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ABSTRACT

 Elastic wave velocity and thermal expansion of four kinds of volcanic rocks at high temperatures were measured.The wave velocity was measured by means of X-cut quartz transducers.An increasing elastic wave velocity with a rise in temperatures was observed in dacite from Showa-shinzan volcano and also in basalt from Mihara volcano,while a decreasing wave velocity was observed in andesite from Aso volcano.The stepwise increase in wave velocity of thermally treated Showa-shinzan dacite was observed at a certain temperature between 200 and 300℃,while this stepwise velocity increase was not observed in a virgin specimen in the first heating run.The wave velocity of Hakone dacite decreased with a rise in temperature from room temperature to 150℃ and then it increased at higher temperatures and again decreased stepwise at temperatures above 573℃.
 Thermal expansion of rock specimens was measured by a dilatometer.The Remarkable difference of thermal expansion curves was related to the crystalline forms of free silica in rocks,namely quartz or cristobalite.
 The temperature variation of porosity was obtained from the difference between the measured and the calculated thermal expansion curves.The relationships between elastic wave velocity,thermal expansion,and content of cristobalite were discussed.An increase in wave velocity is generally correlated to the decrease in porosity.The inversion of alpha to beta cristobalite is related to the stepwise increase in wave velocity of Showa-shinzan dacite.

INTRODUCTION

 In the previous paper [7],a new method of measurement of elastic wave Velocity in rocks at high temperatures by means of ultrasonic impulse transmission Was presented,and the results were discussed for several kinds of Volcanic rocks.An increase in elastic wave velocity with a rise in temperature was observed in the rocks from Mihara(basalt)and Showa-shinzan(dacite)volcanoes.This phenomenon was from first considered a characteristic of the recently ejected new volcanic rocks.In general,the elastic constants of many substances decrease with a rise in temperature,with exceptions of amorphous or glassy substances.These exceptional cases in crystalline substances are known in a narrow temperature range where a phase transition such as the inversion of alpha to beta quartz may occur.The positive temperature coefficient of elasticity of rocks is exemplified by Wilberns sandstone(less than 1,000 bars,below 100℃)[4],Ellenburger dolomite(less than 5,000 bars,below 120℃)[4],Barrisfield granite(less than 1,000 bars,below 100℃)[5],Showa-shinzan dacite(1 bar)[7,9,10] and Mihara basalt(1 bar)[7,10].Sakuma inferred the existence of quenched glassy substance in Mihara basalt and its crystallization processes at high temperatures.The increase in elasticity with temperature was,however,observed in the specimens in which glassy substances are not detected even by the microscopic and X-ray analysis.If this increase in elasticity could not be explained by the properties of the constituent substances themselves,it must be attributed to the temperature variation of the structure of substance or to the mode of aggregation of the constituent grains.On account of the fact that the negative temperature coefficient of the elasticity is observed under a certain low pressure,it is expected that the looseness of aggregation in a broad sense may play an important role.A compaction process may have a tendency to become more predominant than a loosening process between constituent grains and their crystal lattice with a rise in temperature.The porosity is one of the parameters expressing the looseness of the aggregation.Moreover,the existence of microcracks or fissures may produce significant effect on the physical properties such as strength,plasticity,and elasticity or viscosity.This paper deals with the foregoing relations of volcanic rocks by means of measurement of elastic wave velocity and thermal expansion.

EXPERIMENTAL APPARATUS AND PROCEDURE

ArraySupersonic apparatus
 The present apparatus is almost the same as that reported in the previous paper [7],in which the writers suggested the use of a quartz transducer up to the temperatures of 1,000℃ or more in utilization of piezoelectricity of beta-quartz.The piezoelectric constant of beta-quartz gradually decreases with a rise in temperature,nevertheless it has a sufficient magnitude for practical use at least up to 800℃.It was,however,found very difficult to keep quartz transducers,electrodes,and the specimen safely stuck together in a definite state throughout a wide range of temperatures.Thus,the compressional force of 1-10 kg/cm^2 was applied to the specimen and transducers in order to stick them together.However,the force was not uniform sometimes and transducers ruptured occasionally.Thus,some of the measurements at the temperatures above 700℃ or at a cooling run from high temperatures may not be accurate enough.The quartz transducers used in the present experiments are all X-cut plate,3mm thick.
 First,the arrival time of dilatational wave was read,and the distortional wave was read in a later phase.Then,the arrival time was confirmed,refer-ring to that obtained at the temperatures above 550℃,where the amplitude of the distortional wave becomes predominant over that of the dilatational wave.The errors in successive readings of time from photographic records were very small,being estimated at less than 4percent in a velocity determined by a series of experiments.These errors are chiefly due to the uncertainty in the determination of wave front or arrival time.

Dilatometer
 As seen in Fig.1,a specimen of rectangular prism is set in a fused silica pipe one end of which is closed convex inward.The specimen is pressed on this closed end of the silica pipe through a fused silica rod.The silica pipe is horizontally set in the central part of an electric furnace.The elongation of the specimen is transmitted to the outside of the furnace,and the relative displacement between the outer pipe and the inner rod is measured by several methods such as(1)the optical method using the light deflexion with a me-chanical lever,(2)the direct method with dial gauge,and(3)the electrical method with a differential transformer.In the case of the optical lever and the direct method,the magnification was of the order of 10^3 under a stable working condition,where the precautions to prevent friction effect were required.In the case of the electrical method,it is possible to obtain the magnification of the order of 10^5 or more,even though the working condition is rather un-stable.By means of the output of the differential transformer the elongation of the specimen was detected,and its continuous records for temperature variation were automatically taken by a pen recording galvanometer system.

Temperature measurement and control
 The temperature was measured always at about the center of the specimen by the alumel-chromel or platinum-platinum rhodium thermocouples.The heating rate was controlled by the electric Omer of the furnace,and the cool-ing rate by regulating the volume of cold air or nitrogen gas sent into the furnace.The rate of temperature change was 3-9℃ per minute.The errors of thermal expansion were less than 3percent in the case of specimen 100mm in length.The errors in temperature measurement were about 1 percent in centigrade.

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FIG.1.Schematic diagram of dilatometer.

ROCK SPECIMEN

Array The measurements were carried out on the four kinds of volcanic rocks.The nomenclatures,localities,and constituent minerals of the rock specimens are listed in Table1 and their chemical compositions are listed in Table2.The mineral compositions of the rock specimens determined by norm analysis are given in Table3.The crystalline form of free silica in rocks,quartz or cristobalite was determined by X-ray analysis.
 All the specimens were cut off from solid blocks collected from various fields and were worked into a suitable size and shape.The specimens for the measurement of elastic wave velocity were all rectangular prism 1.5 to 5.71cm in length and(1.5 to 2.00)^2cm^2 in cut end and those for the measurement of thermal expansion were 2 to 10cm in length and(0.5)^2cm^2 in cut end.During the preparation,the specimens may have been affected by such factors as cutting,polishing,and cementing the specimen with quartz transducer.

Density and porosity
 The bulk density ρ_b is given by the ratio of weight to the apparent volume of the specimen which is a rectangular prism in shape,the length of whose edge being measured by a micrometer.The true density pt,as is called,gener-ally means the ratio of weight to the volume of a solid part or substantial part of the rock.The other parts of the rock occupied by the solid part,are the void spaces or pores.
 The specimen was first heated in water and then slowly cooled.This treatment may result in a full saturation of the open void space with water.The increment of weight of the specimen represents the volume of the void space,and we obtained the porosity P_0 as regards the open pore which may be connected to the outside of the rock by fissures or cracks.Thus we get

   P_0 =ρ_t−ρ_b/ρ_t×100.

 However,such a true density is somewhat affected by the grade of treatment or by the mechanical history of the specimen.It varies with the temperature and the duration of heating,or the size of the specimen.The effect of size seems to be partly due to the mechanical history imparted on the specimen during the preparation.
 The 「powder density」 ρ_p is the density of crushed and pulverized rock specimens,and is measured by a pycnometer with water as an immersion liquid.The powder density is expected to be that of the solid part of rocks.Then the total porosity P_t is given by

     P_t=ρ_P ρ_b/ρ_b×100.

 For comparison of these densities with the real density pr expected from the mineral composition,calculation of ρ_r is made from the norm,where the ratio of cristobalite to quartz in the norm quartz is given by X-ray analysis.The density of cristobalite is assumed to be 2.3 g/cm^3.All the densities thus obtained are listed in Table4,which indicates that the powder density is sys-tematically small as compared with the calculated real density.This may be due to the very small closed pores or inclusions left in the grains of the powder.

Free silica in rocks
 In order to determine crystalline form and fraction of free silica in rocks,X-ray analysis was carried out by the diffractometer.Crystalline forms of free silica in the present rock specimens were of quartz and cristobalite.The internal standard method was employed for quantitative analysis of them.In order to get the coefficient of internal standard,artificial cristobalite containing only a trace of quartz and tridymite,was prepared from silica gel by heating for five hours at 1500℃.Many types of cristobalites have been found in respect of their complex structure and defects in the crystal [2].The diffraction lines of X-ray of both artificial and natural cristobalites in the present rock specimens were very sharp and each of these cristobalites was considered to be an ordered crystal.The intensity of X-ray diffraction was assumed to be identical in both cristobalites,but systematic errors may arise from this assumption.Errors of this internal standard method are estimated at 5 percent for the fraction of cristobalite or quartz in rocks.These errors were estimated from the fluctuation of intensity of X-ray diffraction under identical conditions.The percentage of total silica content in rocks is,therefore,obtained from the X-ray method.Independent of this the silica percentage can be obtained from norm analysis.In Table5,the norm silica is compared with that determined by the X-ray method.The norm is calculated from the chemical composition which was already reported in the literatures.These two values of the silica percentage are concordant within the range of errors in the cases of Showa-shinzan dacite and Hakone dacite,which contain large amounts of silica.On the other hand,they are discordant significantly in the cases of Mihara basalt and Aso andesite.In the case of Aso andesite,cristobalite and quartz are detected by X-ray analysis,but the existence of olivine is confirmed by both microscopic observation and norm analysis..This result is somewhat conspicuous.However,the results of the measurement showed characteristic thermal expansion at the temperature of about 200℃,similar to the case of Showa-shinzan dacite,containing 30 percent cristobalite.In the case of Mihara basalt,the silica percentage determined by the X-ray method is smaller than that determined by norm analysis.The smaller value of silica content seems to be more reliable,since it is suggested by the measurement of the thermal expansion.This circumstance will be described later.

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TABLE1. ROCK SPECIMENS
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TABLE2. CHEMICAL COMPOSITION
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TABLE3. MINERAL COMPOSITION FROM NORM ANALYSIS
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TABLE4. SOME PHYSICAL CONSTANTS OF ROCK SPECIMENS
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TABLE5. CONTENTS OF CRISTOBALITE AND QUARTZ

EXPERIMENTAL RESULTS

 As already reported in the previous paper [7],the elastic waves through the rock specimens were photographed on an oscilloscope screen.Fig.2 shows some examples of the records of the wave patterns obtained.
 The velocities of longitudinal and transverse waves,determined at various temperatures,were plotted in Fig.3.As seen in Fig.3,the wave velocity varies with a rise in temperature and,as already pointed out [7],a certain range is noted in the value of wave velocity even in the same specimen and at the same temperature;this may be due to heterogeneity,anisotropy,and difference in the past history of the rock specimen.
 The thermal expansion curves obtained by the present experiments are shown in Fig.4.As is found,the degree of fluctuations in thermal expansion coefficients is small as compared with that of the case of wave velocity.The porosity variation with temperature is shown in Fig.6,where a slight hysteresis can be seen.
 Showa-shinzan dacite.——As seen in Fig.3,the elastic wave velocity of dacite from Showa-shinzan volcano gradually increased with a rise in temperature at the first heating run.Especially,it increased sharply stepwise at a certain temperature between 200 and 300℃ in the thermally treated specimens.It was found that this stepwise increase in velocity took place not only in the second heating and the cooling run,but also in the specimens heated in hot water at 100℃ for 24 hours.It is quite likely that this abnormal change at temperatures between 200 and 300℃ is caused by the presence of cristobalite in the specimens.It can be seen that the value of wave velocity has a range in one and the same specimen even at a constant temperature.
 The hysteresis of thermal expansion was observed at about 200℃ and also at an early stage of cooling process.With respect to the expansion curves the elongation at the beginning of cooling at 900℃ seems to be a thermal relaxation,while the permanent elongation at room temperature did not take place.The hysteresis at about 200℃ may be affected by the inversion of alpha to beta cristobalite.The maximum thermal expansion was observed at 220℃ in the first heating run and at 180℃ in the cooling and the second heating run.Nevertheless,the characteristic expansion at 573℃ was not observed at all.The calculated expansion is significantly large as compared with the observed value.It is,therefore,considered that the porosity decreases with a rise in temperature as in the case of Mihara basalt.
 Hakone dacite.裕he characteristic variations of elasticity of Hakone dacite are noted as follows:The significant wave velocity was found to decrease with temperatures ranging from room temperature to 150℃.At an early stage of cooling run the wave velocity is always few percent larger than those in the heating run below the inversion point of alpha to bata quartz.The elastic wave velocity decreased stepwise at the temperatures above 573ーC,and the permanent decrease in wave velocity was caused by the cooling run.As far as the present experimental accuracy is concerned,the rate of temperature change did not influence the value of wave velocity.The hysteresis curves of the thermal expansion were slightly observed,where the cooling runs from both 1,000 and 500℃ followed a similar course,but the permanent elongations did not take place.The significant expansion,due to the abnormal expansion of quartz,was observed at the temperatures between 500 and 600℃.However,the discontinuity of expansion in the quartz crystal at 573℃ seems to have been smoothed out in rocks.Accordingly,the abnormal expansion at nearly 200℃,expected from the existence of cristobalite,was not entirely observed.The observed expansion was smaller than that calculated in the temperature range from 200 to 600℃.
 Aso andesite.—As seen in Fig.3,the elastic wave velocity in andesite from Aso volcano decreased with the rise in temperature.The decrease in velocity in the cooling run is larger than that in the heating run.The attenuation of elastic waves was very large,which may be due to the presence of many visible cracks.
 The abnormal expansion was observed at 250℃ in the heating run and at 230℃ in the cooling run.The expansion differences between the first and the second run were very slight.The shrinking curve for the cooling run from 500℃ nearly followed the expansion curve in the heating run,although a slight hysteresis loop over 400℃ was recognized.The large hysteresis or the permanent expansion was observed at the temperatures above 700℃.The elonga-tion of 0.003 percent for ten minutes took place when the specimen was kept at the constant temperature of 1,000℃.This measurement up to 1,000℃ was carried out at the increasing rate of 5℃ per minute.The results may be significantly affected by the rate of temperature change at the temperatures above 700℃.
 Mihara basalt.裕he elastic wave velocity in basalt from Mihara volcano generally increased with the rise in temperature except below 150℃.The velocity in the second and the cooling runs seems to be larger than that in the first heating run.
 The thermal expansion at the temperatures above 700℃ became gradually large and was similar to the case of Aso andesite.This large expansion at the temperatures above 700ーC was not permanent,and recovered at room temperature when the specimens were cooled.The shrinking curve in the cooling process from 500℃ followed a curve similar to that of heating,but some slight differences were detected at the initiation of cooling.The distinctive expansions at about 200 and 573℃,expected from the mineral composition,were not ascertained even by the accurate examination.These facts may suggest that the small quantities of quartz and cristobalite(10 percent in total from the norm)were not affected by the thermal expansion in bulk or that the real fraction of free silica was not so large as that obtained from the norm.The smaller content of free silica in this rock specimen is inferred from X-ray analysis.The measured expansion curve is generally lower than that expected from the mineral composition,and the void space diminishes corresponding to a rise in temperature.

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FIG.2.Examples of screen view of elastic waves through the rock specimen.(a)
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FIG.2.(Continued)(b)・(c)
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FIG.3.Relationship between temperature and elastic wave velocity.(a)
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FIG.3.(Continued)(b)・(c)
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FIG.3.(Continued)(d)
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FIG.4 Calculated and measured thermal expansion curves.(a)・(b)
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FIG.4.(Continued)(c)・(d)

DISCUSSION AND CONCLUSION

Array Since the groundmass of the present rock specimen is composed of very fine grains,the mineral composition was calculated from the chemical composi-tion by norm analysis.This calculated mineral composition does not represent a real composition.However,the compositional properties of rocks may be given by this norm in the present discussion.Using this mineral composition,the thermal expansion and the elastic wave velocity were calculated for com-parison with the measured values.
 Much discussions have been made on the methods of expressing the elastic properties of an aggregate by the elastic constants of each constituent grain.However,any of those methods will do for a rough order estimation in the present discussion.Here we take the compressibility of rocks β as the weighted mean of the compressibility [1] of each mineral’s volume,neglecting the effect of pores.Assuming λ=μ and μー3/5β(λ,μ:Lame’s elastic constants),the dilatational wave velocity V_D,and distortional wave velocity V_s are given by

     V_D=√9/5/√(β・ρ_b),   V_s=√3/5√(β・ρ_b).

As far as the writers are concerned,the data of the elastic properties of cris-tob;elite have not yet been reported.The density of cristobalite at room tem-perature is 2.3,being extremely low as compared with that of quartz or other rock forming minerals.Since,as is generally known,material of low density is more compressible,the compressibility of cristobalite was assumed to be twice as large as that of quartz.Owing to the lack of data we were unable to estimate the temperature variation of elastic wave velocity in each mineral.The calculated and measured maximum wave velocities are listed in Table 4.
 As seen in Table4,the measured elastic wave velocities are found to be so small that it may be concluded that the elastic wave velocities are not substantially governed by the properties of constituent materials but rather by the mechanical looseness of the structure of rocks.
 The thermal expansion curve expected from the norm is represented by the weighted summation of each expansion curve [1] of constituent minerals by volume fraction,assuming a homogeneous deformation without the effect of void spaces or fissures.The calculated results thus obtained are superimposed on the measured curves in Fig.4.Two dotted curves,(NC_r100)and(NQ _u100indicate the expansion curves which are respectively calculated under two assumptions:(NC_r100)norm silica is represented by cristobalite alone,and(NQ_u100)norm silica is represented by quartz alone.The curve X_n indicates the calculated one,in which the ratio of cristobalite to quartz in norm silica is given by the result of X-ray analysis.The curves(X)indicate the calculated expansion given under the assumption that the total free silica percentage in the rock is given by X-ray analysis.For this calculation,the thermal expansion curve of cristobalite(Fig.5)measured by Hummel [6] was used in a slight modification that the transition temperature of alpha to beta cristobalite is shifted to be applied to that of cristobalite in the present volcanic rocks.Since there are many kinds of cristobalites,shifting of inversion temperature may be allowed,nevertheless the uncertainty of the magnitude of thermal expansion remains.
 The differences between the calculated and measured thermal expansion curves are related to the change in the void space in rocks.If the calculated thermal expansion is larger than the measured value,the void space at that temperature is smaller than that at room temperature.Accordingly,the temperature variation of the void space or porosity can be obtained from the difference between the measured and the calculated thermal expansion curves.The temperature variations of porosity are shown in Fig.6.
 In Figs.6 and 7 the variations of porosity are compared with those of the elastic wave velocity.Decrease in porosity at high temperatures was observed in the Showa-shinzan dacite,Mihara basalt,and Hakone dacite(below 600℃),and the wave velocity in such rocks at high temperatures is evidently larger than that at room temperature.The Aso andesite has very small changes in porosity and its elastic wave velocity decreases with a rise in temperature.The decrease in porosity and the increase in velocity are well correlated with one another in the first order approximation.Therefore,the elastic wave velocity decreases or increases depending upon the structural property such as porosity of rocks which is determined by the measurement of the thermal expansion and by the mineral composition.
 Another type of variations of wave velocity is observed,however,which are not correlatable with the change in porosity.The significant decrease in wave velocity at the temperatures between room temperature and about 150℃ does not seem to be accompanied by the increase in porosity.This phenomenon is,in some cases,accompanied by the increase in elastic wave attenuation as is recognized by the decrease in amplitude of elastic waves through the specimen.At an early stage of cooling,the elastic wave velocity is generally larger than that in a heating run under the same temperature,even though the thermal expansion or porosity in a cooling run is larger than that of heating.Such a phenomenon may be due to the development or dissipation of small cracks or fissures,which may be caused by thermal stress or pressure in rock specimens.The rocks are composed of various anisotropic minerals,having variable crystallographic orientations.Thus,the temperature change may be related to the change in stress at each contact point of constituent mineral grains.The various state of stress is considered at every point:compressional,extensional,or etc.The average stress is equal to the external pressure,i.e.atmospheric pressure in the present case.The spontaneous expansion of rocks(cf.Aso andesite)observed at high temperatures may result from a great increase in internal pressure due to thermal stresses.The dissipation of microcracks or fissures may occur due to such pressure at a place where the stress is favorable to the closeness of cracks.This process may take place at high temperatures where the substance is thermally activated.On the other hand,microcracks may be developed where the stress is favorable to the growth of cracks.Thus,number of cracks in the rock varies with the rates of processes of development and dissipation of microcracks.A decrease in porosity or void space leads to an increase in the contact area among grains or fissures,making the cohesion more powerful.The change in elastic wave velocity may be accompanied by the variation of such compactness or looseness determined by the processes mentioned above.
 There is a question what kinds of structure and what kinds of rock are related to the mechanical processes mentioned above.The porosity or looseness does not decrease in Aso andesite(erupted in 1933)at a high temperature,whereas the porosity of Showa-shinzan dacite(erupted in 1940),Mihara basalt(erupted in 1950),and Hakone dacite(below 600℃)(erupted in Pliocene)decreases with temperature.This difference may be neither due to the difference in the age of rocks nor due to the chemical composition.
 The stepwise increase in wave velocity observed in Showa-shinzan dacite may be an effect of the inversion of alpha to beta cristobalite.It is strange that this stepwise change is not observed in the specimen which has not been treated thermally in the laboratory.There exist many kinds of cristobalites according to a degree of disorder in the crystal lattice.The inversion temperature generally covers the range over several tens of degrees in centigrade.The inversion point(or inversion region)is situated at about 260℃ in every order crystal which was crystallized at a high temperature,and the disorder crystals have several inversion points between 75 and 260℃.Since about 5 Percent volume change is accompanied by the inversion,the porosity in Showa-shinzan dacite decreases at this inversion temperature and the rock becomes more compact in a heating run.On the other hand,the elastic constant of cristobalite may be small at temperatures higher than this,since the density of beta cristobalite(or high temperature cristobalite)is smaller than that of alpha cristobalite( or low temperature phase),the difference being 5 percent.It is,therefore,expected that these two effects on the velocity change are cancelled together in virgin specimens by some mechanisms,and that the former effect is predominant over the latter in the case of thermally treated specimens.
 It was observed that the cristobalite content of Showa-shinzan dacite decreased and the quartz content increased in the range of a few percent when the rock specimen were heated at 500℃ for 30 minutes.Such changes in contents of cristobalite and quartz may result from the transformation of cristobalite to quartz,since the cristobalite is a metastable modification of quartz.The transformation of cristobalite to quartz takes place even in a case that the powder of the specimen for X-ray analysis is prepared in a crushing pot.From the above evidence,considerable amounts of quartz in volcanic rocks are supposed to have been transformed from cristobalite during the geologic time.The volume difference between cristobalite and quartz is 7.6 percent.Then,it is quite significant that the porosity increases in cristobalitebearing rocks due to the transformation of cristobalite to quartz.The physical properties of acidic rocks will change at a considerable rate,especially in vol-canic regions,since such a transformation may be accelerated by stress,vapour or high temperature.The physical properties,such as elastic wave velocity,thermal expansion,strength and so on,are much affected by the presence of free silica and its crystalline form,as well as by changes in mineral composi-tion and resulting changes in structures.Thus,we conclude that the tem-perature variation of elastic wave velocity in rocks may well be explained by considering the change in thermal property of constituent minerals of rocks as well as the change in structure of rocks.
 In conclusion,the writers wish to express their thanks to Messrs.T.Tani-gawa,S.Matsunami,and T.Kano for their help in the present experiments.Appreciation is also due Dr.H.Kuno,Tokyo University,who permitted us to use his rock specimen.The expenses for the present study were defrayed in part from the Grant in Aid for Researches of Ministry of Education.

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FIG.5.Thermal expansion curves of cristobalite [4] and quartz.
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FIG.6.Variation of porosity with temperature,calculated from norm(N)and from silica contents given by X-ray(X).
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FIG.7.General tendency of dilatational wave velocity variation with temperature.

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