Measurements　of　elastic　wave　velocities　in　volcanic　rocks　at　high　temperatures　by　means　of　ultrasonic　impulse　transmission.PartI

ABSTRACT

　A　new　method　of　measurement　for　elastic　wave　velocities　in　rocks　at　high　temperatures　by　means　of　ultrasonic　impulse　transmission　is　presented.This　method　consists　of　the　direct　measurement　of　wave　velocities　by　utilizing　the　piezoelectricity　of　a　beta-quartz　crystal.It　is　shown　that　there　are　several　kinds　of　cut　in　the　orientation　of　a　beta-quartz　crystal　generating　or　receiving　the　longitudinal　or　transversal　wave,or　both　waves.In　our　experiments,these　beta-quartz　crystal　cuts　did　not　change　in　phase　to　tridymite　at　870℃,presumably　due　to　a　sluggish　inversion.The　efficiencies　of　transducers　were　not　reduced　even　at　870℃,and　the　measurement　could　be　made　up　to　about　1000℃.Thus　there　is　a　possibility　of　using　direct　measurements　for　high　temperatures　above　1000℃.
　The　rock　specimens　used　are　all　volcanic　rocks　which　were　collected　from　several　localities:Mihara　volcano,Izu　Oo-shima;Showa-shinzan　and　Usu　volcano,Hokkaido;Hakone　volcano,Kanagawa　Prefecture;Shidara,Aichi　Prefecture.Some　of　the　results　obtained　are　noted　below:
　1）Longitudinal　and　transversal　wave　velocity　through　volcanic　rocks　from　Showa-shinzan　and　Mihara　volcanoes　increases　with　a　rise　in　temperature　up　to　about　800℃,while　that　through　volcanic　rocks　from　Shidara　and　Hakone　volcano　decreases　with　a　rise　in　temperature.The　longitudinal　wave　velocity　generally　varies　more　than　the　transversal　wave　velocity.
　2）The　increase　of　elasticity　with　a　rise　in　temperature　seems　to　be　a　characteristic　of　the　recently　erupted　new　volcanic　rocks,while　the　decrease　of　elasticity　is　observed　in　the　old　volcanic　rocks.This　seems　to　be　mostly　due　to　the　differences　in　the　structures　of　volcanic　rocks.
　3）The　increase　of　Poisson’s　ratio　with　a　rise　in　temperature　is　generally　remarkably　large.

INTRODUCTION

　The　elastic　properties　of　rocks　at　high　temperatures　have　not　been　duly　studied,because　of　many　difficulties　in　technique　for　measurements　at　such　temperatures.In　particular,there　are　quite　a　few　experimental　data　on　the　rigidity　modulus　and　Poisson’s　ratio　of　rocks　at　elevated　temperatures.Young’s　modulus　of　rocks　at　high　temperatures　elevated　up　to　about　1000℃　has　been　determined　by　several　methods　of　measurement:the　static　measurement　by　the　bending　method　[14],the　dynamic　measurement　by　the　resonance　method　[1,3,7],and　the　longitudinal　wave　velocity　measurement　by　the　ultrasonic　impulse　transmission　method　[6,15]　have　been　reported.In　these,the　static　method　is　unsuitable　for　the　measurement　of　elasticity　of　rheological　substances　such　as　rocks,because　of　the　reciprocal　action　of　their　elasticity　and　viscosity.It　is,therefore,desirable　to　use　the　dynamic　measurement,a　fact　that　is　well　known.However,even　when　the　resonance　method　is　used,it　is　rather　difficult　to　derive　the　torsional　vibration　in　rock　samples,particularly　at　high　temperatures;therefore　Young’s　modulus　has　been　obtained　mainly　by　the　bending　vibration　method.On　the　other　hand,Hughes,Pondrom,and　Mims　[5]　have　begun　to　use　the　method　of　measurement　of　wave　velocity　of　ultrasonic　impulse　transmitted　through　rocks.This　method　has　proved　more　effective　from　various　view　points,but　it　is　mostly　restricted　to　the　temperatures　of　about　550℃　and　below.This　is　because　there　is　no　suitable　transducer　which　can　sufficiently　endure　at　higher　temperatures.To　overcome　this　difficulty,a　scheme　has　been　devised　[2]　for　maintaining　the　transducer　at　room　temperature　and　for　transmitting　the　ultrasonic　impulses　through　the　rock　samples　by　means　of　a　rod　wave　guider,which　has　one　end　fixed　to　the　transducer　and　the　other　end　closely　attached　to　the　specimen.By　such　a　method,only　the　longitudinal　wave　seems　to　be　obtained　because　of　the　modification　of　the　ultrasonic　impulses　in　the　wave　guider　mentioned　above.
　The　authors　carried　out　the　experiment　by　paying　attention　to　the　piezoelectricity　of　a　high　quartz,called　beta-quartz,and　found　a　possibility　of　direct　measurement　of　both　longitudinal　and　transversal　wave　velocities　in　rocks　for　high　temperatures　up　to　1000℃　or　higher.Accordingly,by　this　direct　measurement,which　differs　from　that　used　before,the　measurement　of　elastic　wave　velocities　in　volcanic　rocks　was　carried　out.The　present　paper　deals　with　the　experimental　method　used　and　lists　some　of　the　results　obtained.

EXPERIMENTAL　APPARATUS　AND　PROCEDURE

　The　ultrasonic　apparatus　has　been　constructed　for　the　measurement　of　elastic　wave　velocities　in　rocks.This　principal　apparatus　is　similar　to　that　used　by　Nagumo　[12].A　block　diagram　of　the　apparatus　is　shown　in　Fig.1　and　the　photograph　of　the　experimental　arrangement　of　the　apparatus　in　Fig.2.The　apparatus　is　constructed　as　it　is　generally　made　and　consists　of　a　pulse　generator,pulse　amplifier,sweep　circuit,time　mark　circuit,and　cathode-ray　oscillograph.Its　main　characteristics　are　the　following:The　pulse　generator　provides　an　output　pulse　accurately　synchronized　with　the　trigger.The　output　pulse　has　a　rise　time　of　about　0.1-0.5　μ　sec　and　a　peak　amplitude　of　about　200　volts.Furthermore,the　pulse　is　repeated　at　every　1　kc　per　second.The　time　marks　are　given　at　every　1.00　or　0.20μ　sec,while　the　maximum　sweep　velocity　is　5cm　per　microsecond　at　the　trace　on　the　screen　of　the　oscilloscope.The　pulses　are　impressed　on　a　quartz　crystal　which　generates　very　sharp　elastic　pulse　waves　in　the　rock　specimen.These　waves　are　received　at　the　opposite　end　of　the　specimen　by　a　similar　crystal.The　quartz　crystals,as　well　as　the　bariumtitanates　that　were　used　for　room　temperatures,were　employed　commonly　as　a　driver　and　a　receiver.The　output　of　the　receiving　crystal　goes　through　an　amplifier　to　a　cathode　ray　oscilloscope.The　amplifier　has　a　flat　response　up　to　1mc　per　second　with　a　gain　of　110db　andthen　gradually　falls　off.
　It　has　been　proved　that　small　rock　specimen　is　convenient　for　the　high　temperature　experiment,and　therefore　a　pulse　adjuster　having　a　minimum　variable　rise　time　of　0.2μ　sec　and　a　time　mark　of　0.20　it　sec　have　been　made　for　the　purpose　of　our　experiments.In　any　event　a　device　to　increase　sweep　velocity　and　to　amplify　the　gain　for　the　high　frequency　region　extending　to　15-30mc　per　second　is　now　under　construction.
Transducer
　X-　and　Y-cut　quartz　crystals　are　mostly　used　for　the　experiment　of　ultrasonic　impulse　transmission;while　low　quartz,designated　alpha-quartz,changes　into　high　quartz,designated　beta-quartz,at　573℃.The　inversion　is　spontaneous　and　accompanied　by　an　abrupt　change　in　the　directly　observable　properties,even　though　the　change　is　not　too　great.Moreover,an　electric　twinning　is　easily　producible　in　the　neighbourhood　of　the　transition　point.From　these　circumstances　the　reliable　measurement　for　high　temperatures　has　been　carried　out　in　safety　only　at　temperatures　below　about　550℃.It　was　found,however,that　beta-quartz　had　piezoelectricity,so　this　beta-quartz　was　used　as　a　transducer.In　the　case　of　beta-quartz,the　so-called　X-　and　Y-cut　crystals　like　as　in　the　case　of　alpha-quartz　are　available　only　for　the　transversal　wave　measurement,while　a　special　transducer　is　needed　only　for　the　measurements　of　longitudinal　waves　or　for　both　longitudinal　and　transversal　waves.Various　kinds　of　cuts　in　the　orientation　of　the　crystal　axis　of　a　quartz　crystal　are　illustrated　in　Fig.3.Generally,we　should　like　to　call　transducers　made　from　such　cuts　as　β-cut　crystals.The　β-X-　and　β-Y-cut　crystals　for　longitudinal　waves　have　the　same　characteristics　at　temperatures　above　573℃　and　they　are　used　only　for　the　measurement　of　longitudinal　waves.However　the　characteristics　of　　β　-X　-cut　crystal　are　different　from　those　of　β-Y-cut　at　temperatures　below　573℃.The　plane　of　the　electrode　of　this　type　of　transducer　is　perpendicular　to　the　plane　of　the　sound　radiation,even　though　this　may　cause　inconvenience　in　practical　use.A　,β-45°-cut　crystal　is　used　for　the　measurement　of　both　longitudinal　and　transversal　waves;it　is　most　effective　to　take　about　40-50°　for　the　angle　θ　in　Fig.3.
　The　piezoelectric　constants　of　beta-quartz　crystal　up　to　626℃　have　been　obtained　by　Cook　and　Weissler　[4].As　seen　in　Fig.4,the　piezoelectric　constant,d_14,of　beta-quartz　is　of　almost　the　same　order　as　d_11　of　alpha-quartz,and　therefore　it　is　sufficiently　useful　for　practical　purposes.As　seen　in　Fig.4,d14,_β　seems　to　have　a　tendency　to　decrease　rapidly　with　a　rise　in　temperature.It　was　found　from　the　results　obtained　from　practical　use,however,that　it　did　not　change　too　much　with　a　rise　in　temperature.
　At　temperatures　above　870℃　beta-quartz　is　usually　inverted　into　tridymite　which　has　no　piezoelectricity,but　in　the　present　experiments　beta-quartz　did　not　change　in　phase　to　tridymite　at　870℃,this　being　presumably　due　to　a　sluggish　inversion.Thus　the　transition　did　not　really　take　place.The　measurements　could　be　carried　out　with　the　beta-quartz　in　the　same　condition　until　a　temperature　of　960℃　was　reached.This　temperature　of　960℃　is　the　melting　point　of　silver,the　substance　used　as　a　cementing　material　to　fix　the　transducer　to　the　rock　specimen.Consequently,in　this　case　the　transducer　became　useless　at　960℃　because　of　the　melting　of　the　silver.According　to　the　results　of　differential　thermal　analysis,beta-quartz　does　not　seem　to　be　inverted　into　tridymite　until　at　least　1200℃.Therefore　this　has　opened　a　possibility　to　measure　directly　the　elastic　wave　velocity　of　rocks　by　means　of　ultrasonic　impulse　transmission　at　temperatures　above　1000℃.
　In　the　cooling　process　from　temperatures　above　the　inversion　point　of　alpha-　to　beta-quartz（573℃）,an　electric　twinning　was　generally　produced　in　the　alpha-quartz　crystal　under　573℃,and　the　experiment　could　not　be　continued　under　the　same　conditions.In　some　cases　it　is　possible　to　prevent　[16]　the　electric　twinning　by　imparting　a　suitable　static　stress　and　electric　field　to　the　transducer　before　the　temperature　in　question　is　attained.
　At　high　temperatures　the　transducer　is　sometimes　broken　down,so　we　made　the　transducer　self-producing　The　dimension　of　the　transducer　used　was　changed　according　to　the　size　of　rock　specimen,namely（1.0～1.5）×（1.0～　1.5）×（0.2～0.4）cm3　for　X-cut　and　Y-cut　crystals　and　1.0×1.0×1.0cm3　or　1.2x0.4×0.6cm3　for　β-X-　and　β-Y-cut　crystals.
Method　of　experiments
　First,a　transducer　and　an　electrode　cemented　to　both　ends　of　the　rock　specimen.A　mixture　of　sodium　silicate（water　glass）and　graphite　powder　or　Dupont　silver　conductive　coating　was　used　for　this　cementing　material.It　was　found　that　the　silver　conductive　coating　was　fairly　good　for　this　experimental　purpose,but　that　it　could　not　be　used　above　960℃,its　melting　point.The　sodium　silicate　in　this　mixture,however,was　found　to　be　a　good　substance　to　attach　firmly　the　rock　specimen　to　the　transducer　at　high　temperatures,particularly　above　800℃,but　was　found　to　be　somewhat　inadequate　at　comparatively　low　temperatures,because　the　electrode　or　transducer　cemented　to　the　rock　specimen　is　sometimes　fall　off　due　to　an　air　bubble,probably　caused　by　the　dehydration　of　the　sodium　silicate.
　Both　ends　of　the　rock　specimen　having　the　electrode　and　transducer　thus　cemented　were　covered　by　a　special　fire　brick,the　outside　of　which　was　electrically　shielded　by　painting　the　mixture　of　sodium　silicate　and　powder　of　graphite　over　it.These　features　are　illustrated　by　the　photograph　of　the　rock　specimen　prepared　for　the　experiment,as　shown　in　Fig.5.
　Since　the　elastic　constants　of　alpha-and　beta-quartz　crystals　are　given　by　E.W.Kammer　et　al.[9,10]　up　to　800℃,the　so-called　response　delay　time　of　the　transducer　against　a　pulse　can　be　calculated　for　various　types　of　transducers　up　to　800℃.In　the　neighbourhood　of　a　temperature　of　573℃　the　elastic　property　of　the　quartz　crystal　varies　rapidly　according　to　the　variation　in　temperature.Moreover　the　elastic　wave　velocity　of　the　rock　specimen　becomes　rather　large　in　the　neighbourhood　of　1-2cm　away　from　the　driver.To　eliminate　these　influences,two　rock　specimens　with　a　different　length　were　measured　at　the　same　time　during　one　experiment,and　the　delay　time　induced　was　cancelled　out　from　the　observation　of　apparent　time　difference　of　impulse　transmission　through　them.Thus　the　velocities　of　longitudinal　and　transversal　waves　directly　transmitted　through　the　specimen　were　accurately　determined.In　this　case,the　uncertainty　of　the　absolute　velocity　does　not　usually　exceed　2　per　cent　and　is　no　greater　than　5　per　cent　even　in　the　worst　condition.The　errors　induced　are　chiefly　due　to　the　obscurity　of　the　rise　of　the　pulse　and　to　the　uncertainty　of　the　identification　of　the　pulse.Accordingly,our　experimental　apparatus　is　being　continuously　modified　so　as　to　increase　the　accuracy　of　measurements.
　To　elevate　the　temperature　an　electric　furnace　about　35　cm　in　length　and　about　10　cm　in　diameter　was　used.This　furnace　was　horizontally　set　and　was　filled　with　nitrogen　gas　for　the　purpose　of　preventing　the　oxidation　of　the　specimen.The　rock　specimen　was　horizontally　placed　on　a　steel　plate　set　in　the　center　of　the　furnace.The　temperature　was　always　measured　at　about　the　center　of　the　specimen.The　thermocouple　leads　passed　through　insulated　porcelain　tubes　to　the　cold　junction,from　which　copper　connections　were　carried　to　a　potentiometer.Chromel-alumel　or　platinum-platinum　rhodium　thermocouples　were　used　in　conjunction　with　the　manufacture’s　calibration　table;the　temperature　measurement　was　thus　made　with　the　maximum　error　of　about　±5℃.It　was　necessary　to　allow　a　little　time　for　the　specimen　itself　to　reach　the　temperature　of　the　furnace;in　this　case　the　rate　of　change　in　temperature　was　200-300℃　per　hour.

ROCK　SPECIMEN

　The　rock　specimens　used　in　this　experiment　were　all　volcanic　rocks　and　were　cut　to　suitable　length　by　a　diamond　saw　from　solid　rocks　collected　from　several　localities.The　ends　of　the　specimens　were　ground　smoothly　to　a　plain　parallel　finish　before　the　measurements　were　made.The　specimens　were　all　rectangular　prisms,1.2　to　1.5　cm　in　width　and　2.0　to　6.0cm　in　length.The　names　of　the　rock　specimens　are　listed　in　Table1　together　with　their　localities,their　longitudinal　and　transversal　wave　velocities　at　room　temperature,their　densities,and　their　cutting　types　from　which　the　transducers　were　made.The　names　of　the　rock　specimens　listed　are　given　according　to　the　classification　of　volcanic　rocks　by　Kuno　[11].The　chemical　and　petrographical　studies　of　some　kinds　of　rocks　used　were-already　carried　out　by　a　number　of　investigators　[11,13,17,18].Their　chemical　compositions　are　listed　in　Table2.The　specimens,after　the　silver　coating,were　placed　in　the　apparatus　
for　ultrasonic　impulse　transmission.

RESULTS

　By　means　of　the　apparatus　iust　mentioned　above　the　elastic　waves　through　the　rock　specimens　were　photographically　taken　on　an　oscilloscope　screen.
　Top　curve　of　each　record　represents　time　marks,1　microsecond.Middle　and　lowest　curves　of　each　record　represent　the　longitudinal　and　transversal　waves　through　the　rock　specimens,the　lengths　of　which　are　6.00　and　3.00　cm　respectively.Fig.6　shows　some　examples　of　the　records　of　the　wave　patterns　obtained.The　incident　and　received　wave　pulses　are　shown　on　the　records.The　wave　trains　received　show　two　sharply　distinguishable　phases,the　first,a　smaller　one　corresponding　to　the　longitudinal　wave　and,the　second,a　larger　one　corresponding　to　the　transversal　wave.
　The　velocities　of　longitudinal　and　transversal　waves,V_1　and　V_t,were　obtained　from　the　relationship　between　the　length　of　the　specimen　and　the　times　of　the　first　and　the　second　phases　respectively.The　values　of　V_1　and　V_t　thus　determined　for　some　examples　of　specimens　are　given　in　Table3.The　variations　in　these　velocities　with　a　rise　in　temperature　are　shown　in　Figs.7　and　8.Furthermore,Young’s　modulus　E,rigidity　modulus　μ,and　Poisson’s　ratio　σ　were　computed　from　the　longitudinal　and　transversal　waves:

【数式】

These　values　were　plotted　against　the　temperatures,as　shown　in　Figs.9　and　10.
　As　seen　in　Figs.7　and　8,the　longitudinal　wave　velocity　of　rocks　such　as　the　1950　lava　of　Mihara　and　the　1944　lava　of　Showa-shinzan　decreases　slightly　at　a　temperature　around　100℃　or　200℃　and　then　increases　somewhat　more　when　the　temperature　rises　to　about　700-800℃;on　the　other　hand,the　velocities　of　rocks　from　Hakone　and　Usu　volcanoes　and　Shidara　decrease　only　with　a　rise　in　temperature.
　The　velocity　of　the　transversal　wave　varies　with　a　rise　in　temperature　in　a　similar　way　to　the　longitudinal　wave,although　its　variation　is　not　so　great　as　that　in　V_1.The　phenomenon　of　the　increasing　wave　velocity　with　the　increasing　temperature　may　be　seen　in　the　recently　erupted　rocks,such　as　basalt　from　Mihara　and　hypersthene　dacite　from　Showa-shinzan.On　the　contrary,a　decreasing　wave　velocity　may　be　seen　in　the　comparatively　old　rocks,such　as　two-pyroxene　andesite　from　Hakone　and　Usu　volcanoes　and　rhyolite　from　Shidara.
　With　respect　to　Young’s　modulus　Sakuma　[14]　found　that　the　lava　of　Showa-shinzan　and　Oo-shima　increased　its　value　remarkably　with　a　rise　in　temperature　up　to　nearly　700-800℃,after　which　its　value　began　to　decrease;the　maximum　value　it　attained　was　about　1.5　to　2.0　times　as　great　as　its　initial　value　at　room　temperature.The　present　results　also　show　a　tendency　to　increase　E　when　the　temperature　rises　as　seen　in　Fig.9,but　the　value　of　increase　is　found　to　be　a　little　less　than　the　amounts　above.The　difference　between　the　two　cases　depends　upon　the　differences　in　the　method　and　specimens　used.The　temperature　variation　of　μ　is　also　seen　in　Fig.9;the　maximum　increasing　value　it　attained　was　about　1.8　times　as　great　as　its　initial　value.This　increase　of　elasticity　with　a　rising　temperature　will　be　seen　also　in　the　rocks　from　Showa-shinzan（S）.On　the　other　hand,a　decreasing　elastic　constant　with　a　rise　in　temperature　may　be　seen　in　the　rocks　from　Shidara（K）and　Usu（G-1）,as　shown　in　Fig.10.
　The　Poisson’s　ratio　σ　varies　rather　greatly　according　to　the　increase　of　temperature,as　shown　in　Figs.9　and　10.As　a　whole,a　has　a　tendency　to　increase　the　value　with　a　rise　in　temperature　except　for　the　rocks　from　Shidara.Since　σ　is　a　function　of　the　ratio　of　V_1　to　V_t,even　a　slight　change　in　V_1　and　V_t　has　much　influence　upon　σ.This　variation　of　σ　is　caused　by　a　great　increase　of　V_1　rather　than　by　any　decrease　of　V_t.Thus　it　is　interesting　to　note　in　this　phenomena　that　the　rocks　are　in　a　sense　to　become　harder,not　softer,when　a　larger　value　of　σ　with　a　rise　in　temperature　is　given,so　far　as　the　present　temperature　ranges　are　concerned.
　In　any　event　there　are　two　kinds　of　variation　types　in　the　variation　of　the　elasticity　and　temperature　of　volcanic　rocks.The　increase　of　elasticity　is　quite　similar　to　the　results　concerning　amorphous　silica　[8].It　is,however,noted　that　this　increase　of　elasticity　does　not　always　depend　on　only　the　amount　of　silicate,as　given　in　Table　2.Then　the　increase　of　elasticity　seems　to　be　a　characteristic　of　the　new　volcanic　rocks　recently　erupted　and　the　decrease　of　elasticity　a　characteristic　of　the　old　volcanic　rocks.This　may　be　considered　the　main　differences　in　the　structures　of　rocks.
　Furthermore,the　thermohysteresis　phenomena　were　observed　in　the　andesite　from　Hakone.Its　velocity,V_t,in　the　cooling　process　following　a　heating　to　about　1000℃　is　quite　different　from　that　in　the　heating　process　above　600℃.Such　phenomena　were　already　observed　in　the　case　of　the　basalt　from　Oo-shima　[14].Consequently,if　the　rocks　are　subjected　to　a　high　frequency　region　of　ultrasonic　impulse,a　thermohysteresis　has　much　influence　upon　their　elastic　constants.

SUMMARY

　An　ultrasonic　apparatus　has　been　constructed　for　the　measurement　of　elastic　wave　velocity　in　rocks.By　utilizing　the　piezoelectricity　of　beta-quartz　crystal　the　direct　measurement　of　longitudinal　and　transversal　wave　velocities　of　ultrasonic　impulses　transmitted　through　rock　specimens　was　carried　out　at　high　temperatures　up　to　about　1000℃.The　rock　specimens　used　were　all　volcanic　rocks　such　as　hypersthene　dacite,two-pyroxene　andesite,basalt,and　rhyolite.These　were　collected　from　several　localities　such　as　Mihara　volcano,Oo-shima;Showa-shinzan　and　Usu　volcano,Hokkaido;Hakone　volcano,Kanagawa　Prefecture;Shidara,Aichi　Prefecture.The　results　obtained　are　summarized　as　follows:
　1）Longitudinal　and　transversal　wave　velocities　through　volcanic　rocks　from　the　Showa-shinzan　and　Mihara　volcanoes　increase　with　a　rise　in　temperature　up　to　about　800℃,while　those　through　volcanic　rocks　from　Shidara　and　Hakone　volcano　decrease　with　a　rise　in　temperature.The　longitudinal　wave　velocity　generally　varies　more　than　the　transversal　wave　velocity.
　2）The　temperature　variation　of　Young’s　modulus　of　rocks　is　generally　remarkable　compared　with　that　of　the　rigidity　modulus.
　3）An　increase　of　elasticity　with　a　rising　temperature　seems　to　be　a　characteristic　of　the　recently　erupted　new　volcanic　rocks　and　a　decrease　of　elasticity　a　characteristic　of　the　old　volcanic　rocks.This　seems　to　be　the　main　difference　in　the　structures　of　volcanic　rocks.
　4）Poisson’s　ratio　varies　according　to　the　temperature　variation　and　generally　increases　with　a　rising　temperature.The　variation　with　temperature　of　the　longitudinal　wave　velocity　contributes　to　this　phenomena　more　than　the　transversal　wave　velocity　does.
　5）The　thermohisteresis　of　volcanic　rocks　seems　to　have　a　great　influence　upon　the　variation　in　elasticity.

ACKNOWLEDGMENT

　In　conclusion,the　authors　wish　to　express　their　thanks　to　Mr.K.Suwa,who　made　the　classifications　of　the　rock　specimens.The　expenses　for　the　study　were　partly　defrayed　from　the　Grant　in　Aid　for　Scientific　Research　given　by　the　Ministry　of　Education.

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