E L A S T I C A N I S O T R O P Y O F I G N E O U S A N D M E T A M O R P H I C R O C K S

VLADISLAV BABUSKA

Geophysical institute, Czechosl. Aead. Sci., Prague*)

1. I N T R O D U C T I O N

Research into the elastic parameters of rocks is a necessary part of geopkiyscal investigations of the upper parts of the Earth. One of the important properties of rocks is their elastic anisotropy, which in some cases effects the interpretation of the results of seismic measurements, and which can also yield valuable information about the properties of rocks in the deeper layers of the Earth 's crust and of the upper mantle [1, 2]. The purpose of this paper is to get an idea of the range of values of the coefficient of elastic anisotropy with the main types of igneous and metamorphic rocks under laboratory conditions, and to study the relation between elastic ~tnisotropy, the structure of the rocks and the preferred orientation of minerals. In the present paper, an inextens- ire summary of some of the results of the investigation of elastic anisotropy are given, to which 150 samples of igneous and metamorphic rocks of the Bohemian Massif were subject. Detailed results, together with the petrographic characteristics of the samples, will be published in a separate paper.

Lately, a number of authors has investigated elastic anisotropy and its relation to the structure of rocks [3-- 8]. Apart from one exception, paper [4], all the authors agree on the fact that the velocity of elastic waves in the direction parallel to the schistosity, or the stratification, of the rocks is larger than in a perpendicular direction to this plane element. Birch [3] concludes that anisotropy, caused by stratified structures, changes significantly with increasing pressure. At high pressures, when the porosity of the rocks has been reduced to a minimum, elastic aniso- tropy is mainly caused by a certain regular orientat ion of crystals or inhomogeneities in the rocks. Balakrishna [5] considers the spatial orientation of a mineral to be the main cause of elastic anisotropy in rocks. Shimozuru [6] differentiates between two kinds of generation of elastic aniso- tropy with sedimentary rocks. The first is a result of plane, or periodically repeated plane, forma- tions (e.g. in schists), and the second depends on the ordering of grains in the individual minerals (sandstone).

Lately some authors have been investigating in greater detail the relation between elastic aniso- tropy and the preferred orientation of micas and amphiboles. Brace [9] investigated the depend- ence of one elastic parameter, the linear compressibility of rocks, on the preferred orientat ion of mica, calcite and quartz. The determined compressibility anisotropy he then compares with an anisotropy calculated for a certain direction, which leads to the conclusion that it is possible to calculate a certain physical property of a rock in a given direction providing the preferred orienta- tion of the minerals is known.

A certain disadvantage of all these papers is in that their authors only measure the elastic properties.of the rocks in a few directions, the choice of which is mostly random and frequently unsuitable [I0]. The usually adopted system of three mutually perpendicular directions of mea- surement is sufficient in case of sedimentary rocks and some metamorphic rocks, with which the choice of directions is facilitated by the stratification, or the schistosity, of the rocks. With most igneous rocks and with a number of metamorphic rocks, however, it is very difficult to determine three directions of measurement in such a way as to determine the maximum value of the coef- ficient of anisotropy. Apar t from this, it is impossible to determine a detailed spatial characteristic of elastic anisotropy with the individual types of rocks from three directions of measurement.

*) Address: BoS~ni II, Praha 4-Spo[ilov.

Studla geoph, et geod. 12 (19G8) 291

V. Babu.r

At the same time, however, the preferred orientation of minerals with which in some cases these results are compared, characterizes the rock, to a certain extent, in space as a whole. That is why a method was developed and equipment constructed [11, 12] to enable the determination of a spatial characteristic of / ' -wave velocity anisotropy, and the real value of the coefficient of ani-

stropy.

2. METHOD OF M E A S U R E M E N T

Elastic anisotropy was determined from the velocities of longitudinal elastic waves, measured at atmospheric pressure and normal temperature, in rock samples. In contrast to the hitherto currently used method of measurement in three mutually perpendicular directions, which in most eases are insufficient for a unique determination of the maximum and minimum velocities and the coefficient of elastic anisotropy of the rock, the individual samples were measured either in nine different directions (18-sided polyhedrons), or in 133 different directions (spherical samples). The suggested-method of investigating the elastic anisotropy on spherical samples enables a continuous sampling of the elastic anisotropy on spatially oriented spheres, using a semi- automatic record of the time of transit of an elastic impulse through the sample. A detailed description of the equipment is in [12].

The velocities of ultrasonic waves were introduced into Schmidt's plane projection, using velocity isolines diagrams of elastic anisotropy were constructed and these were investigated with a view to the preferred orientation of minerals (calcite, dolomite and quartz). The magnitude of elastic anisotropy was determined by the coefficient of anisotropy k, defined analogously with Birch [3] as k = (vj, max -- v e min)/ve, where v e is the average value of the maximum and mini- mum velocities of longitudinal waves.

3. VELOCITIES OF LONGITUDINAL WAVES AND ELASTIC A N I S O T R O P Y

3.1. I g n e o u s R o c k s

Among the measured samples a number was acid, intermediate, bas ic and ultra-

basic (Tab. 1) and some of the samples were volcanites. All the ul t rabasic and a num- ber o f basic igneous rocks were subject to secondary changes o f the minerals (espe- cially the serpentinization of olivine). That is why their velocities are considerably lower

than would seem judging by their chemical composit ion.

Besides the generally known dependence of the increase of P-wave velocities on the

increase of rock density (Fig. la), it was also observed that the lower the velocity o f the rock the higher the value o f the coefficient of anisotropy (Fig. l b ) . This ten-

dency is connected with the fact that a considerable part of the elastic anisotropy at atmospheric pressure is caused by the system of pores which always decrease the velocities, and in most cases, in which they follow certain prescribed discontinuities

in rocks, also increase the coefficient of elastic anisotropy.

The magnitude o f the coefficient o f anisotropy k with the individual types varies

with the mineral content and the genesis of the rock. Effusive and hypabyssa l rocks

in most cases show a lower anisotropy than their abyssal equivalents.

292 s ~ a geoph, et geod. 12 (1968)

Elastic Anisotropy of Igneous and Metamorphic Rocks

Table I. Igneous rocks.

Rock I N u m b e r density v~ ax I v~ i" v~ ean [ o f (mean) ~ vo/ma x

samples g l cm 3 kmts km/s kmfs . . . . k%,.~a.

granite 9 2-63 granodior i te 7 2-67 granodiori te porphyry 3 2"66 quar tz diorite 4 2" 82 pyroxene diorite 2 2-68 diorite 2 2.98 quar tz diori te porphyry

(cataclastic) 2 2-65 gabbro 9 2-83 nori te 6 2-96 pyroxeni te 2 3-04 troctoli te 11 2" 81 serpentinized duni te t 2"76 serpent inized peridoti te 4 2"79 olivine nephel ini te l 3-16 nephel ine basanite 1 3-01 olivine basal t 4 3-05 sodali te phonol i t e 2 2"51 tephri te 1 2-53

6"01 4"24 5"07 12"2 3"4 6-0t 4-23 5"15 14"9 3"2 6-12 5-81 6:00 1-6 1"5 6'65 5-96 6"26 6"9 1"9 5"53 4-93 5'27 7-2 3"5 6-70 5"98 6-40 6-5 2"4

5"76 5"13 5"47 I1"0 7-15 5.56 6"57 5"I 7"08 5"65 6"69 8"9 6-91 6.37 6'62 8-I 6'46 5'62 6"03 13.6 5"87 5"56 5"71 5.4 6-36 5'52 5-88 9"2 6-83 6"71 6-77 1'7 6"36 6'29 6"32 1-1 6-73 6-36 6"51 3-6 6"08 5"97 6"01 1'8 5"71 5'52 5-61 3'4

8'8 1"3 0"9 3"9 4"1 5-4 3'7 1-7 1'1 1"2 1"3 3"4

6"5 7"6 1"5 4"2 5'3 4"4

9"9 3'7 4"4 6'0 6"7 5"4 6"5 1"7 1'1 2"0 1"5 3"4

4

10

D 2

, 3$ 5~

5ZC

5,

fQ2e

5 ~ kx

a) b)

Fig. 1. a) Mean velocity Vv versus density @ for volcanites (9 samples); I - - olivine nephelinite, 2 - - nephel ine basanite , 3 - - olivine basalt, 4 - - sodalite phonol i te , 5 - - tephrite, b) Mean velo- city v v versus coefficient o f elastic anisot ropy k for 29 samples of acid and in termedia te igneous rocks; 1 - - granite, 2 - - granodiori te , 3 - - granodiori te porphyry , 4 - - quartz diorite, 5 - - diorite,

6 - - quar tz diorite porphyry.

Studia geoph, et geod. 12 (1963) 293

V. Babua~ka

3.2. M e t a m o r p h i c R o c k s

A number of samples of marbles, do lomi te marbles , granuli tes, quar tz i tes , gneisses,

amphibol i tes , hornb lende gneisses, serpentini tes and eclogites, be long ing to this

group was measured. The highest velocities were de te rmined with the eclogites

(maximum upto 8.14 km/sec), which also d isp lay the lowest an i so t ropy o f the whole

group (3.4,% on an average). Similar ly as in the case o f igneous rocks, a significant

dependence o f P-wave velocities on density (Fig. 2a), and a decrease of the coefficient

o f a n i s o t r o p y with increasing m e a n P-wave

r ~ So velocity (Fig. 2b) was also obse rved with

i the metamorphi tes .

= j

J ' I i , . s o I

~ i i i E z0c

l ao z ~ i 5~ ~ ! i %

I i 5 o 3 ~ 2

! ] = i 40[ 60 , [

6O i j

1

Fig. 24) Mean velocity v e versus density 0 for metamorphic rocks, b) Mean velocity v e versus coefficient of elastic anisotropy k for metamorphic rocks (37 samples); 1 -- marble and dolomite marble, 2 -- quartzite, 3 -- gneiss, 4 -- amphibolite and hornblende gneiss, 5 -- granulite,

6 - serpentinite, 7 and 8 -- two types of eclogite.

Table 2. Metamorphic rocks.

Rock

marble dolomite marble quartzite gneiss hornblende gneiss amphibolite amphibole schist granulite serpentinite eclogite

Number 1 density ] of (mean) !samples g/cm 3

37 ! 2-72 4 2-75 8 2"72 4 2"65 3 2-94 5 t 3-00 3 i 3-02 2 ] 2'65 2 t 2 - 3 2

10 3.40

v~ ax km/s km/s

U~ can

im/s k%m~x k%~"in

!

7"14 6"84 6"10 6"05 6"61 6"99 7"01 5"30 4"18 8"14

3"81 5"85 4"09 4"69 5"96 5"66 5"71 4"84 3"63 6"27

6"06 6"31 5"14 5"26 6"28 6-44 6"29 5"08 3"88 7"55

27'2 10"3 18"1 22"1

7"7 15"7 8"5 9"1

13"8 11"3

5"1 5"9 3"7 6"7 7"2 5-3 3"8 7"8

11"9 I"4

1116 8-3

11"2 11-I 7"5

10'5 6"0 8-4

12"8 3"4

~-94 Studia geoph, eg Eeod. IZ (1968)

Elastic Anisotropy o f Igneous and Metamorphic Rocks

Special attention should be devoted to marbles and dolomite marbles, which dis- play a substantial variability of values of the mean velocity and the coefficient of anisotropy (mean P-wave velocity ranges from 4.4l to 6.68 km/sec). The high elastic anisotropy (with three of the samples k > 20~o) is caused on the one hand by the high elastic anisotropy of calcite (28.1~), and on the other hand by the expressive effect of the intergranulars. Figure 3, similarly as with the foregoing types of rocks,

.,TO~

' i '�84 i �9 ' '

F ig . 3. M e a n v e l o c i t y v e v e r s u s coef f ic ien t o f e l a s t i c a n i s o t r o p y k fo r m a r b l e a n d d o l o m i t e m a r b l e

(41 s ample s ) .

shows the tendency of decreasing the coefficient of anisotropy with increasing mean P-wave velocity. From the position of the points of the graph corresponding to the individual samples, it is possible to judge the contribution of the intergranular effect on elastic anisotropy. With samples, the mean velocity of which is in the neigh- bourhood of 6-50 km/sec, the anisotropy is directly proportional to the degree of preferred orientation of calcite according to its internal structure. With samples, the mean velocity of which is lower than 6 km/sec, the inter~anular effect is ex- pressively applied, which decreases the velocity and simultaneously in most cases in- creases the coefficient of their elastic anisotropy.

4. E L A S T I C A N [ S O T R O P Y A N D R O C K S T R U C T U R E

In a number of marbles, two samples of quarzite and one sample of dolomite marble, granodiorite and granite the relation between elastic anisotropy and the preferred orientation of calcite, dolomite and quartz was investigated. Special atten- tion was devoted to marbles, which are very suitable for this purpose from the point of view of methodology. They are monomineral rocks the only component of which is practically calcite, expressively elastically anisotropic and well determined with respect to its elastic properties as well as its experimental deformation. The mutual comparison of elastic anisotropy diagrams with diagrams of the preferred orientation of calcite a regular dependence of the spatial distribution of P-wave velocities on the

Studla geoph, et geod. 1~ (t968) 295

V. B a b u J k a

preferred orientation of calcite grains was found. The maxima of the optical axes of calcite are either identical with the minimum of P-wave velocities, o r they form an angle of less than 30~ on the other hand, the velocity maxima always fall within the minimum accumulation of optical axis projections (Figs. 4 - 8).

The relationships between elastic anisotropy and the structure of the rock are also significant. The directions of maximum velocity are always approximately parallel with the plane of foliation, and at the same time the more expressive the foliation,

a) b) Fig. 4. Marble S 9/1 (locality Jesenn~ near Semily, k = 9-4~~,). a) Orientation diagram of e axes in 200 calcite grains. Contours at 6/o,~176 4~, 30,,~,, 2 ~ and 1 ~ per l~/o area. b) Diagram of elastic anisotropy, isolines of velocities v e are constructed between 6-30 km/sec and 6.80 km/sec in

steps of 100 m/sec.

0 0

Fig. 5. Marble S 5 / i (locality Str~i~.n~, k = 17'1~o). a) Orientation diagram of e axes in 300 calcite grains. Contours at 4~, 3~, 2 ~ and l~r. per 1~ area, S refers to the foliation plane, b) Diagram of elastic anisotropy, isolines of velocities v e are constructed between 5-60 km/sec and 6-50 km/sec

in steps of 100 m/sec.

296 Studia geoph, et geod. 12 (1968)

Elastic Anisotropy of [#nevus and ;~,[etarnorphic Rocks

the more remarkable and mostly also the more continuous the belt of the highest velocities they form (Figs. 5,6). The direction of the velocity minimum and the direc- tion of the velocity maximum, and therefore also the foliation, providing it is devel- oped, form an angle of between 80 and 90 ~ It" lineation is developed, its direction is parallel with the direction of the maximum velocity.

The main cause of elastic anisotropy in igneous and metamorphic rocks is, on the one hand, the preferred orientation of minerals according to the internal structure

0

a) b) Fig. 6. Marble S 6/1 (locality Str~.~n~, k = 5.8,%o). a) Orientation diagram of c axes in 200 calcite grains. Contours at 5/o, ~ 4/o,~176 2/o~ 1,/o~ per IT;; area. S refers to the foliation plane, b) Dia- gram of elastic anisotropy, isolines of velocities v e are constructed between 6.40 km/sec and

6.70 km/sec in steps of 50 m/sec.

0 0

o) b)

Fig. 7. Marble S 2a (locality ~ r n ~ Dil l , k = 6-2~). a) Orientation diagram of c axes in 200 calcite grains. Contours at 6~ 5~~ 4~, 3~o, 2~ and 1~~ per 1~~ area. S refers to the fol iat ion plane. b) Diagram of elastic anisotropy, isolines of velocity v e are constructed between 6-40 km/sec

and 6.75 km/sec in steps of 50 m/sec.

Studia geoph, et geod. 12 (1968) 297

V. Babu.~ka

and, on the other hand, the orientation and the construction of the intergranular system, which is in close connection with the preferred orientation of minerals accord- ing to their external shape. The contribution of both these components, even within one rock type, varies very considerably, the extremely high elastic anisotropy being mainly caused by the intergranular system, as has been observed with metamorphic rocks. An idea of the mutual relationship of these two main factors, effecting the

1 0

! a) b)

1 c)

Fig. 8. Marble M 38a (locality Nedv~dice).

a) Orientation diagram of c axes in 200 calcite grains. Contours at 6~, ..'i.,'i~ T,.o,a*t 3 ~ , 2,0/~ and 1 ~

per 1 ~ area. S refers to the foliation plane.

b) Diagram of elastic anisotropy, isolines of ve- locities vp are constructed between 3.90 km[sec and 4.90 km/sec in steps of 100 m/sec;k = 27-270.

c) Diagram of elastic anisot ropy of the same sample after the saturation of intergranulars by oil. Isolines of velocities v• are constructed bet- ween 6.20 km/sec and 6-70 km/sec in steps of

o/ 100 mlsec; k = 9io.

elastic anisotropy and of their contribution to the value of the coefficient of aniso- tropy can be formed from the measurements carried out on samples M 38a and M 38d, which have an exceptionally open system of intergranulars, apparently owing to weathering. When the system of pores, i.e. the minute intergranulary spaces, was filled with lubricating oil in a vacuum, the P-wave velocity increased in all directions and simultaneously a decrease in elastic anisotropy was observed (with sample M 38a from 2770 to 9,%). However, it is interesting that the position of the maximum and the

298 Studia geoph, e~; geod. lZ (1968)

Elastic Anisotropy of 19neous and ~VIetarnorphic Rocks

minimum of P-wave velocities with both the samples remained the same, and that the configuration of velocity isolines practically remained unchanged (Fig. 8). The character of the anisotropy did not change after introducing the lubricant into the pores, and it thus seems that both the causes of the elastic anisotropy, i.e. the pre- ferred orientation of the grains and the opening and the orientation of the inter- granular system, although of a different mechanism, are independent and that they effected the elastic anisotropy of these rocks in the same sense.

o) b)

Fig. 9. a) Granite M 21c (locality Mr',i~otin, k = 12"2~), diagram of elastic anisotropy; isolines of velocities v l, axe constructed between 4"75 kin/see and 5-25 kin/see in steps of 50 m/see. b) Norite R 10 (locality Star~ Ransko, k = 8-9,*/o), diagram of elastic anisotropy; isolines of velo-

cities vp are constructed between 5-70 kra/s and 6-15 kin/see in steps of 50 m/see.

Owing to considerable progress in the research into the deformation of marbles under laboratory conditions, it is also possible to make certain conclusions about the relation between deformation and the anisotropy of P-wave velocities. A number of authors mention the fact that recrystallized grains of calcite show tendencies to take up under the effect of oriented pressure a postion in which the crystallographic axis c is parallel to the axis of the main pressure [13 - 15], or to form with it an angle of between 20 to 30 ~ [16]. At the same time, DeWitte [17] points out that the minimum of calcu.lated P-wave velocities agrees with the direction of axis c, and the minimum of the measured velocities deviates from this axis by about 30 ~ . It is thus possible to assume that with samples of marble, tectonically deformed by one-sided pressure, the elastic anisotropy of which is mainly caused by the preferred orientation of calcite grains (owing to the high anisotropy of calcite these are predominant), the directions of the velocity minimum approximately indicates the direction of the main pressure to which the rock was subject.

Wkile with dolomite marble a similar relationship in the diagram of elastic aniso- tropy with respect to the preferred orientation of dolomite grains as with marbles

Studia geoph, et geod. I% (1968) 299

V. Babulka

was found, with quarzite, granite and granodiorite, with which the preferred orienta- tion of quartz was investigated, no unique correlations with the anisotropy diagram could be established.

Samples of volcanites, which were only measured in 9 directions (on samples having the form of a 18-sided polyhedron), display small values of the coefficient of anisotropy (k < 2~, only in one case k = 3-6%). Nevertheless volcanites display ordered diagrams of anisotropy with a well defined maximum and minimum of

a) b)

Fig. 10. a) Olivine.basalt S 15 (locality list[ n. L., k = 3-6~Q, diagram of elastic anisotropy: isolines of velocities v e are constructed between 6.51 km/s and 6-71 km/sec in steps of 20 m/sec. b) Sodalite phonolite S 16b (locality Bflina, k = 1 '3~), diagram of elastic anisotropy; isolines

of velocities v e are constructed between 5'98 km/sec and 6-04 km/sec in steps o f 20 m/sec.

velocities, which form an angle of between 60 and 90 ~ (Fig. 10). Owing to the fact that measurements were carried out only in nine directions, it is necessary to consider the elastic anisotropy diagram to be simplified if not idealized, as certain details will be missing which it would have been possible to include had the measurements been made in 133 directions on spherical samples. However, the measurements prove that volcanites have a certain expressive anisotropic structure, which is substantiated by a continuously changing series of velocity values on the elastic anisotropy diagram.

5. ELASTIC ANISOTROPY AS A P E T R O S T R U C T U R A L E L E M E N T

Elastic anisotropy is one of the features of the anisotropic state of a rock. During the creation and development of a rock, the crystals try to take up a position in the field of force which is most convenient [18], and which is dependent on the orienta- tion of the acting stresses with respect to the internal structure and external limits of the crystals. There exists, therefore, a relation between the elastic anisotropy of rocks and the external field of force, in which the rock was created and to which it was subject during the time of its development. It was found that in some cases it is

300 Studla geoph, eL geod. I;Z (1968)

Elastic Anisotropy of Igneous and Metamorphic Rocks

possible to estimate, e.g., the character of the deformation process, similarly as from the preferred orientation of minerals and the elastic anisotropy. As has been men- tioned in the previous chapter, the direction of minimum velocity in crystalline limestones corresponds, to the direction of the main pressure in the deformation ellipsoid.

Diagrams of elastic anisotropy have the same symmetry as the diagrams of preferred orientation of minerals for corresponding samples. The main difference is in that the anisotropy diagrams usually have only one maximum and one minimum velocity, and that they create a more compact impression as regards their structure in compar- ison to the diagrams of preferred orientation, which are usually more dissected. This is logical as the value of the P-wave velocity in a certain direction contains the effects of the orientation of all grains through which the elastic impulse has passed, and also the intergranular effects and the contingent inhomogeneities in the composition of the rock. But most of the samples measured, due to their size (diameter of spherical samples d = 80 ram), may be considered to be statistically homogeneous. On the other hand, the thin section of the rock, on which the preferred orientation was de- termined, represents only a very small volume of the sample. Besides, the series of 200 grains, which is usually used in determining the preferred orientation of calcite and quartz, is usually not representative of the sample investigated. Stauffer [19] mentions the necessity of using between 2000 and 4000 measurements in cases of some inexpressive anisotropic structures, which seems impracticable owing to the labo- riousness, of the method. The larger the series which this author used, the simpler the rock structure seemed, and the configuration of isolines, in his diagrams of preferred orientation approximated to our diagrams of elastic anisotropy. In this connection the use of elastic anisotropy for purposes of petrostructural analysis seems hopeful, because even samples with a very low coefficient of anisotropy (e.g. 1~o to 2% in the case of volcanites) display a considerably expressive type of structure with well defined directions of maximum and minimum velocities.

The advantage of elastic anisotropy diagrams is in that they provide data on the P-wave velocities in space as a whole, which are continuous and their degree of detail, dependent on the number of directions in which velocities have been measured, is optional. The diagrams of preferred orientation, on the other hand, only yield information about a certain section of space, where the ma:dma of the optical axes or other crystallographic elements have been found.

The problem of determining the ratio of the effects of the individual factors causing elastic anisotropy, especially the ratio of the effect of grain orientation and the inter- granular effect, remains to be solved. Although it is possible, to a certain extent, to estimate this ratio from the ratio of the coefficient of anisotropy and the mean-P-wave velocity (under the assumption that the mean velocities of the mineral components are known), measurements on spherical samples under high pressures, when the effect of the intergranularies is considerably supressed, are necessary for the detailed study of anisotropy.

Studia geoph, et geod, lZ (1968) 3 0 [

V. Babugka

6. CONCLUSION

The paper presented gives a review of the elastic an i so t ropy of the m o s t impor t an t

types of igneous and me tamorph ic rocks , invest igated on the basis of P - w a v e velocity

measurements carr ied out on po lyhedra l and spherical samples. A spa t i a l representa-

t ion o f elastic an iso t ropy of rock types was obta ined, and with some o f the samples

this was studied in re la t ion to the prefer red or ienta t ion o f minerals and to t h e s t ructure

o f the rocks. Wi th the samples of marbles , a regular dependence of the spa t i a l distr i-

but ion of P-wave velocities on the prefer red or ienta t ion o f calcite g ra ins was found.

The results obta ined, suggest tha t elastic an iso t ropy, apa r t f rom its s ignif icance as

a pe t rophys ica l characterist ic, may also in some cases yield supp l e me n ta ry da ta on

the pet ros t ructura l analysis.

The author wishes to thank Dr. J. Van~:k and Ing. Z. Pros for their help with the experimental work and for their valuable discussion of this paper.

Received 9. 10. 1967 Reviewer: J. Buben

References

[1] D. L. Ande r son : Recent Evidence Concerning the Structure and Composition of the Earth's Mantle. Physics and Chemistry of the Earth. Pergamon press 1965, 1.

[2] E. I. Bajuk, M. P. V o l a r o v i c h , K. Kl ima , Z. Pros, J. Van~k: Velocity o f Longitudinal Waves in Eclogite and Ultrabasic Rocks under Pressures to 4 Kilobars. Studia geoph, et geod., 11 (1957), 271.

[3] F. Birch: The Velocity of Compressional Waves in Rocks at I0 Kitobars. Part 1, Journ. Geophys. Res., 65 (1960), 1083; Part 2, 66 (1961), 2199.

[4] B. B. KpaBeu: Flpo mBH,aKocri npy',~:m, lx KoaHsam, Ta anizi'rpormm z~e~KHX ~e'raz, iopt~i'~rpax nopi~. ,~onoBhi AH YCCP, J~_ 4 (1961), 295.

[5] C. Banaxpam~a: Ynpyrae cBo~fca'Ba rleKoTop~ax ropmax nopo~ Hna0rrr. I/hB. AH CCCP, �9 H3~Ka ~:vta~r,J~_ 5 (1966), 3.

[6] D. Sh imozuru : Elasticity of Rocks and Some Related Geophysical Problems. Japan. Journ. Geophysics, 2 (1960), No 3, 2.

[71 O. I,I. Caaae~a: Hccae~omanHe c noMomlo y~,rpa3ByKa cKopocrefl pacnpoc'rpaaeni~a ynpy- rr~x BOnH n ynpyrHx napaMeTpoB a o6pa3L~ax FOpHblX llopo~ IlpM O~IOCTOpOr~HOM ~aBJIeH~H.

Tpylb~ H~3 AH CCCP, JN'_o 27 (1962), 77.

[8] N. I. Chr i s t ensen : Compressional Wave Velocities in Metamorphic Rocks at Pressures to 10 Kilobars. Journ. Geophys. Res., 70 (1965), 6147.

[9] %V. F. Brace: Relation of Elastic Properties of Rocks to Fabric. Journ. Geophys. Res., 70 (1965), 5657.

[10] V. Babugka: Velocity of Compressional Waves and Elastic Anisotropy of Some Igneous and Metamorphic Rocks. Travaux. Inst. G6ophys. Acad. Tchtcosl. Sci. No 223, Geofysi- k~ilni sbornik 1965, Academia, Praha 1966.

[ l l l Z. Pros, V. Babu~ka: A Method for Investigating the Elastic Anisotropy on Spherical Rock Samples. Ztschr. f. Geophys. 33 (1967), 289.

[12] Z. Pros, V. Babugka: An Apparatus for Investigating the Elastic Anisotropy on Spherical Rock Samples. Studia geoph, et geod., 12 (1968), 192.

302 Studla geoph, et geod. I~ (1968)

Elastic Anisotropy of l#neous and Metamorphic Rocks

[13] D. T. G r i g g s , F. J. T u r n e r , I. B o r g , J. S o s o k a : Deformat ion of Yule Marble. Part V -- Effects at 300~ Bul l Geol. Soc. Am., 64 (1953), 1327.

[14] M. F r i e d m an: Petrofabr ic Techniques for the Dete rmina t ion of Principal Stress Direct ions in Rocks . Proc. o f Intern. Conf. in Santa Monica, Califf. Am. elsevier publ. comp. , New York 1964.

[15] W. B. K a m b: Theory of Preferred Crystal Orientat ion Deve loped by Crystall ization U n d e r Stress. J. Geol. , 67 (1959), 153.

[16] L. W. W e i s s : A study of Tectonic Style. Univ. Calif. (Berkeley). Publ. Geol . Sci., 30 (I 954), 1.

[17] A. J. de W i t t e : On Elastic Wave Propaga t ion in Crystals with Appl icat ions to Calcite and Quartz. Univ. of Illinois, Technical Repor t (1962).

[18] G . . l . F . M a c D o n a l d : Orientat ion o f Aniso t ropic Minerals in a Stress Field (Discussion). " R o c k de fo rmat ion" , Geol. Soc. Am. Mere., 79 (1960), 9.

[19] M. R. S t a u f f e r : An Empirical Statistical Study of Three-Dimens ional Fabr ic Diagrams as Used in Structural Analysis. Can. J. Earth Sci., 3 (1966), 473.

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