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Possible cryptic tectono-magnetic fabrics in ‘post-tectonic’ granitoid plutons of the Canadian Shield
EPSL ELSEVIER
Earth and Planetary
Science Letters 137 (1996) I 19- 127
Possible cryptic tectono-magnetic fabrics in ‘ post-tectonic’ granitoid plutons of the Canadian Shield Graham J. Borradaile Geology Depurtment, Received
Lakeheud
*,
Manfred M. Kehlenbeck
Uniurrsity, Thunder Bay. Onl. P?B SEI, Canudu
11September 1995; revised 7 November 1995; accepted 14 November 1995
Abstract Two late Archean granitic plutons forcefully intruded and thermally metamorphosed Archean schists. Feldspar magatrysts aligned concentrically with the margins during inflation. Substantial tectonic deformation never affected the plutons. Nevertheless, both plutons show the same, consistently oriented, cryptic magnetic fabric revealed by anisotropy of low field susceptibility (AMS) from 134 samples. They have an NE-SW vertical magnetic foliation and a magnetic lineation trending 060/ 15. Eigenvalues of the orientation distribution of principal susceptibilities show fhat the magnetic fabrics have almost identical strengths, orientations and symmetry in both plutons. We propose a post-magmatic reactivation of the earlier regional tectonic shortening. This imparted a ‘cryptic tectonic’ magnetic fabric on the plutons that overprinted the magmatic AMS fabric in most outcrops. The plutons’ AMS fabrics are subparallel to the much older schistosity of the country rocks. Because multidomain magnetite provides > 99% of the low field susceptibility of the rocks, it controls the AMS. However, we see no alignment of the magnetite grains. Thus, magnetic anisotropy may be due to stress alignment of intragranular domain walls and not controlled by grain shape, as usually assumed for magnetite.
1. Introduction
North of Thunder Bay, many post-tectonic, quartz-monzonite plutons [l] intrude Archean metasedimentary rocks of the Shebandowan and Quetico subprovinces. The plutons at Barnum Lake and Trout Lake are typical, forcefully intruding pelitic and semipelitic low grade metasedimentary rocks (Fig. 1). The Trout Lake pluton straddles the boundary with the biotite gneisses and migmatitic rocks of
* Corresponding author: fax and phone: (807).935-27.53; email: [email protected]
0012-821X/96/$12.00 SSDI 00 12-82
0 1996 Elsevier Science B.V. All rights reserved
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the Quetico subprovince (Fig. I>. The plutons are independent to a depth of at least 10 km [2]. Buff to salmon-pink K-feldspar megacrysts of < 3 cm in length are ubiquitous and separated by 3-5 cm of matrix. The matrix is coarse to medium grained and comprises pink oligoclase, quartz and biotite; tourmaline is absent. Minor undulatory extinction of quartz is the only conventional microscopic evidence of deformation. Figs. 1 and 2 show the mean orientation of 100-200 megacrysts for each outcrop. The megacryst foliation is steep and subparallel with the margins near the edges of the pluton and is parallel to aligned xenoliths. The megacryst fabric is clearly magmatic [l]. We cannot
120
GJ.
Borradaile,
MM. Kehlenbeck/Earth
und Plunetary
identify any penetrativeregional tectonic fabric in the plutons, neither in the field nor in thin section. Contact metamorphism within 1 km of the plutons thermally overprints the low grade regional metamorphism. The aureole of the Barnum Lake pluton possesses sillimanite, cordierite, garnet and staurolite and both intrusions show homfels textures in their
I
1 ,MAP
Science Letters 137 (1996)
119-127
aureoles. Thus, the plutons post-date regional deformation and metamorphism. The deflection of the regional schistosity (Fig. 1) suggests a forceful emplacement of the plutons during their inflation. We identify cryptic preferred orientations from the anisotropy of magnetic properties of rocks [2-71. Anisotropy may be measured from magnetisation
AREA
LEGEND AEROMAGNETIC
Quartz
Monzonite
porphyry
Mafic
Metavolcanic
Rocks
Metasedimentary Pink and grey Biotite
schist
; Pillow
biotite
gneisses
Schistosity, -_--
lavas 5%
Rocks
MAP
planar
cleavage
and
linear
field
data
86
; migmotites *c
Magmatic
structure
average
orientation
k - feldspar
of
megacrysts
Fig. 1. The Trout Lake and Barnum Lake plutons in northwest Ontario. Trends of the primary schistosity and stretching lineation are shown in the metamorphic rocks. The average orientation of 100-200 K-feldspar megacrysts (black bars) reveals a feeble magmatic foliation in suitable outcrops. This is generally subparallel to the granite margins. The lower right inset map shows part of the national aeromagnetic map-the Barnum Lake pluton shows the stronger signal. (The declination/inclination of the Earth’s magnetic field in this area is 004/68.)
G.J. Borradaile, M.M. Kehlenbeck/Eurth
a) Trout
121
and Planetary Science Letters 137 (1996) 119-127
Lake Pluton
b) Barnum
/
AMS site with MS
Lake Pluton
foliation trajectory
Feldspar megacryst foliation
::-
Fig. 2. Maps at different scales show mean alignments of K-feldspar megacrysts (black bars = means of 100-200 measurements). Trajectories show the magnetic foliation for principal AMS sites (0) based on site means of two to six samples. [n] = number of AMS determinations in each pluton.
induced by a weak field, in different directions through a sample. This is the anisotropy of low field magnetic susceptibility CAMS). We present the results of our study on the magnetic fabrics defined by the principal susceptibilities k,,,, kint and k,i,. These directions normally correspond to principal strain or principal stress directions where the pre-existing magnetic fabric is sufficiently overprinted. We calculated the directions and magnitudes of these principal values. For each intrusion, the data are subjected to eigenvector analysis and their orienta-
tion distributions are contoured hemisphere stereonets.
on equal area lower
2. Magnetic mineralogy The two small plutons show positive magnetic anomalies that predominate over strong regional signals from greenstone terrains (Fig. 1). Low field susceptibility was measured with a Sapphire Instruments SI2B anisotropy instrument, using an RMS
Table 1 Stereograms in Figs. 7 and 8 show eigenvectors only for the maximum susceptibilities (k,,, ) in order to simplify comparisons. Eigenvectors for the minimum susceptibilities show a near-perfect inverse correlation with those for k,,, . Such symmetrical arrangements are typical of well-defined, partial-girdle orientation distributions [17]. Thus, the E,,, and E,,,i, directions for k,,, are, respectively, the E,i” and Emax directions for k,i,
Pltion
n
mean IJSl
s.dev. IJSI
b
kclt
kmh
Evector(max)
Evector(max)
Evector(max)
trend/plunge
trend/plunge
trend/plunge
E,;
E,
(for k_)
Trout Lake
83
15116
10625
060110
331153
146l20
0.58; 0.33
Barnum Lake
51
27695
8374
061l20
225165
144103
0.59: 0.28
G.J. Borradaile,
122
M.M. Kehlenbeck/Earth
and Planetary
field of 0.6 Oe and various frequencies (750-13800 Hz). We did not detect a frequency dependence and the data presented are for 13800 Hz. The measurement unit used to present low field susceptibility is PSI (10e6 SI units on a volume basis). The Barnum pluton has twice the susceptibility of the Trout Lake pluton, which is also reflected in the aeromagnetic anomalies (Fig. 1). Table 1 shows mean susceptibilities calculated from the tensor of the anisotropy of low field susceptibility. This table also shows the directions and magnitudes of the maximum eigenvalue for the orientation distributions of k,,,, kint and kmi,. The Barnum pluton has a unimodal frequency distribution of mean magnetic susceptibility (Fig. 3). The spatial distribution of mean susceptibility is heterogeneous within outcrops and even within hand samples. The Trout pluton samples have a bimodal frequency distribution of mean susceptibility (Table 1). Neither pluton shows geographical control (e.g., chilled margin effect) on the distribution of susceptibility values. Consequently, the petrological factors that influence mean susceptibility must act equally throughout both intrusions on a scale larger than that of an outcrop (100 m*>. The bimodal susceptibility
25
20
n 15
5
0 0
loooo2ocQo3mtU4oooo5oooO6oooo
k in micro-S1 Fig. 3. Frequency distribution of mean susceptibilities for the two intrusions. Each mean susceptibility was calculated from the average of twelve differently oriented measurements for each sample during AMS determination. Each sample had a volume of 10.55 cm3.
Science Letters I37 (1996)
-400
119-127
0
H CmT)
400
Fig. 4. Hysteresis loop for a typical sample. H = induction field; M = magnetisation; MS = saturation magnetisation. The almost negligible positive gradient due to the net contribution of the paramagnetic mat% silicates and diamagnetic matrix were subtracted from this loop to isolate the ferromagnetic effects. High M, (saturation above 200 mT) and a narrow waist (near the origin) indicates that magnetite dominates.
for the Trout Lake pluton hints at two petrological processes (e.g., two ages or two textures of magnetite (Fig. 3)). The reason for this is unknown but may relate to more extensive oxidation (pinker colour). Paramagnetic mafic silicates have susceptibilities of < 1000 PSI and form < 10% by volume. Thus, we expect a net contribution of = 100 PSI per sample due to silicates. This represents 0.7% of the susceptibility of the average Trout pluton sample, and 0.3% of the susceptibility of the average Barnum pluton sample (Table 1). The remainder (> 99.3%) of the susceptibility can only be due to magnetite, which is confirmed both from petrographic observation and further magnetic measurements. Problems in the interpretation of magnetic fabrics can occur where minerals produce inverse fabrics. Single domain magnetite and tourmaline are likely candidates in granitoids [6]. However, tourmaline is absent and the magnetite content would swamp its signal anyway. A Micromag alternating gradient force magnetometer provided hysteresis data [9]. These show that ferromagnetism dominates the low field susceptibility measured in routine AMS determinations. The narrow waists of the loops near the graph origin, high saturation magnetisation, and saturation above 200 mT show that multidomain magnetite predominates. Figs. 4 and 5 show hysteresis parameters, coercivity (H,), coercivity of remanence (E&J, satu-
G.J. Borradaile, M.M. Kehlenbeck/Earth
and Planetary Science Letters 137 (1996) 119-127
123
a 1
Hcr/Hc
b
IO
20
30
Her mT 40
Fig. 5. The multidomain character of the magnetite [14]. M, = remanent magnetisation; MS = saturation magnetisation; H,, = coercivity of remanence; H, = coercivity. Lines seapmte the MD, PSD and SD fields. The MT/M, vs. H,,/H, plot confirms the mutidomain character of the magnetite [ 151.
ration remanence (M,) and saturation magnetisation (M,) that confirms the mutidomain character. -Curie balance determinations for mineral separates from typical samples confirm Curie points for magnetite in all samples. A Curie point for hematite is just detectable in the pinker samples of the Trout Lake pluton (Fig. 6). 3. Cryptic fabric directions revealed by magnetic anisotropy The anisotropy of low field induced magnetic susceptibility CAMS) was studied using a redesigned
SI2B instrument lent by Sapphire Instruments (PO Box 285, Ruthven, Ont. NOP 2G0, Canada). This instrument has a noise level of < 0.02 PUSI under favourable laboratory conditions. The samples’ high susceptibility permits a definition of k,,, and &, directions with a precision of better than 2” at the 95% confidence level. Naturally, where two principal susceptibilities were of similar magnitude, the precision was low for those axes but very high for the third direction. Eigenvector analysis of the orientation distributions shows kmin axes with a mean trend and plunge of 144/20 for the Trout Lake pluton and 144/03 for
G.J. Borruduile, MM. Kehlenbeck/Earth
124
and Planctury Science Letters 137 (1996) 119-127
the Barnum Lake pluton (Table 1). kmi, axes define the pole to the ‘magnetic foliation’ and commonly indicate a dominant shortening direction. The mean k max values are 060/ 10 and 060/20 for the Trout and Barnum Lake plutons. Generally, structural geolaxes as reflecting maximum ogists interpret k,,, stretching and relate k,i, to the pole to schistosity. Where the initial AMS fabric (e.g., magmatic) is sufficiently tectonically overprinted, k,,, , kint and k,i, may represent finite strain axes. Otherwise, ephemeral stress events can induce such alignments. The correspondence of these directions for two separate intrusions is remarkable, and argues against individual magmatic fabrics (Table 1, Figs. 7 and 8). Six cores marred the usually similar and consistent preferred orientations of the magnetic susceptibility axes (Figs. 7 and 8). Their k,,, and kmi, directions were swapped with respect to the mean (eigenvector) values. This is usually due to the inverse fabric effect of single domain magnetite [6,8,10,11]. Small magnetite grains that encompass one magnetic domain cannot have their magnetisation increased along the longest axis; by definition, magnetisation in this direction is already saturated. Consequently, this direction shows the minimum low field susceptibility and the susceptibility ellipsoid has its long axis parallel to the short axis of the grain and vice-versa. Thus, for these anomalous samples (and a selection of samples with normal AMS fabrics) we measured the anisotropy of anhysteretic
0 = mm
A = int
+ = min
Fig. 7. Equal area lower hemisphere stereograms for Barnum Lake pluton. 0, A and + = attitudes of maximum, intermediate and minimum eigenvectors for the distribution of k,,, axes. The eigenvectors for k,i, show a nearly perfect inverse correlation with those for k,,, (Table If. Contours = 25 and 50% of peak value. Data are contoured using 324 counting positions and a counting cell whose diameter varies according to the number of samples [ 161. (a) Maximum susceptibility directions contoured. (b) Intermediate susceptibility directions contoured. (c) Minimum susceptibility directions contoured. (d) Maximum and minimum susceptibility directions. Contours show directions that have Pj > 1.1 (i.e., the most eccentric fabric ellipsoids for minimum susceptibility directions with T > 0).
remanence (AARM) [8]. AARM that the true single domain shape the general AMS trends (Table these for the six aberrant, inverse ‘.
‘.
f
wy I 0
‘1,
\
ellipsoids revealed fabric conforms to 1). We substituted AMS samples.
4. Why are the AMS fabrics ‘tectonic’?
1, \ --_ L -‘.
(n=2751
n= 51
I
I
I
I
1
I
I
loo
200
300
400
500
600
700
c
Fig. 6. Curie points are well defmed near 570°C (magnetite) but the pinker sample from the Trout Lake intrusion also shows a Curie point near 67O”C, suggesting hematite. The curves show the decay of saturation magnetisation during heating. n = number of temperature determinations.
Fig. 2 shows the mean foliation for feldspar megacrysts and the site mean AMS foliations and their trajectories. The megacryst alignment is subparallel to the margins at the edges of the plutons. The AMS foliation trajectories are discordant with the magmatic fabric of the megacrysts. However, some AMS sites do show incomplete overprinting of a
G.J. Borrudaile.
M.M. Kehlenbeck/Eorth
and Plunetmy
Science Letters 137 (1996) 119-127
125
eigenvectors only for the distribution of k,,, . However, the orientation distributions of all three principal susceptibilities are highly symmetrical, as with typical tectonic fabrics. Thus the eigenvectors for k,i, correlate inversely with those for k,,, (Table 1).
0 =
max
A=
int
+ = m,n
n=83
Fig. 8. Equal area lower hemisphere stereograms for Trout Lake pluton. (a) Maximum susceptibility directions contoured. (b) Intermediate susceptibility directions contoured. (c) Minimum susceptibility directions contoured. (d) Maximum and minimum susceptibility directions. Contours enclose directions for samples with P, > I. I (i.e.. the most eccentric fabric ellipsoids). Those associated with the maximum directions have T < 0 whereas those associated with minimum directions have T > 0. For conventions and other detail, see Fig. 7.
primary, magmatic AMS. A more rigorous analysis of the orientation distribution of all k,,,, kint and kmin axes is possible using contoured stereonets and eigenvectors calculated for the orientation distribution of the maximum, intermediate and minimum principal axes. Stereogram contours for principal susceptibilities for the Barnum Lake and Trout Lake plutons are shown in Figs. 7 and 8 respectively. Eigenvectors for the orientation distribution of maximum susceptibility directions are superimposed on each diagram [ 121 and eigenvector analysis for all axes is given in Table 1. To avoid confusion we point out that the orientation distribution of each susceptibility axis (e.g., k,,,) has three eigenvectors (Emax, Eint, Emi,) for indicating the critical concentration of each susceptibility axis. For clarity, the stereograms show
The following suggests that the AMS fabric is dominantly tectonic and most unlikely to be due to magmatic processes in two separate intrusions: (1) The magnetic foliation has a remarkably similar strike in each pluton (Table 1, mean kmi, poles of 146/20 and 144/03). Both intrusions show a remarkably similar angular distribution of k,,, (Fig. 7c and 8~). (2) Mean k,,, shows directions of 060/ 10 and 061/20 in the two intrusions. (3) The strength of the preferred orientations for the distributions of the k,,,. kinr and kmin axes is nearly identical (at 0.6:0.3:0.1) in both intrusions (Table 1). (4) In both intrusions k,,, forms a partial girdle in the k,,,- kint plane (Figs. 7 and 8a). This is also expressed by the similar eigenvalues mentioned under point (3). The hint of a girdle around the perimeter of the stereogram is partly an artifact of projection, and is unsupported by the eigenvector analysis. The orientation of this girdle is inappropriate for it to be a vestige of a magmatic AMS fabric. (5) For the Barnum Lake pluton, the k,,, axes of the most ablate AMS ellipsoids cluster around the mean k,i, (Fig. 7d). (6) For the Trout Lake pluton, the most oblate fabrics cluster around the mean k,i,, and the k,,, axes of the most prolate fabrics cluster around the mean k,,, (Fig. 8d). These six observations are incompatible with a concentric ballooning magmatic fabric in two independent intrusions. We suggest that the closely similar AMS fabrics are due to a regional stress that imposed a similar ‘cryptic tectonic’ fabric on the two intrusions. The AMS fabrics follow the regional NE-SW tectonic trend. Despite the poor distribution of outcrops, it is unlikely that these fabrics are concentric magmatic fabrics affected by sampling bias. We argue that the evidence for ‘late cryptic tectonic’ AMS (Figs. 7 and 8) is as compelling as the arguments for the concentric magmatic megacryst fabric (Fig. 2).
126
GJ. Bormdaile, MM. Kehlenbeck/Earth
and Planetary Science Letters 137 (1996) 119-127
5. Origin of the cryptic AMS magnetite fabrics
tation. However, as in many similar studies, we detect no preferred alignment of magnetite grain outlines. Thus, we suspect that domain structure within the poorly aligned magnetite grains controls AMS. The intensity of magnetic fabric (mean Pj> for the Trout Lake pluton is double that of the Barnum Lake pluton (Fig. 9a). We recall that the Trout Lake pluton has a bimodal frequency distribution of mean susceptibility (Fig. 3). However, graphs of Pj VS. k, and T vs. k, reveal that the lower susceptibility mode for the Trout pluton shares the same distribution of Pj and T (Fig. 9b,c). Thus, even if their petrological histories differed, perhaps with more oxidation of the Trout pluton (Fig. 3), this did not change the AMS. This argues for a common origin of the AMS in the two intrusions (i.e., tectonic rather than magmatic). Samples of high mean susceptibility do not have principal directions concentrated in any
Anisotropies of magnetic susceptibility are shown using T to represent shape and Pj to represent the eccentricity of the ellipsoid [13]. T = + 1 for an oblate ellipsoid (= flat magnetite grains), T = - 1 for a prolate susceptibility ellipsoid ( = rod-shaped magnetite grains). Neutral ellipsoids (with the axes max/int = int/min) have T = 0. Pj ranges from unity upwards. Separating shape from eccentricity on orthogonal axes makes interpretation much simpler than with the Flinn diagram from structural geology. The symmetry of T with shape, together with the logarithmic nature of the parameters, is also advantageous. Oblate and prolate fabrics are equally common (Fig. 9a). Such diverse fabric shapes can still produce the net magnetic foliation (Figs. 5 and 6) if the grains possess a strong preferred dimensional orien-
To
0
Barnum
l
Trout
Loke
Lake
-1
To
Pj
I.00 0
IO
20 k
30
in IO”
40
SI
50
60
;
,
,
I
,
,
0
IO
20
30
40
50
k in IO”
60
SI
Fig. 9. Jelinek graphs. T = + 1 for ablate (perfect disc) ellipsoids; T = - 1 for prolate (perfect rod) ellipsoids; Pj = a measure of eccentricity of ellipsoid indicating intensity. (a) Both plutons have a wide range of fabric ellipsoid shapes, and flat ellipsoids are not particularly dominant. Trout Lake samples have a larger Pj range. (b) and (c) Neither tbe shape (T) nor intensity (Pj> of the fabric ellipsoids correlates with mean susceptibility.
G.J. Borruduile.
M.M. Kehlenbeck/Eurih
und Plunetury Science Letters 137 (1996) 119-127
particular direction. This is true for both intrusions; the bimodal frequency distribution of mean susceptibility in the Trout Lake intrusion is not expressed in the orientation distribution. This also argues for a common tectonic component to the AMS fabrics.
127
the measurements of AMS, Anne Hammond prepared the samples and Sam Spivak drew some of the diagrams. We thank Rob van der Voo and the two anonymous readers for perceptive and constructive reviews. [ RV]
6. Conclusions References (1) Both intrusions show marginal, magmatic alignments of feldspar megacrysts. Inflation of the plutons produced magmatic fabrics as the country rocks were pushed aside. We cannot detect evidence for penetrative, regional deformation of the plutons in the field or under the microscope. (2) Anisotropy of low field susceptibility CAMS) reveals a consistent NE-SW magnetic foliation and a subhorizontal magnetic lineation in both intrusions. Moreover, the eigenvalues of the orientation distributions are equal for the two intrusions. Therefore we argue that these ‘post-tectonic’ intrusions share a common late ‘cryptic tectonic’ fabric. This may have been the result of a reactivation of the pre-intrusion stress field because the AMS foliation and lineation are nearly parallel to the pre-intrusion tectonic schistosity and stretching lineation. (3) The Pj and T parameters show that the magnetite susceptibility fabrics range from rod to disc shapes, with a slight preponderance in the oblate field (Fig. 9). Magnetite grain shape alignment is not readily detectable and penetrative deformation is absent. Why then are the AMS orientation distributions so well defined? A preferred arrangement of significant magnetic domains within large multidomain magnetite grains may be the explanation. In this way the almost isotropic shape fabric of mutidomain magnetite grains can be independent of the strong orientation fabric shown by principal susceptibilities (Figs. 7 and 8). This may be stress-induced, rather than strain-induced as argued in most studies of metamorphic AMS fabrics.
Acknowledgements NSERC funded this research through an operating grant to G. Borradaile. Gina Borradaile helped with
[l] M.M. Kehlenbeck, The Barnum Lake pluton, Thunder Bay, Ontario, Can. J. Earth Sci. 14, 2157-2167, 1977. [2] M.M. Kehlenbeck and S.P. Cheadle, Structural cross-sections based on a gravity survey of parts of the Quetico and Wawa subprovinces near Thunder Bay, Ontario, Canada, Can. J. Earth Sci. 27, 187-199, 1990. [3] F. Hrouda, Magnetic anisotropy of rocks and its application in geology and geophysics, Geophys. Surv. 5, 37-82, 1982. [4] W.D. MacDonald and B.B. Ellwood, Anisotropy of magnetic susceptibility: Sedimentological, igneous, and structuraltectonic applications, Rev. Geophys. 25(5), 905-909, 1987. [5] G.J. Borradaile, Magnetic susceptibility, petrofabrics and strain, Tectonophysics 1.56, l-20, 1988. 161 P. Rochette, M.J. Jackson and C. Aubourg, Rock magnetism and the interpretation of anisotropy of magnetic susceptibility, Rev. Geophys. 30, 209-226, 1992. [7] D.H. Tarling and F. Hrouda, The Magnetic Anisotropy of Rocks, Chapman and Hall, 1993. [8] M.J. Jackson, Anisotropy of magnetic remanence: A brief review of mineralogical sources, physical origins and geological applications, and comparison with susceptibility anisotropy, Pure Appl. Geophys. 136, l-28, 1991. [9] P.J. Flanders, An alternating-gradient magnetometer, J. Appl. Phys. 63, 3940-3945, 1988. [IO] D.K. Potter and A. Stephenson, Single domain particles in rocks and magnetic fabric analysis, Geophys. Res. Lett. 15, 1097-I 100, 1988. [I 11 J.F. Nye, Physical Properties of Crystals, Oxford University Press, 1985. [12] P.J. Diggle and N.I. Fisher, SPHERE: a contouring program for spherical data, Comput. Geosci. II, 725-766, 1985. [I 31 V. Jelinek, Characterization of the magnetic fabrics of rocks, Tectonophysics 79, T63-T67, 198 I. [I41 R. Day, M.D. Fuller and V.A. Schmidt, Magnetic hysteresis properties of synthetic titanomagnetites, J. Geophys. Res. 81, 873-880, 1977. [I51 P.J. Wasilewski, Magnetic hysteresis in natural materials, Earth Planet. Sci. Lett. 20, 67-72, 1973. 1161 P.Y. Robin and E.C. Jowett, Computerized density contouring and statistical evaluation of orientation data using counting circles and continuous weighting functions. Tectonophysics 121, 207-223, 1986. [17] N.I. Fisher, T. Lewis and B.J.J. Embleton, Statistical Analysis of Spherical Data, Cambridge University Press, 1992.
Earth and Planetary
Science Letters 137 (1996) I 19- 127
Possible cryptic tectono-magnetic fabrics in ‘ post-tectonic’ granitoid plutons of the Canadian Shield Graham J. Borradaile Geology Depurtment, Received
Lakeheud
*,
Manfred M. Kehlenbeck
Uniurrsity, Thunder Bay. Onl. P?B SEI, Canudu
11September 1995; revised 7 November 1995; accepted 14 November 1995
Abstract Two late Archean granitic plutons forcefully intruded and thermally metamorphosed Archean schists. Feldspar magatrysts aligned concentrically with the margins during inflation. Substantial tectonic deformation never affected the plutons. Nevertheless, both plutons show the same, consistently oriented, cryptic magnetic fabric revealed by anisotropy of low field susceptibility (AMS) from 134 samples. They have an NE-SW vertical magnetic foliation and a magnetic lineation trending 060/ 15. Eigenvalues of the orientation distribution of principal susceptibilities show fhat the magnetic fabrics have almost identical strengths, orientations and symmetry in both plutons. We propose a post-magmatic reactivation of the earlier regional tectonic shortening. This imparted a ‘cryptic tectonic’ magnetic fabric on the plutons that overprinted the magmatic AMS fabric in most outcrops. The plutons’ AMS fabrics are subparallel to the much older schistosity of the country rocks. Because multidomain magnetite provides > 99% of the low field susceptibility of the rocks, it controls the AMS. However, we see no alignment of the magnetite grains. Thus, magnetic anisotropy may be due to stress alignment of intragranular domain walls and not controlled by grain shape, as usually assumed for magnetite.
1. Introduction
North of Thunder Bay, many post-tectonic, quartz-monzonite plutons [l] intrude Archean metasedimentary rocks of the Shebandowan and Quetico subprovinces. The plutons at Barnum Lake and Trout Lake are typical, forcefully intruding pelitic and semipelitic low grade metasedimentary rocks (Fig. 1). The Trout Lake pluton straddles the boundary with the biotite gneisses and migmatitic rocks of
* Corresponding author: fax and phone: (807).935-27.53; email: [email protected]
0012-821X/96/$12.00 SSDI 00 12-82
0 1996 Elsevier Science B.V. All rights reserved
I X(95)00220-0
the Quetico subprovince (Fig. I>. The plutons are independent to a depth of at least 10 km [2]. Buff to salmon-pink K-feldspar megacrysts of < 3 cm in length are ubiquitous and separated by 3-5 cm of matrix. The matrix is coarse to medium grained and comprises pink oligoclase, quartz and biotite; tourmaline is absent. Minor undulatory extinction of quartz is the only conventional microscopic evidence of deformation. Figs. 1 and 2 show the mean orientation of 100-200 megacrysts for each outcrop. The megacryst foliation is steep and subparallel with the margins near the edges of the pluton and is parallel to aligned xenoliths. The megacryst fabric is clearly magmatic [l]. We cannot
120
GJ.
Borradaile,
MM. Kehlenbeck/Earth
und Plunetary
identify any penetrativeregional tectonic fabric in the plutons, neither in the field nor in thin section. Contact metamorphism within 1 km of the plutons thermally overprints the low grade regional metamorphism. The aureole of the Barnum Lake pluton possesses sillimanite, cordierite, garnet and staurolite and both intrusions show homfels textures in their
I
1 ,MAP
Science Letters 137 (1996)
119-127
aureoles. Thus, the plutons post-date regional deformation and metamorphism. The deflection of the regional schistosity (Fig. 1) suggests a forceful emplacement of the plutons during their inflation. We identify cryptic preferred orientations from the anisotropy of magnetic properties of rocks [2-71. Anisotropy may be measured from magnetisation
AREA
LEGEND AEROMAGNETIC
Quartz
Monzonite
porphyry
Mafic
Metavolcanic
Rocks
Metasedimentary Pink and grey Biotite
schist
; Pillow
biotite
gneisses
Schistosity, -_--
lavas 5%
Rocks
MAP
planar
cleavage
and
linear
field
data
86
; migmotites *c
Magmatic
structure
average
orientation
k - feldspar
of
megacrysts
Fig. 1. The Trout Lake and Barnum Lake plutons in northwest Ontario. Trends of the primary schistosity and stretching lineation are shown in the metamorphic rocks. The average orientation of 100-200 K-feldspar megacrysts (black bars) reveals a feeble magmatic foliation in suitable outcrops. This is generally subparallel to the granite margins. The lower right inset map shows part of the national aeromagnetic map-the Barnum Lake pluton shows the stronger signal. (The declination/inclination of the Earth’s magnetic field in this area is 004/68.)
G.J. Borradaile, M.M. Kehlenbeck/Eurth
a) Trout
121
and Planetary Science Letters 137 (1996) 119-127
Lake Pluton
b) Barnum
/
AMS site with MS
Lake Pluton
foliation trajectory
Feldspar megacryst foliation
::-
Fig. 2. Maps at different scales show mean alignments of K-feldspar megacrysts (black bars = means of 100-200 measurements). Trajectories show the magnetic foliation for principal AMS sites (0) based on site means of two to six samples. [n] = number of AMS determinations in each pluton.
induced by a weak field, in different directions through a sample. This is the anisotropy of low field magnetic susceptibility CAMS). We present the results of our study on the magnetic fabrics defined by the principal susceptibilities k,,,, kint and k,i,. These directions normally correspond to principal strain or principal stress directions where the pre-existing magnetic fabric is sufficiently overprinted. We calculated the directions and magnitudes of these principal values. For each intrusion, the data are subjected to eigenvector analysis and their orienta-
tion distributions are contoured hemisphere stereonets.
on equal area lower
2. Magnetic mineralogy The two small plutons show positive magnetic anomalies that predominate over strong regional signals from greenstone terrains (Fig. 1). Low field susceptibility was measured with a Sapphire Instruments SI2B anisotropy instrument, using an RMS
Table 1 Stereograms in Figs. 7 and 8 show eigenvectors only for the maximum susceptibilities (k,,, ) in order to simplify comparisons. Eigenvectors for the minimum susceptibilities show a near-perfect inverse correlation with those for k,,, . Such symmetrical arrangements are typical of well-defined, partial-girdle orientation distributions [17]. Thus, the E,,, and E,,,i, directions for k,,, are, respectively, the E,i” and Emax directions for k,i,
Pltion
n
mean IJSl
s.dev. IJSI
b
kclt
kmh
Evector(max)
Evector(max)
Evector(max)
trend/plunge
trend/plunge
trend/plunge
E,;
E,
(for k_)
Trout Lake
83
15116
10625
060110
331153
146l20
0.58; 0.33
Barnum Lake
51
27695
8374
061l20
225165
144103
0.59: 0.28
G.J. Borradaile,
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and Planetary
field of 0.6 Oe and various frequencies (750-13800 Hz). We did not detect a frequency dependence and the data presented are for 13800 Hz. The measurement unit used to present low field susceptibility is PSI (10e6 SI units on a volume basis). The Barnum pluton has twice the susceptibility of the Trout Lake pluton, which is also reflected in the aeromagnetic anomalies (Fig. 1). Table 1 shows mean susceptibilities calculated from the tensor of the anisotropy of low field susceptibility. This table also shows the directions and magnitudes of the maximum eigenvalue for the orientation distributions of k,,,, kint and kmi,. The Barnum pluton has a unimodal frequency distribution of mean magnetic susceptibility (Fig. 3). The spatial distribution of mean susceptibility is heterogeneous within outcrops and even within hand samples. The Trout pluton samples have a bimodal frequency distribution of mean susceptibility (Table 1). Neither pluton shows geographical control (e.g., chilled margin effect) on the distribution of susceptibility values. Consequently, the petrological factors that influence mean susceptibility must act equally throughout both intrusions on a scale larger than that of an outcrop (100 m*>. The bimodal susceptibility
25
20
n 15
5
0 0
loooo2ocQo3mtU4oooo5oooO6oooo
k in micro-S1 Fig. 3. Frequency distribution of mean susceptibilities for the two intrusions. Each mean susceptibility was calculated from the average of twelve differently oriented measurements for each sample during AMS determination. Each sample had a volume of 10.55 cm3.
Science Letters I37 (1996)
-400
119-127
0
H CmT)
400
Fig. 4. Hysteresis loop for a typical sample. H = induction field; M = magnetisation; MS = saturation magnetisation. The almost negligible positive gradient due to the net contribution of the paramagnetic mat% silicates and diamagnetic matrix were subtracted from this loop to isolate the ferromagnetic effects. High M, (saturation above 200 mT) and a narrow waist (near the origin) indicates that magnetite dominates.
for the Trout Lake pluton hints at two petrological processes (e.g., two ages or two textures of magnetite (Fig. 3)). The reason for this is unknown but may relate to more extensive oxidation (pinker colour). Paramagnetic mafic silicates have susceptibilities of < 1000 PSI and form < 10% by volume. Thus, we expect a net contribution of = 100 PSI per sample due to silicates. This represents 0.7% of the susceptibility of the average Trout pluton sample, and 0.3% of the susceptibility of the average Barnum pluton sample (Table 1). The remainder (> 99.3%) of the susceptibility can only be due to magnetite, which is confirmed both from petrographic observation and further magnetic measurements. Problems in the interpretation of magnetic fabrics can occur where minerals produce inverse fabrics. Single domain magnetite and tourmaline are likely candidates in granitoids [6]. However, tourmaline is absent and the magnetite content would swamp its signal anyway. A Micromag alternating gradient force magnetometer provided hysteresis data [9]. These show that ferromagnetism dominates the low field susceptibility measured in routine AMS determinations. The narrow waists of the loops near the graph origin, high saturation magnetisation, and saturation above 200 mT show that multidomain magnetite predominates. Figs. 4 and 5 show hysteresis parameters, coercivity (H,), coercivity of remanence (E&J, satu-
G.J. Borradaile, M.M. Kehlenbeck/Earth
and Planetary Science Letters 137 (1996) 119-127
123
a 1
Hcr/Hc
b
IO
20
30
Her mT 40
Fig. 5. The multidomain character of the magnetite [14]. M, = remanent magnetisation; MS = saturation magnetisation; H,, = coercivity of remanence; H, = coercivity. Lines seapmte the MD, PSD and SD fields. The MT/M, vs. H,,/H, plot confirms the mutidomain character of the magnetite [ 151.
ration remanence (M,) and saturation magnetisation (M,) that confirms the mutidomain character. -Curie balance determinations for mineral separates from typical samples confirm Curie points for magnetite in all samples. A Curie point for hematite is just detectable in the pinker samples of the Trout Lake pluton (Fig. 6). 3. Cryptic fabric directions revealed by magnetic anisotropy The anisotropy of low field induced magnetic susceptibility CAMS) was studied using a redesigned
SI2B instrument lent by Sapphire Instruments (PO Box 285, Ruthven, Ont. NOP 2G0, Canada). This instrument has a noise level of < 0.02 PUSI under favourable laboratory conditions. The samples’ high susceptibility permits a definition of k,,, and &, directions with a precision of better than 2” at the 95% confidence level. Naturally, where two principal susceptibilities were of similar magnitude, the precision was low for those axes but very high for the third direction. Eigenvector analysis of the orientation distributions shows kmin axes with a mean trend and plunge of 144/20 for the Trout Lake pluton and 144/03 for
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the Barnum Lake pluton (Table 1). kmi, axes define the pole to the ‘magnetic foliation’ and commonly indicate a dominant shortening direction. The mean k max values are 060/ 10 and 060/20 for the Trout and Barnum Lake plutons. Generally, structural geolaxes as reflecting maximum ogists interpret k,,, stretching and relate k,i, to the pole to schistosity. Where the initial AMS fabric (e.g., magmatic) is sufficiently tectonically overprinted, k,,, , kint and k,i, may represent finite strain axes. Otherwise, ephemeral stress events can induce such alignments. The correspondence of these directions for two separate intrusions is remarkable, and argues against individual magmatic fabrics (Table 1, Figs. 7 and 8). Six cores marred the usually similar and consistent preferred orientations of the magnetic susceptibility axes (Figs. 7 and 8). Their k,,, and kmi, directions were swapped with respect to the mean (eigenvector) values. This is usually due to the inverse fabric effect of single domain magnetite [6,8,10,11]. Small magnetite grains that encompass one magnetic domain cannot have their magnetisation increased along the longest axis; by definition, magnetisation in this direction is already saturated. Consequently, this direction shows the minimum low field susceptibility and the susceptibility ellipsoid has its long axis parallel to the short axis of the grain and vice-versa. Thus, for these anomalous samples (and a selection of samples with normal AMS fabrics) we measured the anisotropy of anhysteretic
0 = mm
A = int
+ = min
Fig. 7. Equal area lower hemisphere stereograms for Barnum Lake pluton. 0, A and + = attitudes of maximum, intermediate and minimum eigenvectors for the distribution of k,,, axes. The eigenvectors for k,i, show a nearly perfect inverse correlation with those for k,,, (Table If. Contours = 25 and 50% of peak value. Data are contoured using 324 counting positions and a counting cell whose diameter varies according to the number of samples [ 161. (a) Maximum susceptibility directions contoured. (b) Intermediate susceptibility directions contoured. (c) Minimum susceptibility directions contoured. (d) Maximum and minimum susceptibility directions. Contours show directions that have Pj > 1.1 (i.e., the most eccentric fabric ellipsoids for minimum susceptibility directions with T > 0).
remanence (AARM) [8]. AARM that the true single domain shape the general AMS trends (Table these for the six aberrant, inverse ‘.
‘.
f
wy I 0
‘1,
\
ellipsoids revealed fabric conforms to 1). We substituted AMS samples.
4. Why are the AMS fabrics ‘tectonic’?
1, \ --_ L -‘.
(n=2751
n= 51
I
I
I
I
1
I
I
loo
200
300
400
500
600
700
c
Fig. 6. Curie points are well defmed near 570°C (magnetite) but the pinker sample from the Trout Lake intrusion also shows a Curie point near 67O”C, suggesting hematite. The curves show the decay of saturation magnetisation during heating. n = number of temperature determinations.
Fig. 2 shows the mean foliation for feldspar megacrysts and the site mean AMS foliations and their trajectories. The megacryst alignment is subparallel to the margins at the edges of the plutons. The AMS foliation trajectories are discordant with the magmatic fabric of the megacrysts. However, some AMS sites do show incomplete overprinting of a
G.J. Borrudaile.
M.M. Kehlenbeck/Eorth
and Plunetmy
Science Letters 137 (1996) 119-127
125
eigenvectors only for the distribution of k,,, . However, the orientation distributions of all three principal susceptibilities are highly symmetrical, as with typical tectonic fabrics. Thus the eigenvectors for k,i, correlate inversely with those for k,,, (Table 1).
0 =
max
A=
int
+ = m,n
n=83
Fig. 8. Equal area lower hemisphere stereograms for Trout Lake pluton. (a) Maximum susceptibility directions contoured. (b) Intermediate susceptibility directions contoured. (c) Minimum susceptibility directions contoured. (d) Maximum and minimum susceptibility directions. Contours enclose directions for samples with P, > I. I (i.e.. the most eccentric fabric ellipsoids). Those associated with the maximum directions have T < 0 whereas those associated with minimum directions have T > 0. For conventions and other detail, see Fig. 7.
primary, magmatic AMS. A more rigorous analysis of the orientation distribution of all k,,,, kint and kmin axes is possible using contoured stereonets and eigenvectors calculated for the orientation distribution of the maximum, intermediate and minimum principal axes. Stereogram contours for principal susceptibilities for the Barnum Lake and Trout Lake plutons are shown in Figs. 7 and 8 respectively. Eigenvectors for the orientation distribution of maximum susceptibility directions are superimposed on each diagram [ 121 and eigenvector analysis for all axes is given in Table 1. To avoid confusion we point out that the orientation distribution of each susceptibility axis (e.g., k,,,) has three eigenvectors (Emax, Eint, Emi,) for indicating the critical concentration of each susceptibility axis. For clarity, the stereograms show
The following suggests that the AMS fabric is dominantly tectonic and most unlikely to be due to magmatic processes in two separate intrusions: (1) The magnetic foliation has a remarkably similar strike in each pluton (Table 1, mean kmi, poles of 146/20 and 144/03). Both intrusions show a remarkably similar angular distribution of k,,, (Fig. 7c and 8~). (2) Mean k,,, shows directions of 060/ 10 and 061/20 in the two intrusions. (3) The strength of the preferred orientations for the distributions of the k,,,. kinr and kmin axes is nearly identical (at 0.6:0.3:0.1) in both intrusions (Table 1). (4) In both intrusions k,,, forms a partial girdle in the k,,,- kint plane (Figs. 7 and 8a). This is also expressed by the similar eigenvalues mentioned under point (3). The hint of a girdle around the perimeter of the stereogram is partly an artifact of projection, and is unsupported by the eigenvector analysis. The orientation of this girdle is inappropriate for it to be a vestige of a magmatic AMS fabric. (5) For the Barnum Lake pluton, the k,,, axes of the most ablate AMS ellipsoids cluster around the mean k,i, (Fig. 7d). (6) For the Trout Lake pluton, the most oblate fabrics cluster around the mean k,i,, and the k,,, axes of the most prolate fabrics cluster around the mean k,,, (Fig. 8d). These six observations are incompatible with a concentric ballooning magmatic fabric in two independent intrusions. We suggest that the closely similar AMS fabrics are due to a regional stress that imposed a similar ‘cryptic tectonic’ fabric on the two intrusions. The AMS fabrics follow the regional NE-SW tectonic trend. Despite the poor distribution of outcrops, it is unlikely that these fabrics are concentric magmatic fabrics affected by sampling bias. We argue that the evidence for ‘late cryptic tectonic’ AMS (Figs. 7 and 8) is as compelling as the arguments for the concentric magmatic megacryst fabric (Fig. 2).
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and Planetary Science Letters 137 (1996) 119-127
5. Origin of the cryptic AMS magnetite fabrics
tation. However, as in many similar studies, we detect no preferred alignment of magnetite grain outlines. Thus, we suspect that domain structure within the poorly aligned magnetite grains controls AMS. The intensity of magnetic fabric (mean Pj> for the Trout Lake pluton is double that of the Barnum Lake pluton (Fig. 9a). We recall that the Trout Lake pluton has a bimodal frequency distribution of mean susceptibility (Fig. 3). However, graphs of Pj VS. k, and T vs. k, reveal that the lower susceptibility mode for the Trout pluton shares the same distribution of Pj and T (Fig. 9b,c). Thus, even if their petrological histories differed, perhaps with more oxidation of the Trout pluton (Fig. 3), this did not change the AMS. This argues for a common origin of the AMS in the two intrusions (i.e., tectonic rather than magmatic). Samples of high mean susceptibility do not have principal directions concentrated in any
Anisotropies of magnetic susceptibility are shown using T to represent shape and Pj to represent the eccentricity of the ellipsoid [13]. T = + 1 for an oblate ellipsoid (= flat magnetite grains), T = - 1 for a prolate susceptibility ellipsoid ( = rod-shaped magnetite grains). Neutral ellipsoids (with the axes max/int = int/min) have T = 0. Pj ranges from unity upwards. Separating shape from eccentricity on orthogonal axes makes interpretation much simpler than with the Flinn diagram from structural geology. The symmetry of T with shape, together with the logarithmic nature of the parameters, is also advantageous. Oblate and prolate fabrics are equally common (Fig. 9a). Such diverse fabric shapes can still produce the net magnetic foliation (Figs. 5 and 6) if the grains possess a strong preferred dimensional orien-
To
0
Barnum
l
Trout
Loke
Lake
-1
To
Pj
I.00 0
IO
20 k
30
in IO”
40
SI
50
60
;
,
,
I
,
,
0
IO
20
30
40
50
k in IO”
60
SI
Fig. 9. Jelinek graphs. T = + 1 for ablate (perfect disc) ellipsoids; T = - 1 for prolate (perfect rod) ellipsoids; Pj = a measure of eccentricity of ellipsoid indicating intensity. (a) Both plutons have a wide range of fabric ellipsoid shapes, and flat ellipsoids are not particularly dominant. Trout Lake samples have a larger Pj range. (b) and (c) Neither tbe shape (T) nor intensity (Pj> of the fabric ellipsoids correlates with mean susceptibility.
G.J. Borruduile.
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und Plunetury Science Letters 137 (1996) 119-127
particular direction. This is true for both intrusions; the bimodal frequency distribution of mean susceptibility in the Trout Lake intrusion is not expressed in the orientation distribution. This also argues for a common tectonic component to the AMS fabrics.
127
the measurements of AMS, Anne Hammond prepared the samples and Sam Spivak drew some of the diagrams. We thank Rob van der Voo and the two anonymous readers for perceptive and constructive reviews. [ RV]
6. Conclusions References (1) Both intrusions show marginal, magmatic alignments of feldspar megacrysts. Inflation of the plutons produced magmatic fabrics as the country rocks were pushed aside. We cannot detect evidence for penetrative, regional deformation of the plutons in the field or under the microscope. (2) Anisotropy of low field susceptibility CAMS) reveals a consistent NE-SW magnetic foliation and a subhorizontal magnetic lineation in both intrusions. Moreover, the eigenvalues of the orientation distributions are equal for the two intrusions. Therefore we argue that these ‘post-tectonic’ intrusions share a common late ‘cryptic tectonic’ fabric. This may have been the result of a reactivation of the pre-intrusion stress field because the AMS foliation and lineation are nearly parallel to the pre-intrusion tectonic schistosity and stretching lineation. (3) The Pj and T parameters show that the magnetite susceptibility fabrics range from rod to disc shapes, with a slight preponderance in the oblate field (Fig. 9). Magnetite grain shape alignment is not readily detectable and penetrative deformation is absent. Why then are the AMS orientation distributions so well defined? A preferred arrangement of significant magnetic domains within large multidomain magnetite grains may be the explanation. In this way the almost isotropic shape fabric of mutidomain magnetite grains can be independent of the strong orientation fabric shown by principal susceptibilities (Figs. 7 and 8). This may be stress-induced, rather than strain-induced as argued in most studies of metamorphic AMS fabrics.
Acknowledgements NSERC funded this research through an operating grant to G. Borradaile. Gina Borradaile helped with
[l] M.M. Kehlenbeck, The Barnum Lake pluton, Thunder Bay, Ontario, Can. J. Earth Sci. 14, 2157-2167, 1977. [2] M.M. Kehlenbeck and S.P. Cheadle, Structural cross-sections based on a gravity survey of parts of the Quetico and Wawa subprovinces near Thunder Bay, Ontario, Canada, Can. J. Earth Sci. 27, 187-199, 1990. [3] F. Hrouda, Magnetic anisotropy of rocks and its application in geology and geophysics, Geophys. Surv. 5, 37-82, 1982. [4] W.D. MacDonald and B.B. Ellwood, Anisotropy of magnetic susceptibility: Sedimentological, igneous, and structuraltectonic applications, Rev. Geophys. 25(5), 905-909, 1987. [5] G.J. Borradaile, Magnetic susceptibility, petrofabrics and strain, Tectonophysics 1.56, l-20, 1988. 161 P. Rochette, M.J. Jackson and C. Aubourg, Rock magnetism and the interpretation of anisotropy of magnetic susceptibility, Rev. Geophys. 30, 209-226, 1992. [7] D.H. Tarling and F. Hrouda, The Magnetic Anisotropy of Rocks, Chapman and Hall, 1993. [8] M.J. Jackson, Anisotropy of magnetic remanence: A brief review of mineralogical sources, physical origins and geological applications, and comparison with susceptibility anisotropy, Pure Appl. Geophys. 136, l-28, 1991. [9] P.J. Flanders, An alternating-gradient magnetometer, J. Appl. Phys. 63, 3940-3945, 1988. [IO] D.K. Potter and A. Stephenson, Single domain particles in rocks and magnetic fabric analysis, Geophys. Res. Lett. 15, 1097-I 100, 1988. [I 11 J.F. Nye, Physical Properties of Crystals, Oxford University Press, 1985. [12] P.J. Diggle and N.I. Fisher, SPHERE: a contouring program for spherical data, Comput. Geosci. II, 725-766, 1985. [I 31 V. Jelinek, Characterization of the magnetic fabrics of rocks, Tectonophysics 79, T63-T67, 198 I. [I41 R. Day, M.D. Fuller and V.A. Schmidt, Magnetic hysteresis properties of synthetic titanomagnetites, J. Geophys. Res. 81, 873-880, 1977. [I51 P.J. Wasilewski, Magnetic hysteresis in natural materials, Earth Planet. Sci. Lett. 20, 67-72, 1973. 1161 P.Y. Robin and E.C. Jowett, Computerized density contouring and statistical evaluation of orientation data using counting circles and continuous weighting functions. Tectonophysics 121, 207-223, 1986. [17] N.I. Fisher, T. Lewis and B.J.J. Embleton, Statistical Analysis of Spherical Data, Cambridge University Press, 1992.