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ABSTRACT

 The elastic dilatational wave velocity in crystalline schists from Sanbagawa metamorphic terrain,Shikoku,southwest Japan,is measured under hydrostatic pressure up to 5kilobars.Although the porosity is usually less than 1 per cent,the velocity at low pressure is very low,and the large hysteresis of velocity with a change of pressure is present.The empirical formula representing the effect of pressure P on the velocity V is derived;V V_o;CP AP^(−n),where V_o:CP is the velocity of pore−free state at high pressure,C is a constant Showing the pressure derivative of velocity,A and n are numerical parameter showing the effect of porosity on the velocity.The velocity anisotropy amounts to about 40 per cent at ordinary condition,and decreases with increasing pressure.However,the anisotropy remains at 10 to 12 per cent even in pore−free state at high pressure.The tectonic b−axis and c−axis show respectively the maximum and the minimum velocities.The porosity effect is largest along the tectonic c−axis,but it decreases more rapidly with pressure,when compared with the effect along the tectonic b−axis.Owing to the porosity effect,the velocity even at 10kilobars is still lower than that of pore−free state by 0.2km/sec.
 Sanbagawa metamorphic terrain is composed of three distinctly different types of rocks;silicic schist with density of 2.7 to 2.9g/cm^3 and velocity of 6.0 to 6.5km/sec,basic schist with density of 2.9 to 3.2g/cm^3 and velocity of 6.5 to 7.5km/sec,and basic and ultrabasic rocks with high density.Based on these data,the seismological structure in metamorphic terrain is tentatively discussed.

INTRODUCTION

 The analyses of the travel time curves of seismic waves have been providing the information about the internal structures of the earth.Since 1940,systematic studies of the crustal structures have been carried out by means of explosion seismology,and the local variations of the structures have been explored in Japan.In almost all the cases,the crustal structures thus obtained are two−dimensionanal profiles of the crustal and subcrustal regions,and they consist of several layers characterized by different velocities of the dilatational wave.By comparing these results with the laboratory determination of the elastic constants of several kinds of rocks,the rocks composing the particular layers in the profiles of the earth’s crust have been tentatively identified.For example,the layers having the dilatational wave velocity of about 6km/sec and 7km/sec are called granitic and basaltic(or gabbroic)layers respectively.However,we do not know what these granitic and basaltic layers are.From the considerations on the genetical processes of the earth’s crust,we do not always agree with the view that the upper and the lower parts of the crust are respectively composed of granite and basalt(or gabbro)of igneous origin.If the crust is generated by the quiet solidification of magma as in the case of Skaergaard,the layers of granitic and gabbroic rocks may overlie the upper mantle of ultrabasic rocks.However,this may not always be the case.
 Age determination of rocks has shown that the continental crust was growing by some processes around the older mass of the crust.Gravels,sand,clay and the inorganic solution derived from the pre−existing crustal substances and also the products of volcanic activity are transported from the continental region to the oceanic area.Most of them are laid down at the continental margin.Especially near the island arc regions,the sediments as well as the oceanic crust are supposed to be pushed into or pulled down to the earth’s interior.They will be inevitably metamorphosed in varying degree in the earth’s depth.After the uplift of these regions and the removal of the overlying rocks by some processes,the metamorphic terrain might have emerged on the crustal surface.Some of rocks from the regional metamorphic terrains contain high pressure minerals;the existence of which suggests that the pressure environments of the rocks were 10kb or more.When the hydrostatic equilibrium is approximately attained in the earth’s crust,the pressure of 10kb corresponds to a depth of 30 to 40km in the earth’s interior.This depth is identified with that of the Moho−discontinuity in the continental region.Therefore,we have no evidence whatsoever that the deeper parts of the crust,even immediately above or below the Moho−discontinuity,are not composed of the sedimentary rocks and their derivatives,metamorphic rocks.Rather it seems to be quite probable that the deeper parts of the crust are mainly composed of metamorphic rocks,especially in the young island arc areas.In the island arcs such as Japanese islands,it has been difficult to obtain unique crustal structures by seismic refraction exploration,presumably because of the following three reasons;(1)horizontal heterogeneity,(2)vertical heterogeneity and(3)seismic anisotropy of the earth’s crust.
 The resolving power along the horizontal extents by the explosion seismic exploration is limited.In order to identify Pn phase clearly on the seismograms for example,the spread of the span has to be extended to 150km or more.Even excepting the sedimentary veneers which locally cover the surface of the earth’s crust,the horizontal continuity of the uniform rock masses over 100km is not always expected in island arc region.Especially in Japan,the spatial scale of geologic structural unit seems to be relatively small.Nevertheless,the crustal profiles obtained by the explosion seismic exploration are the simple three− or four−layered structure extending over several hundreds kilometers.Such a simple model may be enough to depict the gross picture of the crustal structure;however,we can not get any good information concerning the materials in the depth.
 Even in the case of horizontally uniform layered structure,the velocity contrasts between the layers and the thickness distribution of the layers have some effects on the observed arrival time of the short period seismic waves.In order to clarify this problem,it will be very useful to know the elastic properties of all possible rocks in the crust.At the earth’s surface,we may expect to find out almost all kinds of rocks composing the deeper parts of the earth’s crust,since occasionally there occur such rocks that are supposed to be derived even from the earth’s mantle.
 If the thickness of each layer composing the crust is small compared with the wave length of the seismic waves,the crust will behave like an anisotropic body even though each of the layers is isotropic.It is of much interest to know the elastic property of metamorphic rocks which have an anisotropy recognized even by visual inspections.Birch [2] has shown that the meta−morphic rocks,especially schists and gneisses,show the elastic anisotropy.Christensen [6] made the measurements of acoustic wave velocities in a number of metamorphic rocks of various origins,and discussed the cause of anisotropy.The significant elastic anisotropy observed under ordinary conditions rapidly decreases with increasing pressure.However,it does not always reduce to zero even at high pressure.Schists and gneisses will actually show significant anisotropy even at great depth in the earth’s interior,while some other kinds of rocks such as granite and basalt show a relatively isotropic nature.Therefore,the existence of elastic anisotropy might be a prominent factor for determining the rock species or the fine layered structures in the earth’s interior by seismological methods.In addition to this,the pattern of anisotropy in a horizontal plane may be an indication of the geotectonic trend of the structures.
 According to the geologic study of the basement structures in Japan,they are characterised by the zonal arrangement of several regional metamorphic belts as shown in Fig.1.Among these metamorphic belts,Hida,Ryoke−Abukuma and Hidaka metamorphic terrains are accompanied by a considerable amount of granitic intrusions and they are classified as low pressure−high temperature type metamorphism.The remaining three metamorphic terrains,Sangun,Sanbagawa and Kamuikotan are accompanied by the intrusions of ultrabasic rock masses and occur together with rocks including high pressure minerals such as jadeite.The latter three are classified as high pressure−low temperature type metamorphism(Miyashiro [17]).The present authors are particularly interested in these regional metamorphic terrains of high pressure−low temperature type,since the rocks or rock masses belonging to them are considered as those having been seated in deeper parts of the earth’s crust.
 In southwest Japan,the major tectonic trend of the geologic structures generally lies in northeast to southwest direction.There occur Mesozoic formations(Shimanto group),weakly metamorphosed Paleozoic formations(Chichibu group),Sanbagawa,Ryoke and Sangun metamorphic terrains successively from southeast to northwest.Sangun metamorphic terrain is annealed secondarily by granitic intrusion of a later geologic period,and its exposed area is rather restricted,while Sanbagawa metamorphic terrain,mostly situated in Shikoku island,is a typical regional metamorphic belt having the widest surface area of all metamorphic terrains in Japan.
 In Shikoku,the Sanbagawa metamorphic terrain assumes a belt with a width of about 25km at the surface.It shows the progressive metamorphism of regional type;its northern part is highly metamorphosed and composed mainly of coarser grained crystalline schists,some with porphyroblasts of plagioclase rich in sodium.The ultrabasic intrusion composed of Alpine type dunite occurs in the Higashiakaishi−yama district,which is located in the most highly metamorphosed region of this terrain.The analysis of the mineral assemblage suggests that the pressure environment of the metamor−phism amounts to 10kilobars,which corresponds to the load pressure at the normal Moho−discontinuity(Miyashiro,[17]).
 In this respect the authors have carried out the systematic determination of elastic dilatational wave velocities in crystalline schists from the Sanbagawa metamorphic terrain.
 Previous works on the elasticity of rocks in this area are laboratory measurements by Misawa [15] and the short distance seismic prospecting in Sazare mine by Kitsunezaki [10].Misawa’s measurements were,however,made under the atmospheric condition and the results do not seem useful for the interpretation of the deep structure of the earth’s crust.Kitsunezaki tried to detect anisotropy in situ and obtained 5.0 and 6.4km/sec respectively along the tectonic c− and b−axes of silicic schist.For basic schist,he obtained 6.8 and 7.2km/sec respectively along tectonic c− and b−axes.

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FIG.1.Distribution of regional type metamorphic terrains in Japan(after Miyashiro [17]).

LOCALITY OF THE ROCK SAMPLES

 Sampling of the rock specimens was made mostly along the lines(profiles)traversing the isograds of metamorphism or stratigraphic sequences as shown in Fig.2.The deep geologic structures in this region are not yet known.The surface geology shows several anticlines and synclines,the trends of which being almost parallel to the trend of the Sanbagawa metamorphic belt.Therefore,the metamorphic grading is almost parallel to the stratigraphic sequences,and then the differences of rock samples collected from the different points along a profile are due both to the difference in the metamorphic grade and also to the difference in the composition of the original sedimentary rocks.Each of the formations which occur in the region belongs to the Yoshinogawa group.As for the details of stratigraphy,geologic structures and metamorphic zoning,there have been published a number of papers(e.g.,Kojima [11,12],Miyashiro and Banno [16],Nakayama [18],Hide [7],Iwasaki [9],Banno [1]).The stratigraphic sequences and the sampling localities are listed in Table1.
 The horizontal spacing of the sampling points was scheduled to be 0.1 to 0.3km;however,it was modified owing to conditions of outcrops.In many cases,the rocks at the outcrops were weathered and mechanically brittle.The total number of the collected rock samples amounted to 120;however,the measurements were made for 59 samples which looked to be homogeneous,fresh and also typical of the area.Some of rocks were so weathered that we could not prepare cylindrical specimens.Others had complicated structure,including large grains,secondary veins,foldings of various scale,or layering with different kinds of rocks.
 Along Hadeba−Komata profile,the condition of outcrops was most satisfactory and closedly spaced sampling was possible.The profile traverses the boundary of metamorphic zones II and III(the metamorphic zoning in this paper is after Miyashiro and Banno [16])and passes through a narrow area belonging to zone IV.
 The southern part of Hodono−Nahashichiban profile was mainly composed of quartz schists.The southern and northern parts belong to regions of metamorphic zones II and III respectively.
 Alpine type dunite and eclogite occur around the peak of Mt.Higashi−akaishi−yama;however,the fresh outcrop is quite limited in this area.Most of crystalline schists are coarse grained and not suitable for the ultrasonic measurement.Only two specimens(Nos.18 and 19)were measured although they contain the porphyroblasts of garnet with a diameter of up to 5mm.
 To get a profile in a weakly metamorphosed area,we tried to obtain samples from Kokitagawa−Ohashi profile.In this area most of rocks are black schists(quartz schist including graphite),and the rocks were mechanically weak due to small cracks.The collected rock samples were basic schists alone,which occurred as the thin layers in black schist.Not only along this profiles but also in other areas,black schists are not suitable for the acoustic measurement,because they have so many cracks and irregular microfolds of various scale,and also strongly weathered.Therefore,the relatively compact black schist collected by Mr.Masahiro Shibata of Dengenkaihatsu Company from a darn construction site somewhere in Sanbagawa terrain in Shikoku(sample No.10)was also measured.
 At the southern part of Shirataki−Okitagawa profile,basic schists were rather fresh.At the northern part,the sampling was made in Shirataki mining draft,which is working for chalcopyrite ore.
 On Minawa−Oboke profile,most rocks belonging to Oboke and Koboke formations were irregularly deformed sandstone and conglomerate.In some cases the spatial scale of the mesoscopic structures(e.g.,alternation of micarich layers,quartz−rich layers and/or basic schists)was almost the same as the size of the specimen for experimental use.The metamorphic grade of this area belongs to zone I.
 In Bizan−Tsudayama area,rocks were mainly basic schists and the mesoscopic structures were rather simple and small in scale.This profile traverses the metamorphic zones II and IV.The rocks in this region are supposed to be the eastern extension of the Minawa formation in Besshi district.It is not,however,yet known which horizon of Minawa formation corresponds to those occurring in Bizan district.The Sanbagawa metamorphic belt is characterized as a jadeite−glaucophane metamorphism and the Bizan area is said to be typical of it.However,good samples of glaucophane schists with silicic composition could not be obtained.Therefore,glaucophane quartz schists collected by Mr.Katsuro Ogawa of Geolocical Survey of Japan,from the Kwanto district(sample No.1007),were included for the present measurements.
 Three Canadian rock samples collected by Prof.Yasuo Shimazu of Nagoya University and an albitite from Sugajima,Mie prefecture were also measured for comparison.

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FIG.2.Map showing the sampling locality(geologic structure after Hide [7]).
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TABLE1.STRATIGRAPHIC SEQUENCES OF SANBAGAWA METAMORPHIC TERRAIN IN SHIKOKU AND THE SAMPLING PROFILES

PREPARATION OF SPECIMENS

 Three cylindrical specimens were cored from a block of rock sample by a diamond−impregnated boring machine.The orientations of the three specimens are mutually at right angles so as to coincide respectively with three tectonic axes;a,b and c.The tectonic axes are determined by visual inspection;b−axis is along the major lineation in the plane of major lamination,c−axis is the direction perpendicular to the major lamination,and the direction perpendicular to b− and c− axes is a−axis.In most cases,b−axis is most easily determined.However,in some cases,the determination of a− and c−axes involves some ambiguities,the nature of which is due to the lack of clear lamination,the existence of microfolds and/or the complicated shear planes inclined to the bedding plane.
 The size of the specimen is 15mm in diameter and 45 to 50mm in length.Both ends of the specimen are polished to be parallel within 0.005mm.In order to prevent the intrusion of the confining fluid into the texture of rock specimen under high pressure,a thin film of epoxy resin(Araldite)was brought on the cylindrical surface of the specimens.On both ends of the specimen,a 0.02mm aluminium foil or 0.03mm brass foil was fixed by means of the same resin.The metal foil is used as an electric lead for the ultrasonic transducers in contact.
 During the machining of c−specimens(specimens cut paralell to the direction of tectonic c−axis),partings sometimes occurred along the tectonic ab−plane.In such cases,two or three pieces of short cylindrical specimens were glued together by resin.

DETERMINATION OF DENSITY AND POROSITY

Array In most cases,the bulk volume V of the specimens was given by the cross sectional area multiplied by a length of the specimens.The cross section was ordinarily elliptic due to the resistance anisotropy against abrasion.For quartz schists the difference between the largest and the shortest diameter is 0.085mm on the average.This difference sometimes amounted to 0.3mm.
 The pore volume v of the specimen is given by
     ν=(M_2−M_1)/(density of water),
where M_1 and M_2 are respectively the weight of the dried and water saturated specimens.In order to obtain the state of water saturation the specimen is immersed in water and boilded at the ordinary temperature for 0.5 to 1hour in vacuum.This treatment was repeated two or three times with the interval of 0.5hour.This procedure will give rise to the replacement of gas in open void space included in the specimen by water.The dried state is obtained by maintaining the specimens at 110℃ for 20hours.
 In the cases where the cylindrical surface of the specimen was irregular(due to the parting or breaking off of the edge,etc.),the hydrostatic weighing in water was carried out for water saturated specimen.In these cases the intrinsic volume of the specimen is directly obtained.
 Then the porosity φ of open pores in the specimen,bulk density ρb and true density ρt were calculated as follows;
     φ= ν/ V,ρb=M_1/V,ρt =M_1/(V−ν).
The true density given above is not actually the intrinsic density of the specimens,since the volume ν in the above is not related to the volume of the closed pores.

MEASUREMENT OF DILATATIONAL WAVE VELOCITY

 The high pressure system is a very simple one.A steel piston installed with the insulated electric leads is pressed into a steel cylinder by means of a hydraulic ram.The confining fluid is white spindle oil.Pressure in the vessel is given by a force−per−cross section calculation within an uncertainty of 5 per cent,which arises from the frictional force between the piston and the cylinder.The calibration of pressure was made by a manganin resistance gage.
 The travel time of the ultrasonic pulse propagated through the specimen was measured by a phase equalization method with an electric delay line,which was calibrated by a quartz clock.The errors involved in the absolute determination of the travel time is 0.04 microsec;however,this uncertainty is reduced to 0.02 microsec or less for the relative measurements in successive readings during one run.
 The measured travel time requires some corrections.In order to reduce the excess travel time originating from the acoustic wave transmission in epoxy resin and metal foils at the both ends of the specimen,we measured the thickness of the resin,and the dilatational wave velocity in the resin up to 6 kilobars(see Table2).These data are used to reduce the excess travel time of the thin layers of resin.The elastic wave velocity in the resin is very low and the correction due to this effect amounts sometimes to 5 per cent,though it is less than 2 per cent in most cases.
 The correction of the contraction of the specimen length due to pressure was not made.The contraction of the sample by the closure of pores is in the order to ofφ/3;however,it depends on the geometry of pore space.The total porosity is in the order of 0.6 per cent and thus the correction needed for the volocity due to this effect will not exceed 0.6 per cent even along the most compressible c−direction.The correction of the elastic dilatation of the solid part of rocks is only in the order of 0.05 per cent.

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TABLE2.TRAVEL TIME OF ULTRASONIC PULSE IN AN EPOXY RESIN OF 1mm LONG AT ORDINARY CONDITION

RESULT AND DISCUSSION

Array The density,porosity and the dilatational wave velocity are shown in Table3.The velocities listed are the arithmetic average of the data of raising and lowering pressure runs.Fig.3 shows an example of velocity as a function of pressure.
 Hysteresis.—The hysteresis of velocity with a change in pressure is observed for almost all the specimens.The difference of velocities between the raising and the lowering runs shows a maximum in the pressure range between 0.25 and 1kilobars.In some cases it amounts to over 0.5km/sec.Hysteresis is genarally large for such specimen that shows low velocity at lower pressure.Christensen [6] stated that the hysteresis is attributed primarily to the insufficient time for the adjustment of porosity to the changes of external pressure.This effect may be present to some extent;however,there should be another factor because the hysteresis curve was almost reversible and the drifting of velocity at constant pressure was very small when compared with the observed amount of hysteresis.The velocities before and after the high pressure run are almost the same under ordinary condition.
 Frequency density of velocity and density.—Fig.4 shows the frequency density distributions of average velocity at 5 kilobars and average true density for three mutually perpendicular specimens.It is apparent that the rocks are clearly classified into three types.The rocks with density 2.7 to 2.8g/cm^3 are pelitic and psammitic schists which are virtually silicic or quartz schist.The elastic dilatational wave velocity ranges from 6.0 to 6.5km/sec.The rock type having a density of 2.9 to 3.2g/cm^3 and a velocity of 6.5 to 7.5km/sec are basic schist.The last rock type is characterized by a very high density.The occurrence of such high density rocks is quite limited in Sanbagawa metamorphic terrain except the ultrabasic mass at Mt.Higashiakaishi−yama.With few exceptions there is no intermediate type among the three mentioned above.The actual composition of the rock masses in this region is intermediate between silicic schist and basic schist,showing alternation of layers of both rock types.The scale of the layering ranges from the order of centimeter to that of kilometer.The relative number of silicic schists to the basic schists shown in Fig.5 is neither representative of the Sanbagawa metamorphic terrain nor of the region under study.The stratigraphic sequence and the data concerning the relative abundance of basic schist and silicic schist are still lacking in the terrain,partly because outcrops are limited and partly because in some cases their occurrence is lenticular in shape to some extent.
 In order to know how the elastic properties depend on their composition or density,61 specimens are classified into five groups;15 pelitic and psammitic schists for P−group,10 basic schists with density(g/cm^3)of 2.9 to 3.0 for B−1 group,21 basic schists with density of 3.00 to 3.06 for B−2 group,13 basic schists with density of 3.06 to for B−3 group with one exception(No.1404)and 2 high density rocks for miscellaneous group.The comparison of the various properties for different group is made in Table4.
 Velocity as a function of pressure.—The general tendency of the velocity change due to pressure is almost the same as that reported by Birch and Christensen.In order to extrapolate the observed data to those of the high pressure conditions and also to discuss the factors influencing the velocity,we tried to obtain an empirical formula.When the logarithm of the pressure coefficient of velocity(△V/△P km/sec・kb)is plotted against the logarithm of pressure(kb)as shown in Fig.5,this relation is found to be nearly linear;i.e.,
     log(dV/c/P)= log B− mlog P,   (1)
where B and m are constant.When(1)is fitted to each of pressure runs,we have considerable fluctuations,and B ranges from 0.16 to 0.40km/sec per kilobar and m ranges from 0.4 to 1.9.When m > 1,the following relation can be derived from(1)
     V(P)=V_0−AP^n,   (2)
where A=B/(m−1),n=m−1 and V_0 is a velocity at P=∞ and is given by V(P=1kb)+A.According to this empirical formula,V=−∞ for P=0,and thus the application of(2)to the lower pressure range is inadequate.The pressure dependency of velocity represented by(2)is schematically shown in Fig.6.It is apparent that the factor A or B and the exponent n or m respectively represent the magnitude of the porosity effect and the rate of decrease of the porosity effect with pressure.V_0 represents the intrinsic velocity of the rocks,which is supposed to be completely free from porosity.Using(1)and(2)with experimentally determined B and m,an extrapolation of velocity to that of pore−free state is quite possible.The extrapolation by(2)to high pressure is shown in Table 5.On the average,the velocity at 10 kilobars will be 0.08km/sec larger than that at 5 kilobars.In addition,it may be inferred that in the case of crystalline schists the measured velocity even at 10 kilobars may be smaller by 0.2km/sec than the velocity of porosity free state.
 According to(2),dV/dP decreases with increasing pressure and vanishes at high pressure.On the other hand,the precise measurements of the elastic properties of single crystals and also the theory of finite strain elasticity suggest that dV/dP has a finite value.According to the second order finite strain theory of Eulerian formulation we have
     dV/dP= 3 V/2 K,
where K and V are bulk modulus,and the dilatational weve velocity.Assuming isotropy and Poisson’s relation for solid body,the numerical values of dV/dP has to be 0.015 to 0.010km/sec per kilobar for rocks having the intrinsic velocity of 5.5 to 7.5km/sec and density of 2.7 to 3.2g/cm^3.The present measurements gave 0.02 to 0.04km/sec per kilobar at 5 kilobars and the extrapolation by(2)yields a value below 0.01km/sec per kilobar at above 10 kilobars.
 The actual pressure variation of velocity at high pressure is therefore represented by
     V(P)= V_0 +CP−AP^(−n)   (3)
where C=3 V_0/2 K=2.7/ρV_0 is a constant and ρ is density.The second term in(3)increases with pressure,while the third term decreases.We consider a critical pressure where the second and the third terms in(3)have the Same value.A rough estimation gives 9 to 11 kilobars for this critical pressure.Above this,the elastic properties are mainly determined by the intrinsic properties.In order to obtain dV/dP of the rocks completely free from porosity effect,pressure of 20 to 25 kilobars is required.Below this pressure,the porosity effect can not be ignored,and the variation of velocity is mainly due to porosity effect.
 Velocity−density relation.—The mean velocity(mean of three specimens)at 5 kilobars is plotted for the measured true density in Fig.7.Each plot of velocities is not corrected for the shortening of the specimens due to pressure.The average velocities at 1 and 5 kilobars and their extrapolated values to 10 kilobars and to a pore−free state are also shown for each of the four groups.
The contraction of closed pores will give rise to an effective increase of density by several tenths of one per cent.The effect of the shortening of specimens by contraction of pore space on the velocity will be in the order of one third of the total porosity.These two corrections were also made in Fig.7,even though the difference was negligible.
 As a reference,the velocity−density relations for mean atomic weight m of 21 and 22 as presented by Birch [2] were shown in Fig.7.Mean atomic weight of silicic schist is 20.7 from the average of 11 chemical analysis of pelitic and psammitic schists from Besshi and its vicinity(S.Banno [1],p.219,Table2).For basic schist,we have m=21.8 from the average of 11 analysis of schists from Besshi district(S.Banno [1],p.218,Table 1)and m=21.4 from the average of 9 analysis of schists from Bizan and its vicinity(M.Iwasaki [8],p.35,Table 1,and M.Iwasaki [9],p.29,Table 3).Therefore,mean atomic weight of rocks in Sanbagawa terrain is estimated to be 21.6 for basic schists and 20.7 for silicic schists.Birch did not make an extrapolation of velocity measured at 10 kilobars to the pore−free state.In the case of basic schists,the present pore−free velocity is slightly higher,while those at 5 to 10 kilobars agree quite well with the Birch’s formula.In the case of quartz schist,however,Birch’s formula gives the higher velocity than the present result by 0.6km/sec.
 The gradient of the velocity−density relation for the present crystalline schists is almost the same as that of Birch’s formula.As the average property of Sanbagawa crystalline schists,the relationship between the velocity and the density is presented as follows:
     V=2.8ρ−(1.2±0.1)for a pore−free state,
     V=2.8ρ−(1.4±0.1)for the pressure corresponding to the
        lower part of the earth’s crust,
and
     V=2.8ρ−(1.6±0.2)for the pressure corresponding to the
           upper part of the earth’s crust.
 Velocity anistropy.—lastic anisotropy in crystalline schists is extremely large as shown in Table3 especially under ordinary conditions,the maximum velocity difference amouting to 3km/sec or more in some cases.This significant anisotropy decreases with the rise of pressure as shown in Fig.8;however,it still remains at 0.7 to 1.0km/sec(10 to 12 per cent)even under the pore−free condition at high pressures.Birch [3],Brace [4] and Christensen [6] had already discussed some factors influencing the anisotropy of rocks in the porefree state,based on their experimental data and also on the petrofabric investigation of the mineral lattice orientation.The velocity anisotropy at lower pressures is mainly due to the anisotropic distribution of flattened or elongated pore spaces.
 When the wave length of the acoustic wave is shorter than the scales of lineation,lamination and size of elnogated or flattened grains in the specimen,it is expected that the velocity along the tectonic b−axis is highest and that along c−axis is lowest.The observed pattern of the anisotropy is the same as in the above interpretation.However,the effect may not be the main factor causing the observed anisotropy from the following reasons.The scale of the mesoscopic structures such as banding in the present specimens sometimes amounts to 3mm on visual inspection.However,it rarely exceeds 2mm,because we did not measure the samples which have very large structures.The grain size of most constituent minerals is of microscopic scale except for the schists from highly metamorphosed spotted schist zone.The diameter of the largest porphyroblast of albite is almost 3mm;however,the grain shape is equidimensional,and the effect of the grain size seems to be generally unimportant for the anisotropy.The problem arising from the relative scale of wave length and of the structures is present apparently;however,it will be less important.
 Even though the structural scale of the specimens is considered to be infinitesimally small,the intrinsic anisotropy due to the geometry of the structures is still effective.Kumazawa [14] suggested that the factors influencing the elastic anisotropy of the polycrystalline rocks are due to two kinds of structures;the interface structure and the petrofabric structure,and he presented a method of numerical estimation of the effects of both on the elastic constants of any solid aggregate.
 The interface structure is related to the anisotropic orientation distribution of the plane interfaces between any two mineral grains in contact in the rocks.The existence of the interfaces between the grains and resulting mechanical contacts bring about the elastic deformation in both minerals under the constraint of the boundary conditions.The most anisotropic aggregate is of the so−called layered structure,in which the interface orientation lies only along one direction.In this case the orientations of the maximum and the minimum dilatational wave velocity are respectively those propagating parallel and perpendicular to the plane of layering.In the case of schists,the structures would lie between the layered and the random aggregates.The orientation perpendicular to the most predominant interfaces between grains corresponds to the tectonic c−axis and the orientation having the least orientation density of the normal of the grain interface corresponds to the tectonic b−axis.Therefore the nature of anisotropy to be expected from the interfaces structures is the same as that observed for schists.The upper limit of the elastic anisotropy of an aggregate due to interface structures corresponds to the difference between Voigt’s and Reuss’ type averages of the elastic constants of the constituent minerals(Kumazawa [14]).
 According to the numerical estimations [14],the effect of the interface structures on the velocity anisotropy of monomineralic rocks,composed of anisotropic mineral(except mica),amounts to 3 per cent(0.2km/sec)at most.The anisotropy generated by layering of isotropic Poisson’s solid is read by a chart shown in Fig.9.The aggregate is supposed to be a 1:1 aggregate of two kinds of media having the elastic constants,C_1 and C_2 respectively,or such that the frequency density of the elastic constants is uniform from C_0(1−√3a)to C_0(1+√3a),where C_0=(C_1+ C_2)/2,a=(C_1−C_2)/2 and C=ρV^2(The statement on the range of uniform distribution in Kumazawa [14] is incorrect).The velocities of the constituent media are assumed to satisfy Birch’s formula:V=3.16ρ−2.01,for minerals with the mean atomic weight of 21.As seen from Fig.9,a 1:1 layered aggregate composed of minerals having the velocity of 6.0 and 8.5km/sec for example,shows the average velocity of 7.1km/sec and the maximum anisotropy of 0.8km/sec.Assuming the most probable interface structutes for schists,the magnitude of anisotropy of the elastic constants is estimated to be about 1/3 of the perfectly layered structure,and thus the velocity anisotropy(velocity difference in different orientations)is supposed to be in the order of 1/6 of the differerence of velocities given by Voigt’s and Reuss’ averages.Therefore the velocity anisotropy up to 0.15km/sec in the observed amount of anisotroy,can be explained by the anisotropic interface structures.
 The remaining fraction,0.5 to 0.8km/sec,of the observed anisotropy has to be attributed to the petrofabric structures of the constituent anisotropic minerals.Using the thermodynamic theory of the effect of nonhydrostatic stress on mineral lattice orientation(Kumazawa,[13]),we can derive a conclusion that the processes of recrystallization will give rise to such lattice orientation that the elastically stiffest orientation,i.e.,the direction of the least linear compressibility and the most compliant orientation,i.e.,direction of the largest linear compressibility,respectively,prefer to be oriented parallel to the principal axis of tension and to that of compression.In the case of orthogonal crystals,the stiffest and the most compliant orientations defined above correspond to those having the largest and the smallest dilatational wave velocities respectively.In the case of metamorphic tectonites,the principal axes of tension and compression may correspond to the tectonic b−and c−axes respectively,so that the nature of the observed elastic anisotropy conforms fully to that caused by the recrystallization processes of the constituent minerals.The magnitude of the anisotropy is dependent both on the anisotropy of the minerals and on the petrofabric structures.In the case of dunite as an aggregate of olivine(Birch [2])and mica schists and amphibalite(Christensen [6]),the apparent anisotropy seems to be a half of that of the constituent minerals.The elastic anisotropy of ordinary silicate and oxide minerals is generally significant,amounting to 1.5 or 2.0km/sec for velocity difference.Therefore,it is easy to account for the observed anisotropy by the existence of anisotropic petrofabric structures.
 The discussion on the recrystallization mentioned above does not always imply that all of the orientation patterns of minerals is generated by recrys−tallization.The stable grain shape under nonhydrostatic condition was discussed by Kumazawa [13].The stable arrangement of a body under stress is such that the plane of flattened surface of the body is perpendicular to the principal axis of compression and the orientation of elongation is parallel to the axis of tension,irrespective of the physical properties of the substance.For example,the crystallographic c−axis of tourmaline is oriented parallel to the tectonic b−axis in schists(Oyagi [19]),because tourmaline in the metamorphic rocks shows a crystal habit elongated along the crystallographic c−axis.If tourmaline is oriented by recrystallization under stress,crystallographic c−axis has to be parallel to the tectonic c−axis,since the elastic constants along the crystallographic c−axis are smaller than the other orientations.Therefore the preferred orientation of tourmaline by recrystallization will give rise to the decrease of anisotropy and that by dimensional effect will increase the anisotropy.In any case,tourmaline is always a minor constituent of schists and the effect of this mineral is unimportant.
 As discussed by Christensen,micas are one of the most prominent minerals which give rise to the anisotropy of rocks.In addition to their elastic anisotropy,micas have remarkable platy crystal habit.Therefore the existence of micas in rocks increases the anisotropy of rocks by two folds;their platy grain shape resulting from the extreme interface structure and from the elastic anisotropy of micas themselves.The relationship between the preferred orientation of amphibole and the anisotropy of rocks was investigated by Christensen.The orientation of amphibole is caused by recrystallization(Kumazawa,unpublished data).The existence of amphibole and their preferred orientation by recrystallization definitely increases the elastic anisotropy.
 In the case of ordinary rock−forming minerals,the directions of the higher elastic dilatational wave velocity and of the smaller velocity respectively correspond to those of the smaller and the larger thermal expansion,and also to the directions of the close and loose atomic arrangements in the lattice configuration.The crystal habit is generally generated by growth anisotropy which is also controlled by the arrangement of the atoms.Along the direction of the closest packing the minerals generally grow faster than the other directions.The planes of the translation gliding and of cleavage are also intimately related to the atomic arrangement in such a way that they are parallel to the plane or to the direction of the closest packing.A kinetic consideration on mineral orientation by translation gliding also shows that the plane of gliding is parallel to the principal axis of compression for stability.Most of the factors mentioned above provide such mineral orientation that the elastic dilational wave velocity of rocks is largest along the tectonic b−axis and smallest along the tectonic c−axis.
 The magnitude of anisotropy shows a slight decreasing tendency with increasing grade of metamorphism,presumably because of change of mineral composition,such as decrease of mica content.When anisotropy of silicic schists is compared with that of basic schists,there is not large difference,although the mineral compositions are quite different.The relationship between the petrography and the elastic properties is not yet studied well.At any rate the cause of the elastic anisotropy should be the nonhydrostatic stress prevailing in the space occupied by the rocks in the earth’s depth in the geologic past.Thus the detection of the elastic anisotropy by seismological observation is a significant clue for the interpretation of the geotectonic stress in the geologic past.
 Porosity effect.—As discussed in the foregoing section the porosity effect was significantly large and the velocity measured even at 10 kilobars is lowered by 0.2km/sec due to this effect,contrary to what is commonly thought.Fig.6 may suggest that there is a certain statistical relationship between the factor A or B and the observed porosity.As shown in Fig.10 we have a positive correlation between B and porosity φ in most cases,while the plots of n versus φ do not show any apparent correlation.However,the plots of A versus φ are significantly scattered since m,ranging from 0.8 to 1.8,for each high pressure run,involves errors of ±0.2 or more.The plot of B versus φ seems to be represented by a linear relation;
     B=α+βφ.
Therefore,using n obtained from the average velocity−pressure relation(Table5),A is represented as follows:
     A=a+bφ,
where a=α/n and b=β/n are constant.The accurate determination of a and b is of course impossible.We may,however,make a rough estimation;a=0.1−0.3km/sec,and b=0.4−0.8km/sec.The parameters a and b are statistically larger for the specimens cut parallel to the tectonic c−axis and smaller for the tectonic b−axis.The fact that a> 0,implies that there remains some porosity effect even if the observed porosity of open pore vanishes,and thus a is related to the effect of pore space which we could not measure directly.Let us now consider the state with no porosity effect,A=0,then we have φ=−a/b.Then alb ranging from 0.1 to 0.5 per cent,represents the upper limit of additional porosity of open pores.The closed pore will not have large effect on the elasticity than the open pores.
 The porosity affects the elastic properties along the tectonic c−axis most effectively and the decreasing rate of the effect with the increasing pressure is also largest along this direction.This fact shows that the pore space is not spherical but is significantly flattened or elongated,as discussed by Walsh [20,21] and Christensen [6].Ordinarily grain shapes in the crystalline schists are flattened parallel to the tectonic ab plane and are elongated along the tectonic b−axis.Pore spaces are assumed to exist between the grain boundaries as intercrystalline fissures or cracks.The cleavage planes in the constituent minerals will have an effect analogous to flattened pore space.
 Summing up the above results,we obtained a porosity and pressure dependency of velocity as follows;
     V=V_0±CP−(a+bφ)P^(−n),
where a,b and n are the constants dependent on the geometry and distribution of pores.We have such an experience that the velocity at ordinary condition is considerably lower for well machined small specimen than that of a big piece of rock sample This fact suggests that most of pores and the porosity effect might have arised during the process of sampling and machining the rock specimen.Therefore the actual velocity of rocks in the shallow part of the crust may be higher than that predicted by(4).In order to take this factor into consideration,the observed specimen porosity φ in(4)may be replaced by porosity φ’ of rocks in situ.
 The effect of other factors.—The present measurements were made for dried specimens.When the pore space in the rock specimen is filled with liquid such as water,the change of velocity with pressure is quite different.Under the natural condition,any pore should be filled with water;in most cases,however,the actual porosity may be so small that the effect of interstitial water may be rather small,though definitely present.

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TABLE3.LOCALITY,BULK AND TRUE DENSITIES,POROSITY OF CRYS TALLINE SCHISTS AND THE DILATATIONAL WAVE VELOCITY AS A FUNCTION OF PRESSURE
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FIG.3.Example of pressure−velocity relation.
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FIG.4.Frequency distributions of mean velocity at 5 kb and of true density.The specimens are classified into four groups:P,B−1,B−2 and B−3,depending on density.Specimen 1404 is excluded from this clas
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FIG.5.Example of relation between log P and log(dV/dP)
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TABLE4.AVERAGE DENSITY,POROSITY,VELOCITY AND MAXIMUM VELOCITY ANISOTROPY OF SILICIC SCHISTS AND THREE GROUPS OF BASIC SCHISTS
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TABLE5.NUMERICAL VALUES OF PARAMETERS;TO 10 KILOBARS AND THOSE
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表:B,n AND A,AND THE EXTRAPOLATED VELOCITY OF PORE−FREE STATE
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FIG.6.Schematic representation of pressure dependency of velocity in terms of parameters;A and n.
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FIG.7.Velocity−density relation for crystalline schists.
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FIG.8.Change of velocity anisotropy with pressure,
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FIG.9.Nomogram for dilatational wave velocity of a 1:1 layering structure composed of two isotropic media with velocity of V_1 and V_2,density of ρ_ and ρ_2,and elastic constant of ρ_1V_1^2 and ρ_2V_2
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FIG.10.Relationship between the observed porosity and the parameters;B and n.Open circle:c−specimen,cross:a−specimen,and dot:b−specimen.

SEISMOLOGICAL STRUCTURE IN THE METAMORPHIC TERRAIN

Array Though the elastic properties of the Sanbagawa metamorphic rocks are not always representative of the metamorphic rocks in the other regions,it seems to be a general characteristic that the metamorphic rocks of regional types have predominant anisotropy;furthermore,they show the lamination structures consisting of two apparently different rock types;silicic and basic schists.Although the difference of their average velocities amounts to 1km/sec,the velocity of basic schists along the tectonic c−axis and that of quartz schists along the tectonic b−axis have almost the same value due to anisotropy.
 In the first approximation for the actual rock body in the deeper part of the earth’s crust,we consider a horizontal layering of crystalline schists with silicic and basic compositions.As in the case of Sanbagawa and also of other metamorphic terrains,the tectonic trend is supposed to lie approximately in a horizontal plane.When the fraction of quartz schist,for example,is given,the bulk properties of the rocks(the wave length of seismic wave is supposed to be sufficiently large compared with the spatial scale of the layering)can be estimated by an aggregate theory.If the average density ρ is estimated from gravity data for example,the average chemical composition,
i.e.the fraction f of quartz schist is approximately obtained from
     ρ=fρ_1+(1−f)ρ_2
where ρ_1 and ρ_2 are the densities of quartz schist and of basic schist respectively.
 The elastic wave velocity obtained by the explosion seismic exploration is,however,mainly concerned with the velocity of the wave propagated in a horizontal plane.Therefore,the velocity obtained from the seismic refraction method is not representative of the bulk properties of rocks in situ in a three−dimensional sense.Summing up the data presented in the foregoing sections,the bulk and the horizontal properties of the crystalline schists are shown in Table6 and Fig.11.For example,the horizontal velocity along the trend of the tectonic structure(maximum velocity)is 0.4 to 0.5km/sec higher than the average velocity of three−dimen−sional sense.In this case the apparent velocity−density relation is approximately given by
     V=2.8ρ−(1.0±0.1),
while that perpendicular to the trend of the tectonic structure(minimum velocity in a horizontal plane)appears to be normal;
     V =2.8ρ−(1.4±0.1).
On the average,the horizontal velocity will appear ca.0.2km/sec higher than the bulk average of the rocks in situ.
 The maximum elastic anisotropy which will be observed from the horizontal velocities,will be 0.3 to 0.4km/sec.This is one half of the maximum anisotropy existing in the region.When the region is folded with the axes parallel to the tectonic trend,the anisotropy will increase since the horizontal minimum velocity will be some mean of the velocity along the tectonic a−axis and that along the c−axis.On the other hand,the progress of metamorphic reaction which reduces the contents of micas and the other significantly anisotropic minerals,will decrease the anisotropy.
 At any rate,the existence of elastic anisotropy would be diagnosed as belonging to the nature of the metamorphic rocks of the regional type or the olivine rocks or rock masses which have been deformed by stress.An example of the seismic anisotropy in a horizontal plane in the continental region is that reported by Brown et al.[5] on the continental shelf,south of New York.In this area,the azimuth of the maximum velocity is parallel to the tectonic trend inferred from the land geology in the vicinity.
 In Japan and its vicinity,no evidence has been reported for the elastic anisotropy in a horizontal plane.In Fig.12 several velocity profiles obtained by the Research Group for Explosion Seismology of Japan are shown together with the expected velocities of crystalline schists in the earth’s crust.The observed velocity of rock mass is intermediate between those of basic schists and silicic schists.The layer with the velocity of 6.8km/sec on the 139゜E profile may be a case of an anisotropic rock mass.The 139゜E profile and the Miboro east profile both in the central Japan are mutually crossing at right angles.The difference in velocities;0.8km/sec,from 20 to 35km depth may be attributable to the anisotropy in a horiozntal plane.The direction of the Miboro east profiles is almost perpendicular to the tectonic trend of northeast Japanese island,and the higher velocity on 139゜E profile is expected.
 Another rock mass,which may be anistoropic is the layer having the velocity of 7.6 to 7.7km/sec on the Ishibuchi−Hokota profile in northeast Japan,and on the Miboro west profile.The layer with the velocity of 7.5 to 7.9km/sec spreads almost over Japanese islands and they are supposed to belong to the upper mantle.This seems to be likely from the positive gravity anomaly on the Ishibuchi−Hokota profiles.However such a possibility can not be discarded that the tectonic b−axis of basic schists or some kinds of ultrabasic rocks is aligning parallel to the profile at the depth of 20 to 30km,because both profiles are parallel to the trends of the exposed metamorphic terrains and also to the arch of the Japanese islands.If the above interpretation is the case,the average velocity of rocks in this layer should be smaller by about 0.3km/sec than that by seismological observation.In any way,the existence of anisotropy is not incompatible with the data obtained up to present.In order to derive some definite conclusion concerning with the anisotrpy in the earth’s crust,further seismological evidence is necessary.
 In conclusion,we like to stress the possibility of anisotropy in the depth of the earth’s crust,based on the genetic consideration of metamorphic terrain and on the present data of the elastic wave velocity of Sanbagawa metamorphic rocks.

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TABLE6.PHYSICAL CONSTANTS OF CRYSTALLINE SCHISTS IN CONNECTION WITH THE SEISMOLOGICAL APPLICATION The range of actual scattering is also shown.Desity in g/cm^3 and velocity in km/sec
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FIG.11.Elastic properties of metamorphic rock mass composed from silicic and basic crystalline schists.||:velocity along the tectonic trend,Z:vertical velocity,and horizontal velocity perpendicular to
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FIG.12 A.Comparison of the velocity distribution obtained by seismic refraction explora−iton in Japan,and those of crystalline schists measured in the laboratory.|| and L respectively show the horizon

ACKNOWLEDGEMENTS

 We wish to acknowledge Prof.Yasuo Shimazu of Nagoya University for his invaluable comments on the present study.We are indebted to Dr.Masao Iwasaki of Tokushima University,Mr.Kinsuke Uchida of Besshi Mine,Mr.Hirosuke Agui of Shirataki Mine,Mr.Ishin Horinouchi of Akaishi Mine,Dr.Yoshiteru Kono of Kanazawa University,and Mr.Ryuichi Shichi of Nagoya University for their help in sampling work.We owe to Mr.Shigetoshi Takahasi and Mr.Gunzo Takamatsu for the construction and maintenance of high pressure instrumentation,and to Mr.Isuzu Hiraiwa for machining the rock specimens.We also owe to Dr.Kokichi Ishioka of Nagoya University for his comments on the petrological problems.The expenses for the present study were partly defrayed from the Grant in Aid for Scientific Research given by the Ministry of Education.

REFERENCES

[1] BANNO,S.,Petrologic studies on Sanbagawa crystalline schists in the Besshi−Ino district,central Shikoku,Japan:J.Fac.Sci.,Univ.Tokyo,Sec.2,15,203−319(1964).
[2] BIRCH,F.,The velocity of compressional waves in rocks to 10 kilobars,Part1:J.Geophys.Research,65,1083−1102(1960).
[3] —,The velocity of compressional waves in rocks to 10 kilobars,Part2:J.Geophys.Research,66,2199−2224(1961).
[4] BRACE,W.F.,Relation of elastic properties of rocks to fabric:J.Geophys.Research,70,5657−5667(1965).
[5] BROWN,M.V.,NORTHROP,J.,FRASSETTO,R.,and GRABNER,L.H.,Seismic refraction profiles on the continental shelf south of Bellport,Long Islsnd,New York.Bull.Geol.Soc.Am.,72,1963−1706(1961).
[6] CHRISTENSEN,N.,Compressional wave velocities in metamorphic rocks at pressures to 10 kilobars:J.Geophys.Research,70,6147−6164(1965).
[7] HIDE,K.,Geologic structure and metamorphism of the Sanbagawa crystalline schists of the Besshi−Shirataki mining district in Shikoku,southwest Japan(in Japanese):Geol.Rept.Hiroshima Univ.,No.9,1−87(1961).
[8] IWASAKI,M.,On the glaucophane schists of Bizan district,Tokushima City(I):J.Gakugei,Tokushima Univ.,4,27−40(1955).
[9] —,M.,Metamorphic rocks of the Kotsu−Bizan area,eastern Shikoku:J.Fac.Sci.,Univ.Tokyo,Sec.2,15,1−90(1963).
[10] KITSUNEZAKI,C.,Determinaton of seismic anisotropy of metemorphic rocks in natural condition:Special Contrib.,Geophys.Inst.Kyoto Univ.No.4,83−90(1964).
[11] KOJIMA,G.,Uber das 「Feld der Metamorphose」der Sanbagawa kristallinen,Schiefer —esonders in Bezug auf Bildung des kristallinen Schiefergebietes in Zentral−Shikoku:J.Sci.Hiroshima Univ.,Ser.C,1,No.1,1−18(1951).
[12] —.Contributions to the knowledge of mutual relations between three metamorphic zones of Chugoku and Shikoku,southwestern features of each metamorphic zone:J.Sci Hiroshima Univ.,Ser.C,1,No.3,17−46(1953).
[13] KUMAZAWA,M.,A fundamental thermodynamic theory on nonhydrostatic field and on the stability of mineral orientation and phase equilibrium:J.Earth Sci.,Nagoya Univ.,11,145−217(1963).
[14] —,The elastic constants of rocks in terms of elastic constants of constituent mineral grains,petrofabric and interface structures:J.Earth Sci.,Nagoya Univ.,12,147−176(1964).
[15] MISAWA,S.,Physical properties of crystalline schists distributed along Dosan−line:Railway Techn.Research Rept.,No.401(1964).
[16] MIYASHIRO,A.,and BANNO,S.,Nature of Glaucophanitic metamorphism:Am.J.Sci.,256,97−110(1958).
[17] —,Metamorphic rocks and metamorphic belts:Iwanami,Tokyo(1965).
[18] NAKAYAMA,I.,Tectonic features of the Sambagawa metamorphic zone,Japan:Mem.Coll.Sci.,Kyoto Univ.,Ser.B,26,103−110(1959).
[19] OYAGI,N.,Preferred orientation of tourmaline in crystalline schists from the Sazare mine,in central Shikoku,Japan:Geol.Rept.Hiroshima Univ.,No.12,493−502(1963).
[20] WALSH,J.B.,The effect of cracks on the compressibility of rock:J.Geophys.Research,70,381−389(1965).
[21] —,The effect of cracks in rocks on Poisson’s ratio:J.Geophys.Research,70,5249−5257(1965).