Elastic　dilatational　wave　velocity　in　crystalline　schists　from　Sanbagawa　metamorphic　terrain,Shikoku,Japan

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.

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.

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

　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.

RESULT　AND　DISCUSSION

　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.

SEISMOLOGICAL　STRUCTURE　IN　THE　METAMORPHIC　TERRAIN

　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.

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.

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