Lognormal distribution of inner continental shelf widths and slopes

Lognormal distribution of inner continental shelf widths and slopes

Deep-Sea Research, 1964, Vol. 11, pp. 53 to 78. Pergamon Press Ltd. Printed in Great Britain. Lognormal distribution of inner continental shelf width...

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Deep-Sea Research, 1964, Vol. 11, pp. 53 to 78. Pergamon Press Ltd. Printed in Great Britain.

Lognormal distribution of inner continental shelf widths and slopes MILES O. HAYES I)cfenseResearch Laboratory,The Universityof Texas, Austin,Texas

(Received 28 October 1963) Abstract--Width of the inner continental shelf (distance from shore to 200-ft depth contour) was measured at 2,136 stations located at 50-mile intervals along the coasts of the world. Inasmuch as most coastal areas have lognormal frequency distributions of inner shelf width, a logarithmic grade scale.--' inner shelf width grade scale '--was developed to compare coastal areas statistically. In order to further simplify statistical computations involving this scale, width measurements axe transformed logarithmically to ' delta units' that give equal numeric significance to class intervals on the scale. This transformation involves the substitution : 8 = logs ~0 wher¢ ~, is the numerical value of the inner shelf width in nautical miles. Mean inner shelf width (Ms) for the total area studied (which includes more than 100,000 nautical miles of shoreline) is 9.2 miles and 68 % (4- 1 ol) of the 2,136 measured traverses range between 1"93 and 48 miles. Of the coastal areas investigated, Mindanao has the narrowest inner shelf (M, = 1.1 miles) and Southeast Asia has the widest (M~ = 52 miles). Mean slope of the inner shelf for the total area studied is 0 ° 12.4' (or 22 fl/mile). Steepest mean slope angle for any of the individual coastal areas investigated occurs off the island of Mindanao (1 ° 43"1", or 182 ft/mile). Application of the graphical statistical measures of FOLK and WARD (1957) permits classification of coastal areas of the world into 12 classes. The classification is based on mean inner shelf width of the individual a/ca (M,), and on variation, or graphic standard deviation (oi), of width within the area. Although this is a purely descriptive classification, it has genetic significance in that width (M a) can be related to tectonism and sediment deposition, and standard deviation (oi) can be related to degree and type of mixing of basic width types. Three basic genetic coastal width types are defined: Type A : Young mountain range coasts (strong uplift)--narrow (M 8 = approximately 3.5 nautical miles) Type B : Plateau-shield coasts (tectonically stable)--intermediate (M~ = approximately 10 nautical miles) Type C : Depositional coasts (strong downwarp and rapid sedimentation)---wide (M o = approximately 40 nautical miles) Inner continental shelf width (and slope) can also be related to bottom sediment composition of the inner shelf. Rocky bottoms are most common on narrow inner shelves (steep slope; < 2.5 miles in width), sand and mud are most common on wider inner shelves (gentle slope; > 20 miles in width);.mld shell occurs most frequently on moderately wide inner shelves. Consideration of the relatinn~ip of inner shelf width and slope to physiography and geology of the adjoining land areas reveals an apparent morphologic principle (Principle of Constancy of Inner Continental Shelf Widths and Slopes) that relates inner shelf width (and slope) variation to factors controlling the magnitude of width (and of slope angle). It is as follows : Coastal-areas with essentially uniform physiography and tectonic origin tend to have inner continental shelf widths (and slope angles) lognormally distributed with low dispersion about a mean value determined by the combined factors of type and degree of intensity of tectonic activity and rate of deposition o f bottom sediments. Mean width is modified, in places, by other geological processes, such as faulting and glaciation.

53

54

Mn.~.~ O. HAYEs INTRODUCTION

WHILE engaged in compilation of oceanographic data concerning the inner continental shelf*, I was faced with the problem of quantitatively describing and comparing different coastal areas with regard to width of the inner shelf. A major difficulty stemmed from the fact that widths do not have a ' normal ' distribution if an arithmetic width scale is used as the x-axis of histograms and cumulative and frequency curves. This problem is illustrated in Fig. 1, which shows the extreme skewness that results from plotting width data on an arithmetic scale. Therefore, standard statistical measures could not be applied to width measurements for an area i f they were plotted on an arithmetic scale. Experimentation with a log scale revealed that inner continental shelf widths have a 'loguormal distribution.' This discovery

,° 1 _o

TOTAL AREA

30-

t-._J D--

20-

2: LtJ

n

IOTO 320

0

5

I0

15 20 25 30 35 INNER SHELF WIDTH, NAUTICAL MILES

40

45

50

Fig. 1. Histogram and frequency distribution curve for inner continental shelf width (distance from shore to 200-ft depth contour) for 2,136 stations located at 50-mile intervals along coasts of world. Distribution is plotted on arithmetic inner shelf width scale and is strongly skewed toward wider measurements. Although abscissa is terminated at 50 miles, width population decreases very gradually until maximum measurement of over 320 miles is reached.

necessitated the development of a logarithmic grade scale for inner shelf widths in order to compare different areas by statistical methods. The consequent usage of statistical measures based on the new logarithmic scale permitted other manipulations of inner shelf width data, including classification of coastal areas on the basis of mean width and standard deviation, and investigations into the nature of width and slope variations of the inner shelf. Basic width data were taken from nautical charts of the U.S. Navy Hydrographic Office and the U.S. Coast and Geodetic Survey. For purposes of description, coasts of the world were arbitrarily divided into the 31 areas outlined on the map in Fig. 2. *The portion of the sea floor that extends from shore out to the 200-ft depth contour is here

defined as the ' inner continental shelf.' The 200-ft depth contour was arbitrarily chosen. It bounds approximately the inner one-third of the continental shelf.

"°"e

" . . . . _i.';

eee

.~

...........

~

BOUNDARIES

2:!:'5"'

'.

• -

• • • • = Type A (Young Mountain Range Coasts) X X X X = Type B (Plateau-shield Coasts) I-IHI-II-I = Type C (Depositional Coasts)

Fig. 2. l..ocation o f 31 coastal areas for which inner continental shelf width measurements were made. Coastlines included in statistical summaries o f sample populations o f basic width types (Figs. 13, 14 and 16) are also shown _:

P~

L/I L~

O

@

8

O ~°

56

MILKS O. FIAYKS

All coastal areas of the world, with the exception of extreme polar regions and small islands, were included in the survey (over 100,000 nautical miles of shoreline). METHODS

OF

STUDY

A total of 2,136 measurements were made of inner shelf width by determining length (in nautical miles) of traverses drawn perpendicular to shore and extending out to the 200-ft depth contour. Traverses were plotted on 259 nautical charts and were located at 50-nautical-mile intervals along a ' smoothed curve' of the shoreline. My original intention was to plot these width measurements as cumulative curves and histograms for each coastal area. As data accumulated, however, it soon became apparent that widths were distributed logarithmically and that a geometric grade scale would have to be improvised to deal with the data. A similar problem has been confronted and dealt with by sedimentologists because the grain size of sediments, also, is usually distributed logarithmically. An attempt was made to apply some of their techniques to the width measurements of this study. APPROXIMATE SLOPE I

6"

3"

I

I

-5"0 t

i

-4"0 i

1'30' 0'45' 0"23' O*II' 0"6' I

I

I

I

INNER SHELF WIDTH -3.0 -20 -1"0 0 i

I

0"3' I

0"I.4' 0"0.7' 0"0.35' 0"0.17' I

I

h

DELTAUNITS (~) +1.0 +2.0 +3"0 +4(3 +50

i

i

i

~

t

l

2-5

5

10

20

40

80

]

I

+60

[

i

320

640

15-

to10-

-= t~

0-

0

0-313 0"625 1"25

160

INNER SHELF WIDTH, NAUTICALMILES

Fig. 3. Histogram of inner continental shelf width for 2,136 traverses (total-area) that results from using logarithmic width scale (' inner shelf width grade scale '). Delta scale and approximate slope scale also given. Compare with Fig. 1 for effect of log scale on normality of distribution.

The evolution of a logarithmic grain size scale for sediments began when UDDEN (1898) proposed a grade scale based on a constant ratio of two between successive classes. In order to simplify statistical computations involving this scale, KRUMBE1N (1934) proposed a ' phi scale' for which the symbol phi (if) is defined by the following equation : =

--

log2 ¢

in which ¢ is the numerical value of the grain diameter (or class limit) in millimeters. He thus proposed to use the logarithm (to the base 2) of the diameter instead of the diameter itself.

lognormal distribution of inner continental shelf widths and slopes

57

A scheme very similar to the one Krumbein proposed for sediments is applied to inner shelf width data of this study. An inner shelf width grade scale (' delta scale '), which also has a constant ratio of two between successive classes and has classes plotted equal in width (see Fig. 3), is utilized. The equal units of the inner shelf width grade scale are defined as 'delta units ' and are assigned numbers that give equal significance to class intervals (Fig. 3). The conversion o f ' i n n e r shelf width units' (in nautical miles) to ' d e l t a units' involves the substitution :

8 = log2 ~0 where/z is the numerical value of the inner shelf width in nautical miles. The conversion of logarithmic values (8) to ' inner shelf width equivalents ' (/z) may also be

0.156

"n

Fig. 4. Chart for converting inner continental shelf width measurements from delta units (3) to nautical miles (~). accomplished by construction of a simple conversion chart (nomograph) on semilogarithmic, 4-cycle graph paper (Fig. 4). Delta unit values of inner shelf width grade limits from 0.156 to 640 nautical miles are given in Table 1. The chief advantage of the delta unit system is that it permits application of standard statistical procedures to these width measurements although they have a logarithmic distribution. The resulting symmetry of the inner shelf width distribution for the total area (Fig. 3), as well as that for many local areas, is thought to be justification for utilization of this grade scale of inner shelf widths.

58

M I t ~ s O. HAXr~S

Table 1. Conversion of inner shelf width grade scale limits from I~ to 8. Approximate slope of inner shelf at each grade limit is also given. Grade limit, nautical miles (l~)

8

Approximate slope 12° 6° 3° 1° 30' 0 ° 45' 0 ° 23' 0Oll '

0"156 0"313 0.625 1-25 2'5

5 10 20 40 80 160 320 640

+ + + + + +

0 ° 6'

0 ° 3' 0 ° 1"4' 0 ° 0"7' 0 ° 0"35' 0 ° 0"17'

For purposes of description of individual coastal areas and comparison between areas, twc~graphic statistical measures proposed by FOLK and WARD (1957), graphic mean (Mz)~and inclusive graphic standard deviation (¢u), are used. Graphic measures 99

95

/r

84

//I

L~

n,"

/;

~>5o p.-

d

//

L~

,

/

0"625 q

-4'0

1"25 t

-3'0

2-5 5 I0 20 40 80 INNER SHELF WIDTH, NAUTICAL MILES i

i

1

i

i

-2"0 -1"0 0 +1-(3 +2"0 INNER SHELF WIDTH, DELTA UNITS.

160

i

+5"0

+ ~ 0'

320

+ eo

Fig. 5. C u m u l a t i v e curves o f i n n e r s h e l f width p l o t t e d o n arithmetic-probability p a p e r for n a r r o w e s t ( C u b a a n d Hispaniola) a n d widest (Southeast A s i a ) o f t h e 31 m a j o r coastal areas investigated, a n d for c o m b i n e d total o f all 31 areas.

are used because they are easier to calculate than corresponding measures computed by the method of moments*. * F o r a discussion o f t h e merits o f graphical statistical m e a s u r e s as o p p o s e d to t h o s e o f statistical m e a s u r e s c o m p u t e d by t h e m e t h o d o f m o m e n t s see FRmDrCa~N (1962).

Lognormal distribution of inner continental shelf widths and slopes

59

In order to determine these statistical parameters, inner shelf width data are plotted as cumulative curves on arithmetic-probability paper and percentiles are read directly from the cumulative curves. Data are plotted on arithmetic-probability paper because " much more accurate results are obtained if one plots the cumulative curve on probability paper, because of the superior accuracy of extrapolation and interpolation " (FOLK, 1961, p. 43). Formulas for finding the two parameters are : M8 = (~te + ~so + ~s4) 3 ~z --

884 -- 816 8.s - - ~5 4 + 6.6

where ~ts, 850, and so forth a~e equal to the inner shelf width value in delta units at the indicated percentile of the cumulative curve. Figure 5 gives cumulative curves for three coastal areas. RESULTS Statistical parameters were determined for all coastal areas and are sttmmnrized in Table 2. These data reveal a wide range in inner shelf width characteristics a m o n g the individual areas; however, if measurements from all areas are combined, they form a lognormal distribution. This is demonstrated by the fact that the cumulative curve plots as a straight line on arithmetic-probability paper (Fig. 5; see also Fig. 3). Mean inner shelf width (Ma) for the total area studied is 9.2 miles and 68 ~o (4- l~z)* of the 2,136 measured traverses range between 1-93 and 48 miles. The coastal area made up of Cuba and Hispaniola, which has a mean inner shelf width (Ma) of 1.9 miles ( - - 2"46), has the narrowest inner shelf of the 31 major coastal areas investigated (although the inner shelf off Mindanao, a subdivision of the major coastal area of the ' E a s t Indies and Philippines,' is even narrower; Ma---- 1.1 miles), and Southeast Asia, which has a mean inner shelf width (Ms) of 52 miles ( + 2"48), has the widest. Cumulative curves for the two extreme areas are compared to the total area curve in Fig. 5t. LOGNORMAL D I S T R I B U T I O N

Width A study of width frequency distribution for the 31 individual coastal areas reveals that, like the distribution for the total area, many are lognormal. It is also evident that as long as coastal areas are restricted to a single physiographic province:L the inner shelf width distribution for the area is generally lognormal. If, however, the arbitrarily delineated coastal areas include two or more physiographic units within their boundaries, the width distributions are apt to be non-normal, often polymodal. *This notation means that approximately 68 % of the population ranges between plus and minus one graphic standard deviation from the mean. fThe scale of some charts was such that it was impractical to measure widths of less than one mile. In those areas where this was the situation, the probability plot was extended as a straight line and percentiles read from extrapolated portion of the curve. Extrapolation is justified on the theoretical basis that normal distributions plot as straight lines on probability paper. SAs used in this paper, a physiographic province is defined as a geographic area with uniform topographic expression, usually brought about by uniform (in time, type, and intensity) geological processes and events. Examples are coastal plains, deltaic plains, block-faulted mountain ranges, and so forth.

60

MILES O. HAYES

F o r e x a m p l e , c o n s i d e r t h e i n n e r s h e l f o f t h e n o r t h e r n G u l f o f M e x i c o (Ms = 42 m i l e s ; o-i = 0 " 9 ) 8 , w h i c h is l o c a t e d o f f t h e u n i f o r m p h y s i o g r a p h i c p r o v i n c e o f t h e G u l f C o a s t a l Plain, a n d t h e i n n e r s h e l f o f t h e w e s t e r n c o a s t s o f t h e U . S . a n d C a n a d a (Ms = 3.4 m i l e s ; o-i = 1"38), w h i c h lies a d j a c e n t to the relatively u n i f o r m Pacific C o a s t m o u n t a i n .ranges. I n n e r s h e l f w i d t h f r e q u e n c y d i s t r i b u t i o n s for b o t h areas h a v e relatively l o w g r a p h i c s t a n d a r d d e v i a t i o n s , are u n i m o d a l , a n d p l o t as n e a r l y s t r a i g h t lines o n a r i t h m e t i c - p r o b a b i l i t y p a p e r ; hence, t h e y are l o g n o r m a l d i s t r i b u t i o n s . T h e s a m e is t r u e o f i n n e r s h e l f w i d t h d i s t r i b u t i o n s for m a n y o t h e r c o a s t a l a r e a s t h a t are m a d e u p o f o n l y o n e p h y s i o g r a p h i c unit. T h e r e f o r e , t h e r e s u l t a n t c o n c l u s i o n is t h a t i n n e r s h e l f w i d t h f r e q u e n c y d i s t r i b u t i o n s for a r e a s w i t h u n i f o r m g e o l o g i c a l h i s t o r y , u n i f o r m t e c t o n i c h i s t o r y , a n d so f o r t h ( o n e p h y s i o g r a p h i c p r o v i n c e ) f o r m a n o r m a l c u r v e if p l o t t e d o n a l o g scale (' d e l t a scale '). A l t h o u g h t h e w i d t h d i s t r i b u t i o n s f o r i n d i v i d u a l c o a s t a l a r e a s o f u n i f o r m p h y s i o g r a p h i c types t e n d to be l o g n o r m a l , m e a n w i d t h has a w i d e r a n g e a m o n g t h e i n d i v i d u a l areas, r a n g i n g f r o m relatively n a r r o w (1.1 miles) to v e r y w i d e (52 miles) (see T a b l e 2).

Table 2.

Inner continental shelf width data for coastal areas o f the world. Location of areas given (by numbers) in Fig. 2.

Coastal area

Number of traverses

Width at ( M 8 - loI)

M8

Width at (Ms + 1oi)

8

miles

8

miles

8

oi

m//e:

1. NE Siberia

73

+ 0-23

11.7

-- 1"12

4.60

+ 1.65

31-0

1"638

2. East Asia

61

-- 0-58

6"8

-- 2"32

1"95

+ 1"34

25"0

1.678

3. Japan

67

--

1.55

3.4

-- 2.98

1.27

--

0.08

9'5

1"518

4. China, Formosa and Hainan

57

¢ 1"86

36'0

-- 0"45

7.40

+ 3"70

130.0

2'158

5. SE Asia

39

-F 2.40

52.0

+ 0"80

17"40

-~ 3"61

121'0

1.37a

278 21 24

-- 0"12 -- 3"19 -- 1"72

9"2 1.1 3"0

-- 2"96 -- 4.90 -- 3-22

1"27 0-33 1"07

H 2"88 - - 1"41 ÷ 0.06

73'0 3.8 10.4

2"708 1"768 1"708

14 26 44 40

+ 2"20 + 0"56 - - 2"08 + 1"11

46-0 14"7 2"4 22.0

÷ ----

2"93 3-20 0"30 3'65

76'0 81"0 8"1 125.0

0"878 2"268 1-548 2"378

63 46

--

0"13 + 2"02

9"2 40.0

-- 2"80 + 0'05

1'42 10"50

+ 3.00 ÷ 3'55

80"0 115"0

2-77~

Central

6. East Indies and Philippines (M) Mindanao (L) Luzon (MP) Malay Penin.

(J) (C) (S) (NG) (B)

Java Celebes Sumatra New Guinea Borneo

1.39 26"00 1"80 2"90 0.346 0"90 1-10 4"65

÷ + -+

1 "62~

7. Australia a n d Tasmania

154

+ 0-82

17.8

-- 1"31

4.00

-- 2"78

68'0

1-978

8. New Zealand

44

-- 0"72

6"0

-- 1"86

2"70

÷ 0"38

13"0

1"198

9. Bay of Bengal

45

+ 1.30

24.0

+ 0-21

11-70

+ 2"40

53"0

1 '068

49

+ 0'88

18.5

-- 0.17

8.90

÷ 1.83

35.0

0-998

10. West India

L o g n o r m a l distribution o f i n n e r continental shelf widths a n d slopes

61

Table 2--continued

Number

Width at ( M e -- l o i )

Mo

of

Coastal area

Width at (M~ + loi)

oI

traverses miles I

11. O m a n a n d A d e n I Gulfs i

54

1"31

4"0

-- 2"77

1"48

+ 0'23

12. Persian G u l f

26

:- 1'69

32'0

0'83

5'60

+ 3"31 I

11"9

1 "460

99"0

2"13o

/

13. R e d Sea

52

14. SE Africa

79

15. M a d a g a s c a r

40

16. West-Central Africa 17. N W Africa, W. Spain a n d Portugal 18. M e d i t e r r a n e a n Sea

5-0

-- 3'47

0"90

+ 0"84

18"0

2.090

4-9

2'44

1"83

+ 0"50

14"2

1 '480

~ 0"08

10.6

1"08

4"70

+ 1"20

23"0

1"18o

70

- 0-04

10'0

1"09

4"70

+ 0'98

19"8

1"17o

63

+ 0"21

11.6

1'46

3'70

+ 2.00

40"0

1.61o

1'88

2"7

- 3'60

0"82

-- 0.15

9"0

1-69o

135

1.05 - - 10l

--

19. W e s t e r n E u r o p e a n d British Isles

82

0.00

10"0

- 2"20

2"18

+ 3.00

80-0

2-390

20. Baltic Sea

50

1"10

21 "4

÷0'12

10"90

+ 2.00

40.0

1 "040

21. E a s t e r n C a n a d a

70

-

1"79

2.9

-- 3'38

0-96

-- 0"30

8"1

1.65o

22. E a s t e r n U.S.

32

+

1 "42

27-0

-- 0"39

7"60

+ 2.70

65'0

1.37o

23. C u b a a n d Hispaniola

45

-- 2'40

1"9

-- 4"35

0"49

-- 0"24

8'4

2"11o

24. N o r t h e r n G u l f o f Mexico (U.S.)

21

+ 2"07

42"0

+ 1"27

23-80

+ 2"96

76'0

0.900

25. E a s t e r n C e n t r a l America

54

+ 0"74

16"5

--

107

+ 1'32

26. N o r t h e r n a n d Eastern South America

1"38

~.80

+

3"10

~5"0

2"390

25-0

0"18

8-90

+ 2"63

51"0

1"420

27. S o u t h e r n S o u t h America

49

--

0"41

7"5

2"38

1.92

+ 1.60

30'0

1"840

28. W e s t e r n S o u t h America

69

-- 1"72

3"0

3 "09

1.18

-- 0"33

7"9

1"37o

29. W e s t e r n Central America

79

- - I "20

4"3

-- 2"95

1"29

+ 0"54

14"6

1"658

30. W e s t e r n U.S. and Canada

33

--

1"53

3"4

-- 2"90

1"33

0"28

8"2

1 "290

+ 1-09

21.0

-- 2"40

1.90

+ 4"30

197"0

2"870

0-12

9-2

2"38

1"93

+ 2-16

48"0

2"230

31. A l a s k a TOTAL

AREA

59 2,136

--

--

62

Mn~s O. HavBs

Of the coastal areas investigated, types of areas particularly noteworthy for having lognormal distributions are :

Examples Western U.S. and Canada Western South America Southeast Africa Japan Madagascar New Zealand Bay of Bengal Northern Gulf of Mexico Baltic Sea

Type Long, straight, tectonically uniform coastlines

Large islands or island groups with relatively uniform physiography throughout Marine embayments with relatively uniform physiography of the adjoining land mass

0

1.25

2.5

5

10

20

40

80

160

320

640

BUTION )BY .ITY PLOT

0

0'313 0"625

I'25

2'5

5

10

20

40

80

16(3

INNER SHELF WIDTH, NAUTICAL MILES

Fig. 6. Histograms illustrating lognormal distribution of inner continental shelf widths for long, straight, tectonicallyuniform coastlines. (Upper) Southeast Africa--79 traverses, (Lower) Western South America169 traverses.

The lognormality of width distributions from these type areas are demonstrated in Figs. 6-8. A histogram demonstrating the bimodality of distributions produced when two distinct physiographic provinces are included within a single coastal area is given in Fig. 9. Three histograms illustrating the extreme polymodality that results from including measurements off several different physiographic provinces within a single coastal unit are given in Fig. 10.

Lol~.ormal distribution of inner continental shelf widths and slopes

63

Slope As originally designed, this study was concerned with inner shelf width only, but a discussion of inner shelf slope should not be omitted. Tangents for average slope angles of the inner shelf of coastal areas are readily calculated from the original inner shelf width measurements, because x (inner shelf width) is determined by direct

30.

MADAGASCAR 20-

10"

~O Z

O

I-a0

0

1~5

2.5

5

10

20

40

80

160

320

640

20"

Im O $.--

RIBUTION !ED BY

10"

~ILITY PLOT

t~

O" O-- f

~0

INNER SHELF WIDTH,

NAUTICAL MILES

Fig. 7. Histograms illustrating lognormal distribution of inner continental shelf widths for large islands or island groups. (Upper) Madagascar 40 traverses,

(Middle) Japan--67 traverses, (Lower) New Zealand 4A,traverses. measurement and y is a constant (200 ft). Slope angles thus calculated for the grade limits of the 'inner shelf width grade scale' are given in Table I. Similar to the inner shelf widths, inner continental shelf slope angles closely approximate a lognormal distribution for the total area. This is evident from the

64

Mxt,ES O. HAYES

3o4 BAY OF BENGAL

20-

I-

0 _J

"o 1 4

o

o

30

z w u u.,

TIC SEA 20-

10"

0

o

~.'~s

2-s

s

lo

20

INNER SHELF WIDTH,

4o

8o

l~o

3~o 6~o

NAUTICAL ~ILES

Fig. 8. Histograms illustrating lognormal distribution o f inner continental shelf widths for marine embayments. (Upper) Bay of Bengal (Thailand border to Madras, India) - - 45 traverses (Lower) Baltic Sea - - 50 traverses. 40-

o_ 30-

o

20-

w

~_ 1o-

0 - m 1.25

2.5

5

IO

20

INNER SHELF WIDTH,

40

80

160

320

6~I0

NAUTICAL MILES

Fig. 9. Bimodal distribution pattern of inner shelf widths in the coastal area extending from southern China border to southern Thailand border (based on 39 traverses). Bimodality is due to inclusion of two physiographic units, hilly coast o f Vietnam (narrow mode) and Gulf o f Thailand (wide mode), within one coastal unit.

Lognormal distribution of inner continental shelf widths and slopes W E S T E R N E U R O P E A N D B R I T I S H ISLES

20"

z

10.

N

°

I-,.

65

0

i

i

i

i

i

i

~

i

i

I

I

I 160

~ 320

1

20EAST INDIES AND PHILIPPENES

o I--

10-

u-

o

~

I-"

0

ac Lu

20-

I

~"

I"

I

~

I 10

I 20

I

I

I

I 80

ALASKA

10-

0 0

t 1"25

I 2'5

I 5

INNER SHELF WIDTH,

40 NAUTICAL

i 640

MILES

Fig. 10. Histograms illustrating polymodal distribution of inner shelf width measurements that results from inclusion of several physiographic units within single coastal unit. (Upper) Western Europe and British Isles - - 82 traverses, (Middle) East Indies (New Guinea, Celebes, Borneo, Java, Sumatra, and Malay Peninsula) and Philippines--278 traverses, (Lower) Alaska--59 traverses. slope values calculated for the grade limits of the ' inner shelf width grade scale ' (Table 1 and Fig. 3). When inner shelf width is doubled, slope is decreased by approximately one halC For example:

Width (miles) 5 10 20

Tangent

Slope

0.00660 0.00330 0.00165

0 ° 22.7' 0 ° 11.3' 0 ° 5.7'

However, this relationship does not hold up as well when the magnitude of slope angle is increased :

Width (miles)

Tangent

Slope

0.039 0.091 0.187

0.8391 0.3640 0-1763

40 ° 20 ° 10°

Nevertheless, it is evident from the approximate lognormal distribution of the lowangle, total area population, that had original data been collected as slope angles rather than as widths, and had a logarithmic slope scale been devised to fit the data, the slope angle distribution would be close to lo~normal.

66

~

O. I-IAvrS

Some insight into the nature of slope angle distribution on the inner shelf can be gained from a study of slope data (as inferred from width measurements) for individual coastal areas, and from comparing them with findings of similar studies on landform slopes. STRAHLER(1950) discussed slope frequency distribution of erosional land forms. He demonstrated that slope frequency distributions show a wide range in mean slope angles for different areas, but that slope angles for a single area are generally distributed symmetrically about the mean and have low dispersion, that is, they approach a normal curve in their distribution. He further concluded that these findings were an expression of a ' morphologic l a w ' . . . (Law of Constancy of Slopes) • . . "relating slope to other form f a c t o r s " (p. 684). It is as follows (p. 685) : "Within an area of essentially uniform lithology, soils, vegetation, climate and stage of desudopment, maximum slope angles tend to be normally distributed with low dispersion about a mean value determined by the combined factors of drainage density, relief and slopeprofile curvature." With three exceptions, there is much similarity between Strahler's findings and the results of this study. Exceptions are : 1. The major exception is that landform slope distributions are usually' n o r m a l ' distributions and are plotted on an 'arithmetic scale,' whereas inner continental shelf slope distributions closely approximate ' l o g n o r m a l ' distributions and must be plotted on a ' l o g scale.' 2. Slope angles are much less for the inner continental shelf than for the landforms described by Strahler, which have slopes up to 60 °. 3. The factors determining the magnitude of slope angle are different in many respects for the two environments. SHEPARD (1950) stated that the average slope of the continental shelf (0-600 ft) is 0 ° 07' and that it is somewhat steeper on the inner, than on the outer part. The

2.0

o-i 16&&iS

1.0 ••-

0

-3"0

22_2__

UNIMODAL POLYMODAL

-2.0

I 0

-I1,0

L +1.0

I +2-O

+3'0

M8 Fig. 11. Mean inner shelf width (Ma) vs. graphic standard deviation (oi) for 40 coastal areas. Ten classes are arbitrarily delineated to providledes~ptive basis for classifying individual coastal areas.

Lognormal distribution of inner continental shelf widths and slopes

67

m e a n slope o f the i n n e r c o n t i n e n t a l shelf for the total area o f this study (calculated using Mo = 9.2 miles as x) is 0 ° 12.4' (or 22 ft/mile), which agrees with Shepard's statement that slope o f the i n n e r p a r t of the c o n t i n e n t a l shelf is steeper t h a n the average for the whole shelf.

Table 3. Inner shelf width classification o f coastal areas. Numbers and letters assigned to coastal areas in column three correspond to those shown on graph in Fig. 11, and also to those given in Table 2 and Fig. 2. Class

Description Exceptionally narrow (av. = 1.5 miles); not uniform, some wide areas off bays and other localities

Representative areas 23) Cuba and Hispaniola M) Mindanao

II

Very narrow (av. = 3.0 miles); very uniformly narrow

(18) (C) 21) L) 28) 3)0 )

Mediterranean Sea Celebes Eastern Canada Luzon Western South America Japan Western U.S. and Canada

III

Narrow (av. = 4.8 miles); very uniformly narrow

(11) (29) (14) (8)

Oman and Aden Gulfs Western Central America SE Africa New Zealand

IV

Narrow (av. = 6"2 miles); exceptionally narrow zones plus some wide zones

(13) Red Sea (2) East Central Asia (27) Southern South America

V

Medium width (av. = 9.4 miles); heterogeneous, some wide areas and some narrow ones

(6) East Indies and Philippines (NG) New Guinea (19) Western Europe and British Isles

VI

Medium width (av. = 10"8 miles); moderate widths uniformly distributed

(16) (15) (18) (1)

West Central Africa Madagascar NW Africa, Spain and Portugal NE Siberia

VII

Wide (av. = 18.4 miles); some very wide areas but also some relatively narrow ones

(J) (25) (7) (31) (S)

Java Eastern Central America Australia and Tasmania Alaska Sumatra

VIII

Wide (av. = 23 miles); uniformly wide

(10) (20) (9) (26)

IX

Very wide (av. = 36 miles); not (12) Persian Gulf uniform, some exceptionally wide (4) China and Formosa areas plus some relatively narrow ones I (B) Borneo

X

Exceptionally wide (av. = 50 miles); uniformly very wide

Western India Baltic Sea Bay of Bengal Northern and Eastern South America (22) Eastern U.S

! (24) Northern Gulf of Mexico (U.S.) i (MP) Malay Peninsula (5) SE Asia (Ch) China (minus Formosa and Hainan)

68

M~L~S O. HAYES INNER

SHELF

WIDTH

CLASSIFICATION

Determination of statistical parameters of inner shelf width measurements makes it possible to classify coastal areas with regard to inner shelf width characteristics. One such classification, which is based on mean inner shelf width (M~) and graphic standard deviation (~I), is given in Fig. 11 and Table 3. Figure 11 is a diagram of Ma vs. gz that has 40 coastal areas plotted on it. These areas, which include the 31 coastal areas outlined on the map in Fig. 2 as well as further subdivided portions

30

:

A YOUNG MOUNTAIN

RANGE COASTS (MEAN)

~i!,!i~;~

/~ii-:~ii...

2"0

I'O

PLATEAU-SHELD' COASTS (MEAN)

~ -~o -

-

-2o

-~O

~

/

~

A / UNIMOOAL '/

6

+I'.o

¢---...-----.----~ ~DEPOSITIONAL COASTS(MEAN)

+~

,~o

MS, DELTAUNITS

3~

2.0

t.0

1'25

2.5

5 IO M8, NAUTICAL MILES

~

40

80

Fig. 12. (A) M~ vs. or! diagram showing areal distribution of unimodal and polymodal inner shelf width distributions of individual coastal areas (modality determined by visual inspection of histograms). Mean values for sample populations of basic width types also given. (B) M8 vs. crl diagram showing areal distribution of basic inner shelf width types among individual coastal areas (compare with Fig. 11). Type A (Young Mountain Range) Coasts are narrowest (M~ = approximately 3-5 miles), Type B (Plateau-shield) Coasts have intermediate widths (Ms = approximately 10 miles), and Type C (I)epositional) Coasts are widest (M~ = approximately 40 miles). Coastal areas made up o f only one ofthese major types, as well as those made up of A + B and B + C, generally occur in unimodal zone (diagram A) a n d have- tow standard deviations. If the two extreme width types, A and C, arc mixed within coastal area, however high standard dvviations result. Inner shelf width distributions for coastal areas made up of width types A and C are generally bim~dal and plot in major peak of sine curve of polymodal distributions (diagram A).

Lognormal distribution of inner continental shelf widths and slopes

69

of those areas, plot into 12 arbitrarily delineated classes. Coastal areas occurring within the same class have similar properties with regard to mean width (Ms) of the inner continental shelf in the area, as well as to the consistency, or uniformity (az), of widths within the area. Verbal descriptions and representative areas for each class are given in Table 3. This classification is purely descriptive as presented in Fig. 11 and Table 3. If the data are studied further, however, several genetic implications are apparent. To understand the genetic significance of this classification, one must know what determines width and how specific width types are distributed within the individual coastal areas. In Fig. 12 A, coastal areas occurring in the unimodal zone in the vicinities of -- 1.56, 0"06 and -k 2"06 compose three distinct coastal width types. The three coastal width types are named Type A (Young Mountain Range Coasts) for those near -- 1"58, Type B (Plateau-shield Coasts) for those near 0"08, and Type C (Depositional Coasts) for those near ÷ 2.0~. These width types were originally recognized by simply studying the geology (literature survey) of land areas adjoining the coastal zones. Consider the following examples occurring at the specified widths on the M8 vs. at diagram in Fig. 12 A : Width near -- 1"58 (3-5 miles) (Type A)

Western South America Western U.S. and Canada

Width near 0"06 (10 miles) (Type B)

West-Central Africa Madagascar

Width near ~-2-08 (40 miles) (Type C)

Southeast Asia Northern Gulf of Mexico (U.S.)

An immediate observation is that Type A coasts are located adjoining young, tectonically active mountain ranges, that Type B coasts are located adjoining shield and plateau areas, and that Type C coasts are located adjoining areas of rapid sedimentation and general structural subsidence. In order to test these observations further, statistical summaries were made of ' typical samples ' of the three coastal width types. Coastal areas included in each summary were chosen on the basis of the following definitions : Type A. Young Mountain Range Coasts. Coastal zone made up of high mountains (maximum elevations > 5000ft) related to Cenozoic orogenic activity. Bedrock of variable age but principally Tertiary sediments and volcanic rocks. Active tectonic uplift. Mostly short, high-gradient rivers emptying into sea. Type B. Plateau-shieM Coasts. Coastal zone made up of plateaus and moderate mountain ranges related to pre-Cenozoic orogenic activity. Bedrock composed of ancient basement complex of granite and gneiss (in shield areas) and Paleozoic and Mesozoic sediments (in plateau areas). Volcanic complex plateaus also present. Areas tectonically very stable. Numerous moderately long rivers may be present, depending on climate. Type C. Depositional Coasts. Coastal zone made up chiefly of broad, coastal and deltaic plains. Bedrock generally Tertiary and Quaternary sediments. Tectonically subsiding area. Many long, large rivers emptying into sea. Areas to be included in the sample populations were chosen in the following manner. Inasmuch as this was done in the later stages of the study, areas were chosen so as to invoke the least amount of reshuffling of data. Therefore, very complex areas with mixtures of all three coastal width types were generally omitted.

NE Siberia (1) Japan(3) Formosa (4) Luzon (6-L) Mindanao (6-M) Northern New Guinea (6-NG) New Zealand (8) Southern South America (27) Western South America (28) Western Central America (29) Western U.S. and Canada (30) Alaska (31) Total Traverses Percent

Coasial area

1

/

1.

;

: 78 1753 &IO

:zi

t;

: 6

: 3

: 12 9

;

1:

--

--

--

1.26-2.5

11

< 1.25

--

_-

_‘-

_-

_-

11: 25.62

::

:

:x

:

1: 2

26-5

(Total

1

1~

1

8: 18.65

:: 9

13 4

:

6-10 --

1

21-40

i ,

A 13.48

1; 3

12 2

:

_-

_-

5 ‘Y 17 3.82

r

r

r -

2 3

’ Number,Of traverses

1

090

r --: r-i

miles)

1 41-80

widths (naulical

mountain range coasts

traverses = 445)

Inner continentdz2~!f

_I-

i’)pe A-Young

.-

.-

-

-

-

-

1 81-160

/

-

-

-

/ i /

/

--

-

-

321-640

Table 4. Tabulation of inner continental shelf width data for coastal areas selected for statistical summaries of sample populations of each of the three basic inner shelf width coastal types.

71

Lognormal distribution of inner continental shelf widths and slopes

i I I i I I I

I I I

I I I I I i i

I I I

I I-I

I I J t I I 1 I I 1-'~

III--~

e~

~'~'~

'~ I i ~ ' ' - ~

~l

V

i

~ ~ ~~ i

0~~

i ~ I ~'~

I I I""-I-I"

eh

I '~ I ' ' 9

I ~ ~q

I I

I I I I I I~l ~6

II

lilllIllll

-=~..

~4 ~

,~ - . ~ . = ~ I ~

72

MILES O . HAYES

An attempt was made to use those major coastal areas (outlined in Fig. 2) with predominantly one width-type so that the whole area, or a sizeable part of the area, could be used in the tabulation. Also, there was a tendency to choose 'classical areas,' such as shield areas of Africa and Brazil, depositional areas of the northern Gulf of Mexico and the Yellow Sea, and young mountain range coasts of the circumPacific ' ring of fire.' Before inspection and tabulation of width data for the sample INNER SHELF ~*,']DT}q, 9ELTt~ UNIT5 I

-~0 I

-40 I

-~0 I

-~0 i

-I'O

0

~

I

+1"0 +2-0 i

i

+3'0 I

+4',0 I

+5"C I

*6-0 I

20-

~0"

O" ] 20-

REDISTRIBUTION INFERREDBY PROBABILITY PLOT

PLATEAU- SHIELD COASTS

MB= -0-04 B ;

I0-

0 30-

20-

10-

00

0"313 0~25

1,25

2.5

5

I0

INNER SHELF WIDTH,

20

40

80

r60

320

640

NAUTICAL MILES

Fig. 13. Histograms and fitted normal frequency distribution curves for sample populations of the three basic inner continental shelf width types--Type A (Young Mountain Range Coasts), Type B (Plateau-shield Coasts), and Type C (Depositional Coasts). Geographic localities of coastal areas included in each sample population are outlined in Fig. 2, and width measurements from all areas are summarized in Table 4. These populations are distinctly different with regard to width, but they all closely approximate lognormal distributions. populations, geographic areas to be sampled were outlined on a world map. Original width data were then summarized for the different geographic localities indicated on the map with no deviation from the original sampling plan. 1 feel it is necessary to point this out in view of the remarkable separation into three distinct width types

Lognormal distribution of inner continental shelf widths and slopes

73

that resulted from the sample population summaries. Location of areas sampled for the summaries are shown on the map in Fig. 2, and width data for each area are given in Table 4. Results of these summaries, which are based on 1,241 of the original 2,136 measurements, strongly agree with the original conclusion that there are three basic width types. The striking distinction between the three types, as well as the near-perfect lognormality of each frequency distribution, is illustrated in Fig. 13. The near-lognormality of these three sample populations is further demonstrated by the cumulative 9+

~

-

~ ....

i

.....

i--/+

i

++ . . . .

~/I

.... ;+,+/¢-/

~ I

'

]

, o°)" I

/

¢"

~

,( J

' ~++~

~7"

.:+/!

4I

+

I

!

1

0"625 i

-4,0

1'25 i

-3.0

2"5 5 I0 20 40 80 INNER SHELF WIDTH, NAUTICAL MILES i

~

i

i

-2.0 -I.0 0 +1.0 +2.0 INNER SHELF WIDTH, DELTA UNITS

i

+:~0

160

320

I

+4.0

+

+~0

Fig. 14. Cumulative curves o f inner shelf width plotted on arithmetic-probability scale for the three sample populations of basic inner shelf width types.

curves in Fig. 14. Mean inner shelf width (M+) and graphic standard deviation (oz) for the three width type populations are as follows : Type A Type B Type C

M8 -- 1"538; 3.4 miles -- 0-048; 9.6 miles ÷ 2"108; 43 miles

~i

1"588 (1.2-11 miles) 1"608 (3.1-30 miles) 1"528 (15-120 miles)

Another important genetic aspect of the inner shelf width classification is mixing of basic width types within individual coastal areas. In order to investigate this factor in more detail, all coastal areas were examined to determine the amount of each coastal width type (as defined above) occurring within their boundaries. Approximations were made for each area and they are summarized in Table 5.

74

M~LES O. HAYES

Table 5. Approximate amounts of basic width types occurring within individual coastal areas. Coastal type Coastal area

A

1. 2. 3. 4. 5. 6.

7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31.

NE Siberia East Central Asia Japan China, Formosa and Hainan (Ch) China SE Asia East Indies and Philippines ~I~), Mindanao (L)~ Luzon (MID, Malay Peninsula (J) Java (C) Celebes (S) Sumatra (NG) New:Guinea (B) Borneo Australia and Tasmania New Zealand Bay of Bengal Western India Oman and Aden Gulfs Persian Gulf Red Sea SE Africa Madagascar West-central Africa NW Africa, W. Spain and Portugal Mediterranean Sea Western Europe and British Isles Baltic Sea Eastern Canada Eastern U.S. Cuba and Hispaniola Northern Gulf of Mexico (U.S.) Eastern Central America Northern and Eastern South America Southern South America Western South America Western Central America Western U.S. and Canada Alaska

t--½ i-½ >~

>~ >~ >~ H H ~>~ <~ <~ t--½ H H H >~ <~

B

½-i <~ <~

<~ H >t

< ~

H

--

-

-

¼-½ <~

--

i--½

H H H >] ~-~ >~ >~

< <~ <~

<~

<~

~-¼

> <~

--

>~

<~

---

>~ t-q <~ t--½ >~

C

<

t-½ t--½



H

½-~ H

~-i

<

--

t-½

As can be seen in Figs. 12 A and B, the separation of coastal areas into genetic categories with regard to mixing of basic width types is very distinct. Consider the unimodal area of Fig. 12 A, for example. Coastal areas occurring in the narrowest portion of the unimodal zone are mostly Type A coasts*. As width increases, however, coastal areas in the unimodal zone become predominantly mixtures of Type A and Type B inner shelf width types. In the intermediate portions of the unimodal zone (around 0"08), Type B coasts are most common. Wider areas are mixtures of Type B and Type C, and, finally, the widest zones are made up predominantly of Type C coasts. The fact that coastal areas with A + B and B + C mixed width types are unimodal can be explained as the result of mixing of two modes of close proximity on the width *If a width type makes up less than ~ of individual coastal area, it is omitted from consideration (Table 5).

Lognormal distribution of inner continental shelf Widths and slopes

75

scale. When they are mixed, therefore, the resultant distribution is unimodal. When the two extreme end members of width types, A and C, are ,mixed, howe'¢vr, the distribution is polymodal and has a high standard deviation. Therefore, most coastal areas occurring in the peak of the sine curve outlining distribution of polymodal areas in Fig. 12 A are mixtures of coastal width types A and C (see Fig. 12 B). The differentiation of coastal areas on the basis of mixing of width types is very clear and generally valid, as the boundaries for the individual and mixed types in Fig. 12 B indicate. There are a few exceptions, however, that are indicated by letter (W, X, Y and Z) on the diagram (Fig. 12 B). These exceptions will now be discussed individually : w (Eastern Canada). Although this is a predominantly Type B coast according to the original definition, mean inner shelf width is very narrow (M~ ~ 2.9 miles). I can only speculate as to the reasons for this discrepancy, but deepening of nearshore areas of the inner shelf by glacial scour is a possibility. X (Western Europe and British Isles). Although this area belongs in the B + C class according to original definitions (Table 5), it plots in the A q- C zone in Fig. 12 B. a'ype B zones of this coastal area have also been subjected to glacial scour. The high standaul deviation is probably due to mixing of the wide Type C coasts with the narrower than a.~e~age Type B coasts, which have widths equivalent with ordinary Type A coasts. Y (RedSea). Although this area is classifiedas Type B, itisnarrowerthanitshouldbetbeoretically, because of its origin as a fault block zone (graben). It has a high standard deviation owing to the presence of some fairly wide coral reef zones. Z (Malay Peninsula). The fact that this area has a wider inner shelf than it should have theoretically probably indicates the inadequacies of the measuring technique in areas like the Molucca Strait, where width is probably exaggerated toward wider measurements. In summary, width of the inner shelf is generally determined by tectonic activity and sediment deposition. Width may be modified in some areas, however, by processes such as glaciation and faulting. In terms of genesis, then, the inner shelf width classification is based on mean inner shelf width (M~), which is determined primarily by basic width type present, and on graphic standard deviation (al), which is determined by the degree and type of mixing of the three basic width types within the area. In the original descriptive classification (Fig. 11), Classes I and II are composed predominantly of Type A width types, Class I I I is predominantly A q- B, Class VI is predominantly B, Class VIII is predominantly B + C, Class X is predominantly C, and Classes IV, V, VII and I X are predominantly A q- C.

A P P L I C A T I O N S AND CONCLUSIONS

Applications to sedimentology Another phase of the original investigation of oceanographic variables of the inner continental shelf was a study of bottom sediment distribution, the results of which have been summarized and will appear elsewhere (HAYES, in preparation). In attempting to determine controlling factors of bottom sediment distribution on the inner shelf, it was found that width (or slope) can be related to bottom sediment composition. Figure 15 shows the relation of sediment type to inner shelf width (for total area studied). Percentages were calculated for the major sediment types* *Percentage determined by approximation of amount of different bottom types occurring along the traverses for which width measurements were made.

MINESO. HAYES

76

present along all traverses occurring within each delta unit span of the ' inner shelf width grade scale,' and were plotted at the midpoints between grade limits. This diagram indicates that rocky bottoms are most commori on narrow inner shelves (steep slope; < 2-5 miles in width), that sand and mud are most common on wider inner shelves (gentle slope; > 20 miles in width), that shell is most common on moderately wide inner shelves (gentle slope; 20-80 miles in width), and that coral and gravel bottoms show no diagnostic trends with regard to inner shelf width.

0625

a

-,,o

1'25

-

o

2

-

5:0

o

-,'-o

0:0 2O0 0"~ NAUTICAL MILES

o'

+,!o

8O.O

gO

320

,z".o

+ 5:0

+ 4~0

+ 5:O

~-I'" ""lifo ---"~'~50 20"0 40"0

60'0

160

320

DELTA UNITS

=, a.

u

40

~ 5o

j'~uD

I0 ~.~

~25

R;CKY

125

2"5

N A U T I C A L M{LES

Fig. 15. Relationship o f bottom sediment type to inner shelf width (< 200 ft depth) for coasts of the world.

Applications to paleogeography If the assumption can be made that inner continental shelves of ancient seas had width and slope characteristics similar to present day seas*, it is possible to apply some of the data of this study to paleogeography. For example, if the tectonic setting of an area were known, one would possibly be able to predict, with some degree of accuracy, distance from strandline to 200-ft depth contour (or, conversely, distance from 200-ft depth contour to strandline) using approximate distances of 3-4 miles for young mountain range areas, 10 miles for teetonically stable, plateaushield areas, and 40 miles for depositional areas. Width types to be expected in different parts of the ' typical' geosyncline would probably be Type A coasts in eugeosynclinal areas, Type C coasts in miogeosynclinal areas, and Type B coasts around the craton. This is based on the Recent example of the East Indies, where Mindanao, northern New Guinea, southern Java, and other similar areas (eugeosyncline) have Type A coasts, and the interior sea areas of northern Sumatra, western Borneo, and so forth (miogeosyncline) have Type C coasts. Width *This assumption is open to doubt because of effect of Pleistocene sea-level fluctuations and of the somewhat ' atypical' nature of present day seas (in terms of ancient rock record).

Lognormal distribution of inner continental shelf widths and slopes

77

of craton inner shelves is more uncertain, but if they can be equated with stable, plateau-shield areas of present days seas, they would have intermediate widths (Type B).

Applications to geornorphology Probably the major contribution of the delta unit system and other techniques given in this report to geomorphology is that they provide a quantitative basis for description of geomorphic features on the inner continental shelf. Coastal areas are readily compared on the basis of mean width (M~) and graphic standard deviation (crz) of inner shelf widths, for example. Other statistical measures, such as skewness and kurtosis, may also be utilized. 40,r .....

T

~

/ ~

I

I

....

~

--7-

.......



I

r - x - 4B-- ./ .
~

o

t

YOUNG MOUNTAIN RANGE COASTS (A) PLATEAU-SHIELD COASTS (B} DEPOSITIONAL COASTS[C) _ _

l

I

o

-

o I0

#'

/,/ // O0

\

0625 ~-" - 2"5' ~ - I0 - L ~ 40 - - - iNNER SHELF WIDTH, NAUTICAL MILES

----

~

O

UPLFT T ~) STABILITY

b

DOWNWARP t -4(

••1

~

+2"0 +4'0 -2'0 INNER SHELF WIDTH, DELTA UNITS

+6"0

Fig. 16. Relat:onship of tectonism to inner continental shelf width. Upper diagram gives fitted normal curves of sample populations of the three basic width types--Type A (Young Mountain Range. Coasts), Type B (Plateau-shield Coasts), and Type C (Depositional Coasts). Type A coasts (narrow; M8 = approximately 3-5 miles) are generally areas of tectonic uplift, Type B coasts (intermediate width; M~ = approximately 10 miles) are generally areas of tectonic stability, and Type C coasts (wide; M~ = approximately 40 nautical miles) are generally areas of tectonic downwarp, as is indicated in lower diagram.

It is hoped that the discovery of lognormality of inner shelf width and slope distributions will aid in the basic understanding of the continental shelf. Strahler (1950) pointed out a similar relationship for landform slopes (exceptions previously discussed). Width and slope of the inner continental shelf can be directly related to tectonism, and this relationship is illustrated in Fig. 16. Briefly, Type A coasts are located adjoining areas of rapid structural uplift (young mountain ranges), Type B coasts

78

MILES O. HAYES

adjoin tectonically stable areas (shields and plateaus), and Type C coasts adjoin areas of rapid structural subsidence. Rapid sedimentation and building out of wide inner shelf areas accompany structural downwarp along Type C~coasts. As a final conclusion, these findings regarding the geomorphology (width and slope) of the inner continental shelf lead to an hypothesis that may be considered a supplement to Strahler's Law of Constancy of Slopes. This hypothesis is simply that there is a morphologic principle, here termed the Principle of Constancy of Inner Continental Shelf Widths (and slopes), that relates inner shelf width (and slope) variation to factors controlling the magnitude of width (and of slope angle). It is as follows : Coastal areas with essentially uniform physiography and tectonic origin tend to have inner continental shelf widths (and slope angles) lognormally distributed with low dispersion about a mean value determined by the combined factors of type and degree of intensity of tectonic activity and rate of deposition of bottom sediments.

Acknowledgements The author is grateful to Dr. Chester M. McKinney of Defense Research Laboratory, who initiated the original survey, periodically reviewed the work, and critically read the manuscript, and to Mr. Reuben H. Wallace of Defense Research Laboratory, who also periodically reviewed the work. The author is also grateful to Dr. Robert L. Folk, Department of Geology, The University of Texas, who made many helpful suggestions and critically read the manuscript. The work was supported by the Office of Naval Research.

REFERENCES

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