Coaxial deformed and magnetic fabrics without simply correlated magnitudes of principal values

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1 .,. 294 Ph.vsks of the Earth and Planetary Interiors. 35 (1984) Elsevier Science Publishers B.V.. Amsterdam - Printed in The Netherlands Coaxial deformed and magnetic fabrics without simply correlated magnitudes of principal values Graham J. Borradaile Department of Geology. Lakehead Universi(v. Thu"der Bay. Olllario P7B JEt (Callada) John S. Mothersill Principal. Royal Roads Military College Victoria. British Columhia VOS t BQ (Callada) (Received January ; revision accepted April ) Borradaile, G.J. and Mothersill. J.S., Coaxial deformed and magnetic fabrics without ~imply corrclatcd magnitudes of principal values. Phys. Earth Planet. Inter.. 35: Results of a detailed strain analysis of accretionary lapilli in the Borrowdale Volcanic sequence of England indicate a bedding-memory component to the rock's fabric. A simple, new strain analysis method uses variation in thickness of lapilli rims and appears not to be inouenced by the bedding fabric. The orientations of the principal magnetic susceptibilities show a strong correlation with the principal strain orientations. as in other studies. but we can detect no correlation between strain magnitudes and principal susceptibility magnitudes in the same small specimens. I 1. Introduction We have investigated loose samples and outcrops of lapilli tuff from the Borrowdale Volcanic sequence at Kentmere in the English Lake District. The sequence is quite deformed with a single penetrative cleavage. The maximum dimensions of, the inequant feldspar and quartz grains in the tuff are :s; 0.2 mm while magnetite. the main magnetic mineral (Rathore, 1980), has maximum dimensions S 0.02 mm. The maximum dimension of lapilli is - 15 mm.the shapes of the accretionary lapiui and the texture of the slates have been studied by Green (1920). Oertel (1970), Helm and Siddans (1971) and Bell (1981) and the latter authors have used the shapes of lapilli to estimate strain. Such studies usually involve assumptions about the original fabric because the lapilli were not perfectly spherical and may not have been randomly oriented /84/$03.00 (l) 1984 Elsevier Science Publishers B.V. We have used a new strain analysis technique on these strain markers which does not involve assumptions concerning the original degree of preferred orientation of the lapilli nor assumptions about their shape. The strain ellipsoids are then compared with the magnetic susceptibility ellipsoids. 2. Strain analysis Using 80 kg of selected specimens we machined planar surfaces on the better examples. The surfaces were cut parallel to the principal fabric planes which were defined by the well developed single tectonic cleavage and the strong fabric lineation within the cleavage. From enlarged blackand-white photographs of the principal surfaces the outlines of the lapilli were electronically digitised. To expose more than fifty lapilli in any

2 ~ given principal plane it was usually necessary to grind down the surface, re-polish and re-photograph it. When this was necessary the surface was always ground down more than 2 mm to ensure that different lapilli were measured. Care was taken at all times to ensure that the surfaces were parallel to principal planes by marking guide lines on the two other orthogonal plane surfaces. From the digitised outlines of the lapilli the following parameters were determined: major and minor axial lengths of an ellipse of the same moment-of-inertia; orientation of the long axis of that ellipse (4)); sphericity; and area. This was done not only for the outline of each lapillus but also for the inner laminations of which one or two are often present. The bedding-memory of the strained lapilli is Skewness 05~ 1J JiII:f.-+ _:,0 /ryq -bo "5 Fig. 1. Skewness of the angular distribution of lapilli long axes which cluster about the cleavage trace (SI)' The angles of lapilli long axes have been measured in a clockwise sense relative to the trace of bedding (So). The skewness values are small and positive if the cleavage and preferred orientation make a small angle with bedding and are otherwise larger and negative. This indicates the influence of the bedding fabric on the deformed distribution of lapilli long axes clear from the asymmetry of the distribution of the lapilu long axes (Fig. 1). The distributions show a change in degree and sense of skewness which appears to be dictated by the size of the angle between bedding and the cleavage trace in the specimen. Since any study of the Rr/4> kind requires extra information on the original angular distribution (and perhaps also the original shape distribution) of the lapilli a different approach is used here. The multiple concentric layering of many lapilli allows each individual lapillus to act as a strain marker. By analogy with the selvage of lava pillows (Borradaile and Poulsen, 1981) the concentric rims of lapilli (or oolites) may serve as strain markers. The ratio of maximum to mimimum rim thickness is then equivalent to the finite strain ellipse ratio. At high strains the ratio of rim thicknesses may somewhat overestimate the strain owing to ductility contrasts but the strain analysis appears at least as accurate as the harmonic mean estimator of Lisle (1977). Figure 2 shows the correlation between selvage thickness ratio and both the harmonic mean and the arithmetic mean of lapilli shapes. The correlations are significant at the 97.5% level with correlation coefficients of The principal strain ratios (a, b) are listed in the Appendix. T ~ 51 x... a::...; f4]...,. v) I :!i: n:!i: 137 I T - Rf(e) Rh(X) Fig. 2. Correlation between the strain ratio determined from the selvage ratio (ordinate) with the mean elliptical ratio of lapilli {Rd and with the harmonic mean of the elliptical ratios of lapilli (R h)' The number of lapilli in each case is n. The correlations are significant at the 97.5$ level.

3 29 Strain estimates with 'selvages' or 'rims' are worthy of consideration for they require less data than harmonic mean estimates (each marker can provide two strain estimates per rim structure) and fewer assumptions than more complex analyses. Furthermore, the rims provide interesting data on the effects of ductility contrast with increasing strain (cr. Borradaile, 1982, fig. 18), and we have found that lapilli with multiple selvages illuminate the partitioning of strain from the edge of the lapillus to its centre. They also provide a test for the near uniformity o( selvage thickness. 3. Strain and magnetic fabrics Encouraged by the potential of the selvagestrain method we have attempted to reproduce the agreement between shape fabrics and magnetic fabrics produced in an earlier study (Rathore, 1980). Although we have only sampled one outcrop the range of strains we have detected from different specimens within this one outcrop is nearly as great as that in the whole region studied by the previous workers (Fig. 3). Furthermore, since we have the actual specimens used for our strain analysis we were able to drill the cores needed for magnetic susceptibility from the centres of each of the specimens used for strain analysis. These cores were 2.54 cm in diameter and 2.20 cm in length. The maximum, intermediate and minimum susceptibility directions and magnitudes were measured on an SI-l Magnetic Susceptibility and Isotropy unit supplied by Sapphire Instruments of Ruthven, Ontario. This instrument contains a continuous memory program that first measures the magnetic inductance with a standard-size sample inside the single measuring coil in a specified orientation and then measures the background reading for each specimen orientation. The effective precision of this instrument was increased in our study by inserting each core-specimen in the measuring coil in 24 specified orientated attitudes corresponding to directions in the forms (100) (110), which do not correspond to the directions suggested by Hext (193), as well as utilizing a measuring time of 4 s for each orientation. We have checked, by measuring each of the core-specimens 14 times, to ensure that the magnetic susceptibility anisotropy results we obtained In (X/Y) 1 0 o Bell 1981 o Oertel 1970 Helm 8 Siddons 1971 Green 1920 Present Work o 0'5 I o 0 0 o 0 0 o-or , ' In (Y/Z) Fig. 3. Shapes of lapilli in the Borrowdale Volcanic lapilli tuff from previous studies and the present work. Axes of lapilli are X>Y> Z.

4 297 were reproducible. We have used the mean of the maximum, intermediate and minimum susceptibility direction and magnitude measurements of each core-specimen in our comparison with the strain analysis. The magnitudes of the principal susceptibilities are listed in the Appendix. The results were initially as expected. The principal directions of the magnetic susceptibility ellipsoid were close to the maximum extension direction of the specimens and the minimum susceptibilities were nearly perpendicular to the cleavage and plane of flattening. The results were in close agreement to those found by earlier workers. In fact, in our study the correspondence of the directions is shown by the fact that the vector mean and angular deviation of the angles between the maximum susceptibility and the maximum extension direction were ± for the 17 large specimens. There was less satisfaction in the comparison of principal susceptibility values with the principal strain magnitudes. The shapes of the strain ellipsoid and of the magnitude-ellipsoid of susceptibility were determined with a precision which we felt would justify some attempt at correlation. Figure 4 shows the mean ratios of principal values and their standard errors. We have attempted to correlate various anisotropy parameters derived from the principal susceptibilities k\ > k2 > k3 and from the principal strain ratios a X/Y and b Y/Z which yield the normalised values of X, Y and Z from the relationships X= (a 2.b)1/3 Y= (b/a)1/3 Z=(a.b 2 ) 1/3 mox{ lint MAGNI!:TIC SUSCEPTIBILITY DATA -ll *v/ ft I'OS STRAIN + + t +f inti. Imm.---A.v los 110 Hi '0 35 Fig. 4. Shapes or the strain ellipsoids ror the turr determined rrom selvage ratios with their standard error bars and shapes or the magnetic susceptibility ellipsoids with their standard error bars. (Note that the axes or the graph have been compressed). Some selected tie-lines are shown joining shapes or magnetic and strain ellipsoids ror the same small specimens. The data are listed in a table in the Appendix.

5 The parameters were calculated for both strain and susceptibility-magnitude ellipsoids and were correlated. A significance level of a = 0.05 was selected for all tests. Of all the parameters available (Hrouda, 1982) we calculated and tested the following: (1) the principal values themselves, i.e., kl with X, k2 with Y.. ; (2) ratios of the principal values, i.e., k./k 2 with X/Y.. ; (3) the ellipsoid-shape parameter (Flinn's k value) given by (a - 1)/(b/1) where a = maximum/intermediate and b = intermediate/ minimum value; (4) natural logarithms of all of the above to test for suspected power-law relationships; (5) a logarithmic ellipsoid shape parameter (Ramsay's K-value) given by In(a)/ln(b) for both susceptibility and strain ellipsoids; () Jelinek's (1981) T and p' parameters, suggested to us by a referee, determined for the susceptibility and strain ellipsoid; and (7) the logarithmic parameters M; and IV; of Rathore (1979). (Note that Rathore and Henry, 1982, defined M; and IV; differently from Rathore's original usage.) The only correlation which was acceptable at the standard confidence level was the logarithmic parameter of Rathore (1979), when arranged in the manner of his original usage. In this, he plotted all natural strains (IV;) against the logarithms of all the deviations of the principal susceptibilities from a hypothetical "isotropic" susceptibility for the specimen. The magnetic parameters M; were thus analogous to the natural strains. However, in our study there is still no correlation between the maximum principal values (MI with N 1 ; coefficient r = ) nor between the intermediate values (M 2 with N 2 ; r = 0.032) nor between the minimum values (M3 with N 3 ; r = 0.430). However, like Rathore (1980), it is possible to obtain an apparently very strong correlation when all IV; values are plotted against all M; values (Fig. 5). In fact the correlation appears to be "significant" at the 97.5% level with a coefficient of correlation of However, if we inspect Fig. 5 it is clear that the physical significance of this correlation is dubious. The regression line essentially joins three distinct sets of data-those for the maximum, those for the intermediate and those for the minimum principal values. A fairly well defined regression line is possible only because of the distribution of the three tightly-packed groups of data on the scatter diagram, and we see little justification for comparing the three groups against one another. In some other studies, especially strong apparent correlations have arisen where the fabrics are very oblate, i.e., described by ellipsoids which almost have rotational symmetry. This is because the data then group into only two clusters on the graph: NI = N2 and M\ = M 2, forming one cluster, while the data (N 3, M 3 ) form the other cluster. In the present study we suggest that no correlation is apparent between the parameters we have derived from the magnitudes of the principal susceptibilities and from the magnitudes of the principal strains of the same specimens. Although we have only investigated one very large site, the range of strains there is very wide (Fig. 3) and should give enough scatter to test a correlation. Furthermore, our strain analysis method gives results in extremely close agreement with Lisle's harmonic mean estimator (Fig. 2) which has been shown to be a very good strain estimator from Mj maximu'!" v~/ues 1'1 0'00 ({cl l s..-'.. - ' J intermediate 0..Y: values ~ ~. ( /-: 2) -~ ,00 minimum values C(, -= ~ ) -1'00 0'000 N I Fig. 5. The natural strain values N, and comparable magnetic parameters M j calculated according to Rathore (1979). Note the separate grouping of values according to whether they refer to maximum (N., M I ). intermediate (N 2 M 2 ) or minimum values. The regression line is apparently significant with a correlation coefficient 0.92 at the 97.5% level with a slope of 0.07)9 and an intercept of

6 .. comparative studies (Lisle, 1977; Borradaile, in press). Four of our specimens have also been determined by the Geological Survey of Canada (K. Christie and E. Schwarz) using a Kappabridge KLYI instrument developed by Hrouda's group. The anisotropies determined at Ottawa agree closely with the determinations at Lakehead and the correlation coefficient r = 0.992, is significant at the a = 0.05 level. 4. Discussion Although we have been unable to confirm a simple relationship between strain and susceptibility ellipsoid shapes we hope that our work spawns further investigations. It is already known that the degree of correlation that one might expect must be influenced by the strain-response model and particular deformation mechanisms which operate. Magnetic fabrics may differ according to whether active rotation (Ramsay, 197, eq. 3-34), passive rotation (Ramsay, 197, eq and 5-27), localised mass removal (e.g., pressure-solution) or intergranular effects dominate. In practice, there may be more prominent influences, particularly jf metamorphism took place, and combinations of these influences may also control the development of the magnetic fabric. It is already known that some deformation mechanisms differently affect the magnetic and strain ellipsoid development. For example, pressure solution transports silicates and carbonates and concentrates less soluble magnetite. The resulting relationship between susceptibility and strain ellipsoids appears distinct from that in rocks in which pressure solution is less important (Borradaile and Tarling, 1981). In cases of particulate flow magnetite fails to develop a strong preferred orientation, possibly owing to the disorie.nting effects of disaggregation on magnetite grains which are much smaller than the rock-forming grains (Borradaile and Tarling, 1984). An important optimistic aspect is the strong relationship between the orientations of principal susceptibilities and mineral fabric elements. Furthermore, in this and many other studies the principal susceptibilities are also coaxial W1th the 299 principal strain directions, within the limits of detection. Usually there is a one-to-one mapping with k I parallel to X, k 2 parallel to Y, etc. This is a most remarkable feature in view of the non-coaxial nature of most natural strain histories and the spatially heterogeneous and probable diachronous nature of many natural deformation processes. It reconfirms the value of susceptibility studies in evaluating cryptic mineral or strain fabrics over large areas, for example in the Canadian shield (Stott and Schwerdtner, 1981) where it may assist in the delimitation of mineralised zones, or in detailed structural studies of the type already cited. Acknowledgements This research was supported by the following grants from the Natural Sciences and Engineering Research Council of Canada: GJB: grants A81 and E558; JSM grants A4243 and E38. K.W. Christie of the Geological Survey of Canada. Ottawa checked our susceptibility determinations and E. Schwarz helped to arrange this. We thank Frantisek Hrouda for a constructive review. Appendix Principal strain ratios (a,b) and principal susceptibilities (k j x 10- G/Oe/cnr). In parentheses: standard errors for the strain ratios and standard deviations for the principal susceptibilities Nr: (a) (b) k(l) k(2) k(3) (n) (n) A3A: (0.082) (0.108) (0.023) (0.028) (0.029) A7A: (0.082) (0.108) (0.024) (0.01) (0.021 ) AC: (0.082) (0.108) (0.018) (0.039) (0.024) BIA: (0.079) (0.057) (0.017) (0.013) (0.017) B4A: (0.082) (0.115) (0.018) (0.029) (0.037)

7 ' 3'00.. Nr: (a) (b) k,(1) k(2) k(3) (n) (n) BA: (0.08) (0.095) (0.020) (0.015) (0.017) B13A: OS (0.125) (0.112) (0.028) (0.030) (0.024) B14A: (0.12S) (O.lSl) (0.023) (0.027) (0.027) BC: 1.S (0.099) (0.12S) (0.021) (0.015) (0.019) BD: (0.095) (0.090) (0.014) (0.021) (0.021) AP: (0.095) (0.149) (0.015) (0.011) (0.014) B2A: (0.05) (0.059) (0.018) (0.013) (0.01) B3A: (0.130) (0.110) (0.024) (0.025) (0.019) B5: (0.050) (0.080) (0.021) (0.023) (0.032) B8: (0.099) (0.072) (0.027) (0.019) (0.093) BIO: (0.094) (0.03) (0.013) (0.017) (0.017) B2AX: (0.095) (0.00) (0.018) (0.013) (0.01) References Bell. A.M., Strain factorisations from lapilli tuff, English Lake District. 1. Geol. Soc. London, 138: orradaile, G.l. 19S2. Tectonically deformed pillow lava as an indicator of bedding and way-up. 1. Struct. Geol.. 4: orradaile, G.l. in press. Strain analysis of passive elliptical markers: 'success of de-straining methods. 1. Struct. Geol. 8orradaile, G.l. and Poulsen, K.H., Tectonic deformation of pillow lava. Tectonophysics, 79: Borradaile. G.l. and Tarling, D.H The innuence of deformation mechanisms on the magnetic fabrics of weakly. deformed rocks. Tectonophysics, 77: Borradaile, G.l. and Tading, D.H Strain partitioning and magnetic fabrics in particulate now. Can. 1. Earth Sci.. in press. Green, I.F.N., The geological structure of the Lake District. Proc. Geo!. Assoc., London, 31: Helm, D.G. and Siddans, A.W.B., Deformation of a slaty. lapillar tuff in the English Lake District, Discussion. Bull. Geo!. Soc. Am.. 82: Hext, G.R., 193. The estimation of second-order tensors, with related tests and designs. Biometrika, SO: Hrouda. F., Magnetic anisotropy of rocks and its application in geology and geophysics. Geophys. Surv., 5: Jelinek, V., Characterization of magnetic fabrics of rocks. Tectonophysics, 79: Lisle. R.1., Estimation of the tectonic strain ratio from the mean shape of deformed. elliptical markers. Geo!. Mijnbouw, 5: Oertel, G., Deformation of a slaty. lapiljar tuff in the Lake District, England. Bull. Geol. Soc. Am., 81: Ramsay, 1.G., 197. Folding and Fracturing of Rocks. Mc- Graw-Hill, New York, 58 pp. Rathore, 1.S., Magnetic susceptibility anisotropy in the Cambrian slate belt of North Wales and correlation with strain. Tectonophysics, 53: Rathore, 1.S., The magnetic fabric of some slates from the Borrowdale volcanic group in the English Lake District and their correlation with strain. Tectonophysics, 7: Rathore, J.S. and Henry, B., Comparison of strain and magnetic fabrics in Dalradian rocks from the southwest Highlands of Scotland. J. Struc\. Geol. 4: Stott, G.M. and Schwerdtner, W.M., A structural analysis of the Central part of the Shebandowan metavolcanicmetasedimentary belt. Final Report to the Ontario Geosci. Res. Rep., #5349, 44 pp. Ontario Dept. Mines, Toronto. Canada. I ) f 1