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Bathymetric gradients of lineated abyssal hills: Inferring seafloor

spreading vectors and a new model for hills formed at ultra-fast rates

Kelly A. Kriner, Robert A. Pockalny , Roger L. Larson

Graduate School of Oceanography, University of Rhode Island, Horn Laboratory, South Ferry Road; Narragansett, RI 02882, United States

Received 28 July 2004; received in revised form 28 April 2005; accepted 2 May 2005

Available online 18 January 2006

Editor: R.D. van der Hilst

Abstract

Abyssal hill morphology provides a preliminary measure of the direction and rate of seafloor spreading, however, additional

information (e.g., magnetic anomaly data or a nearby mid-ocean ridge) is usually required to verify these estimates. Previous

attempts to identify a unique spreading rate proxy from abyssal hill dimensions (e.g., height, length, width) have largely failed due

to the relatively large scatter of data or the non-linear character of spreading rate trends. We present a new, stand-alone method of

determining both spreading rate and spreading direction using the distribution of azimuths for slopes facing toward and away from

the ridge axis. The spreading rate is determined with the peak height parameter, defined as the difference in the height (maximum

frequency) of the two dominant modes observed in the azimuthal histograms. This parameter exhibits a clear, nearly linear

spreading rate trend and allows half spreading rates to be estimated to within 1020 km/Myr. The spreading direction is determined

with the peak width parameter, which compares the average width of the two dominant modes in the azimuthal histograms. The

wider distribution of slope azimuths is oriented away form the paleo-ridge axis for all spreading rates, and thus spreading direction

can be determined. The trends in the peak height and width parameters are used to constrain a new model of abyssal hill formation

at ultra-fast spreading rates, which require greater off-axis extensional faulting resulting in a few large-throw faults on the outward-

facing hillsides, and many smaller throw faults on the inward-facing hillsides.

2005 Elsevier B.V. All rights reserved.

Keywords: Abyssal hills; seafloor morphology; plate tectonics; mid-ocean ridges; slope analysis

1. Introduction

Abyssal hills constitute 80% of the seafloor and

thus are the most common landform on Earth [1]. The

morphology of abyssal hills is best observed on

relatively young ocean crust flanking mid-ocean ridges

where sediment accumulation has not masked their

appearance. In these settings, the hills are elongateparallel to the ridge axis, have relief of 50500 m, and

characteristic width of 110 km[2]. The proximity of

abyssal hills to the ridge axis suggests these features are

the result of the interplay between tectonic and volcanic

processes occurring within the plate boundary zone.

Once formed, the hills are transported onto the ridge

flanks by plate motion and their basement morphology

is preserved.

Since the early days of seafloor mapping, it has been

realized the general morphology of abyssal hills varies

Earth and Planetary Science Letters 242 (2006) 98 110

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Corresponding author. Tel.: +1 401 874 6926; fax: +1 401 874

6811.

E-mail address:[email protected] (R.A. Pockalny).

0012-821X/$ - see front matter 2005 Elsevier B.V. All rights reserved.doi:10.1016/j.epsl.2005.05.046



as a function of spreading rate; basically, slower

spreading rates generate larger abyssal hills [3]. With

the advent of swath mapping systems, this spreading

rate dependence has become even more apparent and a

three-dimensional description is available. In general,

abyssal hills created at slower spreading rates are higher,wider and longer than those hills created at faster

spreading rates [2]. These relationships led to the

development and refinement of abyssal hill formation

models where tectonic processes dominate at slower

spreading rates and volcanic processes dominate at

faster spreading rates (Fig. 1). At slow spreading rates

(b25 km/Myr, half-rate), back-tilted or listric fault

blocks suggest a predominantly tectonic origin of

abyssal hills [4,5]. At intermediate spreading rates

(2540 km/Myr, half-rate), the split volcano model

suggests tectonic and volcanic processes contributeequally as waxing phases of volcanism create an axial

rise that is subsequently bisected during waning

volcanic phases [6,7]. At fast spreading rates (4060

km/Myr, half-rate), the presence of a steady-state

magma chamber precludes the formation of split

volcanoes at the ridge axis, so the abyssal hills are

generated slightly farther off-axis by the formation of a

graben along the shouldersof the axial high[8]. In this

model, the fault scarp closest to the ridge axis is

subsequently covered by volcanic flows emanating from

the ridge axis.

The goal of many seafloor morphology studies has

been to identify a parameter or set of parameters that

can be used to determine the kinematic setting in

which a parcel of seafloor was created. This would be

particularly useful in sections of the seafloor where

conventional methods of determining spreading rateswith seafloor magnetic anomalies are compromised

due to the lack of correlatable magnetic anomalies in

crust created at northsouth trending mid-ocean ridges

near the magnetic equator and in crust created during

periods of uniform magnetic polarity (e.g., Cretaceous

magnetic superchron, 12184 Ma). Abyssal hill

morphology would initially seem to be an attractive

alternative within these magnetically challenged

regions; however, the spreading rate variability of

these first-order morphologic parameters (relief, width,

length) often is not linear and the scatter is too largeto identify a unique spreading rate. Even when

combined with lower-order parameters (e.g., vertical

skewness and kurtosis), a unique spreading rate cannot

be obtained [2].

In this study, we explore the use of bathymetric

gradients (magnitude and direction of seafloor slope) to

determine the kinematic environment of abyssal hill

formation. Since the abyssal hill formation models

predict asymmetric distributions for volcanism and

tectonism on the sides of abyssal hills facing toward

and away from the ridge axis, our analysis compares the

Fig. 1. Three general models of abyssal hill formation and associated ridge morphologies for a) slow, b) intermediate, and c) fast spreading rates(after Macdonald et al. [8]).

99K.A. Kriner et al. / Earth and Planetary Science Letters 242 (2006) 98110



slope characteristics of the two sides. Our results

indicate spreading rates can be predicted with improved

confidence and the direction of spreading can also be

determined. In addition, a new abyssal hill formation

model is proposed for seafloor created at ultra-fast

spreading rates (N60 km/Myr, half-rate).

2. Data and methods

2.1. Data

Gridded multibeam bathymetry data from 64 areas of

known spreading rates are used in this study (Fig. 2).

Each area consists of lineated abyssal hill topography

located adjacent to a mid-ocean ridge (Fig. 3,Table 1),

encompassing a 5050 km area of seafloor. Extreme

care was taken to ensure the areas were fully imagedwith overlapping swaths and were devoid of transform

faults, anomalously deformed seafloor, or excessive off-

axis volcanism. The bathymetry data were obtained

from the RIDGE Multibeam Synthesis Project [9] as

gridded data sets with grid node spacings ranging from

100 to 300 m (Table 1). The highest resolution (smallest

grid node spacing) is chosen for each area, and is

dependent on the resolution of the imaging systems used

to collect the data. To ensure the different node spacing

did not adversely affect our analyses, additional

bathymetric grids were created from the ping data with

grid intervals increasing in increments of 100 m [10].

The suite of slope analyses, described below in the

methods section, was applied and the results were

consistent for grid intervals less than 500 m. For grid

intervals greater than 500 m, the results deviated

significantly and became quite variable.

Spreading rates for the chosen areas were deter-

mined with two methods. In areas where high-quality

marine magnetics data are available, spreading rateswere determined directly by forward modeling of

magnetic anomaly data obtained from the NGDC

trackline geophysics archive [11]. In the areas where

magnetics data are inconclusive (e.g., near the

magnetic equator), the current spreading rate of the

adjacent ridge is used based on the global plate

motion model Nuvel-1A [12].

2.2. Methods

Abyssal hill asymmetry is evaluated by expanding ona method previously developed by Shaw and Smith

[13,14] and Smith and Shaw [15] that compares the

distributions of bathymetric slopes. With this method,

the surface of an individual grid cell, defined by four

grid nodes, is parameterized by a unit vector oriented

normal to the grid cell surface. The unit vector is then

decomposed into azimuthal and dip components with

the GRDGRADIENT command available with the

Generic Mapping Tools software package [16]. The

distribution of slope angles, as a function of azimuth,

provides a measure of asymmetry in the cross-sectional

shape of abyssal hills. This was the method used be

Smith and Shaw[15] to demonstrate that abyssal hills

created at slow spreading rates are asymmetric in cross-

Fig. 2. General location of the multibeam bathymetry data used in this study. Within each of the four regions marked by boxes, 16 data sets were used,8 from each side of the included spreading ridge ( Table 1). The bathymetry examples inFig. 3are from areas within each of the four boxes.

100 K.A. Kriner et al. / Earth and Planetary Science Letters 242 (2006) 98110



Fig. 3. Examples of lineated abyssal hill topography for a) slow, b) intermediate, c) fast, and d) ultra-fast spreading rates. The shaded box on each map

is an example of a selected region used in our analysis. The double-arrow line indicates the direction of spreading. The histograms in Figs. 4 and 7correspond to the data set location shown in a). The inward and outward facing azimuths are also indicated in a).




Table 1

Bathymetry data locations, spreading rates, grid node spacing, and imaging systems used

Sample

#

Adjacent ridge Bounding coordinates Half-rate

(km/my)

Grid nodes

pacing (m)

Imaging system

W E S N

1 N. Mid-Atlantic

Ridge (Slow spreading)

45.00 44.51 21.77 22.22 11.5 200 Hydrosweep and Seabeam

2 45.79 45.30 21.96 22.41 11.5 200

3 44.84 44.35 22.41 22.86 11.5 200

4 45.65 45.16 22.41 22.86 11.1 200

5 43.02 42.51 28.85 29.30 11.5 200

6 43.76 43.25 29.00 29.45 11.5 200

7 41.91 41.40 29.40 29.85 11.5 200

8 44.01 43.50 29.75 30.20 11.5 200

9 42.51 42.00 28.80 29.25 11.5 200

10 44.27 43.76 29.10 29.55 11.5 200

11 41.75 41.24 30.00 30.45 11.5 200

12 42.71 42.20 30.20 30.65 11.5 200

13 44.75 44.24 23.20 23.65 11.8 200

14 46.11 45.60 23.20 23.65 10.9 200

15

42.51

42.00 28.80 29.25 11.5 20016 43.91 43.40 29.05 29.50 11.5 200

17 Southeast Indian

Ridge (Intermediate

spreading)

109.60 110.27 49.60 49.15 37.1 200 Seabeam

18 109.33 110.00 50.12 49.67 37.5 200

19 101.93 102.60 47.85 47.40 32.4 200

20 101.58 102.25 48.35 47.90 37.2 200

21 114.90 115.57 49.95 49.50 40.5 200

22 114.58 115.25 50.40 49.95 45.9 200

23 112.75 113.42 50.20 49.75 36.0 200

24 112.80 113.47 50.75 50.30 36.0 200

25 108.00 108.67 48.60 48.15 39.1 200

26 107.58 108.25 49.15 48.70 32.2 200

27 107.28 107.95 48.40 47.95 36.8 200

28 106.91 107.58 49.02 48.57 32.2 200

29 103.25 103.92 47.85 47.40 40.8 20030 103.03 103.70 48.45 48.00 36.0 200

31 100.95 101.62 47.45 47.00 36.0 200

32 100.48 101.15 47.95 47.50 33.6 200

33 N. East-Pacific Rise

(Fast spreading)

104.20 103.75 14.45 14.90 42.1 300 SeaMARC II and

Hydrosweep34 104.90 104.45 14.15 14.60 52.7 300

35 104.00 103.55 13.75 14.20 44.9 300

36 104.90 104.45 13.75 14.20 52.9 300

37 103.95 103.50 13.25 13.70 44.4 300

38 104.65 104.20 12.80 13.25 53.4 300

39 103.90 103.45 12.74 13.19 45.8 300

40 104.50 104.05 12.74 13.19 53.8 300

41 103.70 103.25 11.55 12.00 54.7 300

42 104.30 103.85 11.30 11.75 53.7 300

43 103.60 103.15 10.35 10.80 57.7 200

44 104.40 103.95 10.25 10.70 55.7 200

45 104.10 103.65 9.25 9.70 51.7 300

46 104.90 104.45 9.30 9.75 60.7 300

47 103.75 103.30 8.60 9.05 51.0 300

48 104.95 104.50 8.45 8.90 62.7 300

49 S. East-Pacific Rise

(Ultra-fast spreading)

107.60 107.15 7.85 7.40 69.5 100 SeaMARC II and

Hydrosweep and Seabeam50 108.46 108.01 7.70 7.25 69.5 100

51 112.85 112.40 16.70 16.25 75.7 200

52 113.60 113.15 16.70 16.25 75.7 200

53 113.00 112.55 17.50 17.05 79.6 200

54 113.75 113.30 17.50 17.05 76.7 200

55 112.90 112.45 16.50 16.05 73.8 200

56 113.60 113.15 16.50 16.05 73.8 200




section and that this asymmetry decreases or is

statistically insignificant at intermediate spreading rates.

For our study, we utilized the azimuthal distribution

of the vectors to obtain a measure of abyssal hillasymmetry. This method is based on previous work

[14,15]that indicates the majority of slope azimuths are

oriented perpendicular to the abyssal hill lineations. This

results in a bimodal slope azimuth distribution with

histogram peaks that are typically about 180 apart and

centered on azimuths oriented perpendicular to the hills

(Figs. 3a, 4a and 5a). Each peak in the population

distribution is therefore comprised of those slopes on

opposite sides of the abyssal hills.

Two parameters are used to assess the cross-sectional

asymmetry of abyssal hill morphology. The first

parameter, peak height, is the difference in the height

(maximum frequency) of the two dominant modes

observed in the azimuthal histograms (Fig. 4). We

subtract the histogram height of the inward-facing side

(i.e., facing the ridge axis) from the histogram height of

the outward-facing side to obtain a positive or negative

peak height that depends on the sense of asymmetry.

A positive peak height indicates the inward-facing

side of the abyssal hill is steeper than the outward-facing

side. Conversely, a negative peak height indicates the

outward-facing side of the abyssal hill is steeper than the

inward-facing side. The magnitude of the peak heightincreases as the asymmetry increases. A zero peak

height indicates a symmetric abyssal hill cross-section.

The second parameter, peak width, is the

difference in the average peak width (APW) of the

two dominant modes observed in the azimuthal

histograms (Figs. 4, 6). The initial step to calculate the

APW is to sum the peak widths (PWi) for each interval

of 10 (number of slopes) from the base (PW1) to the tip

(PWN) of each peak. Where PW1is determined to be the

larger of the two minimum values (number of slopes) for

both peaks, and interval PWNis calculated at the largest

increment of 10 for that peak. The APW is the sum of

the interval peak widths divided by the number of

intervals calculated (N).

APW N

1

XPWi=N

As with the peak height, the peak width is

calculated by subtracting the APW of the inward-facing

Table 1 (continued)

Sample

#

Adjacent ridge Bounding coordinates Half-rate

(km/my)

Grid nodes

pacing (m)

Imaging system

W E S N

57 113.00 112.55 17.00 16.55 74.7 200

58 113.70 113.25 17.00 16.55 74.8 200

59 113.35 112.90 19.00 18.55 80.6 200

60 114.00 113.55 18.50 18.05 69.9 200

61 113.10 112.65 18.00 17.55 81.6 200

62 113.80 113.35 17.95 17.50 73.8 200

63 113.47 113.00 20.00 19.53 84.5 200

64 114.20 113.75 19.75 19.30 73.8 200

Fig. 4. a) Cartesian histogram for the data set shown inFig. 3a, indicating the percentage of slopes that face each particular azimuth. The two peaks are

centered on azimuths perpendicular to the abyssal hill lineations. The difference in height between the two peaks (peak height) is a relative measure

of the cross-sectional asymmetry of the hills. b) Cartoon explaining that a longer running, more gently sloped hillside has a greater number of equallyspaced data points (taller azimuth peak) than a shorter, more steeply sloped hillside.




side of abyssal hills from the APW of the outward-

facing side.The APW is very similar to other measures of

variance (e.g., standard deviation). Instead of calculat-

ing the range over which 69% of a population occurs for

the standard deviation, the APW defines the average

width of the population curve above some defined

background value. Larger values of the APW indicate

the range of slope azimuths are more broadly distributed

and would suggest an undulating, sinuous or hummocky

topography (e.g, Fig. 5). A smaller APW indicates a

more uniform slope azimuth associated with more

lineated topography. We also experimented with the

standard deviation and kurtosis of the histogram peaks

as measures of azimuthal dispersion; however, the APW

parameter provides the best graphical description of the

key observations when the azimuthal data were

projected onto rose diagrams.

3. Results

The bathymetric slope azimuth distributions for 64

areas (Figs. 2, 3) from a range of known spreading rates

are analyzed. The results are plotted as histograms (e.g.,

Fig. 4a) and rose diagrams (e.g.,Fig. 5a) and the results

are consistent with previous studies that have charac-

terized the linearity of abyssal hill topography with

bimodal distributions [1315]. However, our study has

quantified variations in the plots with the peak height

and peak width parameters to identify observed

changes in abyssal hill morphology as a function of

spreading rate.

Fig. 5. a) Rose diagram for the area shown in Fig. 3a, which is the same histogram data as shown in the Cartesian histogramFig. 4a. The two peaks/

lobes are centered on azimuths perpendicular to the hill lineations. The angular width of the lobes (range in azimuths) is measured as the average

width in degrees of azimuth of the lobe, and is named Average Peak Width (APW). b) A wider rose lobe (greater range of azimuths) is interpreted as a

more volcanic surface, and the narrower lobe (smaller range of azimuths) is interpreted as a smoother, faulted surface.

Fig. 6. The peak width (PW) is calculated at intervals of 10 (number of slopes), from the base to the tip of each peak. The intervals start at the higher of

the two trough values (PW1) and end at the maximum interval for that peak (PWN). The APW (average peak width) is the sum of the peak widthcalculations (1

NPWi) divided by the total number of intervals (N). This is done separately for each peak.




3.1. Abyssal hill asymmetry and spreading rate

A clear trend is observed in the peak height

distribution when the histograms are viewed as a

function of spreading rate (Fig. 7). At slower spreading

rates, the histogram peaks of the outward-facing sides ofthe abyssal hills are taller than the peak for the inward-

facing sides; this pattern is reversed at faster spreading

rates (i.e., the peak height values pass through zero).

To quantify this trend, the peak height parameter (e.g.,

outward-facing peak minus inward-facing peak) is

plotted against spreading rate. It exhibits a roughly

linear decrease as function of increasing spreading rate.

For slow and intermediate spreading rates (b40 km/

Myr, half-rate), the peak height values are all positive,

which indicates the inward-facing slopes are steeper

than the outward-facing slopes. At fast-spreading rates(4060 km/Myr, half-rate), the peak height decreases,

suggesting more symmetric abyssal hills. At ultra-fast

spreading rates (N60 km/Myr, half-rate), the majority of

the peak height values are negative, which indicates

the sense of asymmetry has switched and the outward-

facing slopes are now steeper than the inward-facing

slopes. If enough data points are included in the analysis

(e.g., Fig. 7), the overall trend is nearly linear as a

function of spreading rate.

A similar decrease in abyssal hill asymmetry as a

function of spreading rate has also been observed in

other abyssal hill morphology studies. Smith and Shaw

[15] used conventional Sea Beam multibeam data and

characteristic slope analyses to show the inward-facing

slopes of abyssal hills created at slow spreading rates

were significantly steeper than the outward-facing

slopes. At intermediate spreading rates, the magnitude

of the measured asymmetry decreased to the point where

the difference between inward-and outward-facing

slopes was statistically insignificant. Carbotte and

Macdonald [17] used a range of surface- and deep-

towed side-scan data to show the percentage of inward-facing fault scarps was greatest for slow spreading

ridges. The relative difference in inward- versus

outward-facing scarps decreased linearly as a function

of spreading rate, suggesting a symmetric abyssal hill

cross-section. All of these studies exhibit the same

general trend in the cross-sectional asymmetry as a

function of spreading rate. In our study, however, we

show the sense of asymmetry of abyssal hills created at

ultra-fast spreading rates actually reverses to steeper

outward-facing slopes.

3.2. Comparison of inward-and outward-facing

azimuth distributions

Another pattern is observed when the slope azimuth

distributions are displayed as rose diagrams (Fig. 5).

These plots reinforce the bimodal distribution of slope

azimuths by the presence of two lobes corresponding to

the inward- and outward-facing slopes of abyssal hills.

The interesting aspect of these plots, however, is that the

lobe corresponding to the outward-facing slope is

almost always the wider or broader lobe. We use the

peak width parameter to quantify the relative

difference between the outward-and inward-facing

average peak width. In all cases but two, the outward-

facing slopes have a broader distribution of slopes than

the inward-facing slopes (Fig. 8). The average peak

Fig. 7. peak height values for all 64 data sets plotted versus spreading rate. Positive values indicate the outward-facing side is more gently sloped

(taller azimuth peak), and negative values indicate the inward-facing side is more gently sloped. The mean peak height and 95% confidence limitsare shown for each spreading rate interval. A best-fit line (dashed line) for the individual data points and associated equation are shown.




width is 9 and does not change significantly as a

function spreading rate. The variability of the peak

width is fairly uniform for spreading rates greater than

30 km/Myr (half-rate), but increases for abyssal hills

created at slow spreading rates.

4. Discussion

4.1. Inferring spreading rates

The observed correlation between the peak height

and spreading rate (Fig. 7) suggests this parameter may

be used to infer spreading rates for areas of the seafloor

where such information is lacking. For instance, positive

peak height values would indicate spreading rates

were definitely less than 40 km/Myr (half-rate), and

more than likely less than 60 km/Myr (half-rate).

Negative peak height values would likely indicate

spreading rates greater than 6065 km/Myr (half-rate).

Knowing the difference between abyssal hills created at

fast versus ultra-fast spreading rates may initially seemtrivial; however, there are large portions of the seafloor

for which no spreading rate information is available. For

example, crust created during the Cretaceous magnetic

superchron (12184 Ma) in the southwest Pacific has

estimated spreading rates very near the changeover from

positive to negative peak height values. Since the

spreading rates here are interpolated over a long period

(36 million years), the actual spreading rates likely

varied during this time. The peak height parameter

would be very useful in identifying which sections of

the seafloor in such regions were created above or belowthis threshold spreading rate.

A more precise measure of seafloor spreading rates,

or range of spreading rates, may be obtained by fitting a

regression curve and error estimates to the peak

height data (Fig. 7). Based on the linear trend and the

standard deviation of the peak height graph, the

spreading rate of a given parcel of seafloor can be

determined to within about 1020 km/Myr (half-rate).

The linear trend in the peak height parameter is one of

the measured abyssal hill morphology parameters that

show a nearly uniform and monotonic trend as a

function of spreading rate. Other parameters, such as

abyssal hill roughness[2,18], exhibit a general decrease

as a function of spreading rate; however, the roughness

increases again at ultra-fast spreading rates producing an

ambiguity if this parameter is used to estimate spreading

rate. The combination of the peak height with these

other abyssal hill morphology parameters, such as

seafloor roughness, and abyssal hill height, length or

aspect ratio, may provide even better means for

determining spreading rates.

4.2. Inferring spreading direction

Abyssal hill lineations are frequently used to estimate

the general direction of seafloor spreading, however, in

some situations it is difficult to determine which side of

the abyssal hills point toward or away from the paleo-

spreading ridge, and hence the true spreading direction.

Plots of the azimuthal distribution of abyssal hill slopes,

presented as rose diagrams (Fig. 5a), indicate the

broader lobe coincides almost invariably with the side

of the abyssal hill facing away from the ridge axis oforigin. The peak width parameter quantifies this rose

Fig. 8. peak width values for all 64 samples plotted versus spreading rate. A positive value indicates a larger average width for the outward-facing

lobe and is interpreted as a hillside with a broader distribution of slope azimuths. The mean peak width and 95% confidence limits are shown for

each spreading rate interval.



http:///reader/full/bathymetric-gradients-of-lineated-abyssal-hills-inferring-seaflo

diagram trend and supports the observation that the

wider lobe is consistently associated with the outward-

facing slope (Fig. 8).

Identifying the paleo-spreading direction from multi-

beam bathymetry data alone has many applications. In

tectonically complex areas of seafloor (e.g., microplatesand triple junctions) with variable spreading histories,

knowing the paleo-spreading direction would be

essential for tectonic reconstructions. The relative

direction of the paleo-spreading ridge, as well as its

approximate orientation can be determined by the

peak width method without the need for any other

information about the surrounding area. This can aid in

seafloor reconstruction studies as well as allow study of

areas where other data for identifying spreading

direction, or position relative to a spreading ridge, are

unavailable.Our technique is quick and easy to use, and does not

require extensive pre-editing of the data. It may be

performed while at sea during the collection of new

bathymetry data, as well as on previously collected data

from many different surveys. Thus, it can be used to

help guide a survey in near-realtime or to subsequently

analyze the results.

4.3. Implications for models of abyssal hill formation

The slope azimuth distribution histograms (Figs. 4a,

7) indicate the degree of hill asymmetry decreases as

spreading rate increases (i.e., peak height values

approach zero). A transition occurs from fast to ultra-

fast spreading rates as negative peak height values

become more common at faster rates. For ultra-fast

rates, the peak height is generally negative (Fig. 8)

indicating the outward-facing hillsides are generally the

more steeply sloped sides. These results support

previously proposed models of abyssal hill morphology

and formation for slow to fast spreading rates [8](Fig.

1). At ultra-fast rates, however, the change in the sense

of abyssal hill asymmetry (Fig. 7) does not allow for thesimple extrapolation of formation models applicable to

fast spreading rates. Below we review previous models

for hills formed at slow, intermediate, and fast rates, and

propose new models for hill morphology and formation

at ultra-fast rates.

4.3.1. Slow to fast spreading rates

At slow spreading rates (b25 km/my, half rate),

magma supply is lowest and the crust is relatively cool

and brittle[19,20].Hills formed in this environment are

a result of back-tilted fault blocks and have a largeasymmetry (Figs. 1a and 9a). Large-throw normal

faulting forms the inward-facing hillsides, which creates

a steeper, smoother surface. The outward-facing sides

are relatively unfaulted, creating a rougher and more

gently sloped surface.

At intermediate spreading rates (2540 km/my, half

rate), magma supply is intermittent [19,20]. Axialvolcanoes form during times of higher magma supply

and are then split and rafted away by continued

spreading during times of low magma supply (Figs. 1b

and 9b). Large-throw normal faulting also forms the

inward-facing sides of these hills, though the hillsides

are not as steeply sloped as those of the slow rate hills.

The outward-facing sides are formed by the axial

volcanic flows, resulting in a more gently sloped surface

than the inward-facing side. These hills have a smaller

and more variable asymmetry than the slow-rate hills

(Fig. 7).At fast spreading rates (4060 km/my half rate),

magma supply is more steady state and the crust is

warmer and more ductile [19,20]. Hills created in this

environment result from off-axis rifting of the seafloor

which creates fault bounded grabens, followed by

volcanic flows originating at or near the axis that flow

outward and partially cover the innermost fault scarp [8]

(Fig. 9c). Since the rifts form the valleys between hills,

one rifting episode creates half of two abyssal hills. The

scarp that is covered by volcanic flows forms the

outward facing side of one hill, while the scarp not

covered by flows forms the inward facing side of

another hill. Two rifting episodes result in one complete

hill with a volcanically covered outward-facing hillside.

These hills are usually more symmetric than slow or

intermediate abyssal hills, and occasionally result in a

steeper outward-facing side (Fig. 7), possibly dependant

on the amount of volcanism. Regardless of which side is

steeper, the inward-facing side generally remains the

relatively smoother surface, as indicated by the smaller

peak width (Fig. 8).

4.3.2. New models for ultra-fast spreading ratesThe observations we must satisfy for abyssal hills

formed at ultra-fast rates (N60 km/my half rate) are

that the outward-facing hillsides are generally steeper

and yet always rougher (larger peak width) than the

inward facing hillsides. Ultra-fast spreading rates are

accompanied by greater extensional stresses acting on

the crust. This results in a magma supply that is closest

to steady state and very high volume, with extensive off-

axis volcanism occurring up to several kilometers from

the spreading axis[21]. Hills created in this environment

begin to form similarly to those of fast rates, by off-axisrifting and volcanic flows. More extensive volcanism




and/or greater extensional faulting at ultra-fast ratesfurther modifies the abyssal hills, making them slightly

larger than those of fast rates [2,18] and reversing the

sense of asymmetry (Fig. 7). We now speculate on how

this might happen.

One obvious scenario to explain our results is that

volcanism at ultra-fast spreading rates may include large

sheet flows originating from the ridge axis and flowing

outward into the off-axis rift scarps. These volcanic

flows would cover the outward-facing rift scarps to a

larger extent than at fast rates, making the outward

facing hillsides more gently sloped than those of fastrate hills. However, this would only increase the

asymmetry of ultra-fast hills over that of fast hills,without changing the sense or sign of the asymmetry.

This is not supported by the peak height results,

which suggest a reversal in the sense of asymmetry for

most ultra-fast hills (negative peak height) (Fig. 7).

Another potential scenario is that volcanism at ultra-

fast spreading rates may also include off-axis volcanism,

with off-axis faults acting as conduits to the shallow

magma chamber[21,22]. The rift faults that create the

inward-facing hillsides may extend deep enough to tap

the shallow magma chamber, creating volcanic flows

that partially cover the inward-facing hillsides. Thiswould decrease the steepness of the inward-facing

Fig. 9. Four models of abyssal hill morphology and formation as a function of half spreading rate proposed by this study. The spreading center is to the

right, and the direction of spreading is to the left in all cases. In the new model for ultra-fast rates, fewer and longer throw faults on the outward-facing

hillsides relative to more and shorter throw faults on the inward-facing hillsides causes the observed reversal in the peak height parameter.




hillsides, possibly enough to cause the inward-facing

sides to be more gently sloped than the outward-facing

sides. This would reverse the sense of asymmetry

observed at slower spreading rates. The peak height

results support this model (negative values for ultra-fast

rates) (Fig. 7). However, the volcanic flows would haveto be more extensive on the inward-facing side than

those produced from the near-axis flows that cover the

outward-facing side. This is contradicted by the peak

width results that indicate that the inward-facing side is

always the more planar side (Fig. 8).

A primarily tectonic scenario assumes extensional

stress at ultra-fast spreading rates is partially accommo-

dated by inward-facing listric faults, which causes a

back tilting of the abyssal hills, as they rotate outwards

along these faults. The back tilting results in a steeper

outward-facing hillside and a more gently slopedinward-facing hillside. This would cause a reversal in

the asymmetry of the hills (steeper side outward) while

maintaining the asymmetry in roughness (more planar,

faulted side inwards). This model is supported by both

the peak height results (Fig. 7) and the peak width

results (Fig. 8); however, we question the likelihood of

this model. Though inward-dipping listric faults have

been proposed to occur near the ridge axis [23], we

believe rotation is more likely to occur inwards along

outward-dipping listric faults, which result from the

collapse of the magma chamber at the ridge axis [24

26]. Inward rotation would increase the asymmetry of

the abyssal hills without reversing the sense of

asymmetry, and therefore, not be supported by our

observations.

Our preferred scenario assumes the extensional stress

at ultra-fast spreading rates is partially accommodated

by a large number of small-throw normal faults on the

inward-facing hillsides, and a lesser number of larger

throw faults on the outward-facing side (Fig. 9d). Due to

the age-related thickening and shallow depth of the

lithosphere/asthenosphere boundary layer, the brittle

crust is thinner on the inward-facing side of the hills,making it easier to form many smaller faults. On the

outward side, larger faults form through the thicker

brittle layer, which can accommodate the same amount

of strain over a fewer number of faults. The large

amount of extensional stress created by such high

spreading rates may not be fully accommodated by

increased magma upwelling at the ridge axis, so greater

amounts off-axis faulting are required to accommodate

the increased extension. The additional extension at

higher spreading rates is also consistent with elevated

strain rates predicted by unbending

of the lithospherewithin 15 km of the ridge axis [27]. The larger number

of small faults on the inward side creates a longer

running, more gently sloped surface than that created on

the outward side by the fewer, larger throw faults. This

would cause the inward-facing side to be the more

gently sloped side, giving the hills a reversed sense of

asymmetry. Since the outward-facing scarps wereinitially formed by flows emanating from the ridge

axis, as observed at fast-spreading rates, the hills at

ultra-fast rates should inherit roughly the same peak

width values. The additional off-axis faulting would

likely affect the slope distributions of the inward- and

outward-facing hill sides the same. This model is

supported by both the peak height results (Fig. 7)

and the peak width results (Fig. 8).

5. Conclusions

Our results indicate the distribution of bathymetric

slopes obtained with gridded multibeam bathymetry

data can be used to identify paleo-spreading rates, to

determine paleo-spreading directions, and to evaluate

abyssal hill asymmetry. Paleo-spreading rates are

determined with the peak height parameter, which

compares the peak or maximum frequency of slope

azimuth distributions for the outward-and inward-facing

sides of abyssal hills. Our results indicate the peak

height parameter has higher peaks for hillsides facing

away from the ridge axis at slow spreading rates. This

pattern reverses at ultra-fast spreading rates. When

plotted as a function of increasing spreading rate, the

peak height parameter exhibits a roughly lin ear

decrease, which can be used to obtain an estimate of

paleo-spreading rate. Paleo-spreading direction is iden-

tified with the wider lobe of the slope azimuth rose

diagram, either visually or by calculating the peak

width. The spreading direction is the azimuth at the

center of the wider lobe, assuming orthogonal spreading

(Fig. 8). The variation of abyssal hill asymmetry with

spreading rate is also evaluated using bathymetric slope

distributions. For all spreading rates, the inward-facinghillsides are more uniform (narrower range of slope

azimuths) and are consistent with a tectonic/faulted

origin, while the outward-facing hillsides have a

relatively wider slope azimuth that is consistent with a

volcanic origin (Fig. 8).

The results from this study support previous models

for hill formation at slow, intermediate and fast

spreading rates (Fig. 9 a, b, and c). Slow hills are

formed as back-tilted fault blocks, intermediate hills

form as split volcanoes, and fast hills form by a

combination of rifting and volcanism. We discuss fourscenarios (below) for hill formation at ultra-fast rates.




The first three models are not supported by the results of

our study.

1) Large sheet flows originating at the spreading axis

and covering the outward facing rift scarps would not

result in a reversed sense of asymmetry (Fig. 7).2) Off-axis volcanism, resulting from inward-facing

faults tapping a magma reservoir would cover the

inward-facing scarps. This would create hills that are

not asymmetrical in roughness (Fig. 8).

3) Back tilting of the hills along listric faults would

create hills that reverse the sense of cross-sectional

asymmetry, though we do not believe this model to

be likely.

4) We prefer a model of greater off-axis extensional

faulting resulting in a few large-throw faults on the

outward-facing hillsides, and many smaller throwfaults on the inward-facing hillsides (Fig. 9d). This

model is more likely to create hills that have a

reversed sense of cross-sectional asymmetry and

agree with peak width observations.

Acknowledgments

This research was partially sponsored by the State of

Rhode Island and NSF grants OCE-9818776 and OCE-

9912236 to R. A. Pockalny and R.L. Larson. John Goff,

Deborah Smith, and Rob van der Hilst provided

comprehensive and useful reviews.

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