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The effect of rock fabric on P-wave velocity distribution in amphibolites
Physics of the Earth and Planetary Interiors 114 Ž1999. 39–47
The effect of rock fabric on P-wave velocity distribution in amphibolites V. Vajdova´
a,1
, R. Prikryl ˇ
b,)
, Z. Pros c , K. Klıma ´
c
a
Institute of Hydrogeology, Engineering Geology and Applied Geophysics, Faculty of Science, Charles UniÕersity, AlbertoÕ 6, 128 43 Prague 2, Czech Republic b Institute of Geochemistry, Mineralogy and Mineral Resources, Faculty of Science, Charles UniÕersity, AlbertoÕ 6, 128 43 Prague 2, Czech Republic c Geophysical Institute, Academy of Sciences of the Czech Republic, Bocnı ˇ ´ II r 1401, 141 31 Prague 4, Czech Republic Received 28 November 1997; accepted 26 November 1998
Abstract This study presents contribution to the laboratory investigation of elastic properties and rock fabric of amphibolites. P-wave velocity was determined on four spherical samples prepared from a shallow borehole core. The measurement was conducted in 132 directions under various conditions of hydrostatic pressure Žup to 400 MPa.. The rock fabric was investigated by image analysis of thin sections that enabled precise determination of grain size, modal composition and shape parameters of rock-forming minerals. Laboratory measurement of P-waves revealed pseudoorthorhombic symmetry of rock fabric in amphibolites studied. This symmetry reflects rocks’ macro- and microfabric. Maximum P-wave velocity corresponds to the macroscopically visible stretching lineation. Minimum P-wave velocity is oriented perpendicular to the foliation plane. The average grain size is the main microstructural factor controlling mean P-wave velocity. q 1999 Elsevier Science B.V. All rights reserved. Keywords: P-wave velocity anisotropy; Laboratory measurement; Amphibolites; Rock fabric; Image analysis; Grain size; Shape-preferred orientation
1. Introduction P-wave velocity, as a physical property of rocks, depends on their mineralogical composition, on the rock micro- and macrofabric Žincluding both texture and structure in metallographic meaning., on the presence of defects Žmicrocracks and pores. and on
)
Corresponding author. E-mail: [email protected] Present address: Department of Geosciences, SUNY at Stony Brook, Stony Brook, New York, 21794-2100, USA. 1
physical parameters of mineral skeleton, such as elastic properties, density or porosity. Relationship between P-wave velocity and selected physical parameters was already determined for several rock types. For example, the increase of velocity with increasing density is mentioned by many authors: Birch Ž1960., Babuska ˇ Ž1968. and Kopf et al. Ž1985. among others. The influence of microcracks on P-wave velocity distribution was studied by Babuska ˇ et al. Ž1977. and Jech et al. Ž1985. for instance. The effect of crystallographic preferred orientation of rock-forming minerals on
0031-9201r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 1 - 9 2 0 1 Ž 9 9 . 0 0 0 4 4 - 8
40
V. VajdoÕa´ et al.r Physics of the Earth and Planetary Interiors 114 (1999) 39–47
P-wave velocities was examined by Babuska ˇ Ž1968., Thill et al. Ž1969, 1973., Kern Ž1974, 1993., Kern and Fakhimi Ž1975., Peselnik et al. Ž1977., Volarovich et al. Ž1985., Nicolas and Christensen Ž1987., Siegesmund and Dahms Ž1994. and Barruol and Kern Ž1996. among others. These contributions improved understanding and interpretation of seismic measurements from petrological point of view. Amphibolites belong to common rock types of the Earth’s crust. Surprisingly, a comparative study of P-wave velocities, modal composition and microstructures Žgeometrical aspects of grains. of amphibolites is still missing. This study aims to elucidate how some microstructural parameters of minerals can influence the velocity of P-waves. Amphibolites under study were collected from a shallow borehole in Kutna´ hora crystalline complex, Bohemian Massif, Czech Republic. First, P-wave velocity was determined using ultrasonics on spherical samples in 132 directions at pressure range 0.1– 400 MPa. Volume density of the samples was determined. Then, image analysis was employed for the determination of grain size and shape-preferred orientation of rock-forming minerals and for the determination of modal composition of the rock. The image analysis was carried out on thin sections prepared from the same material as the spherical samples. These data were compared to P-wave velocities. 2. Velocity measurements P-wave velocity measurement was conducted on four spherical samples Ž5 cm in diameter. that were prepared from a borehole core. Velocities of longitudinal waves were determined using pulse transmission method first used by Hughes et al. Ž1949., later modified for the measurements on spherical samples ŽPros et al., 1969. under confining pressure ŽPros and Podrouzkova, ˇ ´ 1974.. The details on the apparatus and technique were given more recently by Pros et al. Ž1998. Žand references therein.. The uniqueness of this apparatus lies in its ability to determine P-wave velocity in any direction on a spherical sample with transmitter Žfrequency 2.5 MHz. and receiver sliding on the opposite sides of the sphere. For practical reasons, the measurements are carried out in 132 independent directions regu-
larly occupying the space ŽPros et al., 1998.. The measurement is conducted at atmospheric pressure and under levels of confining pressure 20, 50, 100, 200 and 400 MPa. Velocities calculated from the travel times are not corrected by applied hydrostatic pressure. There are two procedures on how to present velocity data from current laboratory measurement. First, velocities are represented in the form of isolines in the equal area lower hemisphere projection. This scheme of data presentation gives an idea on the spatial distribution of P-wave velocities in the rock sample at a given pressure level. Second, P-wave velocity is expressed as a function of hydrostatic pressure. This approach enables to observe velocity development in a selected direction through the whole pressure range. Conventionally, maximum, mean and minimum velocities are analysed. Maximum and minimum velocities Ž Õ Pmax and Õ Pmin . define the range of observed velocities at a given pressure level while the mean P-wave velocity Ž Õ Pmean . characterizes the whole rock sample. This parameter is calculated as a weighted average value of velocities measured over the whole sphere. 3. Image analysis Image measurement system of thin sections was used for a quantitative analysis of microstructures. Microstructures are understood as the geometrical features of rock fabric ŽWenk, 1985; PanozzoHeilbronner, 1994. and can be evaluated by several parameters. Thin sections were cut in XZ-plane of
Fig. 1. Orientation of coordinates X, Y, Z related to the macroscopically visible fabric elements. X-direction corresponds to stretching lineation, XY-plane is foliation. Z-direction is oriented perpendicularly to foliation.
V. VajdoÕa´ et al.r Physics of the Earth and Planetary Interiors 114 (1999) 39–47
the finite strain ellipsoid and were prepared from the same part of the borehole core as the spherical sample. The X-axis is direction of macroscopically observable lineation, Z is normal to the macroscopic foliation ŽFig. 1.. Our image analysis ŽPrikryl, 1998. processes the ˇ photographs of thin sections made in a polarizing light microscope. Each mineral grain is outlined and identified on the photograph. Then, the black and white image is scanned and analysed by the image analysis program ŽSIGMASCAN, Jandel Scientific, USA.. About 300 grains of each mineral were analysed in every thin section. First, areas occupied by differ-
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ent minerals are used for the determination of modal composition of the studied rock. Then, Feret diameter is calculated for each analysed grain. Feret diameter equals to a diameter of a circle having the same area as the analysed grain. The typical grain size of a rock is expressed as an average value. Last, lengths of major and minor axes of an ellipse approximating the grain shape are determined. A ratio of major and minor axes is expressed as the aspect ratio. Image analysis also allows to compute the orientation of grain’s longest axes to a given plane. The shape-preferred orientations of grains are then plotted out in the form of rose diagrams.
Fig. 2. Spatial distribution of P-wave velocities presented in the form of velocity isolines projected onto the lower hemisphere equal area projection. Letters X and Z indicate directions of macroscopic lineation Ž X . and pole to foliation plane Ž Z .. Black dots in the centre of diagrams show position of Y-axis. Small circles indicate position of Õ Pm ax Žplus sign. and Õ Pmin Žminus sign., respectively.
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V. VajdoÕa´ et al.r Physics of the Earth and Planetary Interiors 114 (1999) 39–47
4. Results 4.1. Results of P-waÕe Õelocity measurement All samples under study exhibit a well-ordered pattern of P-wave velocities. This pattern is charac-
terized by the single minimum and the single maximum of P-wave velocity ŽFig. 2.. Those P-wave velocity extremes are oriented almost perpendicularly to each other. The general pattern of P-wave velocity isolines in the studied amphibolites gives the evidence of pseudoorthorhombic symmetry.
Fig. 3. P-wave velocity–confining pressure behaviour Žleft. and P-wave velocity anisotropy–confining pressure behaviour Žright. of amphibolites under study. Max and min refer to the maximum and minimum P-wave velocity. Mean is mean P-wave velocity calculated as a weighted average of all 132 measurements.
V. VajdoÕa´ et al.r Physics of the Earth and Planetary Interiors 114 (1999) 39–47
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microcracks are closed, linear increase of P-wave velocity follows. P-wave velocity is influenced mainly by elasticity of mineral skeleton in this part of velocity–pressure behaviour. The highest Õ Pmean over the whole range of applied confining pressure was reached in the sample 01S1. The highest change of a Õ Pmean with increased confining pressure occurred in the sample 10S1 Žfrom 4.820 to 7.171 kmrs.. 4.2. Results of image analysis
Fig. 4. Modal composition of amphibolites under study determined by image analysis from thin sections.
The position of P-wave velocity extremes remains almost the same over the applied range of hydrostatic pressure although the absolute values of P-wave velocity vary significantly. A good agreement can be found between position of maximum and minimum P-wave velocity and the directions of observed lineation and foliation. The isolines pattern is generally stable over the whole range of applied hydrostatic pressure which implies that no significant anisotropic change occurred in the rock fabric of studied amphibolites during the hydrostatic load. The procedure of samples collection from a borehole enables to preserve only the vertical axis direction while the rotation of the borehole core around this vertical axis was lost. The isoline images ŽFig. 2. are presented in the conventional coordinate system used by structural geologists where X corresponds to lineation and Z is normal to foliation. Diagrams in Fig. 3a,b,c,d present the evolution of maximum, minimum and mean P-wave velocity with the applied hydrostatic pressure. Two parts can be distinguished on the curves illustrated in Fig. 3. First, there is a steep non-linear increase of P-wave velocity under lower hydrostatic pressure up to 100–150 MPa. This behaviour is usually explained by the closing of microcracks due to pressure load ŽKern and Fakhimi, 1975; Babuska ˇ and Pros, 1984; Jech et al., 1985; Fountain et al., 1990; Kern, 1990; Hrouda et al., 1993.. After the
Modal composition determined for the studied samples is shown in Fig. 4. There are two minerals composing the rocks studied. Except of 01S1, all the samples are characterized by majority of amphibole. The observed content of this mineral ranges from 42.3 to 65.6%. Plagioclase occurs as the second most abundant mineral. Other two minor minerals occur in the samples studied. Calcite occupies less than 3% and pyrite less than 1% of the samples’ volume. Typical grain sizes of rocks studied are summarized in Table 1. It clearly documents differences in average grain size reaching almost one order in magnitude between the finest grain size Žamphibolite sample 02S1. and the most coarse-grained sample Žamphibolite sample 11S1.. Fig. 5 shows orientation of the long axes of amphibole and plagioclase in the form of rose diagram. Most of the grains are stretched in X-direction and therefore do not deviate from the foliation plane.
Table 1 Summary of some physical and microstructural parameters determined on amphibolites studied Sample
Volume density wgrcm3 x
Õ Pm ean observed wkmrsx
Anisotropy coefficient k w%x
Grain size wmmx
01S1 02S1 10S1 11S1
2.973 2.969 2.949 2.942
6.968 6.842 6.717 6.618
12.8 12.9 13.2 12.9
0.04 0.03 0.08 0.11
Velocity data refers to 400 MPa pressure level. Coefficient of P-wave anisotropy was calculated according to Birch Ž1961.. Grain size is expressed as a diameter of a circle having the same area as the analyzed grain.
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V. VajdoÕa´ et al.r Physics of the Earth and Planetary Interiors 114 (1999) 39–47
Fig. 5. Shape parameters of grains determined by image analysis from thin sections. Rose diagrams on the left show preferred orientation of grains’ long axes in respect to the foliation plane Žhorizontal direction.. Aspect ratio Žright. expresses grains’ elipticity.
The scatter of amphibole grains is distinctly smaller than that of plagioclase. The amphibole is also characterized by more elongated shape Žcompare aspect ratio in Fig. 5..
5. Discussion If most of microcracks are closed at 400 MPa in low porosity rocks, the influence of microcracks on P-wave velocity at such a high confinement can be neglected. The P-wave velocity measured at 400 MPa was therefore used for further comparative analysis.
5.1. P-waÕe Õelocity–confining pressure dependence The steep slope of the first part of P-wave velocity–confining pressure curves indicates that three samples 02S1, 10S1 and 11S1 can be regarded as the rocks containing microcracks. One sample 01S1 seems to be crack free because of its linear P-wave velocity–confining pressure behaviour. The highest P-wave velocity increment can be observed in the Õ Pmin direction for samples 02S1, 10S1 and 11S1. This implies that microcracks tend to be oriented parallel to foliation in amphibolites studied. All the samples under study exhibit high P-wave velocity anisotropy that is usually evaluated by a
V. VajdoÕa´ et al.r Physics of the Earth and Planetary Interiors 114 (1999) 39–47
coefficient of anisotropy. The coefficient of anisotropy is computed using the formula introduced by Birch Ž1961. and modified for measurements in more than three directions ŽBabuska, 1968; Jech et al., ˇ 1985.: Õ Pmax y Õ Pmin k w%x s 100% Õ Pmean In Fig. 3, the diagrams e, f and g show a decrease of this coefficient with pressure in samples 01S1, 02S1 and 10S1. This phenomenon was discussed in literature ŽBabuska, ˇ 1968; Kern and Fakhimi, 1975; Fountain et al., 1990; Kern, 1990; Ji et al., 1993.. The general evolution of the anisotropy coefficient with confining pressure seems to result mainly from two factors: closing of microcracks in lower pressure domain and non-isotropic improvement of elastic connection between particles of the rock at high pressure. The sample 11S1 exhibits the same decrease of the k-coefficient in low confining pressure domain as previous samples, but in high confining pressure domain, the k-coefficient increases ŽFig. 3h.. Ji et al. Ž1993. explain this as a result of different pressure sensitivity in various directions in a sample. 5.2. P-waÕe Õelocity Õs. grain size Comparing average grain size and Õ Pmean at 400 MPa, a negative correlation was found ŽFig. 6..
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There are two possible explanations for this observation. First, it can be explained as an interplay between wavelength of the used signal and a size of rock particles. Then, this problem could be considered as a ‘scale problem’ and could be reversed onto problem of ultrasonic velocity dependence on used signal frequency. Second, the relation shown in Fig. 6 comes from a real difference in elastic properties of the material induced by different grain size of a particular rock. To determine which one of these two alternatives is more likely to explain the observation is beyond our current knowledge. A comparison between observed velocities and velocities calculated by Christoffel’s equation could give some more clues. 5.3. The effect of micro- and macrofabric The foliation planes of amphibolites under study are defined by composite layering of amphibole-rich and plagioclase-rich layers 0.1–1 mm thick. Clearly, such a layering contributes to P-wave velocity minima as it decreases velocity of P-waves propagating perpendicularly to foliation. The best agreement between Z-direction and the direction of Õ Pmin can be found in sample 02S1 Žcompare Fig. 2., that is, the sample with mineral grains oriented most parallel to foliation Žcompare Fig. 5.. The position of Õ Pmin in amphibolites under study is influenced by compositional layering that results from the preferred orientation of rock-forming minerals. This preferred orientation is due to the shape and crystallographic preferred orientation. As the strong relationship between both types of preferred orientation for amphibole was confirmed Že.g., Siegesmund et al., 1994., we have focused only on the analysis of the effect of shape-preferred orientation of minerals on P-wave velocity anisotropy that is less studied ŽChristensen and Szymanski, 1988; Barruol and Kern, 1996.. 5.4. Relationship between P-waÕe Õelocity and mineralogical composition
Fig. 6. Relationship between mean P-wave velocity determined at 400 MPa confining pressure level and average grain size determined by image analysis from thin section.
Comparing P-wave velocities at 400 MPa to volume density of the samples, the well-known dependence ŽBirch, 1961. is obtained. The values in
V. VajdoÕa´ et al.r Physics of the Earth and Planetary Interiors 114 (1999) 39–47
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Table 2 Mean P-wave velocity of rock forming minerals of amphibolites Žafter Babuska, ˇ 1981. and their density Žafter Deer et al., 1966. Mineral
Mean P-wave velocity wkmrsx
Density wgrcm3 x
Amphibole Plagioclase Calcite Pyrite
7.16 6.53 6.49 7.40
3.02–3.45 2.60–2.76 2.72 5.00
Table 1 confirm that a lower density produces a lower velocity of P-waves. Table 2 summarizes the properties of single minerals. Omitting the minerals of small modal representation Žcalcite, pyrite., amphibole is the mineral of high density and high velocity. Then, one would expect that the density and Õ Pmean of a sample will be directly related to the amount of the major rock-forming mineral-amphibole. Comparing the modal amount of amphibole ŽFig. 4. with volume densities and velocities of samples ŽTable 1., the opposite trend is observed. Samples with higher density and velocity show smaller amount of amphibole. This consideration was made without taking modal amount of calcite and pyrite into account. While properties of calcite are very similar to that of plagioclase, pyrite differs significantly from other rockforming minerals of amphibolites studied. Thus, even small amount of pyrite seems not to have a negligible effect on physical properties Ždensity and P-wave velocity. of the rock. Other features that complicate the straightforward relation between density of major minerals and density of the studied rock are voids in the rock. Amount of microcracks and their possible preferred orientation were not determined in this study.
6. Conclusions Amphibolites under study show a significant pseudoorthorhombic pattern of P-wave velocities at all pressure levels. The symmetry of those rocks reflects their microfabric defined by linear orientation of rock-forming minerals and by compositional layering. While direction of maximum P-wave veloc-
ity is oriented parallel to lineation, minimum P-wave velocity is oriented perpendicularly to foliation as confirmed by many previous studies. The more the mineral grains lie elongated in the foliation plane the more the Õ Pmin direction merges the normal to this plane. Mean P-wave velocity proved correlation with volume density of samples. Correlation of velocity and volume density with the modal representation of the major mineral-amphibole is not clearly documented. For correct estimation of velocity in rock from velocities of constituent minerals, also, less abundant minerals must be taken into account. An increase of mean P-wave velocity with decreasing average grain size of samples was observed. This observation could be related to the ‘scale effect’ Žan interplay of the wavelength of the used signal and the size of mineral grains. or to the real difference in elastic properties of rocks with almost identical composition but different grain size.
Acknowledgements The authors are very grateful to Tomas ´ˇ Lokajıcek ´ˇ Ž and Lukas Padjen Geophysical Institute of the ´ˇ Academy of Sciences of the Czech Republic. for their help during high pressure experiments. This work was supported by the Ministry of Education of Czech Republic Žproject G41309.. The authors are thankful to three anonymous reviewers for valuable comments.
References Babuska, ˇ V., 1968. Elastic anisotropy of igneous and metamorphic rocks. Stud. Geph. Geod. 12, 291–303. Babuska, ˇ V., 1981. Anisotropy of Õ P and Õ S in rock-forming minerals. J. Geophys. 50, 1–6. Babuska, ˇ V., Pros, Z., 1984. Velocity anisotropy in granodiorite and quartzite due to the distribution of microcracks. Geophys. J. R. Astr. Soc. 76, 121–127. Babuska, ˇ V., Pros, Z., Franke, W., 1977. Effect of fabric and cracks on the elastic anisotropy in granodiorite. Publ. Inst. Geophys. Pol. Acad. Sci. A-6 117, 179–186. Barruol, G., Kern, H., 1996. Seismic anisotropy and shear-wave splitting in lower-crustal and upper mantle rocks from the Ivrea zone—experimental and calculated data. Phys. Earth Planet. Inter. 95, 175–194.
V. VajdoÕa´ et al.r Physics of the Earth and Planetary Interiors 114 (1999) 39–47 Birch, F., 1960. The velocity of compressional waves in rocks to 10 kbars: Part 1. J. Geophys. Res. 65, 1083–1102. Birch, F., 1961. The velocity of compressional waves in rocks to 10 kbars: Part 2. J. Geophys. Res. 66, 2199–2224. Christensen, N.I., Szymanski, D.L., 1988. Origin of reflections from the Brevard fault zone. J. Geophys. Res. 93, 1087–1102. Deer, W.A., Howie, R.A., Zussman, J., 1966. An Introduction to the Rock-forming Minerals. Longmans, London, 528 pp. Fountain, D.M., Salisbury, M.H., Percival, J., 1990. Seismic structure of the continental crust based on rock velocity measurements from the Kapuskasing uplift. J. Geophys. Res. 95, 1167–1186. Hrouda, F., Pros, Z., Wohlgemuth, J., 1993. Development of magnetic and elastic anisotropies in slates during progressive deformation. Phys. Earth Planet. Inter. 77, 251–265. Hughes, D.S., Pondrom, W.L., Mims, R.L., 1949. Transmission of electric pulses in metal rods. Phys. Rev. 75, 1552–1556. Jech, J., Babuska, ˇ V., Pros, Z., 1985. Quantitative correlation of velocity anisotropy with the distribution of microcracks in rocks. In: Kapicka, ˇ A., Kropacek, ´ˇ V., Pros, Z. ŽEds.., Physical Properties of the Mineral System of the Earth’s Interior. Union Czech. Math. Phys., Prague, pp. 175–183. Ji, S., Salisbury, M.H., Hanmer, S., 1993. Petrofabric, P-wave anisotropy and seismic reflectivity of high-grade tectonites. Tectonophysics 222, 196–226. Kern, H., 1974. Gefugeregelung und elastische Anisotropie eines ¨ Marmors. Contr. Mineral. Petrol. 73, 47–54. Kern, H., 1990. Laboratory seismic measurements: an aid in the interpretation of seismic field data. Terra Nova 2, 617–628. Kern, H., 1993. P- and S-wave anisotropy and shear-wave splitting at pressure and temperature in possible mantle rocks and their relation to the rock fabric. Phys. Earth Planet. Inter. 78, 245–256. Kern, H., Fakhimi, M., 1975. Effect of fabric anisotropy on compressional-wave propagation in various metamorphic rocks for the range 20–7008C at 2 kbars. Tectonophysics 28, 227– 244. Kopf, M., Muller, H.J., Gottesmann, B., 1985. Correlation be¨ tween pyroxene content and Õ P and Õ S under high pressure. In: Kapicka, A., Kropacek, V., Pros, Z. ŽEds.., Physical ˇ ´ˇ Properties of the Mineral System of the Earth’s Interior. Union Czech. Math. Phys., Prague, pp. 168–172. Nicolas, A., Christensen, N.I., 1987. Formation of anisotropy in upper mantle peridotites—a review. In: Fuchs, K., Froidevaux, C. ŽEds.., Composition, Structure and Dynamics of the Lithosphere–Asthenosphere System. Vol. 16, Am. Geophys. Union, Washington, DC, pp. 111–123.
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Panozzo-Heilbronner, R., 1994. Orientation and misorientation imaging: integration of microstructural and textural analysis. In: Bunge, H.J., Siegesmund, S., Skrotzki, W., Weber, K. ŽEds.., Textures of Geological Materials Deutsche Gesellschaft fur ¨ Materialkunde-Informationsgesellschaft-Verlag, Oberursel, pp. 147–164. Peselnik, L., Nicolas, A., Stevenson, P.R., 1977. Velocity anisotropy in a mantle peridotite from the Ivrea zone: application to upper mantle anisotropy. J. Geophys. Res. 79, 1175–1182. Pros, Z., Podrouzkova, ˇ ´ Z., 1974. Apparatus for investigating the elastic anisotropy on spherical samples at high pressure. Veroff. ¨ Zentralinst. Physic Erde. 22, 42–47. Pros, Z., Vanek, ˇ J., Klıma, ´ K., Babuska, ˇ V., 1969. Investigation of wave pattern in ultrasonic transmission through the sphere. Z. Geophys. 35, 287–296. Pros, Z., Lokajıcek, K., 1998. Laboratory approach to ´ˇ T., Klıma, ´ the study of elastic anisotropy on rock samples. Pure Appl. Geophys. 151 Ž2–4., 619–629. Prikryl, R., 1998. The Effect of Rock Fabric on Some Mechanical ˇ Properties of Rocks: an Example of Granites. Doctoral Thesis, Charles University, Prague, 154 pp. Siegesmund, S., Dahms, M., 1994. Fabric-controlled anisotropy of elastic, magnetic and thermal properties of rocks. In: Bunge, H.J., Siegesmund, S., Skrotzki, W., Weber, K. ŽEds.., Textures of Geological Materials Deutsche Gesellschaft fur ¨ Materialkunde-Informationsgesellschaft-Verlag, Oberursel, pp. 353–379. Siegesmund, S., Helming, K., Kruse, R., 1994. Complete texture analysis of a deformed amphibolite—comparison between neutron diffraction and U-stage data. J. Struct. Geol. 16 Ž1., 131–142. Thill, R.E., Willard, R.J., Bur, T.R., 1969. Correlation of longitudinal velocity variation with rock fabric. J. Geophys. Res. 74 Ž20., 4897–4909. Thill, R.E., Bur, T.R., Steckley, R.C., 1973. Velocity anisotropy in dry and saturated rock spheres and its relation to rock fabric. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 10 Ž6., 535–557. Volarovich, M.P., Jefimova, G.A., Balasanyan, V.S., 1985. Velocity anisotropy of elastic waves in rocks and minerals under high pressures and its possible causes. In: Kapicka, A., ˇ Kropacek, V., Pros, Z. ŽEds.., Physical Properties of the ´ˇ Mineral System of the Earth’s Interior. Union Czech. Math. Phys., Prague, pp. 29–36. Wenk, H.R. ŽEd.., 1985. Preferred orientation in deformed metals and rocks: an introduction to modern texture analysis. Academic Press, London, 610 pp.
The effect of rock fabric on P-wave velocity distribution in amphibolites V. Vajdova´
a,1
, R. Prikryl ˇ
b,)
, Z. Pros c , K. Klıma ´
c
a
Institute of Hydrogeology, Engineering Geology and Applied Geophysics, Faculty of Science, Charles UniÕersity, AlbertoÕ 6, 128 43 Prague 2, Czech Republic b Institute of Geochemistry, Mineralogy and Mineral Resources, Faculty of Science, Charles UniÕersity, AlbertoÕ 6, 128 43 Prague 2, Czech Republic c Geophysical Institute, Academy of Sciences of the Czech Republic, Bocnı ˇ ´ II r 1401, 141 31 Prague 4, Czech Republic Received 28 November 1997; accepted 26 November 1998
Abstract This study presents contribution to the laboratory investigation of elastic properties and rock fabric of amphibolites. P-wave velocity was determined on four spherical samples prepared from a shallow borehole core. The measurement was conducted in 132 directions under various conditions of hydrostatic pressure Žup to 400 MPa.. The rock fabric was investigated by image analysis of thin sections that enabled precise determination of grain size, modal composition and shape parameters of rock-forming minerals. Laboratory measurement of P-waves revealed pseudoorthorhombic symmetry of rock fabric in amphibolites studied. This symmetry reflects rocks’ macro- and microfabric. Maximum P-wave velocity corresponds to the macroscopically visible stretching lineation. Minimum P-wave velocity is oriented perpendicular to the foliation plane. The average grain size is the main microstructural factor controlling mean P-wave velocity. q 1999 Elsevier Science B.V. All rights reserved. Keywords: P-wave velocity anisotropy; Laboratory measurement; Amphibolites; Rock fabric; Image analysis; Grain size; Shape-preferred orientation
1. Introduction P-wave velocity, as a physical property of rocks, depends on their mineralogical composition, on the rock micro- and macrofabric Žincluding both texture and structure in metallographic meaning., on the presence of defects Žmicrocracks and pores. and on
)
Corresponding author. E-mail: [email protected] Present address: Department of Geosciences, SUNY at Stony Brook, Stony Brook, New York, 21794-2100, USA. 1
physical parameters of mineral skeleton, such as elastic properties, density or porosity. Relationship between P-wave velocity and selected physical parameters was already determined for several rock types. For example, the increase of velocity with increasing density is mentioned by many authors: Birch Ž1960., Babuska ˇ Ž1968. and Kopf et al. Ž1985. among others. The influence of microcracks on P-wave velocity distribution was studied by Babuska ˇ et al. Ž1977. and Jech et al. Ž1985. for instance. The effect of crystallographic preferred orientation of rock-forming minerals on
0031-9201r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 1 - 9 2 0 1 Ž 9 9 . 0 0 0 4 4 - 8
40
V. VajdoÕa´ et al.r Physics of the Earth and Planetary Interiors 114 (1999) 39–47
P-wave velocities was examined by Babuska ˇ Ž1968., Thill et al. Ž1969, 1973., Kern Ž1974, 1993., Kern and Fakhimi Ž1975., Peselnik et al. Ž1977., Volarovich et al. Ž1985., Nicolas and Christensen Ž1987., Siegesmund and Dahms Ž1994. and Barruol and Kern Ž1996. among others. These contributions improved understanding and interpretation of seismic measurements from petrological point of view. Amphibolites belong to common rock types of the Earth’s crust. Surprisingly, a comparative study of P-wave velocities, modal composition and microstructures Žgeometrical aspects of grains. of amphibolites is still missing. This study aims to elucidate how some microstructural parameters of minerals can influence the velocity of P-waves. Amphibolites under study were collected from a shallow borehole in Kutna´ hora crystalline complex, Bohemian Massif, Czech Republic. First, P-wave velocity was determined using ultrasonics on spherical samples in 132 directions at pressure range 0.1– 400 MPa. Volume density of the samples was determined. Then, image analysis was employed for the determination of grain size and shape-preferred orientation of rock-forming minerals and for the determination of modal composition of the rock. The image analysis was carried out on thin sections prepared from the same material as the spherical samples. These data were compared to P-wave velocities. 2. Velocity measurements P-wave velocity measurement was conducted on four spherical samples Ž5 cm in diameter. that were prepared from a borehole core. Velocities of longitudinal waves were determined using pulse transmission method first used by Hughes et al. Ž1949., later modified for the measurements on spherical samples ŽPros et al., 1969. under confining pressure ŽPros and Podrouzkova, ˇ ´ 1974.. The details on the apparatus and technique were given more recently by Pros et al. Ž1998. Žand references therein.. The uniqueness of this apparatus lies in its ability to determine P-wave velocity in any direction on a spherical sample with transmitter Žfrequency 2.5 MHz. and receiver sliding on the opposite sides of the sphere. For practical reasons, the measurements are carried out in 132 independent directions regu-
larly occupying the space ŽPros et al., 1998.. The measurement is conducted at atmospheric pressure and under levels of confining pressure 20, 50, 100, 200 and 400 MPa. Velocities calculated from the travel times are not corrected by applied hydrostatic pressure. There are two procedures on how to present velocity data from current laboratory measurement. First, velocities are represented in the form of isolines in the equal area lower hemisphere projection. This scheme of data presentation gives an idea on the spatial distribution of P-wave velocities in the rock sample at a given pressure level. Second, P-wave velocity is expressed as a function of hydrostatic pressure. This approach enables to observe velocity development in a selected direction through the whole pressure range. Conventionally, maximum, mean and minimum velocities are analysed. Maximum and minimum velocities Ž Õ Pmax and Õ Pmin . define the range of observed velocities at a given pressure level while the mean P-wave velocity Ž Õ Pmean . characterizes the whole rock sample. This parameter is calculated as a weighted average value of velocities measured over the whole sphere. 3. Image analysis Image measurement system of thin sections was used for a quantitative analysis of microstructures. Microstructures are understood as the geometrical features of rock fabric ŽWenk, 1985; PanozzoHeilbronner, 1994. and can be evaluated by several parameters. Thin sections were cut in XZ-plane of
Fig. 1. Orientation of coordinates X, Y, Z related to the macroscopically visible fabric elements. X-direction corresponds to stretching lineation, XY-plane is foliation. Z-direction is oriented perpendicularly to foliation.
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the finite strain ellipsoid and were prepared from the same part of the borehole core as the spherical sample. The X-axis is direction of macroscopically observable lineation, Z is normal to the macroscopic foliation ŽFig. 1.. Our image analysis ŽPrikryl, 1998. processes the ˇ photographs of thin sections made in a polarizing light microscope. Each mineral grain is outlined and identified on the photograph. Then, the black and white image is scanned and analysed by the image analysis program ŽSIGMASCAN, Jandel Scientific, USA.. About 300 grains of each mineral were analysed in every thin section. First, areas occupied by differ-
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ent minerals are used for the determination of modal composition of the studied rock. Then, Feret diameter is calculated for each analysed grain. Feret diameter equals to a diameter of a circle having the same area as the analysed grain. The typical grain size of a rock is expressed as an average value. Last, lengths of major and minor axes of an ellipse approximating the grain shape are determined. A ratio of major and minor axes is expressed as the aspect ratio. Image analysis also allows to compute the orientation of grain’s longest axes to a given plane. The shape-preferred orientations of grains are then plotted out in the form of rose diagrams.
Fig. 2. Spatial distribution of P-wave velocities presented in the form of velocity isolines projected onto the lower hemisphere equal area projection. Letters X and Z indicate directions of macroscopic lineation Ž X . and pole to foliation plane Ž Z .. Black dots in the centre of diagrams show position of Y-axis. Small circles indicate position of Õ Pm ax Žplus sign. and Õ Pmin Žminus sign., respectively.
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4. Results 4.1. Results of P-waÕe Õelocity measurement All samples under study exhibit a well-ordered pattern of P-wave velocities. This pattern is charac-
terized by the single minimum and the single maximum of P-wave velocity ŽFig. 2.. Those P-wave velocity extremes are oriented almost perpendicularly to each other. The general pattern of P-wave velocity isolines in the studied amphibolites gives the evidence of pseudoorthorhombic symmetry.
Fig. 3. P-wave velocity–confining pressure behaviour Žleft. and P-wave velocity anisotropy–confining pressure behaviour Žright. of amphibolites under study. Max and min refer to the maximum and minimum P-wave velocity. Mean is mean P-wave velocity calculated as a weighted average of all 132 measurements.
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microcracks are closed, linear increase of P-wave velocity follows. P-wave velocity is influenced mainly by elasticity of mineral skeleton in this part of velocity–pressure behaviour. The highest Õ Pmean over the whole range of applied confining pressure was reached in the sample 01S1. The highest change of a Õ Pmean with increased confining pressure occurred in the sample 10S1 Žfrom 4.820 to 7.171 kmrs.. 4.2. Results of image analysis
Fig. 4. Modal composition of amphibolites under study determined by image analysis from thin sections.
The position of P-wave velocity extremes remains almost the same over the applied range of hydrostatic pressure although the absolute values of P-wave velocity vary significantly. A good agreement can be found between position of maximum and minimum P-wave velocity and the directions of observed lineation and foliation. The isolines pattern is generally stable over the whole range of applied hydrostatic pressure which implies that no significant anisotropic change occurred in the rock fabric of studied amphibolites during the hydrostatic load. The procedure of samples collection from a borehole enables to preserve only the vertical axis direction while the rotation of the borehole core around this vertical axis was lost. The isoline images ŽFig. 2. are presented in the conventional coordinate system used by structural geologists where X corresponds to lineation and Z is normal to foliation. Diagrams in Fig. 3a,b,c,d present the evolution of maximum, minimum and mean P-wave velocity with the applied hydrostatic pressure. Two parts can be distinguished on the curves illustrated in Fig. 3. First, there is a steep non-linear increase of P-wave velocity under lower hydrostatic pressure up to 100–150 MPa. This behaviour is usually explained by the closing of microcracks due to pressure load ŽKern and Fakhimi, 1975; Babuska ˇ and Pros, 1984; Jech et al., 1985; Fountain et al., 1990; Kern, 1990; Hrouda et al., 1993.. After the
Modal composition determined for the studied samples is shown in Fig. 4. There are two minerals composing the rocks studied. Except of 01S1, all the samples are characterized by majority of amphibole. The observed content of this mineral ranges from 42.3 to 65.6%. Plagioclase occurs as the second most abundant mineral. Other two minor minerals occur in the samples studied. Calcite occupies less than 3% and pyrite less than 1% of the samples’ volume. Typical grain sizes of rocks studied are summarized in Table 1. It clearly documents differences in average grain size reaching almost one order in magnitude between the finest grain size Žamphibolite sample 02S1. and the most coarse-grained sample Žamphibolite sample 11S1.. Fig. 5 shows orientation of the long axes of amphibole and plagioclase in the form of rose diagram. Most of the grains are stretched in X-direction and therefore do not deviate from the foliation plane.
Table 1 Summary of some physical and microstructural parameters determined on amphibolites studied Sample
Volume density wgrcm3 x
Õ Pm ean observed wkmrsx
Anisotropy coefficient k w%x
Grain size wmmx
01S1 02S1 10S1 11S1
2.973 2.969 2.949 2.942
6.968 6.842 6.717 6.618
12.8 12.9 13.2 12.9
0.04 0.03 0.08 0.11
Velocity data refers to 400 MPa pressure level. Coefficient of P-wave anisotropy was calculated according to Birch Ž1961.. Grain size is expressed as a diameter of a circle having the same area as the analyzed grain.
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Fig. 5. Shape parameters of grains determined by image analysis from thin sections. Rose diagrams on the left show preferred orientation of grains’ long axes in respect to the foliation plane Žhorizontal direction.. Aspect ratio Žright. expresses grains’ elipticity.
The scatter of amphibole grains is distinctly smaller than that of plagioclase. The amphibole is also characterized by more elongated shape Žcompare aspect ratio in Fig. 5..
5. Discussion If most of microcracks are closed at 400 MPa in low porosity rocks, the influence of microcracks on P-wave velocity at such a high confinement can be neglected. The P-wave velocity measured at 400 MPa was therefore used for further comparative analysis.
5.1. P-waÕe Õelocity–confining pressure dependence The steep slope of the first part of P-wave velocity–confining pressure curves indicates that three samples 02S1, 10S1 and 11S1 can be regarded as the rocks containing microcracks. One sample 01S1 seems to be crack free because of its linear P-wave velocity–confining pressure behaviour. The highest P-wave velocity increment can be observed in the Õ Pmin direction for samples 02S1, 10S1 and 11S1. This implies that microcracks tend to be oriented parallel to foliation in amphibolites studied. All the samples under study exhibit high P-wave velocity anisotropy that is usually evaluated by a
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coefficient of anisotropy. The coefficient of anisotropy is computed using the formula introduced by Birch Ž1961. and modified for measurements in more than three directions ŽBabuska, 1968; Jech et al., ˇ 1985.: Õ Pmax y Õ Pmin k w%x s 100% Õ Pmean In Fig. 3, the diagrams e, f and g show a decrease of this coefficient with pressure in samples 01S1, 02S1 and 10S1. This phenomenon was discussed in literature ŽBabuska, ˇ 1968; Kern and Fakhimi, 1975; Fountain et al., 1990; Kern, 1990; Ji et al., 1993.. The general evolution of the anisotropy coefficient with confining pressure seems to result mainly from two factors: closing of microcracks in lower pressure domain and non-isotropic improvement of elastic connection between particles of the rock at high pressure. The sample 11S1 exhibits the same decrease of the k-coefficient in low confining pressure domain as previous samples, but in high confining pressure domain, the k-coefficient increases ŽFig. 3h.. Ji et al. Ž1993. explain this as a result of different pressure sensitivity in various directions in a sample. 5.2. P-waÕe Õelocity Õs. grain size Comparing average grain size and Õ Pmean at 400 MPa, a negative correlation was found ŽFig. 6..
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There are two possible explanations for this observation. First, it can be explained as an interplay between wavelength of the used signal and a size of rock particles. Then, this problem could be considered as a ‘scale problem’ and could be reversed onto problem of ultrasonic velocity dependence on used signal frequency. Second, the relation shown in Fig. 6 comes from a real difference in elastic properties of the material induced by different grain size of a particular rock. To determine which one of these two alternatives is more likely to explain the observation is beyond our current knowledge. A comparison between observed velocities and velocities calculated by Christoffel’s equation could give some more clues. 5.3. The effect of micro- and macrofabric The foliation planes of amphibolites under study are defined by composite layering of amphibole-rich and plagioclase-rich layers 0.1–1 mm thick. Clearly, such a layering contributes to P-wave velocity minima as it decreases velocity of P-waves propagating perpendicularly to foliation. The best agreement between Z-direction and the direction of Õ Pmin can be found in sample 02S1 Žcompare Fig. 2., that is, the sample with mineral grains oriented most parallel to foliation Žcompare Fig. 5.. The position of Õ Pmin in amphibolites under study is influenced by compositional layering that results from the preferred orientation of rock-forming minerals. This preferred orientation is due to the shape and crystallographic preferred orientation. As the strong relationship between both types of preferred orientation for amphibole was confirmed Že.g., Siegesmund et al., 1994., we have focused only on the analysis of the effect of shape-preferred orientation of minerals on P-wave velocity anisotropy that is less studied ŽChristensen and Szymanski, 1988; Barruol and Kern, 1996.. 5.4. Relationship between P-waÕe Õelocity and mineralogical composition
Fig. 6. Relationship between mean P-wave velocity determined at 400 MPa confining pressure level and average grain size determined by image analysis from thin section.
Comparing P-wave velocities at 400 MPa to volume density of the samples, the well-known dependence ŽBirch, 1961. is obtained. The values in
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Table 2 Mean P-wave velocity of rock forming minerals of amphibolites Žafter Babuska, ˇ 1981. and their density Žafter Deer et al., 1966. Mineral
Mean P-wave velocity wkmrsx
Density wgrcm3 x
Amphibole Plagioclase Calcite Pyrite
7.16 6.53 6.49 7.40
3.02–3.45 2.60–2.76 2.72 5.00
Table 1 confirm that a lower density produces a lower velocity of P-waves. Table 2 summarizes the properties of single minerals. Omitting the minerals of small modal representation Žcalcite, pyrite., amphibole is the mineral of high density and high velocity. Then, one would expect that the density and Õ Pmean of a sample will be directly related to the amount of the major rock-forming mineral-amphibole. Comparing the modal amount of amphibole ŽFig. 4. with volume densities and velocities of samples ŽTable 1., the opposite trend is observed. Samples with higher density and velocity show smaller amount of amphibole. This consideration was made without taking modal amount of calcite and pyrite into account. While properties of calcite are very similar to that of plagioclase, pyrite differs significantly from other rockforming minerals of amphibolites studied. Thus, even small amount of pyrite seems not to have a negligible effect on physical properties Ždensity and P-wave velocity. of the rock. Other features that complicate the straightforward relation between density of major minerals and density of the studied rock are voids in the rock. Amount of microcracks and their possible preferred orientation were not determined in this study.
6. Conclusions Amphibolites under study show a significant pseudoorthorhombic pattern of P-wave velocities at all pressure levels. The symmetry of those rocks reflects their microfabric defined by linear orientation of rock-forming minerals and by compositional layering. While direction of maximum P-wave veloc-
ity is oriented parallel to lineation, minimum P-wave velocity is oriented perpendicularly to foliation as confirmed by many previous studies. The more the mineral grains lie elongated in the foliation plane the more the Õ Pmin direction merges the normal to this plane. Mean P-wave velocity proved correlation with volume density of samples. Correlation of velocity and volume density with the modal representation of the major mineral-amphibole is not clearly documented. For correct estimation of velocity in rock from velocities of constituent minerals, also, less abundant minerals must be taken into account. An increase of mean P-wave velocity with decreasing average grain size of samples was observed. This observation could be related to the ‘scale effect’ Žan interplay of the wavelength of the used signal and the size of mineral grains. or to the real difference in elastic properties of rocks with almost identical composition but different grain size.
Acknowledgements The authors are very grateful to Tomas ´ˇ Lokajıcek ´ˇ Ž and Lukas Padjen Geophysical Institute of the ´ˇ Academy of Sciences of the Czech Republic. for their help during high pressure experiments. This work was supported by the Ministry of Education of Czech Republic Žproject G41309.. The authors are thankful to three anonymous reviewers for valuable comments.
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