JOURNAL OF GEOPHYSICAL
RESEARCH, VOL. 98, NO. B10, PAGES 17,911-17,920, OCTOBER 10, 1993
Fault Strain and Seismic Coupling on Mid-Ocean Ridges
PATIENCE
A. COWIE,
1 CHRISTOPHER
H. SCHOLZ,
2 MARGOEDWARDS,
3 ANDALBERTO
MALINVERNO
4
Lamont-DohertyEarth Observatoryof ColumbiaUniversity,Palisades,New York
The contributionof extensionalfaulting to seafloor spreadingalong the East Pacific Rise (EPR) axis
near 3øSand between13øNand 15øNis calculatedusingdataon the displacement
and lengthdistributions
of faultsobtainedfrom sidescansonarandbathymetricdata. It is foundthat faultingmay accountfor of the
order of 5-10% of the total spreadingrate, which is comparableto a previousestimatefrom the EPR near
19øS. Given the paucity of normal faulting earthquakeson the EPR axis, a maximum estimate of the
seismicmomentreleaseshowsthat seismicitycan accountfor only 1% of the straindue to faulting. This
result leads us to concludethat most of the slip on active faults must be occurringby stable sliding.
Laboratoryobservationsof the stability of frictional sliding show that increasingnormal stresspromotes
unstablesliding, while increasingtemperaturepromotesstable sliding. By applying a simple frictional
model to mid-oceanridge faultsit is shownthat at fast spreadingridges(>90 mm/yr) the seismicportionof
a fault(Ws)isa small
proportion
ofthetotaldowndip
width
ofthefault(Wf).TheratioW•q,Vfis
interpreted
as the seismic coupling coefficient Z, and in this caseZ-- 0. In contrast,at slow spreadingrates (540
mm/yr),Ws--Wf,,andtherefore
Z-- 1, whichis consistent
with the occurrence
of large-magnitude
earthquakes
(mr,=5.0to 6.0)occurring,
forexample,
alongtheMid-Atlantic
Ridgeaxis.
INTRODUCTION
teleseismic detection threshold which generally lies in the
The use of high-resolution sonar mapping systems in the
ocean basins has revealed a pervasive fabric of normal faults
that dissectthe seafloor at mid-ocean ridges [Edwards et al.,
1991, Carbotte and Macdonald, 1990; Kong et al., 1988;
Bicknell et al., 1987; Crane, 1987; Searle, 1984; Laughton
range mb = 4.0-5.0 in this geographicarea [Riedesel et al.,
1982].
The teleseismic observations do not preclude
seismicity occurring below this threshold,but large-magnitude
earthquakesin this area are generally either strike-slip events
along transform faults [e.g., Kawasaki et al., 1985] or
and Searle, 1979; Macdonald and Atwater, 1978; Macdonald
intraplate events in young ocean lithosphere [Wiens and
and Lyendyk, 1977; Lonsdale, 1977; Lonsdale and Spiess, Stein, 1984]. However, although seismic deformation appears
1980; Klitgord and Mudie, 1974]. These faults developin a to make a negligible contribution to extension at fast
narrow zone at the ridge axis in responseto extension, and as spreadingcenters,the abundantscarpsof normal faults seenon
seafloor spreading proceeds they become inactive and are
sonar images of the seafloor testify that faulting does play a
preserved as irregular topography on the ridge flanks. The
significant role in the process of seafloor spreading and
fossil fault population on the ridge flanks therefore represents deformation of oceanic crust at all spreadingrates [Rea, 1975;
the extensional strain achieved in the active tectonic zone.
Searle, 1984; Macdonald and Luyendyk, 1985; Carbotte and
The contribution of fault strain to plate separationat slow Macdonald, 1990; Malinverno, 1991; Malinverno and Cowie,
spreading ridges has been estimated by summing the seismic this issue].
momentsof normal faulting earthquakesoccurringat the ridge
The purpose of this paper is to calculate the extensional
axis [Solomon et al., 1988]. Solomon et al. calculated that
strain representedby the fault scarpspreservedon the flanks of
seismic faulting could account for 10% to 20% of the total
the EPR and to compare it with a hypothetical estimate of the
spreadingrate for spreadingrates_<40mm/yr. However, at fast seismic moment release rate assuming no limitation to
spreading centers (>90 mm/yr) most of the earthquakesthat earthquake detection. The strain estimates obtained from the
have been detected occur in swarms of low magnitude events fault population represent the total brittle strain, i.e., both
seismic
and aseismic.
From
these calculations
we can
usually associated with hydrothermal circulation and/or
therefore
determine
the
ratio
of seismic
to aseismic
magmatic intrusions [Riedesel et al., 1982; Macdonald and
Mudie,
1974].
More recently Wilcock et al. [1992]
deformation,which is a measureof the seismiccoupling of the
documented microearthquake activity associatedwith faulting
faults. Bicknell et al. [1987] estimated the percentagefault
on the East Pacific Rise (EPR) but this activity is restricted to
strain on the EPR at 19øS by adding up the displacement on
the region of the overlapping spreadingcenter near 9øN. The
faults imaged along a 110-km-long high-resolution ridgespreadingcenters of the EPR are virtually aseismic above the
perpendicular bathymetric profile. Bicknell et al. estimated a
fault strain of 5.3% (4.2% on the Nazca plate; 6.4% on the
Pacific
plate). The method of summing fault displacementsin
1Nowat Department
of Geology
andGeophysics,
Edinburgh
a cross section assumesthat all the faults extend to infinity
University, Edinburgh, Scotland.
2 Alsoat the Department
of Geological
Sciences,
Columbia along strike. While this assumption is valid for the case of
University, New York.
perfect two-dimensional strain, which may seem a reasonable
3 NowatSOEST,
University
ofHawaii
atManoa,
Honolulu,
Hawaii. approximationfor a mid-ocean ridge, a reliable strain estimate
4 NowatSchlumberger-Doll
Research,
Ridgefield,
Connecticut.
requiresseverallines to be measuredand an averagevalue to be
Copyright 1993 by the American GeophysicalUnion.
determined. The approachused here, derived from the work of
Kostrov [1974], does not rely on the assumption of twoPaper number 93JB01567.
0148-0227/93/93JB-01567505.00
dimensionality because it uses information on both the
17,911
17,912
COW•EET AL.' FAULTINGON MID-OCEAN RIDGES
lengths and the displacementsof all the faults. The total fault
strain is the sum of the geometricmomentsof all the faults in a
deformed volume, where geometric moment is the
displacementon a fault multipliedby its surfacearea.
Summingthe geometricmomentsfor a large numberof faults
is simplified, in this study, by using a scaling relationship
betweenthe displacementon a fault and its length [Scholzand
Cowie, 1990]. A displacement-length scaling relationship
has already been demonstratedfor faults in continental areas
[Cowie and Scholz, 1992a]. This relationship is established
near 3øS on the EPR by correlatingfaults scarpsidentified in a
ridge-perpendicularbathymetric profile with a fault lineation
map produced from side scan sonar images. The strain
estimatesdependon the completenessof the data set for smallscale faulting which is a function of the resolution of the
mapping systemused. We show here how the effect of limited
systemresolutioncan be estimatedby using a functional form
for the distribution of fault lengths and assuming the
distribution can be extrapolated to sub-resolution-scale
faulting.
In this study, we have analyzed the length
distributions
of faults on the flanks of the EPR between
13øN
and 15øN and near 3øS using data from side scansonarimages.
The disparity between the calculated fault strain and the
seismic moment
central California, but in this case the seismicity representsa
small proportion of the total slip occurring on the fault
[Scholz, 1990, p. 312].
STRAIN CALCULATION
From Kostrov [1974] the amount of strain representedby a
populationof faults can be calculatedusing
k=l
where N ris the total number of faults in the populationand V
is thesizeof thefaultedvolume.Mijis thegeometric
moment
of each fault which is given by
Mij= Mo(•inj+ ni•)
where
8
is
a unit
(a)
vector
which
defines
(2)
the
sense
mo= d L Wf
(3)
whereL is the mappedlengthof the fault trace,Wf is its
downdip extent, and d is the displacementon the fault. The
maximum depth of faulting, t, is the depth of the transition
from predominantlybrittle deformationin the upper part of the
crust to ductile deformation at greater depth. Large faults that
break all the way through the brittle layer grow by increasing
theirlengthwhiletheirwidthWf remainsconstant,
i.e., Wf=
t/sin (0) (Figure 1). For small faults with lengthsless than the
dimension
t, the fault surface is approximately
equidimensional
sothatWf--L. Thesizeof thefaulted
volume
V is given by
V=At
inward-facing
outward-facing
fault
of
displacementon the fault, and n is a unit vector normal to the
fault plane. M ois the magnitudeof the geometricmomentand
is given by
release on the EPR is discussed in the context
of a frictional model for faults at mid-oceanridges. The model
is derived from laboratory observations of the stability of
frictional sliding; a model similar to that presentedhere has
already been consideredfor continentalfaults [Tse and Rice,
1986; Scholz, 1988a]. In this model, the portion of the fault
that can slide unstably, and thus produce earthquakes, is
determined by the position of frictional stability transitions
which are controlled by the stressand thermal regimes at the
ridge axis. The model predictsthat slip on active normal faults
at fast spreadingridges is occurring by stable, as opposedto
stick-slip, sliding due to the high geothermal gradient. Stable
sliding on faults may be associatedwith low-level seismicity,
as it is along the creeping section of the San Andreas fault in
(1)
f[ult
seafloor
base of brittle crust
(b)
FIG. I (a) Simplified model for normal faulting at the rise axis showingthe parametersusedin the straincalculation:0 is the
dipof thefaults;t isthethickness
of thefaulted
upper
portion
of thecrust;Wfisthefaultdimension
measured
downdip
in the
planeof the fault. (b) Simplifiedview of "smallfaults",which breakthroughonly a portionof the brittle crustand grow in
both strike and downdip directions,and "large faults" which grow only in their length dimension.
(4)
COWIE ET AL.: FAULTINGON MID-OCEAN RIDGES
where
A is the areal
extent
of the faults
17,913
used in the strain
calculation. An upper estimateof the total strain is obtainedif
we assumeA - D Lmax, where D is the width of the deformed
region measuredperpendicularto the ridge axis and Lmax is the
length of the longestfault. This value for A implies that at the
scale of the largest fault the strain is two-dimensional(and just
equal to the displacementon this fault normalizedby D); faults
shorterthan Lmaxcontributea strainscaledby the ratio L/Lmax.
If, alternatively, we use A equal to the size of survey area in
equation(4), then the value of A is arbitrary. In other words,
in this latter case we are implicitly assumingthat an increase
in the extent of the survey would increase, by the same
proportion, the numbers of faults of all sizes found in that
area. This may be the case for shorter faults, but the largest
faults, which representmost of the strain,will tend to be under
represented(e.g., they might extend out of the area) unlessthe
survey area increasesin multiples of Lmax. Consequently,
using the survey area in the calculation will generally give a
lower strain estimate. We calculateboth upper (A -D Lmax)
and lower estimates (A - survey area). If the faults dip at an
angle 0 (Figure 1), then for faults that dip away from the axis
(outwardfacing faults)the vectors5 andn are
n - (sin (0), 0, cos (0)),
(5a)
(cos (0), O, -sin (0))
d=7L
(7)
where y is a constant that dependson the rock type and the
tectonicenvironmentin which the faults form. Gillespie et al.
[1992] argued that the relationshipis nonlinear if many fault
data sets from different regions and rock types are combined.
The validity of a linear relationshipgiven by equation (7) for
normal faults on the EPR is investigated in this study and
discussed in detail below.
If the distribution of fault lengths has a functional form, we
can write N(L 1, L 2) the numberof faults of lengthbetweenL1
andL2 as
N(L•, L2) = NT
ß
2f(L)
dL
1
(8)
where N T is the total number of faults, and f(L) is the
probability density function of the fault lengths. In this case,
the summationin equation (6) can be reducedto an integration
that can be solved analytically. Although the integral method
uses an idealized (e.g., best fit) length distribution, it has the
advantage that the sensitivity of the strain calculation to the
resolution limit of the data set can also be investigated. For
example, substitutingequations (7) and (8) into equation (6),
the equivalent integral expressionsare
while for faultsthat dip towardthe axis (inwardfacingfaults),
ycos
(0)NT
A
n = (-sin (0), O, cos (0)),
f(L)L2dL
(9a)
(5b)
for large faults (Lmax > t), and for small faults,
(-cos (0), O,-sin (0)).
.t
The only nonzero terms in equation (2) are Mxx (ridge-
7cos
(0)
NT
f(L)
L3dL
Asin
t (0)
ßt
Lmin
perpendicular deformation) and M zz (crustal thickness
changes). We assumethat both inward and outward facing
faults have the samedip and are parallel to the ridge axis. This
assumption is clearly an oversimplification but there is
insufficientdata available to arguefor systematicvariationsin
0. For a fixed valueof 0, MxxandMzz are the samefor both
fault sets. From equation (1), the extensional strain exx
perpendicularto the ridge crest,due to both inward and outward
facing faults, is
cos
(0)•d•L•
A
(6a)
for largefaults (L _>t). For smallfaults(L <_t), exxis
N
cos
(0)sin
(0)•dk(Lk)
2
At
•=•
(6b)
Note that specifyingthe maximum depth of faulting, t, defines
the limit of the large fault population and is necessaryfor
calculatingthe contributionof small faults (equation(6b)).
Equations6a and 6b may be reducedto summationsof fault
lengths alone if the relationshipbetween the displacementon
a fault, d, and its lengthL is known. The usefulnessof sucha
displacement-length scaling relationship is that the strain
may then be calculatedfrom informationon fault lengthsalone
[Scholz and Cowie, 1990]. Cowie and Scholz [1992a, b]
argued that for continentalfaults the relationshipbetween the
maximum displacementon a fault and its length is linear:
(9b)
where Lmax is the longest fault and Lmin is the shortestfault
resolvedin the data set. Using equation(9), we can investigate
the sensitivityof our strain estimatesto the value of Lmin, as
Lmin tendsto zero.
FAULT PARAMETERS
Length Distribution
The lengths of faults were obtained from side scan sonar
images collected on the EPR using the SeaMARC II mapping
system between 13øN and 15øN [see Edwards et al., 1989,
1991] and the GLORIA (Geological LOng Range Inclined
Asdic) mapping system near 3øS [see Searle, 1984]. The
SeaMARC II device images the seafloor using 12 kHz sound
waves
and covers
a 10-km-wide
swath
with
an across-track
resolutionof 5 m [Blackinton et al., 1983]. By comparison,
GLORIA is a lower-resolution system; the Mark II version
operatesat a frequencyof about 6 kHz and coversa swaththat
is up to 60 km wide with an across-trackresolutionof about 30
m [Laughton, 1981; Tyce, 1986]. For the area between 13øN
and 15øN the lengthswere measuredfrom a fault trace map at a
scaleof 1:200,000 using digital SeaMARC II imagesdisplayed
at a 50-m pixel resolution. The fault length data for the area at
3øS on the EPR were compiledfrom analogGLORIA imagesat
a scale of 1:270,000. In the fault length interpretation we
took into consideration
the fact that the SeaMARC
II data were
collected along survey lines oriented at 45ø to the fault fabric
17,914
COWlEET AL.: FAULTINGON MID-OCEAN RIDGES
whereas the GLORIA data were collected along fault-parallel
survey lines. Oblique survey lines make lineation mapping
acrossadjacent swaths more subjectiveand less sensitiveto
structuraldetail whereasfault-parallel lines highlight structural
discontinuities in the fault traces.
Moreover,
(a)
1000
the GLORIA
survey imaged inward and outward facing fault populations
separately. In the SeaMARC II interpretationwe found that the
longer faults actually consistof severalsegmentsand often the
facing direction of segments can change along strike.
Therefore in order to comparethe two data sets,we recombined
the inward and outward facing fault populations interpreted
from the GLORIA images. We also applied a criterion that
segmentsoffset by _<150 m belong to the same fault system.
Note that the resolutionlimit of the SeaMARC II swathimages
usedfor the analysisbetween 13øN and 15øN is about 140 m (=
13-15øN:
II
100
10
3ø8 ß
0
10
NL= NT exp(-• L)
( 1O)
whereNL is the numberof faultswith length>L and,t is the
20
30
40
50
60
70
L (km)
400
(b)
[Gudmundsson, 1987a, b].
Figure 2a showsthe cumulativedistributionsof fault lengths
for the two study areas. Both distributionsare best described
by the function
10 km
A
2(2)l/2(pixel size)), so that offsetsof this size or smaller
cannotbe easily resolved. This scaleis also comparableto the
size of discontinuitiesalong normal faults mapped in Iceland
<L>-
' ' '
300
7
200
reciprocalof the mean fault length <L>. The slopeof the bestfit straight line through the data plotted on log linear axes
lOO
gives the value of /l, which is listed in Table 1. The
probabilitydensityfunctioncorresponding
to (10) is f(L)= •
exp (-/IL).
o
0
10
20
30
40
50
60
Displacement-LengthCoefficient ?'
L (km)
In general, the displacementprofile along the trace of a fault
FIG.
2.
(a)
Cumulative
distributions
of fault lengths obtained from
can be described as bell-shaped or elliptical. The maximum
SeaMARC II imagesat 13ø-15øN(dots)and from GLORIA imagesnear
value occurstoward the centerof the profile. The displacement 3øS (circles). The vertical axis is the numberof faults with length>L.
is fairly constantover at least the central third of the fault trace The slope of the distributionequals the reciprocalmean fault length
and then dies out to zero at the fault tips. A linear correlation <L>. (b) Displacement-length
correlationplot for faultsnear 3øS. The
between the displacement on a fault and its length has been maximum displacementis plotted and is calculatedby assumingan
demonstrated by Cowie and Scholz [1992a] for continental elliptical displacementprofile with the maximum displacementat the
fault midpoint and zero displacementat the fault tips (see text for
faults. They show that the ratio of maximum displacementto
explanation). The error bars represent 10% uncertainty in the
length (which is the parameter 7) ranges between
displacementestimates. The value for yis also shown(equation7).
approximately5.0x10-3 and 6.0x10-2 depending
on the
tectonicsettingand rock type in which the faults form [Cowie
and Scholz, 1992b].
ratio7 rangefromabout2.5x10
-3 to about1.7x10
'2 with a
To constructthe displacement-lengthscaling relationshipfor
the faults near 3øS the lengthswere measureddirectly from the
GLORIA side scanimages (see above). The fault displacements
were determined by measuring fault scarp heights along a
ridge-perpendicularbathymetricprofile in the samearea (taken
from [Lonsdale [1977]). This profile was obtained using the
high-resolution Scripps Institute deep-tow tool which has an
mean value of 6.7x10 -3 + 2.0x10 -3. The scatter in the data
effective vertical resolution of a few meters [Lonsdale, 1977'
Kleinrock et al., 1992]. The scarpheightswere convertedto a
displacementby assumingthe dip of the faults (45ø in this
case). We also implicitly assumedin this conversionthat the
actual offset acrossthe fault is reflected in the bathymetry,i.e,
that sedimentinfilling adjacentto the fault may be neglected.
The measurements
were corrected
to allow
shown in Figure 2b is typical of that observedin continental
fault data sets, and Cowie and Scholz [1992a] attribute this
variation to both the processof fault development and data
collection procedures. S. M. Carbotte and K. C. Macdonald
(Comparisonof seafloor tectonic fabric at intermediate,fast,
and ultrafast spreading ridges, submitted to Journal of
Geophysical
Research,
1993)founda valuefor 7of 8.1x10
-3+
0.8x10-3by correlating
faultscarps
observed
alonga deep-tow
line publishedby Lonsdaleand Spiess[1977] with SeaMARC
II fault lineation mapping near 9øN on the EPR.
STRAIN ESTIMATES
for the fact that the
bathymetric line does not always intersectthe fault where the
displacementis at its maximum value. To do this we assumed
that at a point x from the mid-point of the fault trace the
displacement
is givenby dmax
(1 - (x/L)2)•/2. Thevalues
of the
Strain estimates
have been calculated
for the areas near 3øS
and between 13øN and 15øN using both the summation
expression (equation (6) with d = 7L) and the integration
expression(equation (9)) using the parameterslisted in Table
COWIEETAL.: FAULTINGON MID-OCEANRIDGES
17,91$
TABLE 1. Summaryof FaultParameters
andStrainEstimates
Location
Spreading
Rate
;l
Lma
x
Lsurv
D
mm/yr
1/km
km
km
km
19øS
EPR
160
3øS EPR
15 2
90
0.12
13ø-15øN EPR
94
0.10
37øN
MAR
PercentStrain
Method
4.2-6.4
sum-•
70
8.9
sum-d
53
75
65
3.4-5.2
sum-L
45*
75
65
3.8-5.0
int-L
65
210
150
4.8-15.5
sum-L
75'
210
150
5.1-14.2
int-L
20
11-20
sum-d
•
Here;l is thereciprocal
meanfaultlength;
Lma
x is themaximum
measured
faultlength;
Lsurv
is thelengthof thesurvey
area
measured
parallel
to theridgeaxis;D is thewidthof thesurvey
areameasured
perpendicular
totheridgeaxis.In lastcolumn,
"sum-d"meansthestrainwascalculated
by summing
faultdisplacements
alonga bathymetric
profile;"sum-L"meansthatthe
actual
measured
faultlengths
weresummed,
i.e.EL2;"int-L"means
thatthebestfit length
distribution
(equation
10)wasused
to calculatethe strainusingequation(9) andassuming
L,nin- 0. The lowerstrainestimatein the range(column 7)
corresponds
toA = DLsurv;
thelargest
valuecorresponds
toA = DLma
x. EPRis EastPacific
Rise,andMARis Mid-Atlantic
Ridge.
* This is the best fit value.
õ Valuestakenfrom Macdonaldand Luyendyk[1977].
1' Values taken from Bicknell et al. [ 1987].
1. A faultdip0= 45øanda valuefor7of 6.7x10
'3wasassumed 100
in all the calculations. Upper and lower estimatesrespectively
were obtaineddependingon whetherA = D Lmax or A = D Lsurv,
whereLsurvis the lengthof the surveymeasuredparallelto the
faults. We use a value for t, the maximum depth to which
faulting can occur, of 6 km. As previously mentioned,the
value of t effects the amount of strain attributed
to faults with
length lessthan or equal to t. The contributionof small faults
to the total fault
strain has been estimated
80
60
40
and is shown in
Figure 3. Figure 3 showsthe percentageof total fault strain
accounted for plotted against the value of Lmin for the
parameterslisted in Table 1, where Lmin is the smallestfault
that can be resolvedin the data set. As Lmin tends to zero the
amount of fault strain accountedfor approaches100%. It is
clear from Figure 3 that even if the data set is not completefor
faults less than a few kilometers in length (i.e., L <_t), these
faults contributea small proportion(<10%) of the total strain.
Note that because the distribution of fault lengths is
L=t
20
o
2
4
6
8
10
12
14
16 18 20
shortestfault lengthsampled(km)
FIG. 3. Percentage
of total fault strainas a functionof the resolution
limit for the area between 13øN and 15øN (thin line and squares)and
exponential(equation(10)) the strain convergesmore rapidly the area near 3øS (bold line and circles). The lines were obtainedusing
than it does for a power law distribution which characterizes equation(9) with the bestfit lengthlengthdistribution
functions.The
fault lengthsin
continentalfault populations[Scholzand Cowie, 1990; Walsh pointswereobtainedby summingthe actualmeasured
et al., 1991].
The difference between the curves plotted in
eachcase(equation(6) with d = yL).
Figure3 reflectsthe differencein the valueof Lmax in the two
datasets.If Lma
x is not muchgreaterthanLmin,thentherateof
convergenceof the strain estimateis slow, i.e., the strain
(8.9%) obtained by summing displacementsalong the deeptow bathymetric profile. The upper strain estimate for the
From examinationof equations(6) and (9) it is evident that regionbetween13øN and 15øNis 14.2-15.5%. Usingthe size
the values of the parameters7 and 0 will have a significant of the surveyarea in the calculationsprovideslower estimates
effect on the magnitudeof the strain estimate,yet these are of 3.4 to 3.8% at 3øS and 4.8-5.1% at 13ø-15øN. The mean
also the parameters that are least well constrained. For values of these two extremes are: 4.4% at 3øS and 10% between
example,if a fault dip of 60ø insteadof 45ø is used,then the 13øN and 15øN. There is a large variability in theseresultsand
estimateof strain decreasesby 30%. Similarly, a factor of 2 the rangeincludesthe estimatesof 4.2% and 6.4% obtainedby
uncertaintyin 7introduces a factor of 2 uncertaintyin the Bicknell et al. [1987] for the area near 19øS. S. M. Carbotte
estimate is more sensitive to the resolution limit.
strain
estimate.
In Table 1 the upper estimateof strainfor the area near 3øS
rangesfrom 5.0 to 5.2% which is slightlylower than the value
and K. C. Macdonald (submittedmanuscript,1993) calculateda
strain of 3.1% for the area between 8ø30'N and 10øN on the
EPR and 4.5% for the area between 18øS and 19øS using fault
17,916
COWIEET AL.' FAULTINGON MID-OCEANRIDGES
data from SeaMARC II imagesfor a fault dip of 45ø and y =
8.1x10-3. Note that Carbotteand Macdonaldusedthe size of
the survey area in thesecalculationsso their resultsrepresent
at 21øN [Riedeselet al., 1982]) have foundthat the earthquake
activityoccursin swarmsof low-magnitudeevents(mb _<1.0)
more consistentwith volcanic and hydrothermalactivity than
lower
faulting. More recently, Wilcock et al. [1992] monitored
microearthquakes
at the overlappingspreadingcenternear9øN
on the EPR. These workers interpret the earthquakesthey
observedas normal faulting events. The averageearthquake
magnitudemeasuredwas about mb = 2.0-3.0; however,all the
events were restricted to the vicinity of the overlapping
spreadingcenter itself, and none of the earthquakesrecorded
estimates.
Given the uncertaintiesin the calculationparameters,we can
only conservativelyconcludethat brittle strain along the EPR
axis is of the order of 5 to 10%, with a possiblerangefrom 3
to 15%. In contrast,the only measurementobtaineddirectly
from fault data at the slow spreadingMid-Atlantic Ridge
(MAR) is in the range 10-20%. This measurement,from the
MAR at 37øN where the spreadingrate is 20 mm/yr, was made
by Macdonald and Luyendyk[ 1977], who summedfault throws
alonga deep-towbathymetricprofile. This rangefor the MAR
allows for a factor of 2 variation but, in comparisonwith the
estimatesalongthe EPR obtainedhere,our resultssuggestthat
the strain due to faulting is greaterat slow spreadingridges.
Malinverno
and Cowie [this issue] reached a similar
conclusionfrom a comparisonof topographicroughnesson
the EPR and MAR assumingthat all the roughnessis due to
faulting. An inverse relationship between fault strain and
spreadingrate can be argued, at least to first order, from the
results of this study of the EPR: for spreadingrates >150
mm/yr, exx-- 3-9%; for spreading
rates-- 100 mm/yr,exx-- 515%.
SEISMICITY
In this study we reexamined the Harvard Centroid Moment
Tensor (CMT) catalogueand the Bulletin of the International
SeismologicalCentre (ISC) for the region of the EPR between
20øS and 30øN. It is difficult to evaluateunequivocallythe
seismic activity in this area becauseof poor station control
due
to
the
remoteness
of
continental
seismic
networks.
Furthermore, the CMT catalogue is restricted to only the
largest earthquakesworldwide (usually mb >- 5.0) with good
stationcontrol and which occurredduring the last 15 yearsor
so. The CMT catalogue does have the advantagethat it
providesan estimateof the earthquakefocal mechanism.CMT
solutions in this region are primarily located on transform
faults with focal mechanismsconsistent with strike-slip
motion.
D Ulll•tlll
The 1•.............
indicates
a number
of additional
earthquakesin the area during the last 30 years or so with
magnitudesas low as mb = 3.5 and which are scatteredup to
distancesof a few hundredkilometersfrom the ridgeaxis. The
magnitudes of these events are typically quite well
constrained, particularly for the largest events (_< +0.2
magnitude units), but the location deteriorates rapidly with
decreasing magnitude. For example, according to the ISC
Bulletin, for mb >_5.0 the locationerror is of the orderof only
+5 km, whereasfor 4.5 _<mb _<5.0 the error is about +20 km
and for 4.0 _<mb _<4.5 it is about +50 km. Wiens and Stein
[1984] and Wysessionet al. [ 1991] identified a small number
of large earthquakes (mb >"- 5.0) in this area which they
classified as intraplate due to their distance from the plate
boundary. Otherwise, the largest ISC events approximately
colocate with the CMT
transform faults.
solutions in this area, i.e., on
The majority of the smaller events are
located less than 150 km from a transform fault.
Therefore,
given the uncertainty in their locations, it is possible that
many of the smaller events may also be transform fault
earthquakes.
On-site seismicstudiesof fast spreadingridges(for example,
the Galapagosridge [Macdonaldand Mudie, 1974] and the EPR
were otherwise
located on the rise axis.
The seismicity data from the EPR do not entirely preclude
earthquakeactivity associatedwith normal faulting along the
spreadingcentersif the magnitudelevel of the seismicityis
below the teleseismicdetectionthreshold. Consequently,it is
of interest here to present the calculation of a hypothetical
seismicmomentreleaserate at the ridge axis assumingthere
are no restrictions imposed by detection capabilities. To
obtain a maximumestimatewe assumethat the largestnormal
faultingevent on the EPR that hasoccurredwithin the 30 year
period of the ISC cataloguehas a magnitude5.0, i.e., equal to
the detection threshold, and that the seismicity below this
threshold is distributed according to the global momentfrequencydistributionwith a power law exponentB equalto
0.6 (equivalentto the Gutenberg-Richterb value equalto 1.0).
An earthquake of magnitude 5.0 has a mean slip of a few
centimeters, a source radius of the order of a few kilometers,
anda seismicmomentof about1.0x1017
N m. Integrating
over the distributionof earthquakes,the total momentreleased
by all the earthquakesis about 2 times that releasedby the
largestearthquake[e.g., Wesnouskyet al., 1983, equation4].
Over a 30-year time period thereforethe seismicityaccounts
fora mome.
nt release
rateof about3x1015
(N.m/yr. Seismic
s.train.rateesis relatedto moment
release
rateMo according
to
es- Mo/(2t,
tV) where/2 is the shearmodulus[e.g.,Ekstrom
and England, 1989]. The half width of the fault generation
zone at the EPR axis is approximately5 km (seeEdwardset al.,
[1991] for discussion)' the thickness of the crust is 6 km; 50
km is taken as the maximum fault length Lmax, giving V =
1500km3. Therefore,
if p_= 3.0x!011 N m-2 i• •ed, the
seismic
strainrateis 4x10-9year'l. At a halfspreading
rateof
50 mm/year, a fault may be active for about 100,000 years
before it moves out of the fault generationzone. The total
seismic moment released over this time period producesa
strain of 0.04% which is 2 ordersof magnitudeless than the
calculatedtotal fault strain along the EPR (see Table 1). In
order for the seismicityto accountfor a significantlylarger
strain while remaining below the teleseismic detection
threshold, there would have to be a high level of
microearthquakeactivity (e.g., a B value close to 1.0) which
has yet to be observed in ocean bottom seismic observations
on mid-ocean ridges.
In contrast to the EPR, the CMT catalogue for the MidAtlantic Ridge showsmany large-magnitudenormal faulting
events(mb = 5.0-6.0) locatedon the spreadingcenters[Huang
and Solomon,1988]. By summingmomentsfor earthquakes
on slow spreadingridges, Solomon et al. [1988] showedthat
seismicitycan accountfor 10-20% of the plate separationrate
on slow spreadingridges. This is comparableto the estimates
of fault straincalculatedby Macdonald and Luyendyk[1977],
using a deep-tow bathymetric profile across the MAR near
37øN, and by Malinverno and Cowie [this issue] from seafloor
COWIE ET AL.: FAULTING ON MID-OCEAN RIDGES
topographic roughness. However, there is only one direct
estimate of strain from the MAR, and it may be quite variable
along different portionsof the ridge axis [e.g., Shaw, 1992].
DISCUSSION
first becomesunstablein the shallow part of the crust and has,
in the past, been attributed to the stabilizing effects of low
normal stressor pore fluid effects. The lower transitionTl is
where sliding can again occur by stable slip, by processes
usually attributed to elevated temperatures and the onset of
ductile
Figure 4 shows a summary of the estimates of brittle
deformation from both seismicity data and fault data for fast
and slow spreadingridges. Plate separationat all spreading
rates is clearly dominated by magmatic processesthat create
new crust, but a proportion of the total plate separation is
accounted for by the formation of normal faults at the axis.
According to these and previous calculationsthe contribution
of faulting may be as much as 10-20% at slow spreadingridges
and perhaps a factor of 2 lower (5-10%) at fast spreading
ridges. There is, however, a much greater difference between
the seismicactivity associatedwith the faulting. Whereasthe
seismic moment release rate at slow spreadingridges appears
to be similar
to the brittle
strain rate calculated
from the fault
population, at fast spreading ridges an upper estimate of the
seismic moment release rate can only accountfor perhaps1%
of the strain representedby the faults.
Here
we
show
that
the
fundamental
variation
in seismic
activity with spreadingrate of mid-ocean ridge normal faults
can be explained by a model similar to that of Tse and Rice
[1986], and discussedby Scholz [1988a], for the stability of
frictional sliding on continental faults. This model is based
on the idea that the part of the fault that can slip unstablyand
produce earthquakesis controlled by the position of frictional
stability transitionsand may be only a small part of the whole
fault. The upper transition Tu is the depth at which sliding
100
17,917
deformation
mechanisms.
The stability of frictional sliding dependson three factors,
the first being the critical slip distance 1c, which is the
distance two surfaces in contact must slide, upon a velocity
perturbation,for friction to change from a static to a dynamic
value. The secondfactor is defined by the difference between
two empirical constants(a- b), determined from laboratory
friction experiments, which is the change in the steady state
frictional resistance with sliding velocity. If the frictional
resistance decreases with increasing velocity, then an
instability occurs. If (a- b) is positive, sliding is intrinsically
stable; if (a - b) is negative, sliding may be stable or unstable
depending on the third factor, which is the stiffness of the
sliding system. See Scholz [1990, p. 86] for discussionof
this topic.
Tse and Rice [1986] showedthat for continentalstrike-slip
faults the lower stability transitionTl is the depthat which (a b) changesfrom a negativeto a positivevalue with increasing
temperature. Therefore Tt dependson the geothermalgradient,
and it approximately coincides with the transition from
predominantlybrittle deformation in the upper crust to ductile
flow at greaterdepthsin the crust. From the thermal modelsof
Lin and Parmentier [1989] we estimateda geothermalgradient
in the fault generation zone by averaging the gradients
calculated
at distances
of 1 km and 5 km from the axis.
For a
fast spreading ridge (100 mm/yr full spreading rate) the
average geothermal gradient is approximately 200øC/km,
whereas on a slow spreadingridge (20 mm/yr full spreading
rate) the average gradient is approximately 100øC/km (see
Figure 5). Although the exact relationshipbetweenTl and the
brittle-ductile transition is not well defined, Wiens and Stein
80
60
40
20
0
slow
20mm/yr
fast
100mm/yr
FIG. 4. Summary diagram comparing the partitioning between
magmaticactivity (hatchedpattern), aseismicfault strain (white), and
seismicfault strain (shaded)during seafloorspreadingat fast and slow
spreadingridges. The seismic couplingZ is a measureof the ratio of
seismic strain to total (seismic plus aseismic) brittle strain (see text for
discussion).
[1984] showed that accordingto a simple plate cooling model,
seismicityin the oceansis confined to temperatureslower than
approximately 600øC. Experimental data show that this
temperaturecorrespondsto the onset of ductile deformation in
olivine [Goetze and Evans, 1979]. In this case,Tl will occurat
_<3km in the fault generationzone at fast spreadingridges but
at _<6-8 km in the fault generation zone at slow spreading
ridges (see Figures 5 and 6).
The upper stability transition T u is less well understood.
However, two more detailed explanationshave been recently
put forward. Using an elastic model for the contact between
two rough surfaces,Scholz [1988b] showedthat 1c decreases
with increasing normal stressand calculated that the transition
to unstable sliding occurs above an effective normal stressof
30-40 MPa.
Marone
and Scholz [1988]
showed
experimentally that thick accumulations of poorly
consolidated fault gouge exhibit intrinsically stable sliding,
i.e., (a- b) is positive. Unconsolidatedfault gougeis usually
best developed in the shallow portion of a fault zone and
correlates with the amount of displacement on the fault
[Robertson, 1982]. Bathymetricdata indicatethat fault scarps
on slow spreading ridges can reach heights of 600-800 m or
more, which is at least a factor of 3 larger than that observed
on ridges with intermediate or fast spreading rates [Searle,
1984]. The difference in gouge development that could be
inferred from this difference in fault displacementwould imply
that faults at slow spreading ridges have developed thicker
17,918
COWIE ET AL.: FAULTINGON MID-OCEAN RIDGES
NORMAL
STRESS
,
TEMPERATURE
.
FRICTIONAL
fast-spreading slow-spreadingBEHAVIOR
40 MPa
600øC
600øC
- -
3km
'
I
6km
II
(b)
(a)
_ . _ T1
(c)
unstable
stable
....
slow
fast
(d)
FIG. 5. Frictionalstabilitymodelfor mid-oceanridge faults.(a) Resolvednormalstressas a functionof depthin the crustfor
normal faults in the fault generationzone assumingCoulomb friction, hydrostaticpore pressures,a vertical stressof 28
MPa/km, and a friction coefficientequalto 0.75. (b andc) Temperatureprofilesfor a fast (100 mm/yr full spreadingrate) and
a slow (20 mm/yr full spreadingrate) ridge,respectively,basedon the averagethermalstructurenearthe ridge axis [afterLin
and Parmentier, 1989]. (d) Regionsof stableand unstablefrictionalbehavioron an activefault at the two differentspreading
rates. T, and T! are the frictional stabilitytransitionscontrolledby the mean normal stressand the thermal gradient,
respectively.
gouge and thus may be more likely to exhibit stable slip. As
this is not observed to be the case we investigate instead the
effect of normal stressas suggestedby Scholz [1988b]. For
extensional faulting the maximum principal stressis vertical
and increases with depth in the crust according to o' = pgz,
where z is the thicknessof the overburdenof average density
p, and g is the accelerationdue to gravity. If we assume
Coulomb
friction
with
a friction
coefficient
vertical stress increase of 28 MPa/km,
of 0.75
and a
then the increase in
normal stress with depth in the fault generation zone is 12
MPa/km. Therefore for mid-oceanridge faults, Tu will occurat
about3 km (Figure 5). We assumehere that the positionof Tu,
which depends on the stress regime, does not vary
substantially with spreading rate.
According to this simple model, illustrated in Figure 6, Tl
will be coincident with T u on fast spreadingridges, but close
to the ridge axis where the thermal gradient is higher than the
average,Tl will mostlikely be shallowerthanTu. Thereforeat
fast spreading ridges, active faulting occurs in a region
dominated by stable slip due to the high thermal gradient
(Figure 6). In contrast,on slow spreadingridgesthere is only
a narrow region very close to the axis itself in which TliS
shallower than T u. As the fault generationzone has finite
width, faulting on slow spreadingridges may continueinto the
region where T• is deeperthan Tu, and in fact T• and Tu may be
quite well separated(Figure6).
The seismic coupling of oceanic faults Z can be defined by
the ratio of the seismicwidth of the fault,Ws, to the total down
dip widthof thefault,Wf. ThewidthWsis controlled
by the
positionsof Tu and T•, i.e.,
Ws= r•- ru
rl >ru
sin (0)
Ws
=0
shallowerthan Tu, Ws is zero so that Z equalszero. Although
the model describedabove predicts that Ws is always smaller
thanWf,independent
of spreading
rate,onceanearthquake
has
nucleated, it can rupture the whole fault. This is becausethe
rupture can propagate through the frictional stability
transitions, although they will inhibit the propagation.
Solomon et al. [1988] found that the centroid depth of
earthquakeson slow spreadingridgesis at about 6 km which is
approximately the depth of T l between about 1 km and 5 km
from the axis. The maximum depth of seismic rupture is
probably about twice the centroid depth. Therefore at slow
spreadingrates the effective seismic width Ws, at least for the
largestearthquakes,
maybecomparable
to Wf.
The model derived above provides a simple first-order
explanation for the observed variation in seismic activity as a
function of spreading rate. Hydrothermal circulation at midocean ridges, which often utilizes faults as conduits,may also
influence the seismic activity and should be considered.
Reinen et al. [1991] have found that serpentine,a weathering
product of basalt, is characterizedby stable frictional sliding
((a - b) positive) over a range of confining pressuresfor slow
loading rates typical of plate motion velocities. These
workers conclude that serpentinite should not be the site of
instability initiation although propagation of unstable slip
initiated on anotherportion of the fault may be permitted. The
flux of fluids and thus hydrousalterationof fault zone materials
is probably affected by fault activity, i.e., slip rate. The slip
rate on Holocene and Quaternary faults in the slow spreading
Asal Rift, Djibouti, measuredby Stein et al. [1991], is of the
order of 1-2 mm/yr. By measuring the width of acoustic
shadowsin SeaMARC I side scan images collected along the
EPR axis near 12øN we have estimateda maximum scarpheight
of about 120 m for a fault at a distance of 1 km from the axis
otherwise.
(11)
At fast spreading rates where T• is at the same depth or
(see Crane [1987] for a descriptionof the original data set). If
we assumea dip of 45 ø, this fault has had an averageslip rate
of about 8 mm/yr, assumingthat it started to form fight at the
COWlE ET AL.' FAULTING ON MID-OCEAN RIDGES
17,919
fault generationzone
slow
fast
I •'•
5km
0
5km
i
m
i
., T/ ,
i
maximumdepth
RIDGEAXIS
of faulting
km
FIG. 6. Cross sectionthrough oceaniclithosphereadjacentto the ridge axis accordingto the frictional model shown in
Figure 5. The half-width of the fault generationzone is taken to be 5 km. The left hand side illustratesa slow spreading
ridge,andthe righthandsideillustrates
a fastspreading
ridge. TuandTt aredefinedin Figure5. The shadedareaindicatesthe
regionwhereTt < Tuso that faultsin thisregionslip stably. The hatchedpatternindicatesunstableslip on faultsat a slow
spreadingridge.
axis and was still active when it was imaged. Even if we
assumethe fault to be verticalat the surfacethe slip rate would
have been 6 mm/yr which is 3-6 times higher than in Asal. It
seemsreasonableto concludethat fault slip rate (as opposedto
accumulatedfault displacement)and the thermal structureat the
axis may be the important factors determining the seismic
characteristics
of oceanic
faults.
CONCLUSIONS
Using side scansonarand bathymetricdata from the flanksof
the EPR at 13ø-15øN
and near 3øS we have calculated
that of
the order of 5-10% (with a possiblerange from 3 to 15%) of
the total plate separationrate is achievedby brittle extension
of the oceanic crust at the rise axis.
The contribution
of brittle
deformation to seafloor spreading appears to be negatively
correlatedwith spreadingrate. Specifically, we calculatethat
for spreadingrates greaterthan 150 mm/yr, the fault strain exx
-- 3-9%, which is consistentwith estimatesfrom independent
studies. For spreadingrates of about 100 mm/yr we find that
exx= 5-15%. The only direct estimateof fault strain from the
MAR, where the spreadingrate is 20 mm/yr, is in the range 11
to 20%. This estimate from the MAR is comparable to
calculations
of brittle
deformation
from
the seismic
moment
releasedduring normal faulting earthquakesat the ridge axis.
Seismic coupling, which is defined as the ratio of seismic to
aseismic slip occurring on a fault, appears therefore to be
about 100% on the MAR.
controlled by fault activity and thus slip rate, hydrothermal
effects may be enhancedat fast spreadingridges where fault
slip rates appearto be unusuallyhigh.
The results presentedhere indicate that there are marked
differencesin the seismiccouplingof normal faults forming at
mid-oceanridges with extremesin spreadingrate. It remains
to be demonstratedhow seismiccouplingvariesgraduallyover
the observedrange of slow, intermediate, and fast spreading
rates. The next step toward this ultimate goal is a more
comprehensivecalculation of fault strain at slow spreading
ridgesthan has previouslybeen done. The effect of along-axis
variations in fault development, as documented by Shaw
[1992], should also be examined. Given that large-magnitude
earthquakesdo occur on the MAR and that the stationcontrol
is this area is better than for the central Pacific, a detailed
comparisonof seismicity and faulting should be possible. In
this way, we may be able to establish whether some of the
faulting is aseismiceven at low spreadingrates.
Acknowledgments. The authors acknowledgehelpful discussions
with Neil Mitchell, Dan Fornari, Kim Kastens,and Bill Ryan. Roger
Searlegenerouslyprovidedoriginal copiesof the GLORIA imagesnear
3øS and unpublisheddata on fault lengths. We also thank Suzanne
Carbottefor many helpful commentsand for providingpreprintsof her
work. Marc Parmentier and Eric Bergman provided thorough and
helpful reviews which improvedthe final manuscript.The initial stage
of this project was supportedby NSF contractEAR90-04534, and it
was completedwith the supportof the Office of Naval Researchunder
contract
number
N00014-89-J1159.
In contrast, even if the detection
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M. Edwards, SOEST, University of Hawaii at Manoa, Honolulu, HI
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A. Malinverno, Schlumberger-Doll Research, Old Quarry Road,
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C. H. Scholz, Lamont-Doherty Earth Observatory, Palisades,NY
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(ReceivedOctober 13, 1992;
revisedMay 27, 1993;
acceptedJune 8, 1993.)