The mechanism of the emplacement of the Inyo Dike, Long Valley

The mechanism of the emplacement of the Inyo Dike, Long Valley

JOURNAL
OF GEOPHYSICAL
RESEARCH,
VOL.
93, NO. B5, PAGES
4321-4334,
MAY
10, 1988
The Mechanismof Intrusionof the Inyo Dike,
Long Valley Caldera,California
ZE'EV RECHES
GeologyDepartment,Hebrew University,Jerusalem,Israel
JONATHANFmac
GeologyDepartment,ArizonaStateUniversity,Tempe
We analyzetheintrusion
of the11-km-longInyoDikeatthemarginsof LongValleycaldera,eastemCalifomia.
ThediketrendsN07øWandisdividedintoat leastthreesegments
whicharerotatedby asmuchas25øwithrespect
to themaintrend.The dikeseemsaffectedprimarilyby theregionalstressfield of right-lateralshearof the western
UnitedStatesandby thelocalthermalconditions
of thecrest;thedikeseemsunaffectedby thepreexistingcaldera
marginsandSierra-Nevada
frontalfaultsystem.Thehighheatflow inLongValley calderaimpliesthatcrustalrocks
below3-4.5 km deformby steadystatecreepundertectonicstrainrateandsupportlow to vanishingtectonicshear
stresses.
Theupperrocks,above3-4.5 km, deformby frictionalslipalongfracturesandmaysupporttectonicshear
stresses
ashighas24 MPa. We demonstrate
thatdepthvariationsof tectonicstresses
mayhavea profoundeffect
on the segmentation
androtationof dikes,bothat LongValley andin otherareasof highheatflow. The analysis
placesconstraintson severaltectonicconditions.The Inyo Dike intrudedunder a tectonicstressstatewith a
horizontalmaximumcompression
orientedN07øW.Themaximumextensional
fracturestrengthof thehostrocks
is 1-2.5 MPa, andthe pressuredropwithinthe propagating
Inyo Dike was about0.55 MPa/km.The volatile
overpressure
in the magmachamberwasabout15 MPa during eruptionof rhyoliticlavasat the Inyo Domes.
INTRODUCTION
Seismicactivityandgrounddeformation
since1980havefocused
attentionon Long Valley calderaas a site of incipientvolcanic
activity.The lastmajorvolcaniceventto occurin thisareawasthe
emplacement
of theInyo Domesandassociated
pyroclastic
deposits approximately
550 yearsago;thesefeatureswerefedby an 11km-longdikewe will referto astheInyo Dike. The distributionof
Holoceneventsin LongValley suggests
thatfutureeruptions
will
likely be fed by pipessituatedalongdikes.
The Inyo Dike providesa goodopportunityto analyzetheprocess
of magmapropagationfrom sourceareato the surface,thanksto
detailedstudiesof theregion.The three-dimensional
geometryof
Inyo Craterswerefed by a single11-km-long,northtrendingdike
(Figure 1). Fink [ 1985] mappedgroundcracks,normalfaults,and
phreaticpitson andaroundthedomesandconcludedthattheywere
fed by a N-S trendingdike that dividedinto at least threeNNE
trendingsegmentsas it approachedthe surfacefrom the south
(Figure2). He furthersuggested
that rotationof the segments
increased
upwardandthatthetopof eachsegment
slopedupward
to the north.
Major tectonicfeaturesaroundthe Inyo Domes includethe
roughlyellipsoidalcaldera-bounding
faultsandtheN30W trending
faultsystemof theSierraNevadablock(Figurela ). The immediatevicinity of the Inyo Domescontainsnormalfaultsandvertical
the dike has been resolved on the basis of surface structural features
fractures
trendingmostlyN15øWto N20øE(Figurelb) [Benioff
andmappingof the domes[Fink andPollard, 1983; Fink, 1985; andGutenburg
, 1939;Baileyetal., 1976;Miller, 1985;Fink, 1985;
Mastin andPollard, in press].Threeresearchdrill holesattheInyo Mastinand Pollard, in press].The trendsof the Inyo areaare
Domes provide subsurfacecontrolon the dike geometryand its apparent
alsoin detail.Forexample,a 300-m-longfissure,known
composition[Eichelbergeret al., 1985]. The vast body of geo- asEarthquake
Fault,isfound6 km southof theInyoCratersalong
physicalmeasurements
in Long Valley calderafurtherconstrains theInyotrend(Figure1b); it iscomposed
ofmany2- to20-m-long
the mechanicaland rheologicalconditionsof the upper crustal segments
whosetrendsalternatewithinthesamerangeof N15øW
rockshere [e.g., Hill et al., 1985].
to N20øE (Figure 3).
In this paper we explain the dike geometryin terms of the The presence
of theInyo Dike wasconfh'rned
by thethirddrill
interaction between tectonic stresses and local variations in host
holeof theInyo ScientificDrillingProgram[Eichelberger
et al.,
rock rheology.We evaluaterelationshipsbetweentectonicand 1985]. This slantedhole was sited between Obsidian Dome and
magmaticstressesandestimatethemagnitudeof magmaticpres- SouthGlassCreekDome(Figure1b) whereat a verticaldepthof
sureat depthnecessaryto get the dike to the surface.Application 620m, theholeintercepted
a7-m-widerhyolitedike.Thedikewas
of the model to other volcanoes is also discussed.
surroundedby a 30-m-wide zoneof fractures,someof which were
filled with intrusivepyroclasticmaterial.This dikedidnot ventto
Tu•. Imro Votcnmc
C}tnts
the surface at the drill hole area but fed the 35-m-wide conduit of
Basedon mappingand age datingof pyroclasticdepositsand Obsidian
Dome,about1 km northof thedrill hole.Thepointof
silicicextrusionsin thewesternpartof LongValley caldera,Miller intersection
waswestof a lineconnecting
theventareasof thetwo
[ 1985]proposedthatthethreelargestInyo Domesandtheadjacent domes,suggesting
10' of clockwiserotationat this depth.The
Copyright1988by the AmericanGeophysical
Union.
Papernumber7B7019.
0148-0227/88/007B-7019505.00
directionof thisrotationwasthesamebutthemagnitude
wasless
thanthe25' indicatedby surfacemapping[Fink, 1985].
The sourcefor theInyo lavashasbeenlocatedatthenorthernend
of thechainaccording
to chemical
considerations
[Baileyet al.,
1983],at its southern
portionbasedonstructural
analysis
[Fink,
4321
4322
R•CHESANDFINI(:MECHANISM
OFIm'RUSZON
OFTHEINYODiM
3. Thedeviatoric
tectonic
stress
normal
tothedike,{it'
The dike intrusionis resistedby the following.
Poi•
•
strength
ofthehost
rocks
inthecrust
which
has
• M0_N0_
I• Mono_Inyo
rhyolit
e 4. Pj•,thefracture
to be overcome.
%
.•
Lake
xa
•X*,•
/
•
"X$• •
5. Pva,thepressure
dropinthemagma
duetoviscous
resistance
LONG [••] Moat
latite
VALLEY
'•:•?..•
Ear¾
rh•olite
SYSTEM
•OlassMtn.
rh9olite
to flow of the magma.
6. P,, theelasticresistance
of thehostrockto theintruding
and
dilating dike.
We definethesumof thesestresses
andpressures
asthedriving
• Major
Sierran
frontal
faultspressure
(Pa)of thedike.At depthz belowthesurface
thedriving
,•.'••
• Faults
&fissures
:':.•(•:)'
SouthMoatepicentral
zone
pressureis
•June
••3•' J•
*
M
•5.5
quakes
in
1980
. n OoO•
•
•
o
5'__,•
• 37•
o o ot .
[Pa]•
= Ph+ {it-P• + P•-Pi-P,
(la)
Positivedrivingpressure
indicatesa propagating
dike,whereasa
vanishingdrivingpressure
indicates
a dikethatstopped.
Compressive stressesarepositive.
When the dike intrudesinto a uniform hostrock, threeof theterms
ontherightsideof(la), P•,P!andP,, donotvarysignificantly
with depth,andwe rewrite (la) as
[Pa],= Pc• + [Ph+ {it- P,a,],
'::•::•?
•o•
øø
øøøø
'
(lb)
where
Pco•
=P•-P/-P, isaconstant
foragiven
dikeconfiguration.
Severalinvestigators
havedesignated
the drivingpressure
as
•s•i•
• Mammoth
o,)
Lakes
wherePmisdefinedasthemagma
pressure
inthedike[e.g.Pollard
andMuller, 1976;Delaneyet al., 1986]. From (la) themagma
pressureof previousstudiesis
0
I
Pm=[P,-Pv..•
1,+P•-P•,-P,
I
(lc)
below that the six components
of the driving
Fig. la. Simplifiedgeologic
mapof LongValleycalderaandsurroundingWc demonstrate
area,showingthedistribution
of postBishopTuff volcanicrocks,theInyo/ pressure.
includingthe five components
of the magmapressure
Monovolcanicsystem,majorfaults,andthreeearthquake
epicenters
men- (equation(lc)). maybe separately
calculatedfor theInyo Dike.
rionedin the text [afterHill et al., 1985].
Wefirstcalculate
thehydrostatic
pressure.
P•, fromthegeometry
ofthedike,andthetectonic
stress,
{it,fromthedikeorientation
and
theology.
Then,thesumofconstant
pressures,
P•,
1985] or at severalseparatemagmachambersalong the chain localcrustal
resistance,
P½.•,arecalculated
fromobservations
[Sampsonand Cameron,1987]. While the Long Valley calderais andtheviscous
underlainby a large and shallowmagma chamber,severalgeophysicaltechniques" suggesta much smaller,lesswell defined
dike-like chamber 10-20 km beneaththe Mono [-Inyo] Craters
chain" [Hill et al., 1985].
Geophysicaldatafrom the Inyo areahavebeencollectedaspart
of geothermalexploration,in conjunctionwith the Inyo Drilling
Program,andin ordertomonitorthepotentialfor futureeruptions.
Investigationsconcerningheat flow [Sorey, 1985; Blackwell,
1985], grounddeformation[Savageand Cockerham,1984], and
seismicactivity[Julianand Sipkin,1985] aremostimportantfor
the model developedbelow.
onthedepthof theInyoDike. Finally,themagnitudes
of theelastic
resistance,
P,, andfracture
strength.
Pi, arederived
fromdike
geometry.
,
DEPTH-DEPENDENTPRESS•
Hydrostatic
Pressure,
Ps
Considerthe hydrostaticpressureon a dike which propagates
from a magmachamberat depthH to depthz; meancrustaldensity
is p, andmagmadensity
is p,,.Thelithostatic
pressure
duetothe
crustal
rocksis(p,gH) onthemagma
chamber
and(p,gz)atthetip
of the dike. The hydrostaticpressurein themoltenmagmawithin
EMPLACEMENT OF THE INYO DIKE
thedike decreases
fromthe lithostatic
pressure
(p,gH) at the
depth,
by[p,,g(H-z )] atdepthzbelowthesurface
(Figure
An intrudingdikemaybe envisionedasaninternallypressurized chamber
fracturewhichpropagates
in thecrustdueto its dilationby molten 2b). Thus the hydrostaticpressurein the magmaat depthz is the
magma. The dike extends when the forces which supportits difference,
intrusion exceed the forces which resist the intrusion, and the dike
(p,gH)-[p,,g(H - z )]
stopsunder the oppositeconditions.In the presentsection we
From thishydrostaticpressurewe subtractthelithostaticpressure
evaluatethe balancebetweentheseforcesfor the Inyo Dike.
at depth z and obtain the deviatorichydrostaticpressureof the
The dike intrusionis supportedby the following.
1. P•,,thehydrostatic
pressure
of theintruding
magmawhich
originatesfrom thedensitydifferencebetweenthemoltenmagma
magma,
[ea], = (p,- p•)g (H- z)
(2)
and the solid rock.
Stresses,
{It
2. P•, theoverpressure
in themagmachamber
fromwhichthe Tectonic
Trendselectionofthe
dike. Dikesusuallypropagatenormaltothe
dikepropagates.The mostlikely sourcefor thisoverpressure
isthe
undissolvedvolatiles in the magma [Blake, 1984].
directionof theleastcompressirestressandgrowby infiltrationof
RECHE$
ANDFINK:•/IEcHANISM
OFINTRUSION
OFTHEINYODiem
WILSON
4323
BUTTE
HARTLEY
SPRINGS
FAULT
\
\
OBSIDIAN
x•
•'\
DOME
oocALDERAMARGINoooooooo
øoø
GLASS
NORTHGLASS "•OcUR'•HE
K
oø
øooø
CREEK
DOME
/•/••i••o
ooOøø
NORTH ••
DEADMAN
DOME
•//}
I /
/.,•o
//
oø
o < '•
DEADMAN
SOUTH ,•
0oo-
o
:ooooOO
DEE
•
MAMMOTH
•o
MTN.;
ooooooooooooooooooooOOøøøøøøøø
0
I
2 km
!
Fig.lb. MapoftheInyoDomes
area
showing
rhyolitic
domes,
phreatic
craters,
faults,
cracks,
andcaldera
margins.
Location
marked
in Figurela EF marksEarthquake
Fault[afterFink, 1985].
1b) andthusindicates
localhorizontal
extension
inaNWmagmaintofractures
[e.g.,Anderson,
1938,1951;Delaneyetal., (Figure
thecalderamargin(Figure4a ). No changein
1986].Hostrockenclosing
thetipof agrowingdikeisdissected
by SE directionacross
eruption
style,ormagmacomposition
hasbeen
old,preexisting
fractures
aswellasbynewfractures
induced
bythe domealignment,
[Miller, 1985;Fink, 1985;
propagating
magma.
Themagma
invades
thefractures
havingthe detectedclosetothesetwointersections
1987].Thusthe growingInyo Dike seemsto have
mechanically
mostfavorable
orientation,
regardless
oftheirorigin. Sampson,
boththefractures
andthestress
axesassociated
withthe
TheN07øWalignment
of theyoungInyo Domeschainappears ignored
tectonicfeatures.
unaffected
by two large,preexisting
tectonicfeatures.
The first largestnearbypreexisting
atdepthz,theInyoDikeintrudes
fractures
largestructure
istheactivesystem
ofnormalfaultsthatbound
the Duringitspropagation
trendingNE-SW and
SierraNevadablock.Oneof these,theHartleySpringsfault,trends trendingN07øWandignoresfractures
systems
(Figure4a). Thistrendselection
N30øWandintersects
theInyochainalongthewestsideof South N30øWofthepreexisting
(equation
(la)) is largerfor the
GlassCreekDome(Figure1b). Thisfaultindicates
localhorizon- impliesthatthedrivingpressure
tal extension
in anN60øEdirection(Figure4a). Thesecondlarge N07øW fracture trend than for the other two fracture trends.Of the
stress,
•J,,varieswith the
featureis the conspicuous
marginalzoneandassociated
deep- six termsin (la), onlythetectonic
fracture
trend.
Therefore
we
infer
that
the
magma
intrudedthe
seatedringfaultsof LongValleycaldera.Theringfaultsystem
trendsNE-SW at its intersectionwith the Inyo Craterschain N07øW fracturesbecausethe tectonic stressesassociatedwith this
thanthetectonicstresses
assobetween South Glass Creek Dome and South Deadman Dome trendaremoreintrusionsupporting
4324
RECHES
ANDFXNK:MECHANISM
OFINTRUSION
OFTHEINYODxrm
//•LASS
OBSIDIAN
DOME
JDEADMAN
SURFACE
DIKE
CONTINUOUS
DIKE
NORMAL
,•,10 km
FAULT
(HATCHURES
ON
!
DOWNTHROWN
BLOCK)
/FRACTURE
ZONES
Fig.2a. Schematic
diagram
showing
inferred
dikegeometry
beneath
theInyoDomes.
Notethatthedikeiscontinuous
atdepthand
segmented
near the surface.
ciated with the other trends. We will examine
this inference
in
Thecurvesin Figure4b arenumericalsolutions
forthestress
ratio
R of (3) for the threedominantstructuralsystemsin theInyo area,
In order
formagma
toinvade
anexisting
fracture,
P/=0;thatis, N07øW,N30øW, andN45øE(Figure4a ). ForR < - 1,thedikecould
the magma pressureshould exceed the stressnormal to the notintrudeanyfracture,whichindicatesnegativedrivingpressure;
detail.
fracture's
surface. The orientation
of vertical fractures that can be
for R > 1, the dike could intrude all fractures.For - 1 < R < 1 the dike
dilated
bymagma
pressure,P,,,
weredetermined
fromMohrcircle intrudesfracturestrendingasplottedin Figure4b. Eachstressstate
relationsby Delaney et al. [1986, equation1] (Figure4a ). They isrepresented
by a pointon Figure4b ßfor example,pointG is for
foundthatfractures
trending
atananglea withrespect
to(53would (51trending
N10øEandR = 0.1. Themagmacanonlydilatea
be dilatedby the magmaif
fractureif thepointrepresenting
thestressstateappearsabovethe
tothatfracture.
Consider
(5•trending
N10øE
R = [[(P,•- (51)'3-(Pro-(53)'3'2(p,gz)]/((51
- (53)}> cos(2a) (3) curvecorresponding
(solidlinein Figure4b ). ForR rangingfrom-1. to -0.95 thestress
where(51and(53aretheprincipal
horizontal
tectonic
stresses.
The statesare below all curves, and thusno fracture can be dilated; for
term2(p,gz) appears
in (3) because
themagmapressure
P,•is -0.95 < R < -0.4 onlytrenda canbe dilated;for -0.4 < R < -0.15
definedhere as the deviatoricpressurein the dike (equation2), fractures
trendinga andb canbedilated,andforR > -.15, all three
whereasthemagmapressureis definedby Delaneyet al. [ 1986] as trends
canbedilated(Figure4b ). Forthiscase,tx•= 17ø,at,= 40ø
the absolutepressurein the dike.
andtxc- 35ø(Figure4a ).
OBSIDIAN
/
SURFACE•'
-
•'-
,
0.5km
PIPE
2-4 km
CONDUIT
DOME
The observationthat the Inyo Dike ignoredthe two preexisting
structuresindicatesthat it trendsnormal to the leastcompressive
tectonicstressdirectionduringtheintrusion,N83øE.The developmentof theInyo Dike alonga trendwhichreflectsa regionalstress
field ratherthanlocal structuresis in agreementwith otherstudies
of paleostress;they show relatively uniform regional fields, on
scalesof tens to thousandsof kilometers,which seem to ignore
local structure[e.g., ZobackandZoback,1980;Eyal andReches,
1983]. Further, the fact that the fractures oriented N30øW and
N45øE were not intruded bounds the stress ratio: when the least
compressivestresstrendsN83øE, the ratio is -1.0 < R < -0.65
(Figure4b ); for R > -0.65, fracturestrendingN30øW would also
have been invaded.
Tectonic
stresses in the eastern Sierra Nevada.
Tectonic
stress
dataarenot availablefor the LongValley area,soherewe employ
the regionalstressanalysisof Zobackand Zoback [1980, 1987].
Fig. 2b. Detailedschematic
viewof ObsidianDomesegment
showing
development
ofwidened
pipein centerof segment
andtermination
ofdikeafew They foundthatthe SierraNevadaregionincludesbothstrike-slip
hundred meters below the surface.
andnormalfaulting, andit is transitionalbetweenthe SanAndreas
RECHE$ANDFINK: MECHANISM
OFINTRUSION
OFTHEINYODX•
0
100
200
4325
meters
I
Fig.4a. Idealizedgeometric
relationship
betweentheprincipalhorizontal
stresses,
o• andø3,intheInyoDikeareaandtrends
ofmajorlocalstructural
features'a, trendof Inyo Dike, N07øW;b, trendof HartleySpringsFault,
N30øW;c, localtrendof Calderamargin,N45øE.
andfor normalfaulting [Z,obackand Healy, 1984],
p,.gz= oa
(oavertical)
oz< p,gz
(ozhorizontal)
(4b)
0.5p,gz< o3
(03horizontal)
Theaxesof on•,•in eastern
California
andwestern
Nevadatrend
mostlyin aNNE toN-S directionwith a few casesof NNW (Figure
5). TheN07*Wtrendof on•, deduced
abovefortheInyoDike
(heavy line in Figure 5), appearsto correlatewith the observed
regional
distribution
of trendsof on• (thinlinesin Figure5).
Stressdistributionwith depth. To determinethe depthdistribution of the tectonicstresses
we makethe following deductions.(1)
The stateof stressin theregionof theInyo chainis definedby (4),
whereOhm
• trends
N07øWandOhm
• trends
N83øE.(2) Asthecrust
is continuouslydeformed,the long-termtectonicstresseswithin
thecrustarerepresented
by its yield strength.(3) The rocksin the
upper10km yieldby fracturingwhensubjectedto highstrainrates
accordingto the Griffith-Coulombcriteria.
The yield strengthof the crustis usuallyderivedfor two distinct
rheologies:frictional resistanceto shear along fracturesin the
shallow,brittle rocks,and steadystatecreepin the lower, ductile
Fig.3. Detailedmapof Earthquake
Faultandadjacent
ground
cracksin rocks[e.g.,Kirby, 1983]. The transitionbetweenthetwo rheologic
southern
partoftheInyoChain.Location
indicated
inFigure1b.Notepattern
of bimodal fracture trends. Lines dashed where trends inferred.
STRESS
strike-slipprovinceandtheCordilleraextension
province(Figure
5). Theystatedthat,"detailedobservations
of faultingin theregion
of combinednormalandstrike-slipfaulting(includingbroadlythe
SierraNevada-northernBasin and Rangeboundaryzone and the
Walker Lanebelt of westernNevada)suggesttemporalvariations
(possiblyquitelarge)in bothstressorientation
andrelativemagni-
RATIO
FOR
INYO
DIKE
10
O8
O6
O4
• 02
•
o
tudes"[Zobackand Zoback, 1987].
Forthestrike-slip
events
thestresses
areo.•> o. >> o.m•,and
for normalfaultsthestresses
areo•> o• >> oa,m, where
om•,•,andaura• arethevertical,
maximum
horizontal,
andminimumhorizontalstresses,
respectively[ZobackandZoback,1987].
UsingtheresultsofMcGarr andGay[ 1978],we findforstrike-slip
faulting,
p,gz< o•< 1.5p,gz
o2= p,gz
(o• horizontal)
(o2vertical)
0.5p.gz< o3< p,gz
(03horizontaD
• 04--
b
::•ii
c
-
08
-10_90 70
50
-30 -10 10
30
50
70 90
TREND (degreesfrom north)
a-INYO
(4a)
a
b - SIERRA
½ - CALDERA
Fig. 4b. The stress
ratiorequiredfor dilationby magmaintrudinginto
cracksorientedin directionsN07*W, N30*W, andN45*E (a, b, or c trends
from above)(after equation(3)).
4326
P•cI•ES AS•) Dmc: 1VI•c•,.A•SMOFISr•US•OSOFT.E IS¾OD•
gradients
inthedike.Forexample,
forP.i,= 0.75MPa/km,thedike
wouldpropagatefrom a 10-kmdepthandterminate500 m below
thesurface
if theconstant
pressure
equalled
0.4MPa.WhenP• >
0.4 MPa, the dike continuesto propagate,andit wouldreachthe
/ ///
/
surface
forP•o•> 3.3MPa.Figure7 shows
thatforP•i•= 0.5MPa/
km,thedikewouldreachthesurface
whenP• = 0.8MPa.
Figure7 indicates
thata significant
increase
ofP• isrequired
to
move a dike from a depthof a few hundredmetersto the surface.
This property reflects the profound decreaseof the deviatoric
tectonic
stress,
o,, towardthesurface
(Figure6).
According to Figure 7, for the Obsidian Dome segmentto
terminateat depthsbetween250 and 600 m, the likely pressure
conditions are included in the field marked I. This field is bounded
by0.5< P•i•< 0.75MPa/kmand-0.5< P• < 1.8MPa.
DEPTH-CONSTANT PRESSURES
Elastic Resistance, P
The Inyo Dike is envisioned as an elliptical, vertical crack,
subjected
tointernalpressure,andembedded
in aninfinite,uniform
granite.Similarconfigurations
wereanalyzedby Weertman[ 1971]
whostudiedcrevassesin glaciersandmagmatransportin oceanic
ridges,andPollard andMuller [ 1976] andGudmundsson
[ 1983],
who appliedthe resultsto formsof dikes.
A closedcrackin an elasticplate subjectedto a pressuredifferenceof AP, betweenthe internalhydrostaticpressurein the crack
andtheexternalhydrostaticpressurein thehostrock,woulddilate
Fig.5. Thetrends
oftheaxesofmaximum
horizontal
stress,
on (thin, into an elliptical filled crackof width W andlengthL [Weertman,
short
lines),
forwestern
Nevada
andeastern
Califomia;
these
tr•n•swere 1971,equation15' Pollard andMuller, 1976, equation6]. In the
determinedfrom in-situ stressmeasurements,
earthquakefocal plane solu-
tions,andgeologicalstructures
[afterZobackandZoback,1987].Theblack absenceof tectonic stresses,the dimensions of the crack become
square
isthestudyarea(Figure1) andthethick,longlineisthededuced
trend
AP = (W/L) [{.L/(1- V)]
(5)
ofø•max
fortheInyoDike.
wherep andv aretheshearmodulusandPoisson
ratioof theelastic
behaviorsoccursat about20-km depthin crustwith normalheat
flowbutmayoccurasshallowasafewkilometers
inregionsofhigh
heatflow [Morganand Golombek,1984]. The high heatflow in
LongValley calderasuggests
thattheductile-brittle
transitionis
MAXIMUM
SHEAR
IN INYO
STRENGTH
shallow.
Yield strengthprofilesfor the Inyo areaare calculatedin the
appendixandpresented
in Figure6. This figureshowsthemaxi-
0
2
4
6
8
STRESS
AREA
(MPa)
10 12 14 16 18 20 22 24
mumshearstress,
os= (o• - •3)/2,thatcanbesupported
by the
crustalrocksfor the heatflow andcrustalpropertieslistedin the
appendix.
Figure6 indicates
thattheupper3-4.5km of thecrust
deformby frictional
slip,that• attains
a maximum
valueof 24
MPain the3-4.5kmdeeptransition
zone,andthat•, decreases
to
about3 MPa for heatflow of 300 m%•n-2,or vanishesfor heat flow
of 500 m Wm-2belowa depthof about10 km.
Pressure
Dropdueto Viscous
Resistance,
P•
Theterminationof theInyoDike atdepthslessthan620m implies
thatthedrivingpressure
vanished
atsomedepth0 < z < 620m. By
usingthederived
values
ofPh(equation
(2))andot(Figure6),we
calculate
P• andP•a,whichsatisfy
vanishing
driving
pressure
at
depthsshallowerthan620 m.
Rearranging
(lb) for vanishingdrivingpressure
yields
A• 300 mW/m2
B=500 mW/m2
P•..,= [Ph+ o,Thesolutionfor thisequationis shownin Figure7 by substituting
10
theresultsof (2) andthe appendix.The figuredisplaysthevalues Fig. 6. Theyield strengthof theupper10km of thecrestin theInyo area
of P•mrequired
to propagate
a dikefroma 10-km-deep
magmaasderivedin theappendix.Thediagramindicatesstrengthprofilesfor mean
chamber
totheshown
depths,
forthemarked
P•i•,thepressure
drop heatflow of (a) 500m Wma and(b) 300m Wma.
RECHE$
ANDFmK: M•CHAN•SMOFINTRUSIOS
OFTHEINYOD•
DEPTH-CONSTANT
PRESSURES
During theeruptionof ObsidianDome, the largerpressureat the
topof thedike wasnotsufficientto propagatethedikeupward,due
Peon
(Pc-Pt -Pe) (MPa)
-1.0-0.5
0
I
4327
0
0.5
1.0
1.5
2.0
2.5
3.0
I
I
I
I
I
I
I
3.5
totheresistance
bythefracture
strength
ofthegranite
P/,theelastic
resistance
P,, andtheviscous
resistance
Pvi,(equation
(la)). We
assume
herethattheonlyresistance
topropagation
wasthefracture
strengthof the hostrocks,namely,
P/=[P•]vi•- [P•1•,•
Thus
thecalculated
P!isanupper
limitforthestrength.
Taking
p,=2670kg/m3,p,•=2250kg/m3(molten
rhyolite
[Williams
and
ß
McBirney,1979,p. 29]), andzai
• = 250-600m, we obtainan
,._.
_
::I::: I
-
estimateof thefracturestrengthas1-2.5MPa. Thesevaluesexpress
thein situ,overallmaximumresistanceto yieldingof theintruded
rocksandmay not be directlytransformedinto fracturetoughness
values.
•
I
-
Volatile Overpressure,P
Figure7 shows
thattheconstant
pressure,
P•, ranges
from-0.5
1.4
A: 0.5 MPa/km
1.6'
B: 0.75 MPa/km
to 1.8 MPa for pressuredropdueto viscousresistance
of 0.5 < P
< 0.75 MPa/km. The fracturestrengthand the elasticresistance
were determined above from the dike dimensions, and now the
volatile overpressure,
P can be estimated.
Equation(1b ) indicatesthat
1
2.0
P =P +P/ +P
Fig.7. Theconstant
pressure,
P•, required
topropagate
adikefroma 10
kmdeepchamber
toa depthof2 kmorshallower
underapressure
dropof (a)
0.5 MPa/kmand(b) 0.75 MPa/km.Underpressure
dropof 0.75 MPa/km,
By substituting
theabovederived
valuesof-0.5< P• < 1.8MPa,
1 < Pi<2.5MPa,andP, _--14
MPaintothisequation,
wefinda
P• must
exceed
3.3MPaforthediketoventtothesurface.
Thefieldmarkedvolatileoverpressure
whichrangesfrom 14.5 to 18.3 MPa.
I boundstheconditions
for a diketo terminateat a depthof 250-600m below
the surface.
THE DRn•O
PReSSUrE OF THE INYO DIKE
We examinehere the depthvariationsof the drivingpressureof
plate.Equation(5) showsthe pressurerequiredto overcomethe theInyo Dike (equation(la)), afterthe abovederivationof all its
six pressurecomponents.
We use the followingparametersand
elasticresistance
of theplate;thusP, = AP.
We substitutethe followingvaluesfor theInyo Dike: W = 7 m, results.
L = 11km,!.t= 20 GPa,andv = 0.1(granite),
andfindP,= 14MPa. 1. We assumethat the tectonic shear stressesare equal in
Thusaninternalpressure
of 14 MPa (abovelithostaticpressure
in magnitude and distribution to the shear strengthof the crust
thegranite)isnecessary
todilatean11-km-longfracturein granite (appendixand Figure 6).
into a 7-m-wide
dike.
2. The tectonicstresses
in the SierraNevadaprovinceareeither
of strike-slip faulting (equation (4a)), or of normal faulting
Fracture
Strength,
P!
(equation(4b)). To simplify the following analysis,we suppose
that
duringtheintrusionof theInyo Dike, thestresses
aroundLong
The fracturestrengthof the granitein the Inyo area may be
estimated from the dimensions of the dike. The third drill hole of Valley were of strike-slipfaulting (we will establishthis assumptheInyodrillingproject[Eichelbergeretal., 1985]showedthatthe tion below) (equation(4a)), so that
7-m-thicksegmentof theInyo Dike did notreachthesurfaceand
(6)
terminatedat a depthof lessthan 620 m, about1 km southof
Obsidian
Dome.On theotherhand,the35-m-thick
pipeunderBysubstituting
(6) into(4a),onegetso• + o3_=2(p,gz),andthus
ObsidianDome extendsto the surface(Figure2b ) [Eichelberger the stressratio of (3) becomes
et al., 1985, Figure 3].
DelaneyandPollard [1981] showedthatmagmatransportin a
R _--P,,,/o,
(7a)
quasi-circular
pipe is more efficientthanmagmatransportin a
(4a) and(6)alsoindicate
that(o•+ o2+ o3)/3• p,gz,and
sheetlikedike. Thus piercementof the surfaceby the Obsidian Equations
thus
Domepipeandtermination
of theassociated
dikeareexpected.
The
(7b)
dike and the pipe have the samecomposition[e.g. Vogelet al.,
o,_=o3- (p,gz)_=-(o• - o3)/2= Io, I
1987]andmostlikely werefedby interconnected
conduitsduring
magmapressure,
c•t is thedeviatoric
a singleeruption(Figure2). Thusduringtheeruption,ahydrostatic whereP• is thedeviatoric
tectonic
stress
normal
to
the
Inyo
Dike,
and
c•,
= (c•- c•3)/2,the
balanceexistedbetweenthe pipe and its associateddike. The
crustalshearstrength.
hydrostatic
pressure
atthetopofthedike[Pk]aa•,atdepth
z= zto
v, 3.Theparameters
ofthehostrocks
are:density
p,= 2670kg/m3,
islarger
thanthepressure
atthetopofthepipe[Pk]vi•,'atdepth,shearmodulus!.t= 20 GPa, andPoissonratiov= 0.1 (meanvalues
for graniticrocksin [Clark, 1966]). The densityof the rhyolitic
[Pa]viv,
- [Pa]ai•= (P,- P,•)gzai•
forp, < p,•(equation
(2)).
magma
p,•= 2250kgJm
3[Williams
andMcBirney,
1979,p. 29].
4. Dimensionsof thedike are:widthW _=7 m, lengthL _=11 km,
and depthof sourceH = 10 km.
4328
P•cm•s^NDFm•::IVI•CI-I•N•SM
OFINTRIJSlON
OF'rI-tB
Im,o Dr•m
•-i
i
_1_
i
i
i
i
i
(m•l) H.Ld•(]
I
I
I
I
I
(m •1) HJ.d•t(i
I
I
011
RECHES
ANDFe•K: MECHANISM
OFINTRUSION
OFTHEINYODum
Y
4329
rock.The principalstresses
of the nonuniformfield in front of the
x
diketip aretensional
for positivedrivingpressure,
Pa> 0 [e.g.,
Jaeger and Cook, 1969, section10.12]. We arguehere that the
reduction
of tectonic
stresses associated
with
these tensional
stresses
may explainsegmentationof theInyo Dike androtationof
its segments.
A dike may be modeledasa pressurized
crackcompletelyfilled
with magmaor asa pressurizedcrackwith a leadingmodeI crack
which is not completelyfilled with magma.The stressfield in the
hostrock is essentiallyidenticalfor bothconfigurations(compare
(Jaegerand Cook,[1969, section10.12] for pressurizedcrackand
Lawn and Wilshaw [ 1975, equation3.11], for modeI crack).
The stressesin a plane normal to a planar crack pressurized
uniformly by magma,under plane strainconditions(Figure 9),
werecalculatedbyJaegerandCook[ 1969,section10.12]andLawn
andWilshaw[1975,equation3.11]. FortheInyo Dike, axisXis the
Fn
o,
o• axis(horizontal
andtrending
N07'W), axisY is theo2 axis
Fig.9. Thecoordinate
system
for stresses
atthetip of a pressurized
crack.
andaxisZ isthec•3
axis(horizontal
andtrending
N83'E).
TheY-Zplaneisnormalto theplanarcrack.FortheInyoDike,axisX isthe (vertical),
The stressesare,
o•axis(horizontal
andtrending
N07*W),
axisYistheo2axis(vertical),
and
axisZ istheo3axis(horizontal
andtrending
N83*E).
o•,= (P,•-o,)(O.SC/r)
'a [cos(•)/2)[1 + sin(•)/2)sin(1.5•))]}
oy•= (P,•-q)(O.SC/r)
m[cos(•)/2)[1- sin(•)/2)sin(1.5•))] (9)
5. The following parameterswere estimatedin the aboveanaly-
o,,= (P,•-o,)(O.SC/r)
m[cos(•)/2)[sin(•)/2)cos(•)/2)cos(1.5•))]}
sis:pressure
dropduetoviscous
resistance
P• = 0.5-0.75MPa/km, % = v(% + %)
overpressure
in the magmachamber
Pv= 14-18MPa, fracture where
Cisthedikelength,
r thedistance
from
thediketip,and
•)the
strength
P/- 1-2.5MPa,andelastic
resistance
todikeemplacement
anglewith thedike surface(Figure9). Aspointedoutby Jaegerand
P,_=14MPa.
Cook[1969,
p.263],forP,•>o,theprincipal
stresses
infrontofthe
We nowexaminedepthvariations
of thedrivingpressure
Pa dike,• • 0, andcloseto it, C/r > 2 (Figure9), are tensile.This pro(equation
(1a)),themagma
pressure
P,•(equation
(1c))andtheratio foundreductionof the principalstressesstronglyaffectsthe style
R (equation(7a)). At thedepthof themagmachamber,H, thedike of fracturingin front of the dike as discussedbelow.
intrudedonly the N07*W fractures(seeFigure4b andtext); thus The Sierra Nevada granitesfractureaccordingto the Griffith-1.0 < R < -0.95
z= H
(8a) Coulombyield criteriawhichpredicttwo modesof fracturing:ex-
fractures
for (o• + 303)< 0 (conditions
of smallshear
At depthsshallowerthan620 m wherethedikestopped,nofracture tensional
was dilated; thus
R < -i.0
z < 620 m
stresses
andtensional
c•3asshown
byMohrcircleB inFigure10b),
andshearfractures
when(o• + 3c•3)> 0 (conditions
of largeshear
(8b)
stress
andlargemeanstress,
(o• + 03)/2asshown
byMohrcircle
Usingtheconditionsof (8) andsubstituting
thepressures
listedin A in Figure 10a).
the paragraphabove into (1) and (6), we derive the solution Considerthe Inyo Dike asit propagates
upwardat about10-km
displayed
in Figure8. Thedeviatoric
pressures
Pa, P,•,and0t are depth.Thetectonic
stresses
atthisdepthareo•= 268MPaando3
shownin Figure8a, theirabsolute
values(includingthelithostatic -=266 MPa (Figures6 and10b). (The Mohr circlesin Figure 10 are
load)areshownin Figure8b,andtheratioR = P,•/osisshown
in notto scale.A circleforthestress
stateat 10-kmdepthwitho•_=
Figure8c.Thesolution
in Figure8 isforPv',•
= 0.55MPa/km,Pv= 268MPaando3_=266MPawouldbetoosmalltosee.)Themagma
14.5MPa,P/=1MPa,andP.= 14MPa;thissolution
fitsbestthe intrudesinto rocks subjectedto large lithostaticstressand small
conditionsof (8) andis boundedby the pressures
derivedabove. differentialstress;thisstateof stressis represented
by Mohr circle
In thissolution,the deviatoric
magmapressure
P,• changesb in Figure 10b.The reductionof thestressesin frontof thedike to
linearlywith depthfrom -0.45 MPa at 10-kmdepthto -1.7 MPa at become tensile shifts the Mohr circle b to a new Mohr circle B
the surface(dotted line in Figure 8a), and the deviatorictectonic (Figure 10b). This shift causesthe circle to much the Griffithstressvariesnonlinearlywithdepthasderivedin theappendix(thin Coulombfailure envelopeat a positionwhichindicatestheformaline in Figure8a). The drivingpressureis thedifferencebetween tionof verticalextensionfracturestrendingN07øW,perpendicular
thetwopressures,
Pa= P,•-o,(solidlineinFigure8a).Thedriving totheleastcompressirestress[seeSecor,1965;JulianandSipkin,
pressure
ispositivefor all depthsbelow500 m (namely,it supports 1985, Figure 16]. The dike may now intrudeinto thosefractures
dike intrusion),and negativefor depthsshallowerthan500 m.
(Figure 10d).
DISCUSSION
In theprecedinganalysis,weincorporated
thedepthvariationsof
tectonicstressesin the Inyo area and estimatedseparatecomponentsof drivingpressureof theInyo Dike. We discuss
belowhow
theseresultsmayexplaintherotationof segments
of theInyo Dike.
Dike Segmentation
andRotation
Duringits upwardpropagation
at a depthof 3.5 km the dike
encounters
a largetectonicshearstress
of about15MPa, displayed
by Mohr circlea in Figure10a.The reductionof stresses
in front
of thedike againshiftstheMohr circlea leftwardto a new Mohr
circle A (Figure 10a). However,here the shiftedMohr circle
touchesthefailureenvelopeatapositionwhichindicatesfailureby
shearfractures(Figure 10c).Underthetectonicstressof theInyo
area(equation(6)), theshearfractures
wouldbeverticalstrike-slip
faults(Figure10c).Extensionfracturesdonotformin thetransi-
A propagatingdike generatesa local, nonuniformstressfield
closetoitstipwhichmodifiestheuniformtectonicstressin thehost tion zone due to its large initial shearstresses.
4330
R•CHES
ANDFn•IC:MECHANISM
OFINTRUSION
OFTHEIN¾O
A
GRIFFITH-COULOMB
DIAGRAM
GRIFFITH-COULOMB
10
DIAGRAM
10
9
9-
8
8
7
7-
6-
6-
5-
5
4
4
3
3
2
2
0
o
-1
0
I
NORMAL
2
3
4
5
STRESS/TENSILE
6
7
8
9
lO
STRENGTH
I•
-1
0
| I
I
I
I
I
I
I
I
I
I
2
3
4
5
6
7
8
9
NORMAL
c
STRESS/TENSILE
10
STRENGTH
x,•
z,•
z,•
D
Fig.10.(aandb) Schematic
Mohrdiagrams
forthefracturing
ofcrustal
rocks
during
thepropagation
oftheInyoDike(see
text).
Theheavy
curve
istheGriffith-Coulomb
yieldenvelope.
Circles
bandB (inFigure
10b)indicate
thestates
ofstress
prior
toandafter
theintrusion
ofthedikeatdepths
of10km(see
texO.
Note
thatcircle
Bindicates
extensional
fracturing.
Circles
aandA (inFigure
10a)
indicate
thestates
of stress
priortoandaftertheintrusion
ofthedikeata depth
of3 km(seetext).NotethatcircleA indicates
shear
fracturing.
(c) Thegeometry
ofthefaults
anticipated
fromtheyielding
shown
bycircle
A,displayed
inablock
diagram
(left)anda
stereographic
projection
(right).
(d) Thegeometry
ofthefaults
anticipated
fromtheyielding
shown
bycircle
B,displayed
inablock
diagram
(left)anda stereographic
projection
(right).
The conditions
underwhichthe Inyo Dike coulddilatethese
shearfractures
aredelineated
by (3) andFigure4b.A verticalshear
fracturewhichstrikesfromN20øWto N18øEmaybe intruded
by
thedikefor stress
ratiosR largerthan-0.7 (Figure4b);ourcalculationsof R (Figure8c)indicatethatat 3-kmdepthR _=-0.2 which
is sufficientto dilatethepredictedshearfractures.
The changein the modeof fracturinginvokesa changein the
trendof the dike. The deep extensionalfracturestrendN07øW
(Figure10d),whereastheuppershearfractures
trendiv.tt',erange
N37øWto N23øE(Figure10c).Thereforethepassage
of magma
fromthedeepextensionalfractureto theshallowershearfractures
allowsfor rotationof thedike scgmen,in thetransitionzone.The
changein the fracturingmodewould occurat severallocations
alongthetip of theInyo Dike in thetransitionzone.Thusintrusion
of the magmainto therotatedshearfracturesalsowouldoccurin
severallocationsand the dike shouldhave split into several
segments(Figure 2).
In summary,theprocessdescribedabovedemonstrates
thatthe
InyoDikewouldhavepropagated
fromthemagmachamber
inselfinduced extensional fractures due to small shearstressin the ductile
regionof the crust(Figures10band 10 d). In thetransitionzone
fromductiletobrittletheology,ata depthof about3 km,themode
of fracturing
changes
fromextensional
to sheardueto thelarge
shearstresses
(Figures10aand10c). Thedilationof shearfractures
rather than extension fractures results in rotation of the dike and
segmentation
(Figure2). We thusconclude
thatsegmentation
and
RECHESANDFINK; •[ECHANISMOFIN'I•US•ONOFTHEINYO D•
I ?
1
I
2km
4331
Applicationsof thePresentAnalysis
I
Eventhoughthepresentanalysisisbasedonmeasurements
in and
aroundtheInyo Chain,it mayprovidesomeinsightintoothersheet
•
/ Wahanga
\•
intrusionsin Long Valley calderaand elsewhere.
•
I
Dome •
Rotatedsegmentsof dikesandsillshavebeenobservedin many
locations[e.g.,Pollard et al., 1975;DelaneyandPollard, 1981].
Pollard et al. [1982] proposedthat segmentrotation occursin
,
Dome
x /•.•
(
responseto rotationof theleastcompressirestressaxis.We have
demonstrated
herethattherotationmayalsooccurduetovariations
in hostrock rheologyand fracturingstyle.
One predictionof the currentmodelis theoccurrenceof bimodal
Dome
•••'
Crater
-X
•' •-fracturepatternsaccompanying
dike intrusionasmanifestedalong
theInyo trendin thedetailedstructureof EarthquakeFault(Figure
3). Similar bimodal fracturepatternsoccur in other sitesabove
shallowdikes.The Taraweraeruptionof 1886in New Zealandwas
fedby a 30-km-longN30'E trendingbasalticdikewhosesegments
showa consistent
clockwiserotationof 15' (Figure1la) [Nairn and
/
R•tomahana
•
Cole, 1981]. Regionalmappingin the Taraweraarearevealstwo
Fig. 1la. MapofTarawera
Domecomplex
showing
observed
andinferred mainsetsof faultsorientedN 10'E andN45'E (Figure11b) [Wilson
et al., 1984]. A secondexampleisprovidedby groundcracksalong
positions
of enechelon
basalticdikesegments
(darklines)thateruptedin
1886.Map locationshownin Figure10b[afterNairnandCole,1981].
the trendof Little GlassMountain andadjacentrhyolite domesof
theMedicine Lake HighlandVolcanoin Califomia. The patternsof
vents and faults indicate a NE trending dike whose segments
rotation may be the consequences
of changesin rheology and rotatedclockwise [Fink andPollard, 1983]; in detail however, the
fracturepatternshowsa bimodal distribution(Figure 12). These
fracturingmodeof the crustin a regionof high heatflow.
The proposedmechanismof dike intrusioninto shearfractures patternsindicate possibleapplicationof the presentmodel, but
additionalstudyis requiredto fully ascertainthis suggestion.
explainsandis supportedby severalobservations.
1. The trends of surface fracturesin the Inyo area display Our studyalsooffers an explanationfor two controversialgeobimodaldistributions.This is apparentin the map of large-scale physical observationsin Long Valley caldera. The first case
faultsandfracturezones(Figure1b), aswell asin thedetailsof one concernsthe analysisof focal mechanismsfor threeearthquakes
fracturezone,theEarthquakeFault (Figure3). Althoughdirectin- that occurredin 1980 at depthsof 7-10 km, southof the caldera
clinationsare difficult to measure,all exposedfracturesarevery (locationsshownin Figure la). One interpretationimplies that
steep to vertical. We interpret these fracturesas incipient sub- these are double-coupleshear events associatedwith complex
verticalstrike-slipfractureswhichhavebeendilated.The vertical shearsurfaces[Wallace, 1985; Lide and Ryall, 1985; Priestly et
attitude and the bimodal trend distributionsupportthe above al., 1985),whereasthealternativemodelsuggests
thattheseevents
suggestionthat the strike-slipstressconditionsexistedduringthe indicatedilation phenomenaassociatedwith rapid intrusionof
Inyo Dike intrusion(equation6); however,unambiguous
sheardis- magmaintoNNW-SSE trendingcracks[JulianandSipkin,1985;
placementshave not been documented.
2. The ObsidianDome segmentof theInyo Dike seemsto rotate
?
graduallyas it rises. Surfacemappingsuggestsa trend of about
Rotoma
N18'E (Figurelb), whereasthedrill coreindicatesa trendof N06'E
at 620-m depth (Figure 2b) [Fink, 1985]. The inclinationof the
segmentis unknown.If therotationin theupper620 m is partof a
uniform, gradual rotation from the main Inyo Dike, then this
segmentshouldmerge with the N07øW trendingmain dike at a
depthof about 1200 m. The calculationsin the abovesectionfor
depthof thetransitionzoneindicated3 km; we regardthesedepths
as boundingvalues.
uawa,a
3. Most segmentsof the Inyo Dike appearto be rotatedclockwise,withthepossibleexceptionrepresented
by theNNW trending
fracture zone southeastof Deer Mountain [Mastin and Pollard, in
press](Figureslb and2). We speculate
thatthispreferredsenseof
rotationis causedby releaseof shearstressalongintrudedshear
fractures.Both clockwise and counterclockwisetrending shear
fractureswouldbe availablehi the transitionzone(Figure 10c).If
a clockwisetrendingfracturewere intrudedfirst by the magma,
thenshearstressparallelto thefracturewouldrelax.Relaxationof
the shearstresscausesa local rotationof the horizontalprincipal
stress axes in a clockwise
sense. Because such stress rotation
/
ß
0
t
5
I
10
I
15 km
I
39ø
increasesthetendencyof clockwisefracturesto be intrudedby the Fig. 11b. Mapof faultsinthevicinityof TaraweraComplex,NewZealand.
magma,theprocesswill amplifyitself,leadingto eventualdomi- Note bimodal distribution of orientations. Shaded areas, silicic volcanic
rocks;dashedline, marginof caldera[afterWilsonet al., 1984].
nationby one trend.
4332
R•c•s
^•o Franc:M•canmsM oF IN'mUs•oN OF•-
•
LAVA
I•o
D•rm
i
I BEDS •
/
NATIONAL
/
MONUMENT
/
N
/
/
/
/
/
/
/
/
/
0
OREGON
/// /////
5 km
I
/
/
/
/
/
CALIFORNIA
i NEVADA
/
I
/
I
I
/
/
I
/
I
/
I
i
/
I
I
I
I
I
I
/
/
/
/
/
N
/
/
/
/
/
/
0
100
200
meters
Fig.12.Mapshowing
ground
cracks
overinferred
northeast
trending
silicicdike(s)
northeast
ofLittleGlass
Mountain
rhyolite
flowon
theMedicine
Lake HighlandVolcano,California.Features
indicatedon the insetmap includeLittleGlassMountain(LGM), Big
Glass
Mountain
(BGM),CraterGlass
Flow(CG),Medicine
Lakedacite
flow(MF),Medicine
Lake(ML), caldera
margin(dottedline),
andground
cracktrends
(dashed
lines).Onmaincrackmap,segments
withmorethan5-mhorizontal
separation
indicated
bydotted
lines. Note zigzagpatternof cracktrends.
Chouetand Julian, 1985]. The secondinterpretationis in accord of 8-3 km. The observedsurfacedeformationwouldrequire0.39with thepresentanalysisthatpredictsextensionalfracturingdueto m inflation of the sill and 0.15 m for the dike.
The model of Savageand Cockerhamraisesthe questionasto
magmaintrusionasdeepas 10 km.
The second set of controversial
observations involves recent
whymagmashouldrisefromdepthsof 12km towithin3 km ofthe
on
deformationdata collectedwithin Long Valley caldera.Savage surfacewithouterupting.If anintrusionin 1983haddimensions
and Cockerham [1984] showed that ground deformationthat the order of tens of centimeters, it would have frozen before
occurredin 1983couldbeexplainedby thedilationof anintrusive reachingthesurface.However,ouranalysisindicatesthatevenfor
bodyextendingfrom a depthgreaterthan 10 km to a level about3 a width on the orderof 10 m (for which the coolingrate wouldnot
km below thesurface.Althoughtheexplicitshapeof theintrusion be significant),anintrusioncouldnotreachthesurfaceunlessthe
exceeded
thehostrockfracturestrength
by at
couldnotbeuniquelyresolved,theyindicatedthatthedeformation volatileoverpressure
by thepatternof Holocouldbe accountedfor by inflation of a sill inclined30' between least18 MPa. This constraintis supported
depthsof 12 and8 km thatfedaverticaldikeextendingfromdepths cene silicic activity in the Inyo and Mono Cratersareaswhere
RECHE$ANDFINK: •¾[ECI{ANISM
OFINTRUSION
OFTHEINYODI•
magmaapproachedthe surfacein severallong dikesbut erupted
onlyfromwidepipelikeventssuchastheonepenetrated
bydrilling
beneath Obsidian
Dome.
CONCLUSIONS
o1- o3= (E/Eo)•/•
exp[(Q+ PV)/(nRT)]
4333
(A2)
whereo2ando3arethemaximum
andminimum
principal
stresses,
E is thestrainrate,Eoandn arerockconstants,
Q istheactivation
energy,V is the activationvolume,P is the pressure,R is the gas
constant,and T is the temperature[see also Kirby, 1983].
FollowingLynchandMorgan [ 1987, Tables 1 and2], n = 3, PV =
The analysespresentedhere indicatethe following:
1. Stressfieldsof continentalscalemay prevail andcontroldike
293J/molkm,andforsiliceous
rocks,
Q= 1.4x10
• J/molandEø=
orientationevenin thevicinityof largeandactivetectonicfeatures.
2.5x10-8MPa-3s'•. By substituting
thesevaluesandthetempera2. Variations in crustal rheology and the related variation of
turesderivedfrom (A1) into (A2), we determinethe lowerpart of
fracturing style may cause segmentationand rotation of dikes
the strengthcurvesshownin Figure 6.
without direct rotation of the stress axes. Thus trends of dike
The third stepis determiningthestrengthof thebrittlepartof the
segmentsmay be indicators of rheology as well as of stress
crust
due to frictionalresistancealongshearfractures.For extenorientation.
sionalconditions
it is5.5MPa/km [LynchandMorgan,1987].This
3. Dike geometryprovidesboundsonthemechanical
parameters
strengthcomposesthe upperpart of the curvein Figure6.
of intrusion.For the Inyo Dike we find that extensionalfracture
strengthis 1-2.5 MPa, the elasticresistanceto dike intrusionis
Acknowledgments.The authorsthankRoger Denlinger,David Pollard,
about14 MPa, thevolatile overpressure
in the magmachamberis AgustGudmundsson,
MichaelMalin, andCurtisManleyfor helpfulcom14-18 MPa, andthepressuredropin thepropagatingdike is about ments, Matt Golombek and Mark Zoback for constructivereviews, Sue
Selkirkfor draftingthefigures,andNina De Langefor editorialassistance.
0.55 MPa/km.
by Departmentof EnergygrantDE-FG02-85ER43320
4. Propagationof dikesbecomesincreasinglydifficult as they Researchsupported
aspartof theInyo ScientificDrilling Program,NSF grantEAR 8309500,and
nearthe surfacedueto theupwarddecreasein tensilestrengthand NASA grantNAGW 529 from thePlanetaryGeologyProgram.
thecorresponding
reductionin tensilestressmagnitude.Cessation
of dike rise may thus result from an upward decreasein the
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