Evidence for spreading-rate dependence in the displacement-length
ratios of abyssal hill faults at mid-ocean ridges
DelWayne R. Bohnenstiehl* Department of Earth and Environmental Sciences and Lamont-Doherty Earth Observatory,
Columbia University, Palisades, New York 10964, USA
Martin C. Kleinrock Department of Geology, Vanderbilt University, Nashville, Tennessee 37235, USA
ABSTRACT
New data from the eastern flank of the Mid-Atlantic Ridge
(~25–27°N) show that slow-spreading abyssal hill faults maintain maximum displacement-length ratios that are systematically greater than
those reported on the fast-spreading East Pacific Rise. Lower displacement-length ratios in the fast-spreading environment may reflect the
importance of fault linkage (rather than lateral propagation) in determining the lengths of abyssal hill faults and the limited ability of fault
systems that evolve within an extremely thin lithosphere to acquire
additional displacement during or following linkage.
strain necessary for propagation (i.e., a critical d/L ratio). Field observations
suggest, however, that the self-similar scaling of individual faults also may
be preserved by systems or arrays of nonphysically linked, but mechanically
interacting, fault segments (e.g., Dawers and Anders, 1995; Contreras et al.,
2000). Hence, substantial readjustment may occur prior to, or in the absence
of, physical linkage, the displacement-distance profile of a linkage fault
system adjusting gradually to maintain a shape resembling that expected for
a more isolated fault (e.g., Anders and Schlische, 1994; Dawers and Anders,
1995; Cowie, 1998; Contreras et al., 2000). This is facilitated by the positive
feedback between optimally oriented fault segments within the array (i.e.,
those parallel and coplanar for normal faulting) (cf. Cowie, 1998).
Keywords: mid-ocean ridges, faults, faulting, fault scarps, abyssal hills.
INTRODUCTION
Quantifying the relationship between maximum fault displacement
and fault length has provided significant insight into our understanding of
fault growth and evolution (e.g., Cowie and Scholz, 1992; Dawers and
Anders, 1995; Cartwright et al., 1995). Previous studies characterizing the
relationship between maximum scarp height (d) and fault length (L) within
the abyssal hills of the fast-spreading East Pacific Rise have suggested
maximum throw (the displacement parameter typically reported for normal
faults) versus length ratios that are consistently at the low end of the range
exhibited by terrestrial fault data sets (e.g., Cowie et al., 1993, 1994;
Carbotte and Macdonald, 1994). Here we present the first data quantifying
the d/L scaling of faults in the slow-spreading abyssal hill environment. We
show that faults on the flanks of the Mid-Atlantic Ridge maintain d/L ratios
that are systematically larger than those reported for faults of similar scale
(L = 5–50 km) on the East Pacific Rise, with values approaching both the
terrestrial mean (e.g., Schlische et al., 1996) and those exhibited by much
smaller (L = 0.15–2 km) more isolated faults on the median valley floor of
the Mid-Atlantic Ridge (e.g., Bohnenstiehl and Kleinrock, 1999). These
results imply some variability in the mechanics of fault growth as a function
of spreading rate, which we suggest may reflect the relative ability of slowand fast-spreading faults to acquire additional displacement either during or
following the along-strike growth of faults through linkage.
FAULT GROWTH MODELS
Post-yield fracture mechanics models for the growth of an isolated fault
predict a linear relationship between maximum displacement and length of
the form d = γL, where γ represents a critical shear strain necessary for fault
propagation that depends on the shear strength of the rock normalized by its
shear modulus, as well as the ratio of shear strength to remote loading stress
(e.g., Cowie and Scholz, 1992). In the terrestrial environment, a global
compilation of data indicates that a roughly linear d/L relationship is maintained over ~8 orders of magnitude in fault length, with a mean d/L ratio 0.03
and a range of ~0.001–0.1 (Schlische et al., 1996). Because lengthening
results from segment linkage, as well as simple lateral propagation, this
scale-independent linearity implies that the d/L ratio of a fault that grows by
linkage may evolve toward that expected for a more isolated fault.
Cartwright et al. (1995) suggested that fault growth might be thought of
as a step-like process, in which following linkage the resulting fault preferentially acquires displacement until regaining some critical level of shear
*E-mail: [email protected].
Geology; May 2000; v. 28; no. 5; p. 395–398; 3 figures; 1 table.
METHODS
A 1996 survey aboard the R/V Ewing collected hull-mounted Hydrosweep bathymetry (16 kHz) data and surface-towed HMR1 sidescan data
(11–12 kHz) over an ~75 000 km2 region extending from the ridge axis out
to ~340 km (26 Ma) off axis on the eastern flank of the Mid-Atlantic Ridge
between ~25 and 27°N (Tucholke et al., 1998). A small subset of these data
is shown in Figure 1. Tracklines were run at ~50° oblique to the ridge axis,
with spacings sufficient to provide ~200% sidescan coverage (i.e., ~100% in
both look directions) and nearly 100% Hydrosweep bathymetric coverage.
We utilize a predominantly northeast- or outward-facing sidescan
mosaic gridded at 70 m and coregistered with the bathymetric data. The
HMR1 sonar system can consistently image portions of a fault trace having
>~30 m throw and is capable of resolving fault traces separated by >~200 m
(Cowie et al., 1994). At this scale, mapped faults may represent arrays of
both physically linked and nonphysically linked fault segments that interact
mechanically, rather than simple isolated faults. Our analysis is restricted to
the larger scale faulting (L = 5–50 km) within the upper bounding walls of
the median valley and inactive ridge flanks (beginning ~10 km off axis). The
resolution of these data is comparable to that available on the East Pacific
Rise, where d/L data have been derived from a combination of equivalent
resolution SeaMARC II and GLORIA sonar imagery and high-resolution
bathymetric profiles (e.g., Cowie et al., 1993, 1994; Carbotte and Macdonald,
1994). Hence, we can investigate the mechanics of fault growth by quantifying the relationship between displacement and length at different spreading rates (Table 1).
We defined fault length as the straight line distance between fault tips
within the sidescan imagery. Fault traces were considered linked if separated by <200 m, although offsets to 1 km were allowed between swaths to
account for inaccuracies in instrument heading and navigation. Maximum
throw was determined by extracting from the gridded data a series of bathymetric profiles perpendicular to the fault (Fig. 1); it was not presumed to
occur at the center of the fault trace, although it generally was found to be
within the center third. Maximum scarp height measurements are estimated
to be accurate within 50 m, accounting for bathymetric resolution (~20 m) and
some ambiguity in defining the top and bottom of the fault scarp (Fig. 1).
Sediment thickness is ~10–40 m and volcanism appears to be restricted to
the inner valley floor in this area (Jaroslow, 1996).
DISPLACEMENT-LENGTH DATA AT MID-OCEAN RIDGES
Mid-Atlantic Ridge abyssal hill faults exhibit a positive linear correlation (R2 = 0.65) between maximum scarp height and length, with a mean of
d/L ratio of 0.016 and a range of ~0.009–0.04 (Fig. 2). The d/L ratios of
395
C
C
a
A
b
a
Scarp Height
(m)
b′
low/shallow
C′
BB
43°15′W
Bathymetric Depth
43°25′W
C
–3800
–3900
D
–4000
50
0
a
400 b
300
200
100
E0 0
Scarp Height
(m)
Backscatter
Intensity
43°15′W
43°25′W
250
200
150
100
25°00′N
25°00′N
A
C′
b′
high/deep
Backscatter Intensity
A'
A
~ 5 km
a′
a′
Bathymetric Depth
25°10′N
25°10′N
b
a′
–4100
a′
a
b′
10
5
Distance Along Fault b-b' (km)
500 c
400
300
200
100
0
F 0
15
20
c′
10
Such extensive and systematic overprinting is not supported by the most
complete studies of the active plate boundary zone, which indicate that synchronous volcanism and faulting are restricted to a narrow 1–2-km-wide
zone near the ridge axis (e.g., Carbotte et al., 1997) and that fault throw
increases significantly to distances ~10–30 km off axis (e.g., Lee and
Solomon, 1995; Alexander and Macdonald, 1996).
Table 1 summarizes available d/L data for mid-ocean ridge fault populations at all scales. Previous d/L scaling work on the Mid-Atlantic Ridge
has been restricted to a population of much smaller faults on the median
valley floor of the TAG segment (~26°N), where analysis of high-resolution
DSL-120 sidescan imagery and coregistered bathymetric data indicates a
d/L ratio of ~0.03 (Bohnenstiehl and Kleinrock, 1999). The higher resolution of that data set imposes an inherent bias; however, a first-order comparison of the on-axis TAG and off-axis abyssal hill data sets is reasonable
in this instance because the change in data resolution between the two studies
is met by a proportional change in fault size between the two populations
(Table 1) (cf. Bohnenstiehl and Kleinrock, 1999).
Near-axis studies at an equivalent scale and resolution have not been
conducted on the East Pacific Rise; however, estimates of scarp width and
length made from SeaMARC I sonar data (without bathymetric data) collected on the ridge flanks suggest a d/L ratio of ~0.015 for faults having
lengths of 2–10 km (Cowie et al., 1994). This is similar to that observed at
the larger 5–50 km scale on the Mid-Atlantic Ridge, but it is unclear if these
SeaMARC I data can be compared directly, due to the lack of bathymetric
control on fault displacement and the inclusion of fault segments, which
may have d/L ratios strongly influenced by neighboring fault interactions.
30
20
Distance Along Fault c-c′ (km)
Figure 1. A: Example of HMR1 sonar imagery used in this study (insonified from west-southwest). High-amplitude backscatter returns are
dark. White circles mark tips of four west-dipping fault arrays used in
study, as defined using criteria outlined in text. B: Gray scale image of
Hydrosweep bathymetric data used in study. Faults can be identified by
their characteristic high-amplitude backscatter (C) and steep slopes
(D). Displacement-distance profiles extracted from gridded bathymetry
are shown along faults b-b′ (E) and c-c′ (F).
these faults are therefore systematically greater than those reported within
the abyssal hills of the East Pacific Rise (Fig. 2). The resolution and scale of
both abyssal hill fault data sets, as well as the criteria used to define a fault
in these studies, are quite similar (Table 1), indicating that the observed
spreading-rate dependent variability cannot be attributed to a simple sampling
bias. While volcanic overprinting has been shown to obscure some faulting
locally along the East Pacific Rise (e.g., Alexander and Macdonald, 1996;
Carbotte et al., 1997), >50%–75% of each fault’s total throw would need to
be consistently obscured to account for the observed variation in the d/L ratio.
FAULT GROWTH MECHANICS AND SPREADING RATE
Changes in the d/L ratio of terrestrial faults have been attributed
largely to variations in the shear strength of the brittle lithosphere, associated with either changing lithology (e.g., Dawers et al., 1993) or an
increase in shear strength at depth (e.g., Cowie and Scholz, 1992; Schlische
et al., 1996). In the mid-ocean ridge environment the mechanical properties
of the lithosphere are controlled largely by thermal structure and composition, with rheologic models predicting a brittle thickness of ~4 –10 km
along a slow-spreading ridge and ~1–3 km along a fast-spreading ridge
(within the zone active fault growth) (e.g., Shaw and Lin, 1996). We argue
that the lower d/L ratios observed on the flanks of the East Pacific Rise can
be explained by considering the limits imposed on maximum fault displacement by the presence of a thin lithosphere together with the importance of fault linkage in the lateral growth of abyssal hill faults.
Lateral Fault Growth
Scaled physical models of extensional fault systems illustrate the increasingly important role of fault linkage as the population evolves, with a
more rapid lengthening per unit displacement observed with increasing strain
(Spyropoulos et al., 1999; Ackermann and Schlische, 1999). These models
suggest that the lengthening of faults within populations accommodating
>~10%–15% strain is accomplished primarily by linkage, with a gradual
transition from a lower (<~2.5%) strain regime in which individual faults
nucleate and propagate laterally (Spyropoulos et al., 1999). Strain estimates
TABLE 1. DISPLACEMENT VERSUS LENGTH DATA SETS IN THE MID-OCEAN RIDGE SETTING
Scale range Setting Spreading On/off d/L ∗
(km)
rate (mm/yr) axis mean
9o
N EPR
120
Off
150
Off
5-50
3o S EPR
26o N MAR
25
Off
2-10
12o N EPR
110
0.15-2
26o
3-35
3-55
N MAR
d/L
range
N
0.006 0.003-0.02 35
0.004 0.002-0.008 35
0.016 0.009-0.04 65
Mixed 0.015
0.007-0.03
35
OC Sidescan/bathyemtric
instrument used
(m)
Strain
(%)
Characterization
Reference
1
200
SeaMARC II/ Deep-Tow 5-15
Segmented fault arrays
150
GLORIA/ Deep-Tow
5-15
Segmented fault arrays
200
HMR1/ Hydrosweep
5-20#
?
SeaMARC I / none
5-15
2,3
This study
Segmented fault arrays
Includes some fault segmets 3
0.5-2.5 Dominantly isolated faults
25
0.03 0.015-0.08 30 15 DSL-120/ DSL-120
On
Note: N, number of faults in each environment; OC, offset criteria used to define a fault; MAR, Mid-Atlanric Ridge; EPR, East Pacific Rise;
d/L, maximum scarp height versus length ratio; ∗, determined from least-squares regression constrained at the origin; 1, Carbotte and
Macdonald (1994); 2, Cowie et al. (1993); 3, Cowie et al. (1994); 4, Bohnenstiehl and Kleinrock (1999); #, Jaroslow (1996).
396
4
GEOLOGY, May 2000
Figure 2. Relationship between maximum throw and length for abyssal
hill fault arrays on flank of Mid-Atlantic Ridge (MAR). Vertical error bars
±50 m, horizontal error bars +2.5 km (accounting for portions of fault tip
that may not be properly imaged). Data for abyssal hill fault arrays at 9°N
(triangles) and 3°S (squares) on East Pacific Rise (EPR) are also shown
(Cowie et al., 1993, 1994; Carbotte and Macdonald, 1994). Vertical errors
for EPR data were given as 10% of maximum throw by Cowie et al.
(1994). Horizontal errors +2.5 km. Dashed line is projection of mean displacement-length (d/L) ratio reported for much smaller (L < 2 km) faults
on TAG valley floor (Bohnenstiehl and Kleinrock, 1999). Regression lines
shown above were determined by least-squares fit constrained at origin.
MAR Abyssal Hill Fault Arrays
d/L=0.016 (R2=0.65)
700
Projection of data from
TAG median valley floor:
d/L=0.03 for faults
0.15-2 km in length
500
400
EPR 9o N
d/L=0.006 (R2=0.45)
300
McAllister and Cann, 1996; Searle et al., 1998; Bohnenstiehl and Kleinrock,
1999). These morphologic data confirm that the abyssal hill faults examined
here were formed by the coalescence of numerous smaller segments, as evidenced by observations of anastomosing fault traces in map view, fault
scarps of variable width, and relay-ramp structures accommodating the
deformation between overlapping segments. Linkage-dominated patterns of
growth also have been suggested within the boundary faults of the East
African rift system (reasonable analogs to abyssal hills faults) (e.g., Morley,
1999; Contreras et al., 2000). Seismic stratigraphy indicates that these fault
systems extend to their near final lengths early in their development, with displacement then increasing with little further lengthening (Morley, 1999).
200
3.5o S
EPR
d/L=0.004 (R2=0.40)
100
0
0
10
20
30
Fault Length L (km)
40
50
Throw
within the abyssal hills indicate strains of ~10% (see Table 1), suggesting that
fault linkage, rather than propagation, has been the dominant contributor in
their lateral growth. Within the resolution of our data, most faults appear as a
single scarp (Fig. 1F), with some first-order segmentation (Fig. 1E). A finer
scale segmentation (segment lengths ~2–10 km) is apparent, however, within
higher resolution sonar and bathymetric data sets (e.g., Cowie et al., 1994;
Limits Imposed on Maximum Fault Displacement
The thinness of the lithosphere within the fast-spreading environment
will (1) suppress interactions between large faults that penetrate the brittle
d/L= X (all faults)
Maximum throw locked for MAR abyssal
hill fault array (Time 4S in A)
Maximum throw
slow-spreading environment
Distance along strike
Map View
C
B
A
D
d/L= X
d/L< X
Distance along strike
Map View
Time 2
Fault Throw
Throw
Time 1
L
d/
Maximum throw
fast-spreading
environment
Throw
C
Distance along strike
D
Map View
B
Throw
Time 3
Predicted maximum throw
fast-spreading environment
d/L< X (entire fault array)
Distance along strike
Map View
Throw
Time 4F: Fast-Spreading Evironment
Throw necessary to maintain
a linear d/L relationship
Predicted maximum throw
slow-spreading environment
d/L=X (entire fault array)
Distance along strike
X
Maximum throw
locked on EPR
(Time 4F in A)
d/L< X (entire fault array)
Throw necessary to maintain
a linear d/L relationship
=
Incre
a
as th sing ma
ximu
e fau
m
lt arr
ay ev throw
olves
Maximum Scarp Height d (m)
600
B
kage
Growth by lin
A
Resulting fault array
(Time 3 in A)
Fault Segments
(Time 1 in A)
Fault Length
Figure 3. A: Fault evolution in mid-ocean ridge environment.
Small faults (time 1, cf. Bohnenstiehl and Kleinrock, 1999)
link together forming abyssal hill fault arrays mapped off
axis (times 2–3, cf. McAllister and Cann, 1996; Searle et al.,
1998; Bohnenstiehl and Kleinrock, 1999). Slow-spreading
fault arrays (time 4S, see Fig. 1E) can acquire larger displacements during or following linkage, relative to fastspreading fault arrays (time 4F, cf. Cowie et al., 1994;
Alexander and Macdonald, 1996), and consequently are
more likely to maintain or regain displacement-length (d/L)
ratios consistent with those exhibited at time 1. B: Displacement-length plot showing evolution of fault array and
potential limits imposed by maximum fault displacement on
d/L ratio of evolving mid-ocean fault system.
Map View
Time 4S: Slow-Spreading Environment
A
GEOLOGY, May 2000
Figure 10: Bohnenstiehl and Kleinrock: "Fault scaling at TAG"
397
layer (e.g., Ackermann and Schlische, 1997), and (2) limit the maximum
displacement that faults can obtain (e.g., Shaw and Lin, 1996; Ackermann
and Schlische, 1999). The latter effect has been shown to limit the scale over
which a linear d/L ratio can be preserved in scaled physical models (Ackermann and Schlische, 1999). We summarize the potential consequences of
variable lithospheric thickness on the d/L scaling of mid-ocean ridge fault
populations in Figure 3. Consider a simple model of fault growth in which
a fault’s maximum displacement will continue to increase provided the sum
of the stresses resisting fault growth (i.e., friction, σf , and the stress associated with plate flexure, σe ) does not exceed the stress necessary to initiate
a new fault near the ridge axis (σf + cohesion, σc ) (e.g., Shaw and Lin, 1993,
1996). In this formulation, the stresses resisting fault growth are dependent
on both the fault dip and the effective elastic thickness of the lithosphere,
with a thicker lithosphere and shallower fault dip resulting in larger allowable displacements (Shaw and Lin, 1993, 1996).
The maximum allowable throw on an East Pacific Rise abyssal hill fault
was investigated using the formulation by Shaw and Lin (1996). Their results,
which account for lithospheric thickening off axis, show that for fault dips of
45° a fault growing in fast-spreading oceanic lithosphere should obtain a maximum throw of no more than ~100–200 m. Assuming a d/L ratio of 0.015–
0.030 (Cowie et al., 1994; Bohnenstiehl and Kleinrock, 1999), this implies
that any linking system of faults along the East Pacific Rise that extends to a
length >3–14 km will be incapable of gaining the displacement needed to preserve linearity in the d/L relationship (Fig. 3). This includes many, if not most,
of the faults previously used to constrain the d/L ratio within the fast-spreading environment. East Pacific Rise d/L data sets, therefore, exhibit only a
weak linear correlation, with maximum throws that appear to level off
between ~50 and 150 m and d/L ratios that are systematically less than those
reported on the Mid-Atlantic Ridge (Fig. 2). The presence of a significantly
thicker lithosphere within the slow-spreading environment results in larger
predicted maximum throws (~0.4–1 km) (e.g., Shaw and Lin, 1993). Thus,
synlinkage or postlinkage increases in displacement may allow Mid-Atlantic
Ridge abyssal hill faults to maintain d/L ratios similar to those exhibited by
more isolated faults near the axis and consistent with those exhibited across a
range of scales in the terrestrial environment (Figs. 2 and 3).
SUMMARY
Faults on the eastern flank of the Mid-Atlantic Ridge (25–27°N) maintain d/L ratios that are systematically greater than those reported for structures of similar length on the East Pacific Rise (Fig. 2). High-resolution
sonar imagery (e.g., McAllister and Cann, 1996; Searle et al., 1998), scaled
physical modeling (e.g., Spyropoulos et al., 1999; Ackermann and Schlische,
1999), and terrestrial observations (e.g., Morley, 1999) all indicate that the
lengthening of mid-ocean ridge faults may be accommodated largely by
linkage at the abyssal hill scale. We suggest that the low d/L ratios observed
on the East Pacific Rise reflect the inability of fault systems that evolve
within the thin lithosphere of the fast-spreading environment to acquire
additional displacement during or following linkage. Within the slowspreading environment, larger synlinkage or postlinkage increases in displacement allow abyssal hill faults to maintain systematically larger d/L
ratios that are more consistent with those observed elsewhere.
ACKNOWLEDGMENTS
We thank the crew and scientific party of cruise EW9606, especially Chief
Scientist B. Tucholke and Co-Chief Scientist J. Lin; M. Edwards, B. Appelgate, and
R. Davis for assistance with HMR1 processing; S. Carbotte, C. Scholz, and M. Tolstoy
for discussion; and P. Vogt and an anonymous reader for very constructive reviews.
This work was supported by National Science Foundation grants OCE-9503561 and
OCE-9712230. This is Lamont-Doherty Earth Observatory publication 6044.
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Manuscript received November 8, 1999
Revised manuscript received January 24, 2000
Manuscript accepted February 9, 2000
Printed in USA
GEOLOGY, May 2000