surface-wave propagation in an ocean basin with an anisotropic

Geophys. J. R. astr. Soc. (1981) 64,463-485

Surface-wave propagation in an ocean basin with an anisotropic upper mantle : numerical modelling

s. c. Kirkwood Deparrnient of Ceophj,sics, University of Edinburgh, James Clerk Maxwell Building. Edinburgh EH9 3JZ

Stuart Cramph Institute of Geological Sciences, Murchison House, West Mains Road, Edinburgh EH9 3LA

Received 1980 May 12; in original form 1979 November 20

Summary The characteristics of surface-wave propagation in ocean basins are examined numerically for models with two types of anisotropic alignment in the upper mantle: one resulting from glide-plane slip in olivine with horizontal or vertical slip-planes, and the other from syntectonic recrystallization of olivine in a zone of horizontal shear. Glide-plane slip can cause highly anomalous inclined-Rayleigh particle-motion in the third-generalized mode (corresponding to the isotropic second-Rayleigh mode). The amplitude of this anomaly is rather insensitive to details of the structure. Syntectonic recrystallization can cause an anomalous combination of inclined- and tilted- Rayleigh motion in all modes. The variation with period of the amplitude of the anomaly in the fundamental mode can indicate the approximate depth to the anisotropic layer. In both types of alignment, the sense of tilt and the inclination varies with direction of propagation in a manner characteristic of the structural symmetry.

1 Introduction

The theory of surface-wave propagation in multilayered anisotropic-media has been developed by Crampin (1 970) and Crampin & Taylor (1 971). Crampin & King (1 977) presented numerical results for models representing continental structures, and interpreted polarization anomalies in observations of higher-mode surface waves across Eurasia to indicate extensive anisotropy beneath the Moho. In this paper, we modify the computational procedure of Crampin &Taylor to accept a liquid surface-layer (details in Appendix, and in Kirkwood 1978a), and examine several possible anisotropic ocean-basin structures.

We do not aim to model any particular ocean-basin, but rather try to assess the likely effect on surface-wave polarizations of widespread anisotropic-alignments in the upper- mantle. The models are plane layered with an anisotropic layer, or layers, forming all, or part, of the top 120 km of the upper mantle. All the models are variations on a basic isotropic model, S-ISO, listed in Table 1, representing a stable, simplified ocean-basin some 50 Myr old.

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464 Table 1. Structure of isotropic model of ocean basin S-ISO.

S. C Kirkwood and S. Crampin

Thickness 01 P P

Name (km) (km s- I) (km s- I ) (g s- cm- 3,

water 4.5 1 .so 0 .oo 1 .o sediment 0.5 2.02 0.25 1.9 layer 3 6 .O 6.60 3.80 2.9 layer 4 60.0 8.10 4.40 3.3

60.0 I .48 4.10 3.4 Half-space 8.25 4.55 3.5

crust

Lithosphere Low-velocity-zone layer 5

The velocities and thicknesses assigned to the various layers in S-IS0 are similar to those derived from dispersion studies such as Schlue & Knopoff (1977) and Forsyth (1 975b), except that several thinner layers have been combined in S-ISO. For comparison purposes, the dispersion of the fundamental second Rayleigh and Love modes in t h s structure are shown in Fig. 1 .

2 Observations and theories of anisotropy in the oceanic upper mantle

Several authors have reported observations of upper-mantle anisotropy in oceanic areas. It has been detected at different depths according to the type of study, and in different forms. Refraction experiments have shown an azimuthal variation of between 3 and 8 per cent in P, velocity in the Pacific and Atlantic Oceans (see Hess 1964; Raitt et al. 1969; Raitt et al. 1971; Morris, Raitt & Shor 1969; Keen & Barrett 1971; Keen & Tramontini 1970 among others). Forsyth (1975b) found an azimuthal shear-wave anisotropy of between 2 and 6 per cent in the top 120 km of the upper mantle from the inversion of fundamental Rayleigh- and Love-mode surface waves across the NAZCA plate. The NAZCA plate is an ocean basin which appears to have evolved in a very uniform way with a regular sequence of approximately north-south isochrons. Such regularity is probably essential for azimuthal surface-wave velocity anisotropy to be observed. Most ocean basins have complex tectonic histories, and the limited earthquake to station paths usually cross complicated patterns of isochrons. Thus it

Figure 1. Phase-velocity dispersion of the fundamental and second (first-higher) Rayleigh (FR and ZR, respectively) and Love (FL and Z L , respectively) modes in the isotropic structure S-ISO.

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Oceanic surface waves in an anisotropic upper mantle - I 465

is not surprising that Schlue & Knopoff (1977) were unable to resolve azimuthal anisotropy, for very long paths across the Pacific Basin. They found they could model, to within the errors of their observations, both Love and Rayleigh wave velocities only if shear-wave velocities in the upper mantle varied with the wave type. Their successful models have about 3 per cent difference in SH and SV velocities in the low-velocity zone (LVZ). Forsyth’s (1975b) inversions also suggested that the anisotropy may extend into the LVZ. However, both Schlue & Knopoff (1977) and Forsyth (1975b) inverted their anisotropic observations with isotropic inversion procedures. Such combinations may lead to significant erros in interpreting the anisotropy (Crampin, 1976; Kirkwood 1978b), and the depth of the anisotropy in the upper mantle is unresolved.

Many studies have been made of the possible mechanisms by which upper-mantle anisotropy might be generated. Most authors consider that preferred orientation of olivine, aligned either by glide-plane slip in shear zones (e.g. Hess 1964; Francis 1969; Carter & Av6 Lallemant 1970), or by syntectonic recrystallization (AvC Lallemant & Carter 1970), is likely to be responsible. Seismic anisotropy, related to olivine alignment has been measured in peridotite specimens (Meissner & Fakhimi 1977; Peselnick, Nicolas & Stevenson 1974), and alignment of olivine has been artificially produced in rocks in laboratory deformation experiments (Carter & AvC Lallemant 1970).

In this study we include a range of anisotropic models t o cover the several anisotropic configurations suggested by the surface-wave inversions and mechanism theories: models with anisotropy only at the very top of the lithosphere might explain the P, refraction results; thicker anisotropic layers would be needed to explain the results of surface-wave dispersion studies; an anisotropic lithosphere might be produced if crystalline alignment occurs as the lithosphere forms and is ‘frozen-in’; and an anisotropic LVZ could result from alignment by active strain in that zone. The amount of anisotropy proposed varies, but is generally in the range 4-8 per cent for P-waves (Fuchs 1977).

There are three possible structural symmetries which might result from the different alignment mechanisms proposed:

A transversely isotropic structure, with vertical symmetry axis, would result from alignment of partial-melt pockets in the low-velocity zone as proposed by Schlue & Knopoff (1978) and this could explain the Love-Rayleigh structural incompatibility but not the azimuthal anisotropy. Apart from Forsyth’s (1975b) observations in the NAZCA plate, there is only weak evidence for azimuthal anisotropy, except at the very top of the lithosphere, so such a structure cannot be discounted. However, this study is concerned primarily with surface- wave particle motion, which would not be anomalous in such a structure (Crampin 1975), so this symmetry is not represented in the models.

A structure with two orthogonal, vertical symmetry-planes would result if olivine alignment IS produced by glide-plane slip in a zone of horizontal or vertical shear-strain (Hess 1964; Francis 1969; Carter & AvC Lallemant 1970). This symmetry can be modelled by including an upper-mantle layer incorporating olivine, aligned with one crystallographic axis horizontal. Most models here use transversely isotropic (hexagonal) olivine (TOLIVINE in Table 2), which is symmetrical about the a-axis. This is aligned with the a-axis horizontal, as proposed by Carter & AvC Lallemant (1 970).

A structure yith only one vertical symmetry plane would result if there is olivine alignment by syntectonic reciystallization (AvC Lallemant & Carter 1970). Such symmetry can be modelled by including a layer similarly incorporating hexagonal olivine, but with the a-axis tilted at 45’ to the horizontal.

The anisotropic materials used in the models are formed by combining olivine with isotropic materials in suitable proportions. The elastic constants for olivine have been measured by

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Table 2. Elastic constants, Cjkmn, of anisotropic layers (in 108N m- *),and 01 and p are the compressional and shear wave velocities in the isotropic constituents. The density of all the material is p =3.34g ~ r n - ~ .

AOLIVINE : XTOL5 050 Orthorhonibic olivine (Verma 1960)

i k m n cjkmn i k m n Cjkmn

1 1 1 1 3240 1 1 1 1 2465 2 2 2 2 1980 2 2 2 2 1962 3 3 3 3 2490 3 3 3 3 1962 1 1 2 2 590 1 1 2 2 710 2 2 3 3 780 2 2 3 3 755 3 3 1 1 790 3 3 1 1 710 1 2 1 2 793 1 2 1 2 766 2 3 2 3 667 2 3 2 3 6 04 1 3 1 3 810 1 3 1 3 766

TOLNINE: TTOL2080 : hexagonal olivine symmetrical about a-axis

50 per cent TOLIVINE 50 per centisotropic (a=7.34,p=4.69kms- ' )

20 per cent TOLIVINE 80 per cent a = 7.10 kms-I, p = 3.91 km s- '

i k m n Cjkmn i k ?71 n Cjkmn

1 1 1 1 3240 1 1 1 1 1989 2 2 2 2 2235 2 2 2 2 1788 3 3 3 3 2235 3 3 3 3 1788 1 1 2 2 690 1 1 2 2 6 80 2 2 3 3 7 80 2 2 3 3 698 3 3 1 1 690 3 3 1 1 6 80 1 2 1 2 801.5 1 2 1 2 559 2 3 2 3 727.5 2 3 2 3 545 1 3 1 3 801.5 1 3 1 3 559

XTOL2080: XAOL2080: 20 per cent TOLIVINE 80 per cent 01 = 7.78 km s- I , p = 4.54 km s-

i k m n Cjkmn i k n Cjkmn

1 1 1 1 2254.87 1 1 1 1 2255 2 2 2 2 2052.37 2 2 2 2 2003 3 3 3 3 2052.37 3 3 3 3 2105 1 1 2 2 665.26 1 1 2 2 630 2 2 3 3 710.26 2 2 3 3 668 3 3 1 1 665.26 3 3 1 1 670 1 2 1 2 708.05 1 2 1 2 707 2 3 2 3 671.05 2 3 2 3 681 1 3 1 3 708.05 1 3 1 3 710

TTOWOSO: TAOL5 0 50 5 0 per cent TOLIVINE 5 0 per cent a=5.65kms-l , P=3.27kms-'

i k m n Cjkmn i k m n Cjkrnn

1 1 1 1 2151.75 1 1 1 1 2151.75 2 2 2 2 1649.25 2 2 2 2 1520 3 3 3 3 1649.25 3 3 3 3 1775 1 1 2 2 522.25 1 1 2 2 470 2 2 3 3 567.25 2 2 3 3 565 3 3 1 1 522.25 3 3 1 1 5 70 1 2 1 2 578 1 2 1 2 5 74 2 3 2 3 541 2 3 2 3 511 1 3 1 3 5 78 1 3 1 3 582

20 per cent AOLIVINE 80 per centa=7.78kms- ' ,P=4.54kms- '

50 per cent AOLIVINE 50 per cent a =5.65 km SKI, p = 3.27 km SKI

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A W >

I 1 I

QSH

QSV

5

L U 0' 30' 60' 90'

'I i QSV 5

4 0' :rr! 30' 60' 90' Q S H

100 t o 010 010 to 001 001 to 100 (a) (001)-CUt (1 00) - c u t (010) - c u t

1

m

t c - V 0 > W >

Q P

asii as v

001 to100 100 t o 010 01 0 to 001 (001)-cut (100)- c u t (010)- c u t (b)

Figure 2. Variations of body-wave velocities over quadrants in the three orthogonal synimetry planes fIom elastic constants in Table 2: (a) orthorhombic olivine: AOLNINE, and (b) hexagonal (transversely isotropic) olivine: TOLIVINE; where the b- and c-axes of AOLIVINE have been averaged. QP refers to the quasi? wave, and QSH and QSV to the quasi-shear waves with polarizations parallel and perpendicular, respectively, to the plane of the quadrant. Thus, QSH and QSV are polarized horizontally and vertically when the plane of cut is horizontal.

Verma (1960). These are listed in Table 2, and the associated body-wave velocities are illustrated in Fig. 2. A collection of crystals with a-axes all aligned parallel and with b- and c-axes randomly orientated will have elastic constants and associated velocities as given for TOLI- VINE in Table 2 and Fig. 2. The ratio of aligned olivine to isotropic material is 1 : 4 for models

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468

representing ’weak anisotropy’, I : 1 for ‘strong anisotropy’, corresponding to P-wave aniso- tropies of 4 and 10 per cent respectively. The isotropic materials mixed with the olivine are chosen so that the average seismic velocities are close to those of the isotropic model S-ISO. We obtain the elastic constants of the mixtures by averaging appropriate anisotropic and isotropic constants in the given proportions. This is a first-order approximation, but it is simple, direct and adequate for modelling weak anisotropy.

S. C. Kirkwood and S. Crampin

3 Structural symmetry and characteristic surface-wave polarizations There is one family of generalized-mode surface waves propagating in a layered anisotropic structure. These waves have elliptical polarization in three dimensions, where the character of the polarization is determined by the symmetry structure of the anisotropic media (Crampin 1975; Taylor & Crampin 1978). Several distinct classes of polarization can be identified. The two ofinterest to us here are:

(1) Inclined-Rayleigh polarization, where the motion is elliptical in a vertical plane inclined to the direction of propagation, characteristic of surface waves propagating in a structure with a horizontal plane of symmetry.

(2) Tilted-Rayleigh polarization, where the motion is elliptical in a plane through the direction of propagation, but tilted away from the vertical. T1-Lls is characteristic of surface waves propagating perpendicular to a vertical plane of symmetry.

Earth models containing olivine aligned by ghde-plane slip have two vertical planes of overall elastic symmetry perpendicular to the olivine a- and c-axes, and a horizontal plane perpendicular to the b-axis. The identifiers of such models include the suffix 010. Earth models with olivine aligned by syntectonic recrystallization have only one vertical plane of elastic symmetry, perpendicular to the c-axis. Models of this type are indicated by the suffix 110.

The characteristic polarizations of surface waves propagating in these two types of structural symmetry are illustrated in Fig. 3 . Waves travelling parallel to vertical symmetry planes have pure Rayleigh- or pure Love-type polarizations. Waves travelling in off-symmetry directions, in structures with a horizontal plane of symmetry ((010)-models), have inclined- Rayleigh motion (Fig. 3a). Such polarizations have been observed for higher-mode surface waves propagating across much of Eurasia (Crampin & King 1977). Waves travelling in off- symmetry directions, in structures with one vertical plane of symmetry ((1 10) models), have a combination of inclined- and tilted Rayleigh motion (Fig. 3b): inclined to the direction of propagation and tilted away from the vertical.

A very important difference between anisotropic and isotropic surface waves is that for anisotropic propagation the polarization may identify the direction of propagation with respect to the orientations of the anisotropic structures. In a plane layered isotropic structure the propagation characteristics of surface waves are the same in all directions, whereas in anisotropic media the polarizations vary with the direction. The poIarity of the inclination and the polarity of the tilt each determine one pair of possible azimuthal quadrants of propagation as in Fig. 4. If the wave is both tilted and inclined, as in the (1 10)-model in Fig. 3(b), the quadrant of propagation is uniquely defined by the polarity, which can be used to determine the quadrant in relation to the up-tilted a- and b-axes.

The details of particle motion will vary with the model, and several models will be examined to assess the possible effects on surface waves in the Earth. The dispersion and polarization of different models are described in some detail by Kirkwood (1978a), and the details are summarized in Figs 5 to 16 giving the polarizations of surface waves of the models listed in Table 3.

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Figure 3. Characteristic polarizations of surface waves in models with: (a) two vertical planes of symmetry, and (b) one vertical plane of symmetry. The orientations of olivine crystallographic axes in: (a) (010)-models, and (b) (110)-models are indicated at the centre of each diagram. Angles indicate the convention used for azimuth of wave propagation. Note that pure Rayleigh- and pure Love-type particle motion occurs for propagation parallel to symmetry planes at 0" and 90" in (a), and at 0" in (b).

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470 S, C. Kirkwood and S. Crampin

(a) ( b )

Figure 4. Characteristic azimuthal variation in relative phases of transverse and vertical components of surface-wave polarizations, and amount of: (a) anomalous inclination in (010)-models, and (b) anomalous tilt in (110)-models. Lines SS indicate the directions of planes of structural symmetry. The scale of the anomalies varies greatly from mode to mode and model to model (see Figs 17 and 18).

4 Model phase-velocities and polarizations, and the correspondence between isotropic and anisotropic modes

T h e dispersion of tlie first four generalized modes FG, 2G, 3G and 4G for two anisotropic models, S3T and SIX, are given in Figs 5 and 6 for tlie two symmetry orientations (010) and (110). Model S3T has an anisotropiclow-velocity zone (LVZ), and S1X anisotropic lithosphere. Dispersion is drawn for four directions of propagation at 30" intervals from the (010)-plane of symmetry. In general, the polarizations of the generalized modes alternate between similarity to Rayleigh motion and similarity to Love motion except where, at shorter periods,

Table 3. Model anisotropic structures. All structures are the same as S-IS0 (Table 1) except as indicated.

Model name

s1x s3x S4X A1X C I X S1T S3T S6T A3T S3XT

Location

all of lithosphere all of lithosphere all of lithosphere top of lithosphere base of lithosphere all of LVZ all of LVZ all of LVZ

all of lithosphere and LVZ

top of LVZ

Anisotropic layer Percentage of aligned

Thickness olivine (km) material

60 20* 6 0 50 60 20 10 20 1 0 20 6 0 20 60 50 60 50 10 50

20

1 5 0 120

Name of anisotropic mixture

XTOL2080 XTOL5050 XAOL2080 XTOL2080 XTOL2080 TTOL2080 TTOL5050 T A 0 L5 0 5 0 TTOL5050 XTOL2080 and TTOL5050

X in model name indicates anisotropy in the lithosphere, and T indicates anisotropy in the LVZ. Identifiers are of form IJKijk-mn, where IJK refers to model name, ijk is either (010) or (1 10) denoting anisotropic alignment, and rnn is the total thickness of the anisotropic layer.

* Note that the percentage of aligned olivine in the mixtures should not be confused with the percentage of velocity anisotropy which is much smaller.

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Oceanic surface waves in an anisotropic upper mantle - I 47 1 I I I I I 1

I I I I I

0 40 8 0 120 160 PERIOD I s )

(b) Figure 5. Phase-velocity dispersion of the first four generalized-mode surface-waves, for four different azimuths of propagation, in structures with strong anisotropy in the LVZ: The convention for azimuth is as indicated in Fig. 3(a) and 0). (a) S3T01060, and (b) S3T11060.

modes pinch together and exchange polarization characteristics (Crampin & Taylor, 1971). Thus the FG and 3G modes in Figs 5 and 6 correspond approximately to the isotropic fundamental- and second-Rayleigh modes, and the 2G and 4G modes to fundamental- and second-Love modes. The anisotropic LVZ in S3T has a greater degree of anisotropy than the lithosphere in S1 X, and this is reflected in the amount of surface-wave velocity-anisotropy . The maxima and minima of the phase velocities repeat every 180" azimuth for modes corresponding to isotropic Rayleigh modes, and every 90" for modes corresponding to

S1 X 01 0-60 I I I

0 LO 8 0 12 0 PERIOD ( 5 )

(a)

I I I

3 8 I S1 X I 1 0-60 I I I I

3 0 LO 80 120 PERIOD i s )

(b )

10

Figure 6. Phase-velocity dispersion in structures with weak anisotropy in the lithosphere: (a) SlXO1060, and (b) SlX11060.

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472 S. C. Kirkwood and S. Crampin

FG 20s 60s 18s

i t t 2G

120s 60s 30s 15s

S 3 T 0 1 0 - 6 0

3G 27s 155

- 4 G 15s -

(a )

Figure 7. Polarization diagrams of the f i s t four generalized-mode surface waves in models of oceanic basins. Polarization diagrams are in pairs: the upper plot being a horizontal cross-section, and the lower plot a vertical section parallel to the direction of propagation. All sections are drawn to the same scale. Polarization diagrams for S3T, which has 60 km of strong anisotropy in the LVZ.

isotropic Love-modes. These angular variations are similar to the angular variations of P- and SV-waves (180'1, and SH-waves (90") propagating in olivine structures, as in Fig. 1. The degree of velocity anisotropy is generally rather greater for FG than for 2C, but is similar for both (010) and (1 10) configurations.

The surface-wave polarizations in these two models are lllustrated in Figs 7 and 8. The anisotropic symmetry planes lie in the 0" and 90" directions for (010)-models, and the 0" direction for (1 lO)-models, and in these directions the polarizations are of isotropic Rayleigh- or Love-type. In non-symmetry directions, the polarizations may display strong anomalies from isotropic motion.

Note that the 4G motion at 15 s in the 0' direction in model S3T110 (Fig. 7b) does not fit into the general pattern of anomalies. The dispersion curves of the higher modes at such

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Oceanic surface waves in an anisotropic upper mantle - 1 473

FG 20s 60s 18s

2 G 120s 60s 30s 15s + - " - - I I

I

+ I F X

S 3 T 11 0 - 60

- 4G 15s

Figure 7 (b)

periods are very close together (see Fig. 5b) with many pinches in non-symmetry directions and mode crossings in symmetry directions. The modes change polarization characteristics at such places, and thls is probably what has occurred here, but the exact behaviour is difficult to follow in such circumstances without extensive investigations, and these have not been made.

5 Polarization diagrams

Summaries of polarization diagrams for all models are shown in Figs 7 to 16. The most striking polarization anomalies, that is departures from isotropic purely Rayleigh- or purely Love-type particle motion, are in mode 3G. This mode shows inclined-Rayleigh motion in (010)-models with inclinations of up to 60°, and a combination of inclined and tilted motion in the (110)-models. In the (110)-models, there are also fairly large anomalies in FG and 2G, and smaller effects in the 4G modes. There are no anomalies in the FG and 2G modes in any of the (010)-models except at the shortest periods.

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474 S. C. Kirkwood and S. Crampin

FG 20s 60s 15s

i f ' t

" r t

t f l '.b -b I P

2 G 120s 60s 30s 15s

t b I

I

iir

6

4- I

I P

--t

P

S1 X O I O - 6 0

3 G 26s 15s

(a)

Figure 8. Polarization diagrams for S l X , with 60 km of weakly anisotropic lithosphere.

Typical azimuthal variations for the two types of alignments are shown in Fig. 17. In general, the amplitudes of anomalies vary comparatively slowly with the direction of propagation except close to symmetry directions, where they fall very rapidly to zero. This is the justification for summarizing individual polarization diagrams in Figs 9 to 16, and summarizing the variations with period in Fig. 18.

5.1 E F F E C T S O F D E P T H O F A N I S O T R O P I C L A Y E R

The variation with period of the amplitude of the anomalies is summarized in Fig. 18. The size of the 2G and 3G anomalies usually increases with decreasing period down to about 15 s period. The FG anomalies have a maximum at intermediate periods and become smaller at short periods for models with anisotropy in the LVZ, and increase with decreasing period for models with anisotropy in the lithosphere.

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FG 20s 60s 15s

5 -T: .c;

2 G 120s 60s 30s 15s

f” I -f;. +I.

I

i-c .+ s - tit- I

I

S I X I I O - 6 0

3 G 26s 15s

4G 15s -

Figure 8(b)

The depth range of the anisotropy also affects the maximum amplitude of the anomaly. For example, the anomalies generated in FG and 2G in model S l X l l O at periods of 60 s and less are larger than those in model S3T110, although the latter has a greater degree of intrinsic anisotropy, indicating that the particle motion of these modes and periods is more sensitive to anisotropy in the lithosphere than in the LVZ. Conversely, comparison of S3X and SIT where the former includes a greater degree of anisotropy, shows that anomalies in 3G are more affected by anisotropy in the LVZ. This is particularly marked for the (010)- models.

5.2 C H A N G E S IN D E G R E E O F A N I S O T R O P Y

Models S3T and S3X (Figs 7 and 10) have similar structures to S1T and SIX (Figs 9 and S), respectively, but incorporate a greater degree of olivine alignment. Comparison of the polarization diagrams shows that, in general, an increase in the degree of anisotropy results in a larger increase in the FG and 2G anomalies in the (1 10)-models, but little change in the .?G‘ anomalies in either (1 10)- or (010)-models.

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r

FG

- 4G 15s - -

2G

FG 2G 3G 1 2 0 ~ 6 0 s 17s 120s 60s 3 0 s 15s 2 9 s 15s

t

51 T 01 0 - 60

I FG I 2G 3 G 4G 1120s 60s 17sI 120s 60s 30s 15s 20s 15s 15s

-b

I I

-b I

-

i c : i S I T 1 1 0 - 6 0

Figure 9. Polarization diagrams for S1X with 60 km of weak anisotropy in the LVZ.

4G I FG I 2G 3G 28s 15s 15s 1120s 60s 1 9 s l 1 2 0 s 60s 30s 15s

t T -4

S3XO10-60

4G 15s - -

-i- d

3G 27s 15s 1120s 60s 15s 1120s 60s 30s 15s

I I

I S3X110- 60 (b) I

Figure 10. Polarization diagrams for S3X with 60 km of strong anisotropy in the lithosphere.

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FG 120s 60s 15s 9 28s 15s 15s

2G 120s 60s 30s 15s

I A 3 T 0 10 - 10

6 6

FG 120s 60s 15s

i l l 2G

FG 2 G 3 G 120s 60s 15s 120s 6 0 s 30s 15s 26s 15s

't i 1 -7- d i - 1 I I t f , ;,

6 6

'+ +

120s 60s 3 0 s 15s I

4G 15s

J - + 4

I

A3 T 11 0 - 10

FG 2 G 3G 120s 60s 15s 120s 60s 30s 15s 26s 15s

6 6 H i ' - t . + + f i +

3G 2 8 s 15s

4 G 15s

Figure 11. Polarization diagrams for A3T with a 10-krn thick layer of strong anisotropy in the LVZ

A I X 1 1 0 - 1 0 (b )

Figure 12. Polarization diagrams for A1X with a lOkm thick layer of weak anisotropy in the top of the lithosphere.

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2 G

1120s 60s 15s 120s 60s 30s 15s

ir I

66 3. ".

, I 4 ' $ c

c1 XOIO-10

2 G I 3 6 4G 1120s 60s 15s 120s 60s 30s 15sl 27s 15s 15s

t ? ! - i -

66

c 1 x110-10

Figure 13. Polarization diagrams for C1X with a 10-km thick layer of weak anisotropy at the base of the lithosphere.

2 G 1 3 G 1 4 G 120s 6 0 s 30s 15sI 22s 1SsI 15s 120s 60s 15s

S3XT 010 - 120 (a)

FG 2G I 3 G 1 4 G 120s 60s 30s 1 5 s I 2 4 s 1Ssl 15s 120s 6 0 s 15s

S3XT110- 120

Figure 14. Polarization diagrams for S3XT with uniformly orientated anisotropy in both the 6 0 k m thick lithosphere and the 6 0 k m thick LVZ.

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FG 120s 6 0 s 17s

$ 4 + 90"

J/

479

2 G 3 G 4G 120s 60s 3 0 s 15s 28s 15s 15s

I I +I-- r *=- , 4- ,;7 -1, y I -

t 1 I k * j t ;

'

I

Figure 15. Polarization diagrams for S6T with 60 km of strongly anisotropic orthorhombic-olivine in the LVZ.

-90'

5.3 C H A N G E S IN T H I C K N E S S O F A N I S O T R O P I C L A Y E R S

Figs 11, 12 and 13 show polarization diagrams for models A3T, A1X and CIX, which have only a thin (10 km) anisotropic layer situated at the top of the LVZ, the top of the lithosphere, and the base of the lithosphere, respectively. There are almost no anomalies visible for any mode, except for 3G in model A3T.

Thus, although a rather thick layer is necessary to generate significant anomalies in FG and 2G, a thin layer can generate large anomalies in the 3G mode. Crampin & King (1977) came to similar conclusions in interpreting polarization anomalies of surface waves across Eurasia, although the continental structure made the 3G anomalies more sensitive to litho- spheric rather than LVZ anisotropy.

There are large anomalies on FG, 2G and 3G modes when the anisotropy extends through- out both the lithosphere and the LVZ with the same alignment (model S3XT, Fig. 14), those on 2G being rather larger than the sum of those produced by an anisotropic lithosphere and LVZ in isolation. Those in 3G are similar to those found for an anisotropic LVZ, again indicating that 3G is particularly sensitive to LVZ anisotropy.

The anomalies on FG and 2G in this model, S3XT, are larger than in any other model examined. However, the particle motion is still close enough to isotropic Rayleigh- and Love-motion, respectively, especially at long periods, to easily escape notice unless a specific search is made.

FG 2 G 3 G 4G 120s 60s 15s 120s 60s 30s 15s 2 6 s 15s 15s

1 1 t + + - l - 4 = 1 + + + , i + '+

Figure 16. Polarization diagrams for S4X with 60 km of weakly anisotropic orthorhombicdivine in the lithosphere.

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480 S. C. Kirkwood and S. Oarnpin

m o d e F G 110-mode ls mode 2G 110-models

mode 3G 110-models mode 3G 010-models

Uy!U, T=ZOs U y / U x T .20~

S 3 T

51 x __.__._ ~~

Figure 17. Theoretical azimuthal variation of amplitudes of polarization anomalies in models S3T and S1X having 60 km of anisotropy in the LVZ and the lithosphere, respectively.

5.4 C O M P A R I S O N B E T W E E N O K T H O K H O M B I C A N D H E X A G O N A L O L I V I N E

Most of the models examined here contain anisotropic layers with the hexagonal form of olivine. However, olivine aligned by syntectonic recrystallization is likely to retain the full orthorhombic form of olivine. Comparison of Figs 15 and 16 (illustrating polarization anomalies in models S6T110-60 and S4X110-60, with orthorhombic olivine), with Figs 5(b) and 6(b) (models S3T110-60 and SlXl lO-60, with hexagonal olivine), demonstrate that for many purposes the differences between orthorhombic and hexagonal olivine are neghgible, the only signiflcant difference being an increase in the anomalous vertical com- ponent of ZG, at short periods, in model S6T110. %s might be expected as orthorhombic olivine has a larger velocity variation in any vertical plane than hexagonal olivine (Fig. 2), giving a greater tilting effect on the plane of polarization.

The similarities between orthorhombic and hexagonal olivine can also be seen by comparing the body-wave variations in Fig. 2.

6 Effects of the Earth’s sphericity

Techniques for m o d e h g surface waves in a spherical, gravitating, anisotropic Earth have not ye t been developed. The effects of sphericity in isotropic structures can be modelled by imposing an extra velocity-gradient on a plane-layered structure (Alterman, Jarosch & Pekeris 1961), resulting in increased phase-velocities, especially at long periods, and possibly slight changes in particle motion. Schlue & Knopoff (1978) diqcuss the effect of sphericity on anisotropic structures and derive some empirical formulae for modifying FR velocities in

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Oceanic surface waves in an anisotropic upper mantle - I 48 1

1 o k 1 lo- k mode F G 1

\S3XT - w - \ W T3 0 - E ,S3T

z 1 - , ’

0 I \ \\ ,SIT \ ‘ ).: m -

T3

3

0 - + m - e

A1 X

Period ( s 1

0 01 1

10

3

Figure 18. Variation with wave period of the maximum amplitude of polarization anomalies for several models.

an anisotropic spherical model. In this paper we are not trying to model observed dispersion curves for the various modes, and may neglect the effects of sphericity. The form of the particle motion depends on the local symmetry structure and the amplitude of the anomaly rather appears to be insensitive to the details of the layered structure and will not be affected by the overall sphericity.

7 Conclusions

Large polarization anomalies are likely to occur in the third-generalized surface wave mode, 3G (corresponding to the isotropic second-Rayleigh mode), in the presence of quite small amounts of aligned anisotropic material in the top 12Okm of the oceanic upper mantle. A comparatively thin anisotropic layer in the LVZ could generate significant anomalies.

16

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482

Even larger thicknesses of (010)-model anisotropy, where the olivine has been aligned by ghde-plane slip on horizontal planes, do not cause significant anomalies in other surface wave modes, FG, 2G and 4G. However, when the olivine is aligned by syntectonic recrystallization in a zone of horizontal shear, so that a- and b-axes are inclined to the horizontal, as in (llO)-models, quite large polarization anomalies occur on all modes, provided that a fairly thick (a few tens of kilometres) anisotropic zone is present. In oceanic structures a thick anisotropic zone with comparatively uniform alignments is likely, whereas beneath continents it is possible that the alignments vary with depth (Crampin 1977b). Such layered alignments would severely modify polarization anomalies requiring large thicknesses for their generation.

Glide-plane slip alignments in the real Earth ((010)-models) should show the 3G mode with inclined-Rayleigh wave polarization, with the variation of inclination with azimuth as indicated in Fig. 3(a). Such anomalies have been observed for 3G modes propagating across Eurasia, and can also be generated by thin anisotropic (010)-layers in the continental upper mantle (Crampin & King 1977). It will be difficult to observe such polarizations on seismograms from oceanic paths. Any error in assigning a direction of travel to the wave, due to refraction across an oceanic-continental boundary for example, will cause pure Rayleigh motion t o appear as inclined-Rayleigh motion. More important, the group velocity of the 3G mode is very close to the 2G,4G and higher modes for oceanic paths. Consequently, several interfering wave-trains are frequently recorded on the seismogram. Techniques exist for isolating the velocity dispersion of individual modes along paths where there is multi-mode interference (Forsyth 1975a), but they cannot be applied to isolating the particle motion. Only events in which 3G is preferentially excited will be useful observationally. If observations can be made, the relative phases of the radial and transverse components of polarization, as shown by the t and - signs in Fig. 4(b), should locate the planes of symmetry of the underlying structure. However, since these 3G anomalies vary irregularly with depth, thickness and degree of anisotropy present, little information about these parameters is likely to be resolvable from the observations.

Anomalous polarizations should be observable in any mode, if the olivine alignment in the Earth is similar to the (1 10)-models. Anomalies in 2G should be easiest to observe as, for very long paths, the periods for which anomalies occur arrive after the higher- mode surface waves and before the fundamental mode. They also arrive after most of the body-wave phases for paths longer than about 7000 km. Vertical and transverse components will show coupling on the seismograms. Such coupling cannot result from direction of travel or calibration errors, so that accuracy in measuring these parameters is less important than for observations of the inclined-Rayleigh waves in (010)-models. The pattern of relative phases of vertical and transverse components, as shown in Fig. 4(b), will again indicate the plane of symmetry of the underlying structure.

In all the (1 10)-models examined here, the particle-motion ellipse in mode 2G is tilted towards the direction of the olivine a-axis, as in Fig. 3(b), so that a pattern of relative phases, as in Fig. 4(b), also indicates the direction of alignment of the a-axis w i t h the plane of structural symmetry. This in turn should indicate the sense of shear for alignment by syntectonic recrystallization (AvC Lallemant & Carter 1970).

It seems likely that both ghde-plane slip and syntectonic recrystallization have aligned olivine in the upper mantle, where each mechanism predominates in a different depth range. In such a case, anomalies due to the former alignment will be found only by careful analysis of 3G modes (second Rayleigh). Anomalies due to the latter alignment mechanism will be much more obvious, being displayed best by mode 2G (fundamental Love), as well as by mode FG (fundamental Rayleigh) and the higher modes. Even quite large amounts of


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Oceanic surface waves in an anisotropic upper mantle - I 483 olivine aligned by glide-plane slip might have their effects masked by the presence of a zone with alignment by syntectonic recrystallization.

There are too many possible combinations to present an exhaustive list of the effects of anisotropic symmetries in all possible locations within ocean basins. What we have indicated is that the polarizations o f surface waves may contain much information about the location and orientation o f anisotropy in the upper-mantle. In addition, since the polarizations largely depend on the structure within a few wavelengths of the recording station, the interpretation of polarizations does not have some of the problems associated with the interpretation of dispersion curves of surface waves averaged over very long paths across structures of varying ages.

Acknowledgments

The work of S. Kirkwood was supported by a Research Studentship of the Natural Environ- ment Research Council. The work of Stuart Crampin was also supported by NERC and is published with the approval of the Directors of the Institute of Geological Sciences.

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Avd Lallemant, H. G. & Carter, N. L., 1970. Syntectonic recrystallization of olivine and modes of flow in

Carter, N. L. & AvB Lallemant, H. G., 1970. High temperature flow of dunite and periodite, Bull. geol.

Crampin, S., 1970. The dispersion of surface waves in multilayered anisotropic media, Geophys. J. R.

Crampin, S., 1975. Distinctive particle motion of surface waves as a diagnostic of anisotropic layering,

Crampin, S., 1976. A comment on ‘The early structural evolution and anisotropy of the oceanic upper

Crampin, S., 1977a. A review of the effects of anisotropic layering on the propagation of seismic waves,

Crampin, S., 1977b. Palaeoanisotropy in the upper mantle,Nature, 270,162-163. Crampin, S. & King, D. W., 1977. Evidence for anisotropy in the upper mantle beneath Eurasia from the

Crampin, S. & Taylor, D. B., 1971. The propagation of surface waves in anisotropic media, Geophys. J. R.

Forsyth, D. W., 1975a. A new method for the analysis of multi-mode surface-wave dispersion: application

Forsyth, D. W., 1975b. The early structural evolution and anisotropy of the oceanic upper mantle,

Francis, T. J . G., 1969. Generation of seismic anisotropy in the Upper Mantle along the midaeanic

Fuchs, K., 1977. Seismic anisotropy of the subcrustal lithosphere as evidence for dynamical processes in

Hess, H., 1964. Seismic anisotropy of the uppermost mantle under oceans,Nature, 203,629-631. Keen, C. E. & Barrett, D. L., 1971. A measurement of seismic anisotropy in the Northeast Pacific, Can. J.

Keen, C. E. & Tramontini, C., 1970. A seismic refraction survey on the mid-Atlantic ridge, Geophys.

Kirkwood, S. C., 1978a. Seismic surface-waves and anisotropic alignments in the oceanic upper-mantle,

Kirkwood, S. C., 1978’0. The significance of isotropic inversion of anisotropic surface-wave dispersion,

Meissner, R. & Fakhimi, M., 1977. Seismic anisotropy as measured under high-pressure, high-temperature

J. R. astr. SOC., 4, 219-241.

the upper mantle, Bull. geol. Soc. Am., 81,2203-3220.

Soc. Am., 81,2181-2202.

astr. SOC., 21,387-402.

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mantle’, Geophys. J. R. astr. Soc., 46, 193-197.

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polarization of higher mode seismic surface waves, Geophys. J. R. astr. Soc., 49,59-8.5.

astr. Soc.. 25,71-87,

to Love-wave propagation in the East Pacific, Bull. seism. SOC. Am., 65, 323-342.

Geophys. J. R. astr. SOC., 43,103-162.

ridges,Nature, 221,162-165.

the upper mantle, Geophys. J. R. astr. Soc., 49,167-179.

Earth Sci., 8,1056-1064.

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PhD dissertation, University of Edinburgh.

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conditions, Geophys. J. R. astr. SOC., 49,133-143.

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Morris, G . B., Raitt, R. W. & Shor, G. G . , 1969. Velocity anisotropy and delay time maps of the mantle

Peselnick, L., Nicolas, A. & Stevenson, P. R., 1974. Velocity anisotropy in a mantle peridotite from the

Raitt, R. W., Shor, G . G. , Francis, T. J . & Morris, G. B., 1969. Anisotropy of the Pacifc upper mantle,

Raitt, R. W., Shor, G. G. , Morris, G . B. & Kirk, H. K., 1971. Mantle anisotropy in the Pacific ocean,

Schlue, J . W. & Knopoff, L., 1977. Shear wave polarization anisotropy in the Pacific Basin, Geophys.

Schlue, J . W . & Knopoff, L., 1978. Inversion of surface-wave phase velocities for an anisotropic

Taylor, D. B. & Crampin, S., 1978. Surface waves in anisotropic media: propagation in a homogeneous

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near Hawaii, J. geophys. Rex , 74,4300-4316.

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Appendix: introduction of liquid surface layer to anisotropic calculations

The mathematical treatment of elastic-wave propagation in a plane multilayered anisotropic structure has been developed by Crampin (1970, 1977a) and a procedure for the computation of dispersion and polarization characteristics of normal-mode surface waves has been described by Crampin & Taylor (1971).

Crampin (1970) shows that, for propagation in the x-direction of a plane, multi-layered structure, z > 0, the excitation functions for waves in the half-space are related to the particle velocity and stress at the surface, z = 0 by

(f(l)>f(2),f(3)7 o,o, 0) = G(u/c, w/c, P 3 3 , Pi39 v/c, p23)z=O, (-41) where f(l), f ( 2 ) andf(3) are the excitation functions corresponding to the three downward propagating waves in the halfspace. u , u and li, are the particle velocities at the surface, p33 , p I 3 , and p23 are the normal, transverse, and tangential stress components at the surface, c is the phase velocity along the surface, and G is a 6 x 6 matrix with elements depending on the frequency and velocity of the wave and the elastic constants and thicknesses of the layers.

A solution for this equation can be found by using the boundary condition that stresses vanish at the surface so that

(f(1),f(2),f(3), o,o, 0) = G(h/c. w/c, o,o, u/c, O),=o. (A21

det(J) = 0 (A31

Non-trivial values of u, u and w exist only if

where

g41 g42 g45 i g61 g62 g65 1 J = g51 g52 g55 ,

and g,, are the elements of G. Equation (A3) can be solved numerically by recalculating the matrix G, for different values of frequency o and velocity c, until the position of the zero determinant can be estimated (Crampin & Taylor 1971).

A surface water-layer can be specified by forming the matrix G from the solid layers only, so that, in equation (Al), the velocities and stresses are those at the solid-liquid interface z = d. At this interface, pI3 and p 2 3 and zero are only w and p 3 3 are continuous. The normal

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Oceanic surface waves in an anisotropic upper mantle - I 485 stress p33 can be eliminated by reconsidering the relationship between velocity and stress in the liquid layer, and we can derive an equation of the same form as (A2).

The slowness equation for propagation in the water layer can be solved by the methods of Crampin (1970, 1977a) using elastic constants Cjkmn=6jk 6,, A, where 6ik is the Kronecker delta function, and h is Lami’s constant for the water layer. Ths leads to expres- sions for the velocity and stress in the water layer

w/c = i w q { f ( l ) exp (-iwqz) -f(2) exp (iwqz)) exp {iw(t - x/c) )

p33 = -iwA(l/c + q2c) { f(1) exp (-iwqz) + f(2) exp (iwqz)} exp { iw(t - x/c))

where q = I (@c2 - A ) / A C ~ ) ” ~ I , and p is the density of the water. Omitting the factor exp jiw(t - x /c ) } , the relation between the velocity and stress at the surface of the water layer, z = 0, and the velocity and stress at the solid surface, z = d , can be written

1 (‘44)

where d is the depth of the water layer. The stress across the free surface of the water layer is zero and we have:

( W / C ) z = d =A(W/C)~=O, whereA = cos(wqd),

(p33Iz=d =B(W/c),=,, where B = ipc(sin(wqd))/q.

Matrix G can now be replaced by G’, which has elements

which is the equivalent of (A2), and can be solved in the same way.

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surface-wave propagation in an ocean basin with an anisotropic

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