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Depth distribution and bathymetric classification of some sea-floor profiles
Marine Geology - Elsevier Publishing Company, Amsterdam - Printed in The Netherlands
DEPTH DISTRIBUTION AND BATHYMETRIC CLASSIFICATION OF SOME SEA-FLOOR PROFILES D. C. KKAUSEAND H. W. MENARD Graduate School of Oceanography, University of Rhode Island, Kingston, R.L (U.S.A.) ; Institute of Marine Resources, University of California, San Diego, La Jolla, Calif. (U.S.A.)
(Received October 1, 1963) (Resubmitted December 23, 1964)
SUMMARY Fifteen east Pacific sea-floor profiles of 60 nautical miles length are analysed as to depth of the sea floor and the character of the hills. Mechanical energies of formation of some model hills are discussed. Several profiles have a Gaussian distribution of depths and others seem to have a large component that is Gaussian. Correlation related to repetition of sea-floor slopes along the individual profile is nil. Pigeonhole classification of the profiles on the basis of relief corresponds to geological environments. A rough equation of the number of hills (No) of given height (H) in a 60 nautical mile profile is: N o ------9/15log 10n + a
A rough equation of the number of hills in all fifteen profiles (Nln) relative to their widths is: N15 = 120 W"z/2 which implies that the smaller the hills, the more common they are at an exponential rate. Within their context, the statistical and physical characteristics of the profiles can be related to the geological composition of the sea floor and to some of the geological processes modifying the sea floor. The predictability of the characteristics encourages study of large-scale processes important in the evolution of the sea floor.
INTRODUCTION Abyssal hills cover large areas of the ocean floor, yet little is known regarding their character, their origin, and the geologic processes involved in their formation and Marine GeoL, 3 (1965) 169-193
170
D . C . KRAUSE AND H. W. MENARD
160" 40 °
150"
140 °
130 °
'
120 °
~ILSUn
14 13 8 30"
r. . . .
i
1112 ] e
Hawaiian
]
l Fig.l. Index map showinglocation of profiles in northeastern Pacific. modification. Abyssal hills are less than 500 fathoms (3,000 ft.) or 1,000 m (3,300 ft.) in height by definition. A study was undertaken to examine certain properties of abyssal hills, and to develop a classification indicative of the origin of the hills. The study consists of: (1) depth distributions of the sea floor, and (2) distribution and classification of seamounts, abyssal hills and swells. Fifteen, 60-mile-long profiles of the sea floor of the northeastern Pacific Ocean (Fig.l, 2) were chosen for a detailed analysis of their bathymetric characters. The profiles were recorded on EDO depth recorders on ships of the Scripps Institution of Oceanography (University of California) and the U. S. Naval Electronics Laboratory. Depths were read at three-minute intervals which represent a distance of 0.484-0.632 nautical miles (n.m.) depending upon the ship speed (Table I). The results of this paper are not easily related to the published work regarding analyses of subaerial geomorphology. Most such studies deal with smaller-scale features. More importantly, the subaerial geomorphologic features have been greatly modified by erosion which is virtually unknown in the deep-sea environment although minor downhill movement occurs. The profiles are affected by the materials of the sea floor and the geologic processes which have modified the sea floor. The composition of the sea floor in this study can be broadly divided into three main components: (I) recent, soft sediments, (2) older, stiffer or hard sediments, (3) lava flows. The processes modifying the sea floor locally can be broadly divided into the following main groups: (a) pelagic sedimentation, (b) turbidity current deposition, (c) slumping of sediments, (d) tectonic deformation and (e) volcanism. In certain cases, we can pinpoint the conditions. Profile 15, for example, was chosen to be typical of turbidity current deposition of recent, soft sediment. The steep slopes, especially the longer ones, are generally associated with volcanoes as in profiles 8, 10, 11 and 12. The other conditions, however, are not so easily determined but in certain circumstances will be discussed. Marine Geol., 3 (1965) 169-193
,.L
F,
0.566
0.545 0.484 0.535 0.561 0.571
0.600
0.619 0.561 0.577 0.588
0.571
0.571
0.582 0.632
2 3 4 5 6
7
8 9 10 11
12
13
14 15
Length of 3-min interval (n.m. )
INFORMATION
1
Profile
PROFILE
TABLE I
Capricorn Cascadia
Capricorn
Hawaii '53
Hawaii '53 Hawaii '53 Hawaii '53 Hawaii '53
Hawaii '53
Cusp Cusp Transpac Transpac Hawaii '53
Cusp
Cruise
Horizon EPCER 857
Horizon
Horizon
Horizon Horizon Horizon Horizon
Horizon
Baird Horizon Baird Baird Horizon
Baird
Ship
05h00-10hl0, 30 Sept. 1952 01h00--05h50,29 Sept. 1952
18h00--23h16, 29 Sept. 1953
18h20-23h50, 26 Oct. 1953
00h15-05h25, 4 Oct. 1953 02h00-07h35, 26 Oct. 1953 07h35-13h00, 26 Oct. 1953 13h00-18h20, 26 Oct. 1953
14h00-19h10, 4 Oct. 1953
01h00, 13 Aug. 1953 03h30, 29 July 1953 16h15-22h00, 23 Nov. 1953 09h00-14h30, 3 Nov. 1953 07h00-12h30, 3 Oct. 1953
06h30, 11 Aug. 1953
Date
north of Murray Fracture Zone, large hills, irregular relief north of Murray Fracture Zone, very low hills off Deep Plain, rolling plain east of Hawaiian Arch, large rolling hills west of Patton Escarpment, blocky steep hills south of Murray Fracture Zone, broad high hills south of Murray Fracture Zone, gently rolling deep-sea fan Moonless Mountains Hawaiian Arch Hawaiian Arch, just east of 9 Hawaiian Arch, just east of 10, subdued low hills with seamounts Hawaiian Arch, just east of 11, subdued low hills with seamounts Murray Fracture Zone, top of main ridge, increasinglyhilly to right Murray Fracture Zone, bottom of main ridge nearshore, abyssal plain with one deep-sea channel
Character
-t
~.
r~
k,/
! 800
5~
2400 2400
3000 2400
3000 ! 000
M
Fig.2. Echo sounding protiles of tile 60-mile long sections of the sea flool. Mari#w Geol., 3 !1965) 169-193
Fig.2. Legend see p.172. Marine Geol., 3 (1965) 169-193
174
t). C. KRAUSE AND H. W. MENARD
Limits of echo sounding An echo-sounding profile is an imperfect representation of the sea floor because the most commonly used echo-sounder transducer emits and accepts sound pulses through a vertical solid angle of 60 ° (KRAUSE, 1962). The echo sounder records accurately only when the sea floor is absolutely horizontal and the sea is absolutely calm. It does not record the true shape artd slope of hilly bottom. The depth recorded is rarely from beneath the ship, and the recording inherently smooths the irregularities of lhe floor. Therefore, only a certain amount of informatiort can be obtained from echo-sounding profiles. Care must be taken not to proceed beyond the limits of the assumptions and errors, irtcludirtg navigational eirors. In this study, the depths are measured at 3-min (about 0.571 rt.m.) intervals, and the derived slopes are integrated slopes so that irregularities of less than 1/2 mile width are removed. Also any effect is removed of the hyperbolic echo trace (HOFFMAN, 1957; KRAUSE, 1962) of a single point of the sea floor. Had depths been read at l-rain intervals, the slopes would have been those of the hyperbolic echo rather than those of the sea floor. For slopes up to 15 ° (130 fathoms/0.5 n.m.), the differertce is negligible for a track perpendicular to the slope and therefore is disregarded in this paper. Steeper local slopes have little effect ort the integrated slope. The center of an abyssal hill is rarely crossed. The depths recorded are those of an oblique crossing which 2,6001
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Marine Geol., 3 (1965) 169-193
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Fig.3. Bathymetric profiles divided into abyssal hills. Units in three-minute intervals along profile (total length = 60 n.m.). (Profiles 1-6, see p.174.) Marine Geol., 3 (1965) 169-193
176
I). ('. K R A U S E A N I ) H. W . Mf!NARI3
are complexly related to the true depth (KRAUSE,1962). The necessary parameters arc generally unknown. Nonetheless, the derived distributions and parameters appear to be unique for the profile and can be used for classification purposes. Where abyssal hills are equidimensional, the distiibutions derived from echosounding profiles should not vary significantly for different directions of the ship track. Where they are elongate, different course directions yield different distributions. A course perpendicular to the regional trend will yield the profile with the closest approximation to the sea floor, the steepest slopes, and most features crossed. This will vary with course until a course parallel to the regional tread might yield an almost flat profile. The very few available detailed surveys in the eastern Pacific (KRAuSE, 1961: Fisher in: ARRnENIUS, 1963) indicate that north-south trending elongate hills and ridges are the rule rather than the exception in the study area. All of the profiles except profile 15 are perpendicular to the regional trend and were chosen partly for this reason. Therefore, the derived results are expected to yield the best possible relationships. The main features of the recorded profiles (Fig.2) are shown on the plotted profiles (Fig.3). The data can, therefore, be used with confidence in the succeeding analyses.
Mechanical energy of formation of hills The theoretical minimum mechanical energy required to produce a hill on the sea floor may be derived. Assume that a vertically sided, fiat topped hill has a height h above the local base level. The force per unit area F at the base of the hill is:
F=pgh
(l)
where p = difference in density between the rock and sea water, g .... gravitational constant. The work per unit area Wlequired to raise this hill is: h
W=
I Fdh o
= p gh2 2
(2)
For the whole hill of length I and width w, the total energy of formation Wf is:
WI = 1/2 pgh2lw
(3)
For a ridge o f triangular cross section and half width wa and peak height h, the height h x o f the ridge at a point on the cross section is a function of the width wx from the foot of the ridge: hx =
h Wa
w~
(4)
Marine Geol., 3 (1965) 169-t93
177
DEPTH DISTRIBUTION AND BATHYMETRIC CLASSIFICATION
The work of formation I4//per unit length is: h - WX Wa -Wa Ib
I*
Wf= 2pgJ
J
0
hxdhxdwx = 1/3 pgh~w,
(5)
0
For a conical hill of peak height h and of radius wa at the base, the total energy of formation IV/of the hill is: h - -
Wa Wa Wf= pg J 0
J
~2 x
hxnE(wa-wx)dhxdw~ = 1/12 npgh2wa2
(6)
0
The work required to form these three model hills is proportional to the square of their height from the local mean sea floor. In nature the energy is not so easily determined because slumping removes material from the crests of hills and carries it to depressions. This reduces the topography giving the appearance of a lower formational energy requirement. A calculation from the topography will, however, give a minium estimate of the formational energy. A better estimate would require knowledge of the depth of displaced sediment in the depressions and an estimate of the material removed from the crests.
DEPTH DISTRIBUTION
Profiles Profiles chosen for this study (Fig.2, Table I) show a variety of sea-floor configurations. Each profile represents a sample of a deep-sea abyssal hill province. The profiles lie between the United States and Hawaii (Fig. 1), and the statistics and classifications to be developed will apply specifically to those areas, but it is expected that the principles of the study and most o! the findings will be applicable to areas of abyssal hills throughout the ocean basins. (See section on "Relief---division of the profiles into hills", regarding the measurement of the height and breadth of a hill.) Depths used are uncorrected and based on an assumed sound velocity of 4,800 ft./sec. Corrections would have a trivial effect on the results.
Distribution of depths To find the frequency distribution of depths (Fig.4), the profiles are arbitrarily divided into depth intervals of 20 fathoms, except for the very steep profile 8 where a 50 fathom interval is used. The horizontal extent of the sea floor lying within a depth interval in a profile was measured and divided by the length of the profile (60 n.m.). This gives the percent of sea floor that exists within a given depth interval. M a r i n e Geol., 3 (1965) 169-193
175
D.C. KRAUSEAND H. W. MENARI) 60
10 0 40
PROFILE 15
5O
20
.....
S
iq . . . . . . . .
i.qj l ...... r [ _ L _ ~ 2,000
3,0OO
7
40130 20 10
30
0
20
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20
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13
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lO o 2o lO o 20 10
1
DO0
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3,000
DEPTH (FATHOMS)
1,500 DEPTH (FATNOMS)
Fig.4. Depth distribution of the bathymetricprofiles. For example, a length of 13.5 n.m. of profde 4 lies between the depths of 2,860 and 2,880 fathoms and represents 22.5 % of the total length of the profile (Fig.4). This percentage is plotted against the depth interval to show the distribution of the depths. A narrower depth interval would have smoothed the curves but lowered the percent of the sea floor per depth interval. Profiles 1-5 and perhaps profile 15 have roughly unimodal symmetrical depth distributions. Profiles 7, 8, 10-14 have depth distributions skewed so that the mode is deeper than the median, and in several, a lortg tail to the curve persists to shallower depths. An inspection of the profiles (Fig.2) reveals an explanation of these depth distributions. Profiles 1-5 show more or less uniform provinces of abyssal hills and exhibit the symmetrical depth distributions (Fig.4). Profiles 8 arid 10-13 show seamounts and/or isolated large abyssal hills which cause the pronounced skewness of the depth distribution. The large features add a segmertt of shallower depths to a probable symmetrical depth distribution of a uniform province of abyssal hills. Also note that in profile 8 (Fig.2), the two left profiles of seamourtts appear to be oblique crossings compared to the right seamount profile which appears to have been made directly over the seamount's crest. The reason for the bimodal depth distribution (Fig.4) of profiles 6 and 9 is Marine Geol., 3 (1965) 169-193
179
DEPTH DISTRIBUTION AND BATHYMETRIC CLASSIFICATION
apparent in the inspection of the actual profiles where two distinct levels are seen. The skewed depth distribution of profile 7 must be due to isolated low abyssal hills which rise above a very subdued surface. The symmetrical depth distributions of profiles 1-5 do not show a prominent level for the tops of the hills nor for the depressions between. The mode appears to coincide with the average depth of the region. We are apparently dealing with the random distribution of effects about a mean produced by specific causes. This suggests that a uniform process or series of processes led to the formation of the province of abyssal hills shown in a specific profile. Vertical tectonic deformation, such as folding and faulting, would have a strong tendency to yield such a distribution, because the mechanical energy of formation of a vertical column on the sea floor is proportional to the square of its height from the mean sea-floor depth assuming constancy of volume. The higher the hill, the more energy is required for its formation.
Cumulative distribution of depths The cumulative distribution of depths in each profile is plotted on probability graph paper (Fig.5) to illustrate the relation of the depth to normal Gaussian distribution (a type of bell-shaped frequency distribution). A Gaussian distribution plots on probability paper as a straight line. Whether or not the distribution should be normal is a question that may be asked of nature. As a qualitative judgement based on the study of these few profiles, a uniform-appearing profile seems to have a Gaussinn distribution of depth, which might suggest a simple geological history. Profiles 1-5, 14 and 15 show Gaussian or near-Gaussiart distributions, but others are skewed or polymodal. These seem to be the result of one geologic process such as volcanism superimposed over another such as simple deformation or folding as in profiles 10-12 where the seamounts which are obviously volcanoes stand high above the 99.9 t
5 13
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98 ~
95
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1,ooo
1 0 11
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~,5oo
a,ooo DEPTH (FATHOMS)
I
2,500
I
3,ooo
Fig.5. Depth distribution of the bathymetric profiles plotted on probability graph paper.
Marine Geol., 3 (1965) 169-193
IS0
D.C.
KRAUSE AND H. W . MENARI)
abyssal hills. The volcanoes have a far different geologic history than the abyssal hills and this difference may be seen from the depth distributions (Fig.4, 5).
AUTOCORRELATION FACTORS
The extent of repetition of a pattern o f hills is of considerable geologic interest. That is, do certain similar hills appear at uniform distances ? This is tested by the use of autocorrelation factors, which show if parts of the profile cart be predicted from observing other parts. F. N. Spiess (personal communication~ suggested to the authors the use of the following autocorrelation factor whicb is similar to that ot TUKEY (1949) but normalized so that the absolute maximum value is 1. In a given profile of 60 n.m. length, there are m measurements of depth and m-1 .... n computations of the slope. The autocorrelation factor c is: l n-k
j .... n k
y,
j=~
[s(j) • s(j + k)]
c. . . . . . . . . . . . . 1
J=="
/'/
j
:~
, 1
(7)
[s if) ~1
where j = 1, 2, . . . , n-l, n; j = the sequential rmmber of the calculated slope starting with the first calculated slope at the left end of the profile as j ~ 1 ; k =: 0, 1, 2, . . . , n-2, n-1. The first factor c is calculated with k = 0. The second c is calculated with k .... 1. The sequence of calculating c continues with k increasing by + 1 each time a new factor is calculated from the profile; s ( j ) ~- the slope at the jth point of slope computation. The autocorrelation factor is the ratio of averages of the summed multiplication o f slopes chosen as to their successive positions. The closer the ratio is to + 1 or -1, the better the second or third, etc., chosen slope can be predicted from the first chosen slope in sequence throughout the profile. The closer the ratio is to zero, the poorer is the correlation. The following profiles are examined (Fig.6): 3, 5, 8, 11, 15. The correlation factor is invalid for the low slopes of profile 15. Notice that in most cases the correlation factor rapidly approaches the value of zero and oscillates about it, implying that there is no repetition of pattern. The correlation factor of profile 8 does indicate that the pattern repeats (i.e., is highly predictable) which is obvious from the bathymetric profile (Fig.2) where the three seamounts are equally spaced. Geologically, therefore, there is no evidence in profiles 3, 5 and 11 that a pattern exists for folds of constant wavelength or faults with uniform separation or other such geologic phenomena. The profiles 3, 5 and 11 were chosen as the most likely profiles to show such patterns if they existed. It is, therefore, very unlikely that any periodic geologic pattern exists in profiles 1, 2, 4, 6, 7, 9, 10, 12, 13 and 14. Marine Geol., 3 (1965) 1 6 9 - 1 9 3
DEPTH
DISTRIBUTION
AND
O.B
BATHYMETRIC
CLASSIFICATION
181
PROFILE NO. 3 "
0.4 0.2
-0.4 -O.e -
__1_-~
0.~ 1.C
I
PROFILE NO. 5
o.e o.E 0.4
-0.4 ~
-0.6
~
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PROFILE NO. 8
0.8 0.6 0.4 0.2 0
(3 -0.2 -0.4 - 0 .68 I -
-
PROFILE NO. 11
0.8 ().6
0,4 0,2 -0.2 -0.4 -0.6
-0"80- -
I
10
I
20
NUMBER OF INTERVALS
Fig.6, Plot of correlation factors of some profiles.
RELIEF
Division of the profiles into hills The profiles have also been analysed with regard to their hill character. In order to do this, the profiles had to be divided into hills (Fig.3). Several methods were attempted and the most satisfactory one consisted o f assuming a hill to be a bathymetric elevation bounded by two depressions. The height of the hill is the difference in Marine Geol., 3 (1965) 169-193
182
D. C. KRAUSE AND H. W. MENARD
elevation between the top of the hill and the bottom of the deeper depression. The width or breadth of the hill is the distance between the depressions. There are of course small hills on larger hills, and this was taken into consideration as was the fact that hills also occur on broad rises. In this way, the hills were analysed as genetic units.
Fig.7. PIot of the maximum height versus breadth of abyssal hills. The small dot represents one hill or seamount; the intermediate dot represents two features; the large dot represents three features. The right diagonal line represents the limiting width of the hyperbolic echo trace from the top of a very steep, symmetrical feature of a given height at a depth of 2,800 fathoms. The left diagonal line represents half that width, which is the limiting case of a very steep, very asymmetrical feature ~4th one side very short relative to the other side. Marine Geol., 3 (1965) 169493
DEPTH DISTRIBUTION AND BATHYMETRIC CLASSIFICATION
183
Characteristics of hills The height and breadth of the hills were determined for each profile and are plotted in Fig.7. The frequency distributions of the heights and widths of the hills in the 2C 15 1C
Plus three seomounts
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(FATHOMS)
Fig.8. Frequency distribution of heights of the hills in the profiles.
individual profiles were determined and are plotted in Fig.8 and 9, respectively. The frequency distributions of the peak heights for all of the profiles were all combined with an interval of 5 fathoms in height. The resultant distribution was plotted in several ways of which three appear in Fig.8, 10. The scatter of the points in Fig. 1Gis large. One problem is that the hills of lowest height (5, 10 and 15 fathoms) are often not detected because of the hyperbolic echo effect and the sampling technique. Hills of this low height are probably much more common than shown in Fig. 10. Straight lines were fitted by eye to the data in Fig.10. Keeping in mind the large scatter of points, a rough equation for the distribution of hill heights for a typical profile of 1° latitude length is (derived from a plot on semi-logarithmic graph paper, Fig. 10A):
No = -T~-~ 9 log 10n + 3
(8)
or less satisfactorily (derived from a plot on standard graph paper, Fig.lOB): Marine Geol., 3 (1965) 169-193
184
o . ( . KRALSF AND H. W. MENARI)
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2'0 25 ' 30 -~ 35 40 WIDTHS OF HILL(W) (n.rn,)
45
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Fig.9. Frequency distribution of hill widths in the profiles. No=
H + ~-T'7~
(9)
where N O is the number of peaks per 5 fathom interval with a height H in fathoms. This assumes that the profiles represent a fair cross section of the sea floor. The equations imply that the number of peaks of a given width is roughly inversely proportional to the height of the peaks. The frequency distribution of the hill widths for all the profiles was combined with the number of peaks summed over intervals of 0.25 n.m. (Fig.9, 11). Plotted on log-log graph paper (Fig.11), the distribution shows scatter, but a straight line was fitted by eye to represent the combined distribution. The equation of this line is: N15 =
120 W-~
(10) M a r i n e Geol., 3 (1965) 1 6 9 - 1 9 3
DEPTH DISTRIBUTION AND BATHYMETRIC CLASSIFICATION
185
25
20
15
10 u')
<
5
U.
0
UJ Q.
"'.':... oo
l~D
o
20
100
50
200
o e w o o~D
500
I Ipoo
HEIGHT (FATHOMS)
nhl m
Z
30
2O
15 10 5
20 ,o
,o
Fig.10. Combined frequency distribution of peak heights of the fifteen profiles. Each point represents the total number of peaks existing at that particular height. Height intervals are 5 fathoms. Therefore, the ordinate is number of peaks per 5 fathoms interval. In Fig.10A above a height of 250 fathoms, the points showing the absence of peaks in a height interval have been left off because of the large number of such points (see Fig.3). 100, 8O 6O
°\~°
40 3O
~
25'i
20
,,< i s a_
1
15
2 25 3
4 5 6
8 10
20
30
40
60
WIDTH O F HILL (W) (n.m.)
Fig.ll. Combined frequency of hill widths of the fifteen profiles. Each point represents the total number of peaks per 0.25 n.m. interval for a given width for all fifteen profiles. Marine Geol., 3 (1965) 169-193
186
D . C . KRAUSE AND H. W. MENARD
If these profiles represent a faithful cross section of the ocean floor, then the equation representing a single typical profile of the sea floor 1c of latitude long is: N O = 8 W-]
(ll)
where N O = the number of peaks per 0.25 n.m. with a given width W measured in units ofO.5 n.m. If the number of peaks increased as the width of the peaks decreased merely because of the increased length of profile available, the equation would be: N = k W-a
(12)
However, as the widths of the real peaks decrease in size, the number of peaks increases faster than would occur if the number were merely proportional to the available space. The geologic interpretation of this is that the smaller the hill, the more easily it is formed due to a smaller energy of formation, and the more likely it is to form over and above the linear increase due merely to available space. The plot of the distribution is cut off at 1 ram. because this is the limit imposed by 0.5 mile depth measurements. Profiles classified as to hills
The classification system divides the hills in the profiles into high, medium and low seamounts, abyssal hills and swells (Fig. 12, Table II) based on the heights and widths of the features (Fig.7). The percentages of features in each of the three divisions (i.e., high and low seapeaks and the seamounts; high, medium artd low abyssal hills; high, medium and low swells) were calculated and are plotted in the ternary diagram (Fig.13). The numbers of high, medium and low abyssal hills are further plotted in Fig.14. Excluding the anomalous profiles 8 and 15, the average numbers of abyssal hills per profile are: high relief = 1.7 hills, medium relief = 18.1 hills, low relief = 4.3 hills, total ---- 24.1 hills. The classification as given above, also divides the hills more or less according to their geologic character which is discussed later. The ternary diagrams are then divided into seven sections (Fig.13) and each profile is classified as to the section in which it falls (Table II). Each profile, therefore, has a classification based on the four plots as to where it falls within each plot. ~Ihe zero section is reserved for a profile that has no features in that diagram. The subdivision of the ternary diagram is arbitrary. In this subdivision, the outer sides were divided at 331/a and 66~/3~ and the inner triangle (VII) has sides at 162/3~. As percentages of the diagram's area, the three apex zones (I, III, V) each have 11.1 ~, the three intermediate zones (II, IV, VI) each have 13.9~ and the central zone (VII) has 25 ~. Any random point thus has about twice the probability of falling in the central zone as in any other. This central zone contains the less distinctive profiles and the larger size merely sharpens the characteristics of the other zones. Marine Geol., 3 (1965) 169-193
187
DEPTH DISTRIBUTION AND BATHYMETRIC CLASSIFICATION
10,000
1,000
,500
200
o T
100
T 0
50
LQ "I" .J .J
20
10
1 01
I 1
I 2
I 10
I 30
I 60
100
HILL BREADTH (n.m.)
Fig.12. Classificationof positivebathymetricfeatures. From this, a pigeonhill classification is made (Fig.15) consisting of 4,096 positions formed by dividing the table into 64 large squares and dividing each large square into 64 additional positions. The large squares are numbered 0-VII horizontally and represent the classification for hills of intermediate height. The vertical large squares are numbered 0-VII for the classification of the hills of high aspect. Each large square is then divided into small positions numbered 0-VII vertically for hills and swells of low aspect and finally each large square is divided horizontally into positions numbered 0-VII for the classification of the profiles into high, intermediate or low aspect. Consult Table II and Fig.12, 13 and 14 in the following discussion. The classification of positive bathymetric features (Fig.12) is based on (1) the threefold classification of high, medium, low, (2) the threefold classification of broad, medium, narrow and, (3) inferred geologic origin. The geologic significance of the classification is discussed below. "Seamounts, seapeaks, pinnacles" (H). All of the peaks greater than 500 Marine Geol., 3 (1965) 169-193
188
D.C. KRAUSE AND H. W. MENARD
p, H i g h
,xVe~x' h l g h ~ n d g n aDvssa n~ , , .100- 495 foth,~'t Basle units of claSslficat~or
80-
-
[
C GSS f L a K l O n o r medium relief "M ~,
wldth<5Ofathom~/mH~
ne 9ht
3f(Ifhq~s/fllde~
g/a /
%--#
•
/ m ~
~
=
~
~
.
~
" -
\ <2miles ~ Medium
•
^ [sostat~c swe 30 - 60 m~Ies
•
% EA
~"
ona
/ Low/
13
lo
LOW OOySSal htl5 ~<45 fathoms
,
%
2,
w~de ,
~,o
5e--
-
m, A b y s s a l hills ~ 50-95
fathoms
A Seomounts 500 '~
w ae
_ I O S S l f ZOt~On o f swells L
Height <
•
'
~
10 ...........
C]asslhcatron nrgn rebel
of
-
~e,,gnt ~50 w idt h
o_
.o
...........
-,.
5C$8
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9
•
3
4.
and
Local s w e l l s 2-10
miles
EH
Dinnactes / "~
~
EL 715
12
E~rood Swel[~ ~ 10-30 16 m l 4 e S ~, wide
"
23
,1
4
<-195 fothomo
H gn
SeoDeaks -
200
-495
fathoms
,2,~ 6 1 3 ~
~
~
,
~
~
"
6 Nigh
{
'\
.
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~/~ 8"
and
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Classification high, medium
' • ,.
~50 \ \ 1•
/
~NILLS LOW
--
~
7"v • J• 5 o
L
~
\
10 9
3
.
6.
414 v
,\ -
~MedlUm
Fig. 13. Classitieation o f the bathymetric relief•
fathoms are volcanoes (Fig.2, 3). KUE~L~ (1935) found that the submarine slopes of composite andesitic volcanoes in the East Indies averaged 25 °. Mm,~AROand DIETZ (1951) found slopes not greater than 22-24 ° on the basaltic volcanoes of the Gulf of Alaska seamounts. DmTZ and MENM~D (1953) found flanking slopes of 15 ° on a seamount of the Hawaiian Arch. The highest peak in each of profiles 8, 10 and 11 have the following properties respectively: height/width : 114 fathoms/n.m., 83 fathoms/ n.m., 143 fathoms/n.m.; average slope per interval of 0.571 n.m. (int.) ----- 120 fathoms/ int., 95 fathoms/int., 160 fathoms/int.; average slope ---- 11.9 °, 9.5 °, 15.7 °. These slopes are half of Kuenen's values but are probably more characteristic of basaltic volcanoes. Local slopes equal and exceed Kuenen's figures (25 °, 265 fathoms/int.) but Marine Geol., 3 (1965) 169-193
189
DEPTH DISTRIBUTION AND BATHYMETRIC CLASSIFICATION
should not be confused with the broader averages. Most slopes greater than 100 fathoms/int. (10 °) are volcanic (Fig.3). The height/width division of 50 fathoms/n.m, of the classification is half of the ratio for the above basaltic volcanoes. However. TABLE II BASIC CLASSIFICATION OF ABYSSAL FEATURES1
Profile
H
M
L
12
VI V 0 0 V V 0 VII 0 II II II
II IV V VII VI VII IV II VII VII IV VII
III IV IV III VII III V VI VII III III IV
II III III III III III IV II III III III III
13
V
VII
V
III
0 0 VII
IV 0 VII
III V IV
III V III
0 0 29
1
2 3 4 5 6 7 8 9 10 11
14 15 Total
HML
H 2
M 2
L2
6
15
3
2 0 0 2 1 0 7 0
31 20 23 16 16 11 3 16
5 5 4 3 1 12 2 4
2 3
18 14
5 3
2
11
3
4
18
4
26 0 238
4 6 64
Total 2
24 38 25 27 21 18 23 12 20 25 20 16 26 30 6 331
1 Subgrouped (three out of four classes): 4, 6, 10-4, 9--4, 14-6, 13-10, 11-10,12 (9, 10, 11, 12 areally grouped-see Fig. 1). Independent: 1, 2, 3, 5, 7, 8, 15. Compare to Fig.2, 3. 2 Number of bathymetric features in profile. ~-
~
10
5 0
~ ~ E ~ i bJ
25 2o 15 5 0
- -
~
0
20
o
Fig.14. Number and character of abyssal hills in the profiles exclusive of seamounts, seapeaks, and swells. Marine Geol., 3 (1965) 169-193
190
1). C. KRAUSE AND H. W. MENARD M (HML)
o
I
01234567
~
012345670123456701234567012345670t
m
iv
~ ~4,~R7ol
~ O~.af,
¢~
t o ~ a ~
gI
3 -r
rg
1/
"gr
wn
-~
Fig. 15. Pigeonhole classification of bathymetric profiles according to hills.
oblique crossings of the volcanoes give more subdued profiles so that most or all of the features in "seamounts" and "high seapeaks" of the classification should be volcanic. "Low seapeaks" and "pinnacles" may also be volcanic but rock sampling information is lacking. "Plateaus" are absent in this study. "Ill-defined features" are too small to classify due to the sampling method and physical principles. "Very high to low abyssal hills" (M). The main body of the conclusions of this study is concerned with this group. The height/width boundaries of this group are 50 fathoms/n.m, and 10 fathoms/n.m, with steep features above and swells below. The classification may be considered in terms of energy of hill formation, subject to various assumptions. The relative minimum and maximum mechanical energy of formation based on conical hills in each division is: low abyssal hills: 1-15.6, medium abyssal hills: 6.25-2,500, high abyssal hills: 100-40,000, very high abyssal hills: 1,600-156,000. Marine Geol., 3 (1965) 169-193
~
DEPTH DISTRIBUTION AND BATHYMETRIC CLASSIFICATION
191
"Local to isostatic swells" (L). The swells in general are not represented by seafloor slopes (Fig.3). They are rises in the sea floor upon which sit the abyssal hills and seamounts. "Local swells" may be folds, local accumulations of volcanic material, horsts, etc. "Broad swells" are more in the nature of anticlinoriums, broad outpourings of lava, etc. "Isostatic swells" are so broad that the processes of isostasy are beginning to affect the topography and such swells represent variations and structures in the oceanic crust and mantle. The apex zones (I, III, V) of the ternary diagrams (H, M, L, HML) are the most significant geologically because they show which features numerically dominate the profiles. The intermediate zones (II, IV, VI, VII) show mixed profiles and will be discussed only briefly in the following. H-diagram. Many profiles (see Table II, Fig.15), 3, 4, 7, 9, 14, 15, do not appear because they have no such steep features. The steep features in profiles 2, 5, 6, 13 are dominated by low seapeaks and pinnacles. No profile is dominated by seamounts and high seapeaks. M-diagram. Abyssal hills apparently occur characteristically as mixed groups. No profiles are dominated by very high to medium abyssal hills and ortly one, profile 3, is dominated by low abyssal hills. The remainder of profiles, except for 15, appear in mixed zones, especially the central zone VII which indicates that a complete range of hills from low to very high occurs in each profile. L-diagram. No profile is dominated by isostatic swells, mainly because only two or three such swells may exist per profile. Six profiles, 1, 4, 6, 10, 11 and 14 are dominated by broad swells. Three profiles, 7, 13 and 15 are dominated by local swells, channel levees in the case of profile 15. In each of the three ternary diagrams on the basis of space available for a feature and its relative energy of formation, features should numerically increase from zones I through III to V. Therefore zone V should dominate on such a basis. It does not do so in nature, which indicates the action of other determining factors such as a greater than ~- minimum hill size and hence energy of formation. The physical characteristics of the bottom rock also influence the distribution of that energy. Note that no profile is dominated by zone I. This effect in diagrams H and L is due to the lack of space available for numerically significant features of this size. HML-diagram. Eleven of the profiles are dominated by abyssal hills. One, profile 15, is dominated by its levees. The profiles were also treated as a group and classified. This group tentatively represents the northeastern Pacific sea floor. With regard to both steep features and abyssal hills, the group is mixed, having a complete range of features. The group shows a numerical lack ofisostatie swells compared to local and broad swells which are about equal in abundance to one another. The group is further dominated by abyssal hills. The subgrouping (Table II, bottom) of the profiles based on the ternary classification relates the profiles both topographically and geological. Although the best subgroupings have in common only three of the four classes, a visual examination Marine Geol., 3 (1965) 169-193
192
D . C . KRAUSE AND H. W. MENARI)
of the related profiles (Fig.2, 3) reveals a visual resemblence as well. Profiles 9, 10, 11 and 12 were made across the outer portion of the Hawaiian Arch (DIETZ and MENARO, 1953). Profiles 10, 11 and 12 show good relationships while profile 9 is more subdued probably due to sedimentation and/or lava accumulation. The "independent" profiles, 1, 2, 3, 5, 7, 8, 15, visually differ markedly from one another. Through the above classifications, the profiles are easily classified in what appears to be a natural system and one that allows classification of the sea floor throughout the world. The methods used throughout this paper are easily adaptable to computer techniques for rapid classification of the sea floor on the basis of depths. The ultimate objective would be the same as used by HEEZEN et al. (1959, pl. 20) in their classification of the north Atlantic Ocean, but this would be quantitative rather than qualitative.
CONCLUSIONS
(1) Several profiles (1-5, 15) show a Gaussian distribution of depths and others have a significant portion that may be normally distributed if the depth distribution due to seamounts is removed. (2) No horizontal periodism of the features exists except for the three seamounts of the Moonless Mountains. (3) The frequency of abyssal hills is related, though poorly, to the heights of the hills. (4) The frequency of abyssal hills is related more surely to the widths of the hills. (5) Classification of abyssal hills was made on the basis of height versus width and fits the profiles in a natural way. These ielationships except 2 imply a certain predictability to the examined characters of the sea floor. They also imply that the causal geologic processes leading to the formation of the features acted in a consistent way. The discovery of these processes will lead to the understanding of the mechanism of abyssal hill formation. Certain of the processes have been pinpointed in the text. However, other very important processes and relationships remain to be deduced. For example, it is possible to calculate the energy of formation of those hills, if certain simplifying and perhaps unreal assumptions are made such as the assumption that the hills were formed from vertical deformation of a flat sea floor and neglecting friction. This energy of formation helps define the scale of the causal geologic processes and thus aids in their deduction. The uniformity of the results supports reliability of the deductions, certainly for the areas studied and hopefully for large areas of the sea floor. If this report were to do nothing more than this, it will have served its purpose.
ACKNOWLEDGEMENTS
This work was supported initially by the Long Lines Department of the American Marine Geol., 3 (1965) 169-193
DEPTH DISTRIBUTION AND BATHYMETRIC CLASSIFICATION
193
Telephone and Telegraph Co., and later by the University of California, the University of Rhode Island, and the Office of Naval Research. E. Buffington, F. N. Spiess and D. R. Schirtk suggested many improvements in the paper.
REFERENCES
ARRHENIU$,G., 1963. Pelagic sediment. In: M. N. HILL (General Editor), The Sea, Ideas and Observations on Progress in the Study of the Seas. 3. The Earth beneath the Sere Irtterscience, New York, N.Y., pp.655-727. DmTZ, R. S. and MENARD, H. W., 1953. Hawaiian swell, deep and arch, and the sudsidence of the Hawaiian Islands. J. Geol. 61 : 99-113. HEEZEN, B. C., THARP, M. and EWlNG, M., 1959. The floors of the oceans. 1. The north Atlantic. Geol. Soc. Am., Spee. Papers, 65 : 122 pp. HOFFMAN,J., 1957. Hyperbolic curves applied to echo sounding. Hydrograph. Rev., 34 (2) : 45-55. KRAUSE,D. C., 1961. Geology on the sea floor of Guadalupe Island. Deep-Sea Res., 8 : 28-38. K~AUSE,D. C., 1962. Interpretation of echo-sounding profiles. Hydrograph. Rev., 39 (1) : 65-123. KUENEN, PH. H., 1935. Geological interpretation of the hathymetrical results. Snellius Expedition, Sci. Results Snellius Expedition Eastern Pt. East-Indian Archipelago, 1929-1930. 5. Geol. Results, 1:62-69. MENARO, H. W. and DIETZ, R. S., 1951. Submarine geology of the Gulf of Alaska. Bull. Geol. Soc. Am., 62 : 1273. TUKEY, J. W., 1949. The sampling theory of power spectrum estimates. Syrup. App1. Autocorrelation Anal. Phys. Probl., Woods Hole, Mass., 1949, pp.47-67.
Marine Geol., 3 (1965) 169-193
DEPTH DISTRIBUTION AND BATHYMETRIC CLASSIFICATION OF SOME SEA-FLOOR PROFILES D. C. KKAUSEAND H. W. MENARD Graduate School of Oceanography, University of Rhode Island, Kingston, R.L (U.S.A.) ; Institute of Marine Resources, University of California, San Diego, La Jolla, Calif. (U.S.A.)
(Received October 1, 1963) (Resubmitted December 23, 1964)
SUMMARY Fifteen east Pacific sea-floor profiles of 60 nautical miles length are analysed as to depth of the sea floor and the character of the hills. Mechanical energies of formation of some model hills are discussed. Several profiles have a Gaussian distribution of depths and others seem to have a large component that is Gaussian. Correlation related to repetition of sea-floor slopes along the individual profile is nil. Pigeonhole classification of the profiles on the basis of relief corresponds to geological environments. A rough equation of the number of hills (No) of given height (H) in a 60 nautical mile profile is: N o ------9/15log 10n + a
A rough equation of the number of hills in all fifteen profiles (Nln) relative to their widths is: N15 = 120 W"z/2 which implies that the smaller the hills, the more common they are at an exponential rate. Within their context, the statistical and physical characteristics of the profiles can be related to the geological composition of the sea floor and to some of the geological processes modifying the sea floor. The predictability of the characteristics encourages study of large-scale processes important in the evolution of the sea floor.
INTRODUCTION Abyssal hills cover large areas of the ocean floor, yet little is known regarding their character, their origin, and the geologic processes involved in their formation and Marine GeoL, 3 (1965) 169-193
170
D . C . KRAUSE AND H. W. MENARD
160" 40 °
150"
140 °
130 °
'
120 °
~ILSUn
14 13 8 30"
r. . . .
i
1112 ] e
Hawaiian
]
l Fig.l. Index map showinglocation of profiles in northeastern Pacific. modification. Abyssal hills are less than 500 fathoms (3,000 ft.) or 1,000 m (3,300 ft.) in height by definition. A study was undertaken to examine certain properties of abyssal hills, and to develop a classification indicative of the origin of the hills. The study consists of: (1) depth distributions of the sea floor, and (2) distribution and classification of seamounts, abyssal hills and swells. Fifteen, 60-mile-long profiles of the sea floor of the northeastern Pacific Ocean (Fig.l, 2) were chosen for a detailed analysis of their bathymetric characters. The profiles were recorded on EDO depth recorders on ships of the Scripps Institution of Oceanography (University of California) and the U. S. Naval Electronics Laboratory. Depths were read at three-minute intervals which represent a distance of 0.484-0.632 nautical miles (n.m.) depending upon the ship speed (Table I). The results of this paper are not easily related to the published work regarding analyses of subaerial geomorphology. Most such studies deal with smaller-scale features. More importantly, the subaerial geomorphologic features have been greatly modified by erosion which is virtually unknown in the deep-sea environment although minor downhill movement occurs. The profiles are affected by the materials of the sea floor and the geologic processes which have modified the sea floor. The composition of the sea floor in this study can be broadly divided into three main components: (I) recent, soft sediments, (2) older, stiffer or hard sediments, (3) lava flows. The processes modifying the sea floor locally can be broadly divided into the following main groups: (a) pelagic sedimentation, (b) turbidity current deposition, (c) slumping of sediments, (d) tectonic deformation and (e) volcanism. In certain cases, we can pinpoint the conditions. Profile 15, for example, was chosen to be typical of turbidity current deposition of recent, soft sediment. The steep slopes, especially the longer ones, are generally associated with volcanoes as in profiles 8, 10, 11 and 12. The other conditions, however, are not so easily determined but in certain circumstances will be discussed. Marine Geol., 3 (1965) 169-193
,.L
F,
0.566
0.545 0.484 0.535 0.561 0.571
0.600
0.619 0.561 0.577 0.588
0.571
0.571
0.582 0.632
2 3 4 5 6
7
8 9 10 11
12
13
14 15
Length of 3-min interval (n.m. )
INFORMATION
1
Profile
PROFILE
TABLE I
Capricorn Cascadia
Capricorn
Hawaii '53
Hawaii '53 Hawaii '53 Hawaii '53 Hawaii '53
Hawaii '53
Cusp Cusp Transpac Transpac Hawaii '53
Cusp
Cruise
Horizon EPCER 857
Horizon
Horizon
Horizon Horizon Horizon Horizon
Horizon
Baird Horizon Baird Baird Horizon
Baird
Ship
05h00-10hl0, 30 Sept. 1952 01h00--05h50,29 Sept. 1952
18h00--23h16, 29 Sept. 1953
18h20-23h50, 26 Oct. 1953
00h15-05h25, 4 Oct. 1953 02h00-07h35, 26 Oct. 1953 07h35-13h00, 26 Oct. 1953 13h00-18h20, 26 Oct. 1953
14h00-19h10, 4 Oct. 1953
01h00, 13 Aug. 1953 03h30, 29 July 1953 16h15-22h00, 23 Nov. 1953 09h00-14h30, 3 Nov. 1953 07h00-12h30, 3 Oct. 1953
06h30, 11 Aug. 1953
Date
north of Murray Fracture Zone, large hills, irregular relief north of Murray Fracture Zone, very low hills off Deep Plain, rolling plain east of Hawaiian Arch, large rolling hills west of Patton Escarpment, blocky steep hills south of Murray Fracture Zone, broad high hills south of Murray Fracture Zone, gently rolling deep-sea fan Moonless Mountains Hawaiian Arch Hawaiian Arch, just east of 9 Hawaiian Arch, just east of 10, subdued low hills with seamounts Hawaiian Arch, just east of 11, subdued low hills with seamounts Murray Fracture Zone, top of main ridge, increasinglyhilly to right Murray Fracture Zone, bottom of main ridge nearshore, abyssal plain with one deep-sea channel
Character
-t
~.
r~
k,/
! 800
5~
2400 2400
3000 2400
3000 ! 000
M
Fig.2. Echo sounding protiles of tile 60-mile long sections of the sea flool. Mari#w Geol., 3 !1965) 169-193
Fig.2. Legend see p.172. Marine Geol., 3 (1965) 169-193
174
t). C. KRAUSE AND H. W. MENARD
Limits of echo sounding An echo-sounding profile is an imperfect representation of the sea floor because the most commonly used echo-sounder transducer emits and accepts sound pulses through a vertical solid angle of 60 ° (KRAUSE, 1962). The echo sounder records accurately only when the sea floor is absolutely horizontal and the sea is absolutely calm. It does not record the true shape artd slope of hilly bottom. The depth recorded is rarely from beneath the ship, and the recording inherently smooths the irregularities of lhe floor. Therefore, only a certain amount of informatiort can be obtained from echo-sounding profiles. Care must be taken not to proceed beyond the limits of the assumptions and errors, irtcludirtg navigational eirors. In this study, the depths are measured at 3-min (about 0.571 rt.m.) intervals, and the derived slopes are integrated slopes so that irregularities of less than 1/2 mile width are removed. Also any effect is removed of the hyperbolic echo trace (HOFFMAN, 1957; KRAUSE, 1962) of a single point of the sea floor. Had depths been read at l-rain intervals, the slopes would have been those of the hyperbolic echo rather than those of the sea floor. For slopes up to 15 ° (130 fathoms/0.5 n.m.), the differertce is negligible for a track perpendicular to the slope and therefore is disregarded in this paper. Steeper local slopes have little effect ort the integrated slope. The center of an abyssal hill is rarely crossed. The depths recorded are those of an oblique crossing which 2,6001
. . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Marine Geol., 3 (1965) 169-193
2,700
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2,5O0 2~00 2700 2,800 29OO I000 I
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I
I
[
ONe il3tePvcll = 0.577 n.m.
F,oo ,
A
27°°I- //
/I
~Ot
. . . . . . . . . . . . . . . . . . " " - ~ [
I
I
I
I
I
E : ~ ' - - _~_~-__'~2~/"
I
t
I
i
I
I
i
L
L
I
90
100
One interval =0.585 n.m.
2,500 2.600
2.70O 2.600 2.900 3DO0 3,100
i
I
i
i
L
i
I
One interval :0.571 n.m.
2200 23O0 2AO0
2~00
I
I
I
2700 ~
Ion e
I I I interval :0.571 n.m.
4
2~00 2,900 Oi3e interval : 0 . 5 8 2 n.m. 22OO 2300
0
[
i
,
i
10
20
30
,
,
,--~'~
....
40 50 60 70 One interval : 0 . 6 3 2 nm.
L== ~-T
80
,
Fig.3. Bathymetric profiles divided into abyssal hills. Units in three-minute intervals along profile (total length = 60 n.m.). (Profiles 1-6, see p.174.) Marine Geol., 3 (1965) 169-193
176
I). ('. K R A U S E A N I ) H. W . Mf!NARI3
are complexly related to the true depth (KRAUSE,1962). The necessary parameters arc generally unknown. Nonetheless, the derived distributions and parameters appear to be unique for the profile and can be used for classification purposes. Where abyssal hills are equidimensional, the distiibutions derived from echosounding profiles should not vary significantly for different directions of the ship track. Where they are elongate, different course directions yield different distributions. A course perpendicular to the regional trend will yield the profile with the closest approximation to the sea floor, the steepest slopes, and most features crossed. This will vary with course until a course parallel to the regional tread might yield an almost flat profile. The very few available detailed surveys in the eastern Pacific (KRAuSE, 1961: Fisher in: ARRnENIUS, 1963) indicate that north-south trending elongate hills and ridges are the rule rather than the exception in the study area. All of the profiles except profile 15 are perpendicular to the regional trend and were chosen partly for this reason. Therefore, the derived results are expected to yield the best possible relationships. The main features of the recorded profiles (Fig.2) are shown on the plotted profiles (Fig.3). The data can, therefore, be used with confidence in the succeeding analyses.
Mechanical energy of formation of hills The theoretical minimum mechanical energy required to produce a hill on the sea floor may be derived. Assume that a vertically sided, fiat topped hill has a height h above the local base level. The force per unit area F at the base of the hill is:
F=pgh
(l)
where p = difference in density between the rock and sea water, g .... gravitational constant. The work per unit area Wlequired to raise this hill is: h
W=
I Fdh o
= p gh2 2
(2)
For the whole hill of length I and width w, the total energy of formation Wf is:
WI = 1/2 pgh2lw
(3)
For a ridge o f triangular cross section and half width wa and peak height h, the height h x o f the ridge at a point on the cross section is a function of the width wx from the foot of the ridge: hx =
h Wa
w~
(4)
Marine Geol., 3 (1965) 169-t93
177
DEPTH DISTRIBUTION AND BATHYMETRIC CLASSIFICATION
The work of formation I4//per unit length is: h - WX Wa -Wa Ib
I*
Wf= 2pgJ
J
0
hxdhxdwx = 1/3 pgh~w,
(5)
0
For a conical hill of peak height h and of radius wa at the base, the total energy of formation IV/of the hill is: h - -
Wa Wa Wf= pg J 0
J
~2 x
hxnE(wa-wx)dhxdw~ = 1/12 npgh2wa2
(6)
0
The work required to form these three model hills is proportional to the square of their height from the local mean sea floor. In nature the energy is not so easily determined because slumping removes material from the crests of hills and carries it to depressions. This reduces the topography giving the appearance of a lower formational energy requirement. A calculation from the topography will, however, give a minium estimate of the formational energy. A better estimate would require knowledge of the depth of displaced sediment in the depressions and an estimate of the material removed from the crests.
DEPTH DISTRIBUTION
Profiles Profiles chosen for this study (Fig.2, Table I) show a variety of sea-floor configurations. Each profile represents a sample of a deep-sea abyssal hill province. The profiles lie between the United States and Hawaii (Fig. 1), and the statistics and classifications to be developed will apply specifically to those areas, but it is expected that the principles of the study and most o! the findings will be applicable to areas of abyssal hills throughout the ocean basins. (See section on "Relief---division of the profiles into hills", regarding the measurement of the height and breadth of a hill.) Depths used are uncorrected and based on an assumed sound velocity of 4,800 ft./sec. Corrections would have a trivial effect on the results.
Distribution of depths To find the frequency distribution of depths (Fig.4), the profiles are arbitrarily divided into depth intervals of 20 fathoms, except for the very steep profile 8 where a 50 fathom interval is used. The horizontal extent of the sea floor lying within a depth interval in a profile was measured and divided by the length of the profile (60 n.m.). This gives the percent of sea floor that exists within a given depth interval. M a r i n e Geol., 3 (1965) 169-193
175
D.C. KRAUSEAND H. W. MENARI) 60
10 0 40
PROFILE 15
5O
20
.....
S
iq . . . . . . . .
i.qj l ...... r [ _ L _ ~ 2,000
3,0OO
7
40130 20 10
30
0
20
2C
10
1C 0 l o° Z
20
5
to o
U
0 0 20 10 2c 1c c 10
13
10
'
'2
2()
L
lO o 2o lO o 20 10
1
DO0
~)O
0
9
3,000
DEPTH (FATHOMS)
1,500 DEPTH (FATNOMS)
Fig.4. Depth distribution of the bathymetricprofiles. For example, a length of 13.5 n.m. of profde 4 lies between the depths of 2,860 and 2,880 fathoms and represents 22.5 % of the total length of the profile (Fig.4). This percentage is plotted against the depth interval to show the distribution of the depths. A narrower depth interval would have smoothed the curves but lowered the percent of the sea floor per depth interval. Profiles 1-5 and perhaps profile 15 have roughly unimodal symmetrical depth distributions. Profiles 7, 8, 10-14 have depth distributions skewed so that the mode is deeper than the median, and in several, a lortg tail to the curve persists to shallower depths. An inspection of the profiles (Fig.2) reveals an explanation of these depth distributions. Profiles 1-5 show more or less uniform provinces of abyssal hills and exhibit the symmetrical depth distributions (Fig.4). Profiles 8 arid 10-13 show seamounts and/or isolated large abyssal hills which cause the pronounced skewness of the depth distribution. The large features add a segmertt of shallower depths to a probable symmetrical depth distribution of a uniform province of abyssal hills. Also note that in profile 8 (Fig.2), the two left profiles of seamourtts appear to be oblique crossings compared to the right seamount profile which appears to have been made directly over the seamount's crest. The reason for the bimodal depth distribution (Fig.4) of profiles 6 and 9 is Marine Geol., 3 (1965) 169-193
179
DEPTH DISTRIBUTION AND BATHYMETRIC CLASSIFICATION
apparent in the inspection of the actual profiles where two distinct levels are seen. The skewed depth distribution of profile 7 must be due to isolated low abyssal hills which rise above a very subdued surface. The symmetrical depth distributions of profiles 1-5 do not show a prominent level for the tops of the hills nor for the depressions between. The mode appears to coincide with the average depth of the region. We are apparently dealing with the random distribution of effects about a mean produced by specific causes. This suggests that a uniform process or series of processes led to the formation of the province of abyssal hills shown in a specific profile. Vertical tectonic deformation, such as folding and faulting, would have a strong tendency to yield such a distribution, because the mechanical energy of formation of a vertical column on the sea floor is proportional to the square of its height from the mean sea-floor depth assuming constancy of volume. The higher the hill, the more energy is required for its formation.
Cumulative distribution of depths The cumulative distribution of depths in each profile is plotted on probability graph paper (Fig.5) to illustrate the relation of the depth to normal Gaussian distribution (a type of bell-shaped frequency distribution). A Gaussian distribution plots on probability paper as a straight line. Whether or not the distribution should be normal is a question that may be asked of nature. As a qualitative judgement based on the study of these few profiles, a uniform-appearing profile seems to have a Gaussinn distribution of depth, which might suggest a simple geological history. Profiles 1-5, 14 and 15 show Gaussian or near-Gaussiart distributions, but others are skewed or polymodal. These seem to be the result of one geologic process such as volcanism superimposed over another such as simple deformation or folding as in profiles 10-12 where the seamounts which are obviously volcanoes stand high above the 99.9 t
5 13
99.5r-
,g i ill
98 ~
95
~ ~
9o 8o
1121
6 9
j
Y
i ii
I
/!
i •
5(3 4O
U 2O 0U lO 5 2 1 0.5 ().2 0. 1
1,ooo
1 0 11
i
~,5oo
a,ooo DEPTH (FATHOMS)
I
2,500
I
3,ooo
Fig.5. Depth distribution of the bathymetric profiles plotted on probability graph paper.
Marine Geol., 3 (1965) 169-193
IS0
D.C.
KRAUSE AND H. W . MENARI)
abyssal hills. The volcanoes have a far different geologic history than the abyssal hills and this difference may be seen from the depth distributions (Fig.4, 5).
AUTOCORRELATION FACTORS
The extent of repetition of a pattern o f hills is of considerable geologic interest. That is, do certain similar hills appear at uniform distances ? This is tested by the use of autocorrelation factors, which show if parts of the profile cart be predicted from observing other parts. F. N. Spiess (personal communication~ suggested to the authors the use of the following autocorrelation factor whicb is similar to that ot TUKEY (1949) but normalized so that the absolute maximum value is 1. In a given profile of 60 n.m. length, there are m measurements of depth and m-1 .... n computations of the slope. The autocorrelation factor c is: l n-k
j .... n k
y,
j=~
[s(j) • s(j + k)]
c. . . . . . . . . . . . . 1
J=="
/'/
j
:~
, 1
(7)
[s if) ~1
where j = 1, 2, . . . , n-l, n; j = the sequential rmmber of the calculated slope starting with the first calculated slope at the left end of the profile as j ~ 1 ; k =: 0, 1, 2, . . . , n-2, n-1. The first factor c is calculated with k = 0. The second c is calculated with k .... 1. The sequence of calculating c continues with k increasing by + 1 each time a new factor is calculated from the profile; s ( j ) ~- the slope at the jth point of slope computation. The autocorrelation factor is the ratio of averages of the summed multiplication o f slopes chosen as to their successive positions. The closer the ratio is to + 1 or -1, the better the second or third, etc., chosen slope can be predicted from the first chosen slope in sequence throughout the profile. The closer the ratio is to zero, the poorer is the correlation. The following profiles are examined (Fig.6): 3, 5, 8, 11, 15. The correlation factor is invalid for the low slopes of profile 15. Notice that in most cases the correlation factor rapidly approaches the value of zero and oscillates about it, implying that there is no repetition of pattern. The correlation factor of profile 8 does indicate that the pattern repeats (i.e., is highly predictable) which is obvious from the bathymetric profile (Fig.2) where the three seamounts are equally spaced. Geologically, therefore, there is no evidence in profiles 3, 5 and 11 that a pattern exists for folds of constant wavelength or faults with uniform separation or other such geologic phenomena. The profiles 3, 5 and 11 were chosen as the most likely profiles to show such patterns if they existed. It is, therefore, very unlikely that any periodic geologic pattern exists in profiles 1, 2, 4, 6, 7, 9, 10, 12, 13 and 14. Marine Geol., 3 (1965) 1 6 9 - 1 9 3
DEPTH
DISTRIBUTION
AND
O.B
BATHYMETRIC
CLASSIFICATION
181
PROFILE NO. 3 "
0.4 0.2
-0.4 -O.e -
__1_-~
0.~ 1.C
I
PROFILE NO. 5
o.e o.E 0.4
-0.4 ~
-0.6
~
-08 1.0'
Z 0 F~ .J ~ a:
0
PROFILE NO. 8
0.8 0.6 0.4 0.2 0
(3 -0.2 -0.4 - 0 .68 I -
-
PROFILE NO. 11
0.8 ().6
0,4 0,2 -0.2 -0.4 -0.6
-0"80- -
I
10
I
20
NUMBER OF INTERVALS
Fig.6, Plot of correlation factors of some profiles.
RELIEF
Division of the profiles into hills The profiles have also been analysed with regard to their hill character. In order to do this, the profiles had to be divided into hills (Fig.3). Several methods were attempted and the most satisfactory one consisted o f assuming a hill to be a bathymetric elevation bounded by two depressions. The height of the hill is the difference in Marine Geol., 3 (1965) 169-193
182
D. C. KRAUSE AND H. W. MENARD
elevation between the top of the hill and the bottom of the deeper depression. The width or breadth of the hill is the distance between the depressions. There are of course small hills on larger hills, and this was taken into consideration as was the fact that hills also occur on broad rises. In this way, the hills were analysed as genetic units.
Fig.7. PIot of the maximum height versus breadth of abyssal hills. The small dot represents one hill or seamount; the intermediate dot represents two features; the large dot represents three features. The right diagonal line represents the limiting width of the hyperbolic echo trace from the top of a very steep, symmetrical feature of a given height at a depth of 2,800 fathoms. The left diagonal line represents half that width, which is the limiting case of a very steep, very asymmetrical feature ~4th one side very short relative to the other side. Marine Geol., 3 (1965) 169493
DEPTH DISTRIBUTION AND BATHYMETRIC CLASSIFICATION
183
Characteristics of hills The height and breadth of the hills were determined for each profile and are plotted in Fig.7. The frequency distributions of the heights and widths of the hills in the 2C 15 1C
Plus three seomounts
5, 0
-17
~n
n
n
n
n
n
n
n n
n
n
n
~ ~FFt1111 r - ~
b~.l-,~"l~n
n
~-q
~ 2~-~ rJ ~ n-~ ~
0218
nn
gp n n n ~ ~-~ . . . . . . O
n
5
n
n
n
n
n
n
nn
n
~-q
~n n~
n
n
n
n
n
n
on
Plus three
n
n
n
c-~R~--~ n V h
n
n
n
n
n
n
n
n
n
M
Nnn
n
n seornounts--
N
n
n
n
IFfl4fl o
n
~2'0
4
n
.... HEIGHT
n
, n
,60
40
560
(FATHOMS)
Fig.8. Frequency distribution of heights of the hills in the profiles.
individual profiles were determined and are plotted in Fig.8 and 9, respectively. The frequency distributions of the peak heights for all of the profiles were all combined with an interval of 5 fathoms in height. The resultant distribution was plotted in several ways of which three appear in Fig.8, 10. The scatter of the points in Fig. 1Gis large. One problem is that the hills of lowest height (5, 10 and 15 fathoms) are often not detected because of the hyperbolic echo effect and the sampling technique. Hills of this low height are probably much more common than shown in Fig. 10. Straight lines were fitted by eye to the data in Fig.10. Keeping in mind the large scatter of points, a rough equation for the distribution of hill heights for a typical profile of 1° latitude length is (derived from a plot on semi-logarithmic graph paper, Fig. 10A):
No = -T~-~ 9 log 10n + 3
(8)
or less satisfactorily (derived from a plot on standard graph paper, Fig.lOB): Marine Geol., 3 (1965) 169-193
184
o . ( . KRALSF AND H. W. MENARI)
6O
ALL
¢:'ROF'II-ES
COMBINED
5C 40
]
3c
0
I
[
7
. .n
1
.
.
.
.
.
.
.
.
.
.
.
.
.
,i-~ ;P]
13
_~J'L~11
. . . . . .
_Lm~tmU~....0_
_m--_
_rl .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
I0
~.
9 n
n
in e L .
x:~
.
8
2Ea--~ _ H a - ~7 .1- ~
.
.
.
.
.
E_~
n
n .
.
.
.
.
.
. .
.
.
.
.
.
.
.
.
.
.
.
.
.
. .
.
.
. .
.
.
. .
.
. .
.
.
. .
.
a
.
~ _
',
. .
.
.
.
~ q ', j
5 ~lJl r-It r-, 4
0
~LVL~. .
5 re] o lO
. . . . . . . . . . . . . . . . . .
. . . .
[]
£q
'
~1
. . . . . . . . .
j
3
L__L~nnnn nn [l
2
5
10
...........
15
,~
.
.
.
.
2'0 25 ' 30 -~ 35 40 WIDTHS OF HILL(W) (n.rn,)
45
50
55
60
Fig.9. Frequency distribution of hill widths in the profiles. No=
H + ~-T'7~
(9)
where N O is the number of peaks per 5 fathom interval with a height H in fathoms. This assumes that the profiles represent a fair cross section of the sea floor. The equations imply that the number of peaks of a given width is roughly inversely proportional to the height of the peaks. The frequency distribution of the hill widths for all the profiles was combined with the number of peaks summed over intervals of 0.25 n.m. (Fig.9, 11). Plotted on log-log graph paper (Fig.11), the distribution shows scatter, but a straight line was fitted by eye to represent the combined distribution. The equation of this line is: N15 =
120 W-~
(10) M a r i n e Geol., 3 (1965) 1 6 9 - 1 9 3
DEPTH DISTRIBUTION AND BATHYMETRIC CLASSIFICATION
185
25
20
15
10 u')
<
5
U.
0
UJ Q.
"'.':... oo
l~D
o
20
100
50
200
o e w o o~D
500
I Ipoo
HEIGHT (FATHOMS)
nhl m
Z
30
2O
15 10 5
20 ,o
,o
Fig.10. Combined frequency distribution of peak heights of the fifteen profiles. Each point represents the total number of peaks existing at that particular height. Height intervals are 5 fathoms. Therefore, the ordinate is number of peaks per 5 fathoms interval. In Fig.10A above a height of 250 fathoms, the points showing the absence of peaks in a height interval have been left off because of the large number of such points (see Fig.3). 100, 8O 6O
°\~°
40 3O
~
25'i
20
,,< i s a_
1
15
2 25 3
4 5 6
8 10
20
30
40
60
WIDTH O F HILL (W) (n.m.)
Fig.ll. Combined frequency of hill widths of the fifteen profiles. Each point represents the total number of peaks per 0.25 n.m. interval for a given width for all fifteen profiles. Marine Geol., 3 (1965) 169-193
186
D . C . KRAUSE AND H. W. MENARD
If these profiles represent a faithful cross section of the ocean floor, then the equation representing a single typical profile of the sea floor 1c of latitude long is: N O = 8 W-]
(ll)
where N O = the number of peaks per 0.25 n.m. with a given width W measured in units ofO.5 n.m. If the number of peaks increased as the width of the peaks decreased merely because of the increased length of profile available, the equation would be: N = k W-a
(12)
However, as the widths of the real peaks decrease in size, the number of peaks increases faster than would occur if the number were merely proportional to the available space. The geologic interpretation of this is that the smaller the hill, the more easily it is formed due to a smaller energy of formation, and the more likely it is to form over and above the linear increase due merely to available space. The plot of the distribution is cut off at 1 ram. because this is the limit imposed by 0.5 mile depth measurements. Profiles classified as to hills
The classification system divides the hills in the profiles into high, medium and low seamounts, abyssal hills and swells (Fig. 12, Table II) based on the heights and widths of the features (Fig.7). The percentages of features in each of the three divisions (i.e., high and low seapeaks and the seamounts; high, medium artd low abyssal hills; high, medium and low swells) were calculated and are plotted in the ternary diagram (Fig.13). The numbers of high, medium and low abyssal hills are further plotted in Fig.14. Excluding the anomalous profiles 8 and 15, the average numbers of abyssal hills per profile are: high relief = 1.7 hills, medium relief = 18.1 hills, low relief = 4.3 hills, total ---- 24.1 hills. The classification as given above, also divides the hills more or less according to their geologic character which is discussed later. The ternary diagrams are then divided into seven sections (Fig.13) and each profile is classified as to the section in which it falls (Table II). Each profile, therefore, has a classification based on the four plots as to where it falls within each plot. ~Ihe zero section is reserved for a profile that has no features in that diagram. The subdivision of the ternary diagram is arbitrary. In this subdivision, the outer sides were divided at 331/a and 66~/3~ and the inner triangle (VII) has sides at 162/3~. As percentages of the diagram's area, the three apex zones (I, III, V) each have 11.1 ~, the three intermediate zones (II, IV, VI) each have 13.9~ and the central zone (VII) has 25 ~. Any random point thus has about twice the probability of falling in the central zone as in any other. This central zone contains the less distinctive profiles and the larger size merely sharpens the characteristics of the other zones. Marine Geol., 3 (1965) 169-193
187
DEPTH DISTRIBUTION AND BATHYMETRIC CLASSIFICATION
10,000
1,000
,500
200
o T
100
T 0
50
LQ "I" .J .J
20
10
1 01
I 1
I 2
I 10
I 30
I 60
100
HILL BREADTH (n.m.)
Fig.12. Classificationof positivebathymetricfeatures. From this, a pigeonhill classification is made (Fig.15) consisting of 4,096 positions formed by dividing the table into 64 large squares and dividing each large square into 64 additional positions. The large squares are numbered 0-VII horizontally and represent the classification for hills of intermediate height. The vertical large squares are numbered 0-VII for the classification of the hills of high aspect. Each large square is then divided into small positions numbered 0-VII vertically for hills and swells of low aspect and finally each large square is divided horizontally into positions numbered 0-VII for the classification of the profiles into high, intermediate or low aspect. Consult Table II and Fig.12, 13 and 14 in the following discussion. The classification of positive bathymetric features (Fig.12) is based on (1) the threefold classification of high, medium, low, (2) the threefold classification of broad, medium, narrow and, (3) inferred geologic origin. The geologic significance of the classification is discussed below. "Seamounts, seapeaks, pinnacles" (H). All of the peaks greater than 500 Marine Geol., 3 (1965) 169-193
188
D.C. KRAUSE AND H. W. MENARD
p, H i g h
,xVe~x' h l g h ~ n d g n aDvssa n~ , , .100- 495 foth,~'t Basle units of claSslficat~or
80-
-
[
C GSS f L a K l O n o r medium relief "M ~,
wldth<5Ofathom~/mH~
ne 9ht
3f(Ifhq~s/fllde~
g/a /
%--#
•
/ m ~
~
=
~
~
.
~
" -
\ <2miles ~ Medium
•
^ [sostat~c swe 30 - 60 m~Ies
•
% EA
~"
ona
/ Low/
13
lo
LOW OOySSal htl5 ~<45 fathoms
,
%
2,
w~de ,
~,o
5e--
-
m, A b y s s a l hills ~ 50-95
fathoms
A Seomounts 500 '~
w ae
_ I O S S l f ZOt~On o f swells L
Height <
•
'
~
10 ...........
C]asslhcatron nrgn rebel
of
-
~e,,gnt ~50 w idt h
o_
.o
...........
-,.
5C$8
R LOW seopeoKs
9
•
3
4.
and
Local s w e l l s 2-10
miles
EH
Dinnactes / "~
~
EL 715
12
E~rood Swel[~ ~ 10-30 16 m l 4 e S ~, wide
"
23
,1
4
<-195 fothomo
H gn
SeoDeaks -
200
-495
fathoms
,2,~ 6 1 3 ~
~
~
,
~
~
"
6 Nigh
{
'\
.
\
~/~ 8"
and
lOW r e h e f
/ •.
50~ ,
of
Classification high, medium
' • ,.
~50 \ \ 1•
/
~NILLS LOW
--
~
7"v • J• 5 o
L
~
\
10 9
3
.
6.
414 v
,\ -
~MedlUm
Fig. 13. Classitieation o f the bathymetric relief•
fathoms are volcanoes (Fig.2, 3). KUE~L~ (1935) found that the submarine slopes of composite andesitic volcanoes in the East Indies averaged 25 °. Mm,~AROand DIETZ (1951) found slopes not greater than 22-24 ° on the basaltic volcanoes of the Gulf of Alaska seamounts. DmTZ and MENM~D (1953) found flanking slopes of 15 ° on a seamount of the Hawaiian Arch. The highest peak in each of profiles 8, 10 and 11 have the following properties respectively: height/width : 114 fathoms/n.m., 83 fathoms/ n.m., 143 fathoms/n.m.; average slope per interval of 0.571 n.m. (int.) ----- 120 fathoms/ int., 95 fathoms/int., 160 fathoms/int.; average slope ---- 11.9 °, 9.5 °, 15.7 °. These slopes are half of Kuenen's values but are probably more characteristic of basaltic volcanoes. Local slopes equal and exceed Kuenen's figures (25 °, 265 fathoms/int.) but Marine Geol., 3 (1965) 169-193
189
DEPTH DISTRIBUTION AND BATHYMETRIC CLASSIFICATION
should not be confused with the broader averages. Most slopes greater than 100 fathoms/int. (10 °) are volcanic (Fig.3). The height/width division of 50 fathoms/n.m, of the classification is half of the ratio for the above basaltic volcanoes. However. TABLE II BASIC CLASSIFICATION OF ABYSSAL FEATURES1
Profile
H
M
L
12
VI V 0 0 V V 0 VII 0 II II II
II IV V VII VI VII IV II VII VII IV VII
III IV IV III VII III V VI VII III III IV
II III III III III III IV II III III III III
13
V
VII
V
III
0 0 VII
IV 0 VII
III V IV
III V III
0 0 29
1
2 3 4 5 6 7 8 9 10 11
14 15 Total
HML
H 2
M 2
L2
6
15
3
2 0 0 2 1 0 7 0
31 20 23 16 16 11 3 16
5 5 4 3 1 12 2 4
2 3
18 14
5 3
2
11
3
4
18
4
26 0 238
4 6 64
Total 2
24 38 25 27 21 18 23 12 20 25 20 16 26 30 6 331
1 Subgrouped (three out of four classes): 4, 6, 10-4, 9--4, 14-6, 13-10, 11-10,12 (9, 10, 11, 12 areally grouped-see Fig. 1). Independent: 1, 2, 3, 5, 7, 8, 15. Compare to Fig.2, 3. 2 Number of bathymetric features in profile. ~-
~
10
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25 2o 15 5 0
- -
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20
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Fig.14. Number and character of abyssal hills in the profiles exclusive of seamounts, seapeaks, and swells. Marine Geol., 3 (1965) 169-193
190
1). C. KRAUSE AND H. W. MENARD M (HML)
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I
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Fig. 15. Pigeonhole classification of bathymetric profiles according to hills.
oblique crossings of the volcanoes give more subdued profiles so that most or all of the features in "seamounts" and "high seapeaks" of the classification should be volcanic. "Low seapeaks" and "pinnacles" may also be volcanic but rock sampling information is lacking. "Plateaus" are absent in this study. "Ill-defined features" are too small to classify due to the sampling method and physical principles. "Very high to low abyssal hills" (M). The main body of the conclusions of this study is concerned with this group. The height/width boundaries of this group are 50 fathoms/n.m, and 10 fathoms/n.m, with steep features above and swells below. The classification may be considered in terms of energy of hill formation, subject to various assumptions. The relative minimum and maximum mechanical energy of formation based on conical hills in each division is: low abyssal hills: 1-15.6, medium abyssal hills: 6.25-2,500, high abyssal hills: 100-40,000, very high abyssal hills: 1,600-156,000. Marine Geol., 3 (1965) 169-193
~
DEPTH DISTRIBUTION AND BATHYMETRIC CLASSIFICATION
191
"Local to isostatic swells" (L). The swells in general are not represented by seafloor slopes (Fig.3). They are rises in the sea floor upon which sit the abyssal hills and seamounts. "Local swells" may be folds, local accumulations of volcanic material, horsts, etc. "Broad swells" are more in the nature of anticlinoriums, broad outpourings of lava, etc. "Isostatic swells" are so broad that the processes of isostasy are beginning to affect the topography and such swells represent variations and structures in the oceanic crust and mantle. The apex zones (I, III, V) of the ternary diagrams (H, M, L, HML) are the most significant geologically because they show which features numerically dominate the profiles. The intermediate zones (II, IV, VI, VII) show mixed profiles and will be discussed only briefly in the following. H-diagram. Many profiles (see Table II, Fig.15), 3, 4, 7, 9, 14, 15, do not appear because they have no such steep features. The steep features in profiles 2, 5, 6, 13 are dominated by low seapeaks and pinnacles. No profile is dominated by seamounts and high seapeaks. M-diagram. Abyssal hills apparently occur characteristically as mixed groups. No profiles are dominated by very high to medium abyssal hills and ortly one, profile 3, is dominated by low abyssal hills. The remainder of profiles, except for 15, appear in mixed zones, especially the central zone VII which indicates that a complete range of hills from low to very high occurs in each profile. L-diagram. No profile is dominated by isostatic swells, mainly because only two or three such swells may exist per profile. Six profiles, 1, 4, 6, 10, 11 and 14 are dominated by broad swells. Three profiles, 7, 13 and 15 are dominated by local swells, channel levees in the case of profile 15. In each of the three ternary diagrams on the basis of space available for a feature and its relative energy of formation, features should numerically increase from zones I through III to V. Therefore zone V should dominate on such a basis. It does not do so in nature, which indicates the action of other determining factors such as a greater than ~- minimum hill size and hence energy of formation. The physical characteristics of the bottom rock also influence the distribution of that energy. Note that no profile is dominated by zone I. This effect in diagrams H and L is due to the lack of space available for numerically significant features of this size. HML-diagram. Eleven of the profiles are dominated by abyssal hills. One, profile 15, is dominated by its levees. The profiles were also treated as a group and classified. This group tentatively represents the northeastern Pacific sea floor. With regard to both steep features and abyssal hills, the group is mixed, having a complete range of features. The group shows a numerical lack ofisostatie swells compared to local and broad swells which are about equal in abundance to one another. The group is further dominated by abyssal hills. The subgrouping (Table II, bottom) of the profiles based on the ternary classification relates the profiles both topographically and geological. Although the best subgroupings have in common only three of the four classes, a visual examination Marine Geol., 3 (1965) 169-193
192
D . C . KRAUSE AND H. W. MENARI)
of the related profiles (Fig.2, 3) reveals a visual resemblence as well. Profiles 9, 10, 11 and 12 were made across the outer portion of the Hawaiian Arch (DIETZ and MENARO, 1953). Profiles 10, 11 and 12 show good relationships while profile 9 is more subdued probably due to sedimentation and/or lava accumulation. The "independent" profiles, 1, 2, 3, 5, 7, 8, 15, visually differ markedly from one another. Through the above classifications, the profiles are easily classified in what appears to be a natural system and one that allows classification of the sea floor throughout the world. The methods used throughout this paper are easily adaptable to computer techniques for rapid classification of the sea floor on the basis of depths. The ultimate objective would be the same as used by HEEZEN et al. (1959, pl. 20) in their classification of the north Atlantic Ocean, but this would be quantitative rather than qualitative.
CONCLUSIONS
(1) Several profiles (1-5, 15) show a Gaussian distribution of depths and others have a significant portion that may be normally distributed if the depth distribution due to seamounts is removed. (2) No horizontal periodism of the features exists except for the three seamounts of the Moonless Mountains. (3) The frequency of abyssal hills is related, though poorly, to the heights of the hills. (4) The frequency of abyssal hills is related more surely to the widths of the hills. (5) Classification of abyssal hills was made on the basis of height versus width and fits the profiles in a natural way. These ielationships except 2 imply a certain predictability to the examined characters of the sea floor. They also imply that the causal geologic processes leading to the formation of the features acted in a consistent way. The discovery of these processes will lead to the understanding of the mechanism of abyssal hill formation. Certain of the processes have been pinpointed in the text. However, other very important processes and relationships remain to be deduced. For example, it is possible to calculate the energy of formation of those hills, if certain simplifying and perhaps unreal assumptions are made such as the assumption that the hills were formed from vertical deformation of a flat sea floor and neglecting friction. This energy of formation helps define the scale of the causal geologic processes and thus aids in their deduction. The uniformity of the results supports reliability of the deductions, certainly for the areas studied and hopefully for large areas of the sea floor. If this report were to do nothing more than this, it will have served its purpose.
ACKNOWLEDGEMENTS
This work was supported initially by the Long Lines Department of the American Marine Geol., 3 (1965) 169-193
DEPTH DISTRIBUTION AND BATHYMETRIC CLASSIFICATION
193
Telephone and Telegraph Co., and later by the University of California, the University of Rhode Island, and the Office of Naval Research. E. Buffington, F. N. Spiess and D. R. Schirtk suggested many improvements in the paper.
REFERENCES
ARRHENIU$,G., 1963. Pelagic sediment. In: M. N. HILL (General Editor), The Sea, Ideas and Observations on Progress in the Study of the Seas. 3. The Earth beneath the Sere Irtterscience, New York, N.Y., pp.655-727. DmTZ, R. S. and MENARD, H. W., 1953. Hawaiian swell, deep and arch, and the sudsidence of the Hawaiian Islands. J. Geol. 61 : 99-113. HEEZEN, B. C., THARP, M. and EWlNG, M., 1959. The floors of the oceans. 1. The north Atlantic. Geol. Soc. Am., Spee. Papers, 65 : 122 pp. HOFFMAN,J., 1957. Hyperbolic curves applied to echo sounding. Hydrograph. Rev., 34 (2) : 45-55. KRAUSE,D. C., 1961. Geology on the sea floor of Guadalupe Island. Deep-Sea Res., 8 : 28-38. K~AUSE,D. C., 1962. Interpretation of echo-sounding profiles. Hydrograph. Rev., 39 (1) : 65-123. KUENEN, PH. H., 1935. Geological interpretation of the hathymetrical results. Snellius Expedition, Sci. Results Snellius Expedition Eastern Pt. East-Indian Archipelago, 1929-1930. 5. Geol. Results, 1:62-69. MENARO, H. W. and DIETZ, R. S., 1951. Submarine geology of the Gulf of Alaska. Bull. Geol. Soc. Am., 62 : 1273. TUKEY, J. W., 1949. The sampling theory of power spectrum estimates. Syrup. App1. Autocorrelation Anal. Phys. Probl., Woods Hole, Mass., 1949, pp.47-67.
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