Scholz, 1988 B-Ptransition

8/17/2019 Scholz, 1988 B-Ptransition

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319

Geologische Rundschau 77 /1 ] 319--328 ] Stuttgart 1988

T h e b r i t t l e p l a s t i c t r a n s i t i o n a n d t h e d e p t h o f s e i s mi c f a u l t i n g

By C. H. SCI-IOLZ,Palisades*)

With 4 f igures

Zusammenfassung

Ein einfaches rheologisches Modell ftir Schervorg~inge n der

LithosphEre, das eine weite Akzeptanz erreicht hat, ist das

Zweilagenmodell m it einer oberen sprSden Z one, in der De-

formation tiber Reibungsgleitung entlang diskreter St6rungs-

fl~chen stattfindet, und einer unteren d uktilen Zone. H ier er-

folgt die De for m atio n d utch plastisches Flief~en. Beide Zo-

hen wer den durch einen abrupten spr6d-plastischen Obergang

voneinander getrennt, der vermutlich durch die untere G renze

der nac hweisba ren Seismizit~it angeze igt wird. Expe rimentelle

Un tersuchu ngen wie auch die Deformationsgeftige in Mylo-

niten zeigen hingegen, dai~ ein breites lJbergangsfeld m it semi-

spr6dem Verhal ten zwischen diesen beiden Extremen l iegt .

H ier befindet sich ein B ereich ,,gemischter


2/10

3 2 0 C . H . S CH OL Z

L ' & u d e d e s s t r u c t u r e s m y l o n i t i q u e s a i n s i q u e l e s m e s u r e s

e x p & i m e n t a l e s i n d i q u e n t c e p e n d a n t q u ' u n l a r g e c h a m p d e

transi t ion ~ caract~re , .

K p a T K 0 e c o ~e p x ~a H H e

On14car~a peoa mr14 ,~ec~aa M ozm m, ~a ~ 143yqeH14~ qbeHo-

MeHa IleqbopMaIa14Hwm~a c~IB~ra (cI T2 ), T. e. 14axo~r~Tc~ Ha 1414~r~efI rpa H~ t~e ~14Ha-

M 1 4q ec Ko ro n o B e ~ e r m a ~ p e r m z ~ p er1 40 H e c n o ~ y x p y n -

KHM COCTO~IHHeMMaTep14ayia~ ~TO np14M ep140 COOTBeTCT-

ByeT MaK cHM yMy C14JIt,I 3eMJIeTpflceHH~.

3 o H a M e x ~ y T 1 H T 2 n p o ~ B J ~ e T M e 1 4~ m m ee cs ~ n o B e ~ l e -

14~e N01aCTW-tHO~I xeKyqecT14 B nep 40~I M e ~ I y Ce~C-

M14qeCKO ~I aKTHBHOCTBtO 4 ~14HaM14tIeCK14M cK onb YK e-

HH eM BO BpeM ~l 6OJIBILIHX 3eMJIeTpflceH14I;I.

~)Ta 301-Ia xapaK Tep1 43yeT c~I np14cyT CTB IaeM MHYIOH14TOB

14 TeCHO CB~I3aHHbIX C H14MH nCeB~OT paXHTO B~ a Tagx ~e

0 6 pa 30 B aH / Ie M c g p o c o B . K p o M e

TOFO,

B 3O He n e p e x o ~ a

T1 t l3MeH~IeTCSI Mexa14H3M o6pa3oBaH14It 6 p e~ 1 4 k Tp e-

H14f l. ~)TO 143Me14eH14e BblpaX


3/10

The brittle-plastic transition and the depth of seismic faulting 321

I

W

r ~

STRENGTH

TLE

DUCTILE

B R I T T L E

D U C T I L E

T R A N S I T I O N

Fig. 1. A simple m od el for the rheo logy o f the lithosphere.

th is m ode l w i th obse rva tions of the de form a t ion m e-

chanisms of fau l t zone rocks and ear thquake hypo cen-

tra l depth dis t r ibut ions and found a rough corres-

po nd enc e be tween the br it tle-plas tic t rans i t ion pre-

dicted b y this mo del , the depth a t wh ich evidence for

crys ta l plas t ic i ty can be found in faul t rocks , and the

m ax im um d epths of earthquakes. This seemed to pro-

v ide s t rong co nf i rma t ion fo r th is mo de l and so detai l-

ed re f inements and appl ica t ions were made , in which

of ten minor va r ia t ions in the depth d i s t r ibu t ion of

seismicity were, for example, ascribed to variations in

hea t flo w (SIBSON, 19 84 ; DOSER & KANAMORI, 1986;

SMITH & BRUHN, 198 4).

M ore recent ly, a nu m be r o f fund am enta l dif ficul ties

in this s imple m ode l have been pointed out . H oBBs e t

al. (1986) an d STI~EHLAU 19 86 ) have no ted th at m os t

of the r eg ion in the lower pa r t o f th i s mo de l does no t

cor re spond to the h igh t empera ture f low reg ime but

rathe r to sem i-britt le de for m atio n (CARTER & KmBY,

1978). Thi s i s a mixed m ode of de form a t ion for wh ich

the f low law is no t kn ow n for any ma ter ia l bu t w hich

is fundam enta l ly d i f f eren t f rom h igh t empera ture f low

in that it has a pressure sensitive strength (KIRBY,

1983) . As a consequence , the extrapola t ion of high

tempera ture f low laws into the region of the br i t t le -

plastic tran sition is no t valid. Ru'rT~i~ (19 86 ) has

discussed in de tai l the pro blem s in the use of the te rm

>~brittle-ductile transitiom< fo r wh at is pr op erl y a

britt le-plastic tran sition in the mo del show n in Fig. 1.

The t e rm duc t i l i ty r e fe r s on ly to the prope r ty of

bein g able to sustain a substantial strain with m acro-

scopica l ly hom ogen eous d e forma t ion and i s the re fore

no t mechanism-specific, app lyin g equ ally to semi-

br i t t le and plas t ic deformation. He a lso points out

tha t the t rans i t ion is not abrupt : be ing ini t ia ted by a

trans i t ion f rom br i t t le faul t ing to ca tac las t ic f low

(semi-britt le beh avio r) in w hic h the streng th is stil l

pressure sensi tive, and b e ing con clude d by a t rans i t ion

at greater depth to plasticity, the latter transition oc-

curr ing near the peak in s t rength.

HOBBS et al. (198 6) an d ST~eHLAW 19 86 ) ther efo re

proposed three l aye r mode ls in which the p la s t i c a l ly

f lowing region was separa ted f rom the br i t t le region

by a t rans i t iona l layer of po or ly defined, semi-bri tt le

rheology . In an independent deve lopment , Ts~ &

Rice (1986) explored a model based ent i re ly on a ra te

and state variable friction law similar to that f irst de-

scr ibed by DmTRICH (1978) , in wh ich the y were able

to show tha t th e r e s t r ic t ion o f ea rthquakes to sha l low

depths could be comple te ly expla ined by a t rans i t ion

f rom ve loc i ty weakening to ve loc i ty s t r engthening

with increasing temperature, as predicted by the ex-

per im enta l da ta of STESKY (1975) , w itho ut any re-

quirement for a br i t t le -duct i le t rans i t ion. These two

deve lopments r emoved the unde rp innings of the

lower pa r t o f the m ode l show n in F ig. 1 and l ead one

to suspect tha t the apparent success of tha t m ode l was

mis leading, and tha t the physics of the t rans form ation

fro m se ismic to aseismic faul t ing is fa r mo re com plex.

Th e pu rpose of this paper is to discuss the br i t t le -

plas tic t rans i t ion in m ore de ta il , for bo th the case of

bulk deformation and f r ic t ional s l iding, and to deve-

lop the re f rom a mode l tha t i s more cons i s ten t w i th

these recent findings and the relevent observational

f a c e s .

T h e b r i t t l e - p l a s t i c t r a n s i t i o n

Th e br it tle-plas tic t rans i t ion is usua l ly und ers too d

to mean the t r ans i t ion f rom ent i r e ly br i t t l e behavior

to de forma t ion tha t occur s en t i r e ly by c rys ta l l ine

plasticity. T his transition , even for the simplest crys tal

types , cann ot o ccur a t a surface in P-T4 space but m ust

occur ove r some f i e ld w i th in which the de forma t ion

occurs by a mixture of these processes (PATERSON,

1978). Th is is th e semi-brittle field, referred t o earlier.

Also, since we are here dealing with faults , we must

con sider two cases of the brittle-plastic transitio n, th e

t r ans i tion a s i t occur s in the b u lk d e forma t ion of the

rock, and the t rans i t ion as i t occurs in f r ic t ional s l id-

ing . A t some sha l low depth , f au l t ing occurs pr im ar i ly

by f r ic t ional s l iding (with, presumably, some dis t r ib-


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322 C . H . SCHOLZ

uted de forma t ion w i th in i ts zone of wear produc ts ) by

the mechanism of br i t t le f rac ture of contac t ing asper-

i t ies . At suff ic ient depth, the same deformation takes

place as plas t ic f low in bulk as a con t inu um with in an

associated ductile shear zone. In the transition be-

tween these extremes there is l ike ly to be a region in

which the de forma t ion t akes p lace pa r t ly by f r i c t ional

s l id ing and pa r t ly by bulk de forma t ion . I t i s a com-

m on misconcept ion in geology to cons ide r fr i c tion to

be synonymous wi th br i t t l e behavior , whe reas the

br i t t le process was only involved in the formation of

the s l iding surfaces , and not necessar i ly with the ir

cont in ued s lip. Fr ic t ion of meta ls , for example , occurs

a lmost ent i re ly by the plas t ic deformation of contac-

t ing asper it ies. Thu s the presence of duct i ly deform ed

rock in a faul t zone cannot be used to rule out f r ic -

t iona l s l iding as a contr ibut ing, or even major , me-

chanism of t r anspor t .

The br i t t l e -p la s t i c

t r a n s i t i o n f o r b u l k d e f o r m a t i o n

The br i t t le -plas t ic t rans i t ion for any polycrys ta l l ine

mater ia l wil l take place in a f ie ld somewhat l ike tha t

shown schematica l ly in Figure 2, in which plas t ic i ty

is favored by elevated temperature and pressure. The

br i t t le regime is separa ted f rom the regime of ful l

plas t ic i ty by a semi-br i t t le fie ld in which the deforma-

t ion occurs by a mixture of br i t t le and plas t ic pro-

cesses . For monominera l ic rocks , the width of the

semi-bri t tl e f ie ld w i ll be & m ark ed by the condi t ions

und er whic h the eas iest s l ip sys tem becomes ac t iva ted

on the one s ide and on the other those in which suff i -

c ient s l ip sys tems become ac t iva ted to sa t is fy the von

Mises-Taylor criterion for fully plastic flow (PaTER-

SON, 1978) . For mu l t i - comp onent rocks the semi-

br i t t le f ie ld wil l typica l ly be broader , owing to the

ductili ty contrast of the different mineral species.

The rheology through the semi-br i t t le f ie ld is bes t

il lustrated for calcite marble, which has been studied

across the ent i re f ie ld a long the constant tempera ture

pa th A-B by SCHOLZ 1968) and EDMOND & PmERSON

(1972) . At ro om temp era ture this ro ck typ ica l ly passes

into the semi-br i t t le f ie ld a t qui te low conf ining pres-

sure, in wh ich the beha vior is macro scopica l ly duct ile

but th e interna l con tr ibu t ion of br i t t le processes is re -

vea led by pronounced di la tancy and a s t rong pressure

sensi t ivi ty of the s t rength ( in the exper imenta l l i te ra-

ture this behavior is often referred to as cataclastic

f low, but we avoid this te rm here because i t might

cause confus ion wi th the mechanism of forma t ion of

ca tac las t i tes , which are predominant ly wear products

of friction al sliding). As co nfin ing p ressure is raised,

di la tancy is suppressed and the pressure sens i t ivi ty

decreases, indicating that the role of plastic processes

is increasingly dominant over britt le processes. Final-

ly, a t some cr i t ica l pressure both di la tancy and the

pressure sens i t ivi ty vanish and the rock has entered

the ful ly plas t ic f ie ld. The width of the semi-br i t t le

f ie ld a t room tempera ture is typica l ly about 300 MPa.

Rheologica l da ta of this qual i ty is not ava i lable for

the more refractory silicates in the semi-britt le field.

By infe rence f rom mic roscopic s tud ies o f de form a t ion

textures, however, we can trace the same transition in

~ 1 ~ P L A S T I C

~ N I ~ /F U L L PLASTICITYOF

::D N ~ i ~ OST BRITTLECOMPONENT

~ li~ E M IR I T T L E

A - ~ - B

ONSETOF PLASTICITYOF

ii~ MOST DUCTILECOMPONENT

P R E S S U R E

Fig. 2. Schematic diagram of the

b r i t t l e - p l a s t i c

transition for bulk flow.


5/10


the de fo rma t ion of g ran it e th a t was s tud ied a long the

pa th C-D by TULLIS & Yt~ D (1977, 1980). Fo r d ry

grani te they found tha t the semi-br i t t le f ie ld was

ente red a t abou t 300-400 ~ wi th the onse t o f f low in

quar tz . As tempera ture was increased there was a

gradua l t r ans i t ion f rom abundant mic roc racks , to a

uni form dens i ty of d i s loca t ions w i th r ec rys ta l l i z ed

gra ins and no microcracks , and tha t dis loca t ions did

not becom e dom inan t in f e ldspa r un t i l 550- -650 ~ For

wet granite these transition temperatures were reduced

by 150--200 ~ for b oth feldspar and quar tz .

These experimental results are difficult to extrapo-

la te to na tura l condi t ions , so for the present we must

re ly on geologica l observa t ions to es t imate the condi-

t ions un der wh ich the br it tle-plas tic t rans i t ion occ urs

in na ture . Since both quar tz and fe ldspar have only

limited slip systems, fully plastic flow in those ma-

ter ia ls cannot occur by gl ide a lone , but must be asso-

c iated w ith re cov ery and recrys ta l l iza t ion. F or qua r tz ,

this appears at ab ou t 300 ~ (VoLL, 197 6; Kn~RICH et

a i. , 1 977 ) , and for fe ldspar , a t ab ou t 450--50 0 ~

(WHITE, 19 76; VOLE, 1976 ) . Th us qu ar tz begins to

f low a t abou t the begin ning o f greenschist fac ies me-

tam orph ism, bu t f eldspar does no t beg in to f low unt i l

wel l into the am phib ol i te grade . We take 300 ~ and

450 ~ then , a s the u ppe r and lower bou nds of the semi-

br i t t le f ie ld for quar tzo-fe ldspathic rocks . Between

these two states these rocks behave as composite

materials, w ith qu artz flo win g and the feldspar re-

spon ding in a r ig id , b r i tt l e manne r , fo rmin g porphy -

roc las ts , as is so commonly observed in myloni tes .

Any ex t rapola t ion of a f low law f rom the fu l ly

plastic field into th e semi-britt le field, as was don e in

the m od el illustrated in Fig. 1, will always un der-

es t imate the s t rength there , and tha t underes t imat ion

wil l worsen the fur ther the extrapola t ion is taken.

This is because, as we traverse this field from D to C,

say, plastic m ech anis m s will gradu ally be eliminated,

f i r s t in one component and then in anothe r , which

wil l increase the f low s trength, and microscopic br i t -

tle processes will become increasingly necessary to ac-

com m oda te the st ra in , and which ca r ry w i th them a

pressure sens i t ivi ty of s t rength, w hich was no t inc lud-

ed in the extrapola t ion.

T h e b r i t t l e -p l a s t ic t r a n s i t i o n f o r f ri c t i o n a l s l i d i n g

Just as in the above , where we considered enter ing

the t rans i t ion to the semi-br i t t le f ie ld f rom below, for

th i s p rob lem we mus t a l so cons ide r wha t occur s when

the semi-br i t t le f ie ld is entered f rom the br i t t le s ide

above . On ly in th is c a se we m us t cons ide r h ow i t af -

fec ts f r ic t ional s l iding, s ince tha t is the condi t ion of

deformation tha t occurs there . That is : what a re the

changes in f r i c t ion tha t o ccur when the m echanism o f

shea ring o f asperities changes fro m britt le fracture,

which commonly domina te s f r i c t ion in s i l i c a te rock

at low temperature, to plastic flow, as occurs in the

fr ic t ion o f metals, and a t high tem pera ture , for rock?

As far as it affects the gross frictional strength, the

answer is : no t a t a l l . This is because i t i s fundam enta l

to f r ic t ion th a t the real a rea of con tac t , A is a lways

les s than the nom ina l a rea A , and i s de te rmined b y a

s t rength parameter c lose ly re la ted to the s t rength re -

quired to shear th rou gh A r (BoWDEN& TABOR, 1964).

Since A increases with no rm al s t ress , so mus t the

shear s t ress required fo r s l ip, in a jus t com pen sa t ing

wa y so tha t the s t reng th can be descr ibed with a sim-

ple f r ic t ion coefficient . Fo r this reason roc k f r ic t ion is

independent of l i thology and tempera ture (BYERLE~,

1978; SCHOLZ, 1977). We sho uld therefo re no t expect

tha t the re should be an abrupt t r ans i tion f rom f r i c t ion

to bu lk de forma t ion a t the po in t whe re the f i r s t mi -

nera l becomes duct i le , as is implied in the model

shown in Fig. 1, s ince this t rans i t ion wil l only take

place when the f r ic t ion surfaces become welded, i .e .

A = A , which can be expected to occur on ly much

fur ther into the semi-br i t t le f ie ld. So be low the point

a t which the f i rs t yie lding and f low of minera ls is

observed s t rength should cont inue to increase l inear ly

wi th pressure a long a no rm al f r ic t ion curve . Th e peak

in s t rength should be expected wel l within the semi-

br i t t le f ie ld and no t a t its uppe r bo und ary, as indica ted

in Fig. 1.

The re a re , however , oth er im po rtan t e f fec ts of the

tran sition on friction . T he effect of the britt le-plastic

t r ans i tion on f r i c tion i s show n schem a t ica l ly in F igure

3 . The t r ans it ion a long the p a th A-B was s tud ied b y

SHIMAMOTO (19 86 ), usin g halite as a n ex per im ent al

gouge mater ia l sandwiched be tween sandstone sur-

faces in triaxial fri cti on experimen ts. Since halite be-

comes duct i le a t modera te pressures and room tem-

perature, these experiments are analogous to the mar-

ble exper iments descr ibed above . At the lowest

pressures he found tha t the f r ic t ion was ve loc i ty-

weakening ( the ve loc i ty dependence of f r i c t ion i s

negative) and hence unstable, exhibiting stick-slip. At

higher normal s t ress , when the ha l i te had entered i ts

sem i-britt le field, the rh eo lo gy was stil l fr ictional, in

the sense tha t s t r ength con t inued to r is e sha rp ly w i th

con f ining pressure, b ut th e s ign o f the ve lo c i ty depen-

dence changed , i e f r ic t ion became ve loc i ty-s t rength-

ening, and hence stable. Finally, at the highest pres-

sures, wh ere th e halite was in its fully plastic field, the

s trength of the san dw ich becam e insensit ive to

pressure. A t tha t p oin t t rans la t ion o f the op pos ing sur-


6/10

324 C .H . SCHOLZ

faces was taking place by cont inuous plas t ic shear of

the ha l ite layer, whic h h ad co m ple te ly welded the sur-

faces (SHIMAMOTO& LOGAN, 1986).

Fr ic t ion of grani te w as s tudied a long the pa th C-D

to 700 ~ by ST~SKY 197 5, 1978). H e fo un d the same

pa t te rn , in which a t low tempera ture the f r i c t ion

show ed ve loc i ty-weaken ing and s tick-sl ip, b ut tha t

above 300 ~ wh ere quar tz begins to f low, i t becam e

ve loc i ty- s t r engthening and s tab le . He found tha t the

rheology was f r ic t ional , wi th a s t rong pressure e ffec t

on s t rength, a t a l l tempera tures s tudied, but tha t this

effect was dim inish ed at the high est temperatures. Th e

mo del of Tsz & RICE (1986) was based o n Stesky's

results.

Th e onse t of plas t ic i ty in th e sem i-br i tt le f ield is

thus seen to co inc ide w i th a change f rom ve loc i ty-

weakening to ve loc i ty- s t r engthening in f r i c t ion and

hence to a t rans i t ion f rom an unstable f r ic t ional f ie ld

to a s table f r ic t ional f ie ld. Wh en asper i ty deform ation

is la rge ly br i tt le , ve loc i ty-w eakening can ar ise f ro m a

c lass of environmenta l ly a ided processes of the type

discussed by SCHOLZ & ENGELDER (19 76 ) and DIET-

RICH (1978) . W he n asper it ies beco m e duct ile, how -

ever , they de form accord ing to a f low law w i th an in -

t r ins ic pos i t ive s t ra in ra te dependence and the cor-

re sponding f r i c t ion becomes ve loc i ty- s t r engthening

R A B I N O W I C Z , 1965; SHIMAMOTO,1986) . The t rans i t ion

to cont inuous f low, however , occurs a t much higher

tempera ture and pressure where the surfaces become

welded, nearer the t rans i t ion to ful l plas t ic i ty for bu lk

de forma t ion .

The t rans i t ion f rom unstable to s table f r ic t ion thus

appear s to co r re spond to the t r ans i tion f ro m br i t tl e to

semi-bri tt le beh avior o f the roc k. T here is a lso an im-

por tan t change in the mechanism of wea r a t th i s

bounda ry . A t low tempera ture s wea r occurs by the

br i t t le f rac ture of asper i t ies , resul t ing in the produc-

tion of loose wear particles. This is called abrasive

w e a r R A I 3 I N O W l C Z ,

1965) , and is the p r im ary mecha -

nism of generation of cataciastites. Wear stil l occurs

when the asperities deform plastically, as they would,

in part, in the sem i-brittle field, bu t this typ e of wear,

which i s commonly obse rved for the duc t i l e me ta l s

and is called adhesive wear, occurs by ductile shearing

ou t of asper it ies , of ten with t ransfer of m ater ia l to the

oppos i t e sur face . This wea r mechanism would thus

resul t in rocks with myloni t ic fabr ics and micros truc-

ture , even though the mac roscopic behavior of the

fault was stil l fr ictional. Thus the first appearance of

myloni t ic rocks cannot be taken as f i rm evidence tha t

the re la t ive motion across the shear zone is taken up

ent i r e ly by bulk shea r a s a cont inuum in the shea r

zone . Often, for example , the rocks in shear zones in

the semi-bri tt le f ie ld a re S-C mylon i tes , wh ich con ta in

discrete planes (the C planes) which offset markers

and a long w hic h s lip has thus occu red (e .g. Lis-rn< &

=

~FRCTIONAL PLASTC

I ~ CONTNUUM

STABLE ~ FLOW

\ AD.ES,VE

.

-

I d N S E T O F

r

W E L D I N G

r

I I

P L A S T I C I T Y O F G O U G E

P R E S S U R E

Fig. 3. Schem atic diagram of the brittle-plastic transition for frictional sliding.


7/10


SvoK~, 1984) . In these cases , though the deformation

is dear ly not br i t t le , the shear zone may s t i l l be par-

tially frictional in its character, which in terms of its

rheology means tha t i ts s t rength is s t i l l pressure

dependent .

A s y n o p t i c sh e a r z o n e m o d e l

We are now ready, based on the points made above ,

to incorpora te some improvements in the s imple

mo de l o f Fig. 1 and to deve lop a somewh a t m ore r e -

a l is t ic , though necessar i l ly more complica ted, model

of a shea r zone , which is shown in F igure 4 . Thi s m o-

del is intended for quar tzo-fe ldspathic rocks , so the

pr inc ipa l f iducia l p oints , s ho wn on the le ft ax is , a re

300 o and 450 ~ t aken a s the onse t o f qua r tz and

feldspar plasticity. The depth axis is based on the as-

s u mp t i o n o f a c o m m o n l y us ed g e o t h e rm mo d e l f o r

the San An dreas fault (LAcH~N~UCH & SASS, 1980,

m od el B). This d epth sca le sho uld no t be regarded to o

ser iously s ince even for mu ch of the San And reas faul t

i t unde re s tima te s the d epth o f the t r ans i t ions by 3- -5

k m .

Th e 300 ~ isotherm is taken as T1, the t rans i t ion

from br i t t le to semi-br i t t le behavior . The semi-br i t t le

f ie ld is bounded by T1 a t the top and by the t rans i-

t ion to ful l plas t ic i ty a t T~, a t the bot tom, where

feldspar beco m es plastic. T he tran sition f rom cata-

clastites to m ylo nites (S~BsON, 197 7) occ urs at t he up-

per boundary, T~, which, however , is not a t rans i t ion

f rom f r i c t ion to bu lk f low but a t r ans i t ion f rom

abrasive to adhesive wear, in which the latter is do-

minated by duct i le f low within a f r ic t ional regime.

The a sym met r ic hourg la s s shape of the shea r zone i s

somewhat fanc iful , and is based on a wear model

(ScHoLZ, 198 7) in w hich wear ra te and thus faul t

thickness increases with no rm al s t ress , and h ence

depth. The neck in the hourglass is caused by the

change in wear mechanism, s ince usual ly adhesive

wear is assoc ia ted with much lower wear ra tes than

abrasive

wear (RABINOWICZ,

1965). Th ere is no da ta a t

present to suppor t this idea , and even in the upper

pa r t the re a re obse rva t ions of bo th th ickening and

th inning of f au l t zones w i th depth (F~vG & McEvIL-

~Y, 198 3; ANDERSON et al., 198 3). The hy po the tica l

shape shown would on ly occur i f the rock was of

un iform com po si t ion over a ll depths (ScHoLZ, 1987)

and w ould on ly b e preserved in the case of s tr ike-s lip

faulting.

Th e se ismic b ehav ior o f the faul t is descr ibed us ing

the f r ic t ion rate param eter A -B (RuINA, 1983). I f A-B

is negative, frictio n is velo city-w eake ning and instable;

if i t is positive, i t is velocity-strengthening and stable.

This parameter is plot ted schematica l ly in the middle

frame of Figure 4, and follows c lose ly the in pu t m ode l

b of TsE & Ric~ (1986) , which was based on the re -

sults of SWSKY (1975). We have, in add ition, add ed a

region o f ve loc i ty-s t reng thening near the surface . W e

expect this be havio r because of the presence there o f

unconsol ida ted a nd/o r c lay r i ch f au l t gouge . Such

materials are no t ob served to stick-slip in the labo-

ra tory, and this provides an upper s tabi l i ty boundary,

T4, to expla in why ear thquakes a re not observed to

nucleate at depths less tha n ca. 2 k m on w ell developed

faul ts . The lower s tabi l i ty boundary, where A-B be-

com es posi t ive a t depth, is appro xim ate ly a t T1, as in-

depend ent ly de te rmined f rom Ste sky 's r esu lt s. Thu s

A

( I [ ( D

a c ~ 3 0 0 ~

4 5 0=

Fig. 4. A

F R I C T I O N

G E O L O G IC F A U L T R O C K R A T E

F E A T U R E S M E C H A N I S M S B E H A V I O R( A - B )

S E I S M I C S T R E N G T H

B E H A V I O R

__ •CLAY

I

4 . . . G_O~E

--1 1K M T t ~ , '.~ J '.= ~ - -Q U A R T Z ~ , ~ , 4 = ~ 4 ~ S I T I O N

P L A S T I C IT Y ~ z

/ ~ /

t n Q ~ h

. . . .

A M P H I B O L I T E

( - ) T J + )

_ _ ~ _ ~ U P P E R

S T A B I L I T Y

/ l i l ~ N U C L E A T IO N

9 Z O N E

( S E I S M O G E N I C

I I ~ ~ L A Y E R )

O F L A R G E A R T HQ U A K E

~ 1 ~ 'L O W E R T A B I L IT Y '

M A X I M U M

R U P T U R E E P T H

( L A R G EE A R T H Q U A K E )

~ ~ L O N G ERM

I

/

S S

synoptic shear zone mo del, illustrating the major geological and seismological features.


8/10

326 C .H . SCHOLZ

ear thquakes can on ly nucleate be tween T 4 and T1,

which defines the seismogenic layer. Large earth-

quakes, which rupture the entire seismogenic layer,

a n d ma y a l s o c o mmo n l y b r e a k t h r o u g h t h e t h i n

stable re gio n above T 4 to t he surface, are m ost l ik ely

to o r igina te near the base of the se ismogenic layer

whe re A-B is a m in im um (TsE & RIcE 1986. ) This

same expec ta t ion i s ob ta ined f rom cons ide r ing the

dynam ics of rup ture propaga t ion in a s i tua t ion wh e re

s trength and s t ress drop increase with depth (DA s &

SCHOLZ, 19 83 ). Th at large earthquakes do indeed

typica l ly or igina te f rom near the base of the se ismo-

genic layer has been known for a long t ime, and this

fac t was former ly the source of some cons te rna t ion

(MACELWANE, 19 36) .

I f T 1 i s a bo und a ry be tween ve loc ity-weakening

and ve loc i ty-s t reng thening f r ic t ion, as is the thes is be-

ing explored he re , then mo de l ing has show n tha t dur -

ing a la rge ear thquake rupture wil l extend dynamica l-

ly w ell into the sem i-britt le field below T 1 (DAs,

1982; TSE & RICE, 198 6). As STRELAU (19 86 ) has

noted, seismological evidence is either ambiguous or

c ircular on this po int . Th e dep th o f the deepes t a f ter -

shocks wil l be l imited by T1, s ince tha t is the depth

l imit of nuclea t ion, but they do not necessar i ly, as is

so commonly assumed, de l inea te the tota l depth of

the m a inshock . Ne i the r s ei smic nor geodet ic me tho ds

have had sufficient resolut ion to def ine the m axim um

de pth of faulting. Fo r example, THATCHER (1975)

poin ted ou t tha t the geode t ic da ta for the 1906 San

Francisco earthquake are insufficient to resolve slip

benea th 10 km a t the 1 m leve l. Th e m os t r ecent

seismological techniques appear to bear out this pre-

dictio n, however. J . NABELEK pets. co m m ., 1987) has

foun d, in the case of the 1983 Borah Peak earthquake ,

s ignif icant moment re lease down to a depth of 16

km s, whereas the a f te rshocks cut off abru pt ly a t 12

kms .

We thus con clude tha t large earthquakes wil l pro-

pagate be low T 1 to som e grea ter depth, T 3 and tha t

the region be tween T 1 and T3 is one of a l te rna t ing

behavior , wi th co-se ismic dynamic s l ip and inter-

seismic semi-britt le flow. Th ere is a grow ing bo d y of

geological evidence for such an alternating zone, con-

s is ting of shear zones in wh ich m yloni tes a re fou nd in-

te r laced with pseudotachylytes and brecc ias (SmsoN,

1980; STEL, 19 81 , i986; WEN K ~ WEISS, 19 82 ; PAS-

SCHIER, 1984); HOBBS et al. ( 19 86 ) developed a m od el

of duct i le ins tabi l i ty in an a t tempt to expla in this

phenomena. Their model , however , shows tha t i t i s

unl ike ly for such an ins tabi l i ty to ini t ia te within the

a l te rna ting zone . Assuming the rh eolog y of we t qua r t -

zite and a strain rate of 10-12sec-1, they found that

flow was stable at temperatures greater than abo ut

200 ~ i .e . wel l above T 1. Th us one m ight n ot ex-

pec t

nucleation

with in the a l t e rna t ing zone , bu t one

can use the i r mode l to show tha t an ea r thquake

should be expected to

propagate

well into this zone .

An ea r thquake impinging on T I f rom above wi l l im-

pose there a strain rate some 108 times the in-

terseismic rate, so that the co-seismic strain rate will be

abou t 10-4sec -1, which f rom the ir m odel w il l a llow

progagat ion to much grea ter depth.

The consequences of th i s mode l on the s t r ength of

the l i thosph ere is show n on the r igh t f rame of Fig. 4.

The shear zone s t rength is f r ic t ional f rom the surface

to T3, so it increases w ith dep th over that interval. T 1

represents a change in the m icrom echa nism o f f r ic t ion

f rom br i t tl e to duc t il e which p roduces a change f rom

veloc i ty-weakening to ve loc i ty-s t rengthening and

fro m abrasive wear to adhesive wear, bu t n o significant

break in th e s t rength profi le . HoBBs e t a l . (1986) and

SVRELAU (198 6) bo th intr od uce d transitio nal region s

in the ir s t rength prof i les but for unexpla ined reasons

assumed tha t th e s t rength w as constant be low T 1. As

was pointed out above , however , as long as the

behavior is essentially frictional, regardless of the

micromechanism, s t rength should increase approx-

imate ly l inear ly with normal s t ress , and hence depth.

Thu s the peak in s tr ength shou ld no t occur a t T~ but

a t some greater dep th w here welding has occurred. We

place this approx imate ly a t T 3. Below this depth we

expect the s t ren gth to sag, joining a high tempera ture

f low law a t T 2. Th e welding and s t rength decrease

be low the peak i s p robably no t p roduced by p la s t i c

flow alone, but is aided by , ,pressure solution


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T h e b r i t t le - p l a s ti c t r a n s i t i o n a n d t h e d e p t h o f s e i sm i c f a u l t in g 3 2 7

R e f e r e n c e s

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328 C .H . SCHOLZ

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Scholz, 1988 B-Ptransition

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