mantle flow as shown in studies
by Regan, Anderson, Nataf and Nakanishi. This can be understood
in
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D.L. Andmms 403
terms of orientation of olivine crystals. The large lateral
variation in sur-face wave velocities are partly due to velocity
variations caused by temperature and chemical differences and
partly due to anisotropy. H anisotropy is ignored then erroneous
velocity models will result.
H velocity is anisotropic then Q should be as well. There is
some evidence that there is a Love-Rayleigh discrepancy in Q, just
as there is in velocity. Physical mechanisms of attenuation, such
as dislocation relaxation, are expected to be strongly anisotropic.
H so, the commonly used expressions relating P-wave and S-wave Q
are invalid.
Body Wave Heterogeneity Detailed body wave models now exist for
such diverse tectonic
regions as shields, tectonic, rise and old ocean. Velocities
differ by as much as 10% in the upper 200 km and 4% between 200·
and 670 km. These differences are much greater than can be
explained by temperature alone and partial melting, dislocation
relaxation or anisotropy are implied. The variations are similar to
those inferred from surface wave tomographic results. We now need
detailed attenuation and anisotropy studies in the same areas.
The use of SS, PP, multiple ScS and P 'P' precursors promise to
provide detailed velocity and structural information in regions
inaccessi-ble to other phases. The power of these phases has been
demonstrated particularly by Don Helmberger and Stephen Grand and
their colleagues.
Mineralogical modeling of the new velocity models has led to the
surprising result that the transition region is mainly
clinopyroxene and garnet, rather than olivine. The olivine-spine!
transition gives much greater velocity jumps than observed at 400
km. On the basis of seismic velocities the shallower mantle can be
either peridotite or eclogite. Ridges and tec-tonic regions seem to
be partially molten to depth of at least 300 km.
Anelasticity The effects of attenuation on velocity is now well
understood and
is incorporated into most recent seismic modeling. This effect
reconciled body wave and free oscillation surface wave models. The
frequency dependence of Q is still not understood. A
frequency-independent Q is implausible but a mild frequency
dependence over a narrow frequency range is permitted. Since
absorption is likely to be a thermally activated relaxation
phenomena the absorption band should shift with depth. High Q
regions should hpve a strongly frequency dependent Q. Since
temperature shifts the location of the band laterally variations in
Q (or t*) should be accompanied by a change in the frequency
dependence. Observed Q, or t*, over a given path is the result of
superposition of
-
absorption bands with different center or comer frequencies. The
low-Q parts of the path, of course, dominate. There should not be a
single t• or ,. "' for all locations and depths and attempts to
model waveforms with one or two parameter models are doomed to
failure. Scattering and mode conversion can contnbute to apparent
attenuation. Both a laterally- and depth-dependent absorption band
Q model has not yet been fully exploited. ,. "' is exponentially
dependent on temperature and therefore cannot be treated as a
constant.
Figures The figures give a series of maps at 'various depths and
cross-sections
of shear velocity ( VSV) and shear wave anisotropy (XI). These
parameters are combined in seismic flow maps and cross-sections.
These maps and cross-sections are based on model NNA6 of Nataf,
Nakanishi and Anderson (Geophysical Research Letters, 1984).
XI is the anisotropy parameter (VSH)2 I (VSH)2 - 1 and is
positive for horizontal flow (a-axis horizontal for olivine).
The azimuthal variation map is from Tanimoto and Anderson
(Geophysical Research Letters, 1984) and is for 200 sec. Rayleigh
waves. The lines are oriented in the fast direction. For comparison
is the flow map of Hager and O'Connell.
The station residual maps are from a study by Dziewonski and
Anderson.
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Azimuth Independent Term
A
50° N A .a ..
• A
• Q.
0+1 sec
A-1 sec 30° N
150° w 120° w
~
A ..
A A~
90° w
... CJ-iM1 I ii ~!
till; D
D.L. Allderson 405
60° w
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-
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D.L. A1lderson 407
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-
Scale:
XI: -0.15
NNA6, Seismic Flow Map, depth: 100 km
D.L. Anderson 409
VSV: +0.20 km/sec
+0.15
-
410 Eoollltioft of Earlll Stnu:IMrr 01ld Fvblrr Dirrctions ;,,
•••
Scale:
XI: -0.15
NNA6, Seismic Flow Map, depth: 160 km
-0.20 km/sec
+0.15
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-
Scale:
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.YSV: +0.20 km/sec
-0.20 km/sec
NNA6, Seismic Flow Map, depth: 340 km
D.L. Andmon 411
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250
350
450
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XI: -0.15
NNA6: Flow Map Lat = 35, Lon = -108, Az. = 70
D.L. Andnson 417
+0.15
-
418 Eoohltilm of Earti Strucbtrr 4114 Ftlbm Dirrctions in
.••
2 per cent
Velocities Viscosity profile
260 km depth zls .,, (noise)
.99 • 1.00 1 ()23
.98 •. 99 1018
.89 •. 98 1022
.55 •. 89 1 ()25
Cylindrical EQuidistant
Scale= 75 MY A· upgoing .,.. downgoing