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Shape analysis of Pacific seamounts
Earth and Planetary Science Letters, 90 (1988) 457-466 Elsevier Science Publishers B.V., A m s t e r d a m - Printed in The Netherlands
457
[51
Shape analysis of Pacific seamounts D e b o r a h K. Smith Department of Geology and Geophysics, Woods Hole Oceanographic Institution, Woods Hole, MA 02543 (U.S.A.) Received June 1, 1988; revised version received September 1, 1988 Shape statistics have been compiled from 85 profiles of well-surveyed Pacific seamounts in the height range 140-3800 m. A fiat-topped cone was fit to each seamount's cross-sectional profile maintaining the slopes of the sides as closely as possible. On each profile a basal width db, a s u m m i t width dr, and a m a x i m u m height h, were measured. The height-to-basal-radius ratio is ~h is estimated by the ratio 2 h / d b and flatness f by the ratio d t / d b. Slope angle ¢ = arctan(c) is estimated from c = 2 h / ( d b - dr). Summit height and basal radius are found to be highly correlated (r = 0.93). The 85-point sample mean of the height-to-basal-radius ratio is ~h = 0.21 + 0.08 implying that a seamount's summit height is typically one fifth its basal radius. Despite the high correlation, individual points show some scatter, and there may be groupings into different morphological types. For example, all but one of the seamounts with summit heights above 1000 m have values of ~h that are larger than the sample mean. The 85-point sample mean of flatness is f = 0.31 + 0.18. Data points show a large scatter with values of f varying between 0 (a pointy cone) and 0.69 (a fiat-topped cone). A histogram representation of flatness, however, indicates that certain values of f m a y be more common than others: the histogram shows a bimodal distribution with maxima occurring at values of f in the ranges 0.10-0.20 and 0.35-0.50. Moreover, there is some evidence that the m e a n flatness decreases with summit height so that the preferred shape of a large-sized seamount may be a pointy cone. Slope angle has an 85-point sample mean of q~= 18 _+ 6 ° ; individual values of ~ vary between 5 ° and 36 °. In addition to having a lower than average mean flatness seamounts with heights above 2600 m also have a lower than average mean slope angle (15 ° ). To determine which variables account for most of the observed variation in the seamount shapes, a multivariate principal component analysis was performed on the data using five shape variables (summit height, basal radius, s u m m i t radius, flatness, and slope). The analysis indicates that most of the variation is described by two variables: flatness and summit height.
1. Introduction
To date, quantitative and statistical studies of volcano morphology have been mostly restricted to subaerial volcanoes on Earth (e.g., [1-4]) and volcanoes imaged on the inner planets (e.g., [5-8]) because more high-quality topographic measurements are available for these volcanoes than those found in Earth's oceans. Recently, however, studies of submarine volcano morphology have been greatly benefitting from the rapid increase in the number of seamounts that have been surveyed by bathymetric instruments that provide high-resolution, two-dimensional coverage [9-22]; and emphasis is beginning to be placed on using the signals carried by a seamount's shape to better understand crustal and mantle processes. Wood [4] stated that the morphology of a subaerial volcano is a surface expression of: (1) the 0012-821X/88/$03.50
© 1988 Elsevier Science Publishers B.V.
chemical composition of the magma, (2) eruptive style, and (3) tectonic setting. In addition to these Batiza and Vanko [13] suggested that the following are some of the variables important in controlling seamount shapes: (1) age of the underlying lithosphere, (2) thickness of sediment cover, (3) initial and subsequent conduit geometries, and (4) fracture patterns in the crust and lithosphere. For example, irregular and elongated plan shapes of seamounts have been attributed to magma following existing fractures in the crust [13]; also it has been suggested that seamount slopes are inversely proportional to the rate of magma effusion during eruption [17]. It is obvious that many diverse factors play a role in controlling volcano formation; nonetheless, many volcanoes exhibit remarkable symmetry in their shapes suggesting a more universal control [23,24]. To this end, a number of workers have
458 addressed the problem of whether a seamount's gross topography may vary systematically with size. Menard [25] analyzed wide-beam profile data collected in the Pacific and observed that the cross-sectional profiles of seamounts (excluding those that reach the sea surface) appear to be approximately similar and independent of size. More recently, Batiza and Vanko [13] used Sea Beam surveys of approximately 30 seamounts located near the East Pacific Rise, and data from other well-surveyed seamounts in the literature, to measure seamount flatness (ratio of summit diameter to basal diameter) and median and m a x i m u m slopes. Their analysis, however, yielded no simple trends in these variables. Investigations of the areal statistics of seamount populations in the southern and eastern Pacific by Jordan et al. [26] and Smith and Jordan [27,28] also addressed the problem of modeling seamount shapes. The statistical formulation used in these investigations requires that the shape of a seamount be specified as a function of its size [26]. The specific shape model adopted by Jordan et al. [26] and Smith and Jordan [27,28] approximates seamounts as right-circular cones of constant slope ~, height-to-radius ratio ~h, and flatness f. F r o m a study of profiles constructed for 30 well-surveyed seamounts in the Pacific with summit heights varying from 200 to 4000 m, Jordan et al. [26] obtained mean values of ~h = 0.21, f = 0.21, and q, = 15 °. Although there is a lot of scatter in their data some trends are evident. For example, Jordan et al. [26] found that seamount height is roughly proportional to basal radius. Similar shape studies by Smith [29] and Abers et al. [20], using more extensive data sets, obtained mean values of ~h that differ by less than 5% from the value of Jordan et al. [26]. These results agree with the observations of Taylor et al. [11] who suggested that large seamounts typically have heights that are about 10% of their basal diameters (i.e., 20% of their basal radii). Jordan et al. [26] also noted that even though seamounts with heights less than about 1000 m have flatnesses more or less uniformly distributed between f = 0 (pointy cone) and f = 0.6, there is some suggestion that the mean flatness decreases with increasing height. To investigate the shapes of seamounts, and in particular, to investigate the relationship between seamount shape and size,
this report extends the shape analysis of Jordan et al. [26] to a more comprehensive data set comprising 85 profiles of seamounts in the Pacific Ocean.
2. Shape data Shape statistics have been compiled from 85 cross-sectional profiles representing 70 wellsurveyed Pacific seamounts in the height range 140-3800 m (Table 1). The data include published and unpublished bathymetric surveys as well as unpublished Sea Beam transit swaths (unpublished Sea Beam swaths were generously provided by P. Lonsdale). Seamounts from Sea Beam transit data were chosen as closed contour features greater than 100 m in relief whose summits were contained within the swath. All but nine of the seamounts in the data set are located in the eastern and southern Pacific. Of the 42 seamounts mapped by Sea Beam, 13 are located on the Cocos plate [13], two (Larson's seamounts) are located close to the East Pacific Rise at approximately 2 1 ° N [12], 19 are located between the Clarion and Murray fracture zones (Scripps Institution of Oceanography cruises Bonanza 2, Pascua 5, and Marathon 1), and eight are located along an essentially east-west transit between Tahiti and the East Pacific Rise (Scripps Institution of Oceanography cruise Ariadne 2). The data set also includes nine seamounts located on the Nazca plate that were surveyed using G L O R I A [15]. (The published profiles were derived from the acoustic shadows cast by the seamounts or, if the ship passed directly over the seamount summit, the profile was obtained from the narrow-beam echosounder.) Six additional profiles in the eastern Pacific were constructed from seamounts m a p p e d by the N O A A Pioneer Survey. Four profiles of oceanic volcanoes known to be active (Moua Pika and Rocard, Societies; Macdonald, Australs; Loihi, Hawaii) were obtained from Menard [30]. The final nine seamounts are located in the Western Pacific and Philippine Basin and were surveyed using the N A V O C E A N O multi-beam echosounding system [9]. High-resolution multi-beam swaths and sonar images of the seafloor are still too limited to provide a large inventory of large-size seamounts; therefore only 24 of the seamounts have summit heights above 1000 m, and only 7 have heights
TABLE 1 Seamount shape statistics No.
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 32 33
Height (m)
Basal diameter (103 m)
Summit diameter (103 m)
Flatness
Source/ location
No.
Height (m)
Basal diameter (103 m)
Summit diameter (103 m)
Flatness
Source/ location
1335 935 935 600 1465 1400 1600 1135 1065 935 935 935 800 800 535 535 535 535 1065 1200 1335 650 1400 700 1060 600 500 500 1250 750 390 320 220 330 300 315 370 190 760 700 790 700 730
10.8 8.9 10.2 7.3 9.5 8.1 6.9 7.9 7.7 6.0 8.1 7.9 6.1 6.9 8.8 5.5 5.3 4.5 7.9 9.3 10.0 12.0 12.7 8.8 9.6 6.8 7.7 7.5 8.7 6.5 7.2 5.0 5.3 3.8 7.0 4.0 3.5 5.6 6.5 5.9 6.5 7.5 7.4
1.6 5.3 5.1 1.0 1.6 1.6 2.4 2.5 0.5 0.8 3.3 3.6 2.1 2.5 5.5 2.4 0.3 0.5 1.3 3.8 0.8 7.2 3.7 3.5 3.9 3.4 4.5 4.9 2.6 3.1 3.0 2.6 2.1 1.9 2.9 1.6 0.6 1.9 4.0 1.9 3.4 3.2 2.6
0.15 0.60 0.50 0.14 0.17 0.20 0.35 0.32 0.07 0.13 0.39 0.46 0.34 0.36 0.62 0.44 0.06 0.12 0.16 0.41 0.08 0.60 0.29 0.40 0.41 0.50 0.59 0.65 0.30 0.48 0.41 0.53 0.39 0.50 0.42 0.41 0.17 0.34 0.62 0.32 0.52 0.42 0.35
[13] Cocos plate
34
565 620 650 210 380 560 1280 1360 900 900 925 925 150 345 430 495 880 905 150 165 320 220 185 180 145 140 155 175 190 170 180 440 1380 2780 2760 3800 3000 1760 2700 3500 2650 1600
8.6 7.9 7.2 3.7 4.0 4.0 7.6 7.1 5.8 9.8 13.8 9.2 2.3 4.9 5.8 4.3 7.2 6.8 2.0 1.2 2.1 2.9 2.1 3.3 2.9 3.5 3.4 1.4 2.1 0.9 3.4 2.2 8.9 22.6 21.8 35.7 25.1 15.3 23.2 27.4 15.0 13.7
5.8 5.4 3.3 0.3 2.0 0.8 1.1 1.5 1.7 3.8 5.1 1.5 0.7 2.0 2.2 1.7 4.4 3.8 0.4 0.2 0.4 1.4 0.4 0.7 0.4 0.5 1.6 0.3 0.9 0.1 0.6 0.2 1.7 0.9 0.6 6.4 3.5 3.7 2.1 0.6 0.8 0.0
0.67 0.69 0.46 0.07 0.51 0.12 0.19 0.21 0.29 0.39 0.37 0.16 0.30 0.42 0.37 0.40 0.61 0.56 0.20 0.16 0.19 0.49 0.21 0.20 0.15 0.14 0.47 0.22 0.42 0.11 0.16 0.09 0.19 0.04 0.03 0.18 0.14 0.24 0.09 0.02 0.05 0.00
[9] Phil. Basin
35 36 37 38 39 40 41 42 43 44 45 46 47 48 49
[15] Nazca plate
[Ariadne ~]
[12] Pac. plate 21 o N
50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70
[Bonanza a]
[9] Phil. Basin
[Pascua ~]
[Marathon a ]
[Pioneer Survey a]
Moua Pika b Macdonald b Loihi b Rocard b
[9] NW Pac. Basin
Two profiles were constructed for seamounts that were found to be significantly elongated. a SIO cruise Ariadne 2--transit between Tahiti and EPR; SIO cruises Pascua 5, Marathon 1, Bonanza 2 and NOAA Pioneer Survey --northeast Pacific between Clarion and Mendocino fracture zones. b Profiles of the last four seamounts in the table were obtained from Menard [30].
a b o v e 2600 m. There are no s e a m o u n t s in the data set w i t h s u m m i t heights b e t w e e n 1800 and 2600 m. A flat-topped c o n e was fit to each seamount's
cross-sectional
profile maintaining
the
slopes
of
t h e s i d e s a s c l o s e l y a s p o s s i b l e ( F i g . 1). T h e p r o files w e r e c o n s t r u c t e d
by hand;
on each a basal
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Fig. 1. Cross-sectional profiles constructed for some small seamounts mapped by Sea Beam on SIO cruises Marathon 1 and Pascua 5. Summit height is taken to be the height from the shallowest depth obtained to the average baseline. ~h is estimated by the ratio 2 h / d b, f by the ratio d t / d b , and c by the ratio 2 h / ( d b - dr). Two profiles were constructed for seamounts that were found to be significantly elongated.
w i d t h d b , a s u m m i t w i d t h d t, a n d a m a x i m u m height h, were m e a s u r e d . S u m m i t height is t a k e n to b e the height f r o m the shallowest d e p t h obt a i n e d to the average baseline. ~h is e s t i m a t e d b y the r a t i o 2h/db, f b y the ratio dJdb, a n d ~ b y 4000
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16000
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20000
(m)
Fig. 2. Summit height versus basal radius for 85 cross-sectional profiles of Pacific seamounts. The solid line corresponds to the mean height-to-radius ratio ~h=0.21 obtained by equally weighting the ratios of all 85 profiles. Seamount height and basal radius are highly correlated ( r = 0.95). Notice that all but one of the seamounts with heights above 1000 m have higher than average values for ~w
2 h / ( d b - dr). T h e w i d t h - t o - l e n g t h r a t i o of each s e a m o u n t ' s p l a n s h a p e is less t h a n 2; w i t h i n this limit 15 s e a m o u n t s were f o u n d to b e significantly e l o n g a t e d a n d two profiles were c o n s t r u c t e d (Table 1). Fig. 2 is a p l o t of s u m m i t height versus b a s a l r a d i u s ( r b = d b / 2 ). T h e s a m p l e m e a n o b t a i n e d by equally weighting the values f r o m all 85 profiles is ~h = 0-21+-- 0.08 (shown on the p l o t as a solid line); the m e d i a n is 0.22. T h e m e a n height-tor a d i u s ratio d e t e r m i n e d b y this s t u d y is n e a r l y identical to the one d e t e r m i n e d b y J o r d a n et ai. [26] even t h o u g h the d a t a set used here is m o r e t h a n twice as large. Fig. 2 i n d i c a t e s that h a n d r b are s t r o n g l y c o r r e l a t e d ( r = 0.93); however, individual d a t a p o i n t s show s o m e scatter a n d there m a y be g r o u p i n g s into different m o r p h o l o g i c a l types. F o r example, all b u t one of the 24 s e a m o u n t s with s u m m i t heights a b o v e 1000 m have heightt o - r a d i u s ratios that are greater t h a n the s a m p l e mean; Fieberling Guyot (h=3800 m) has a h e i g h t - t o - r a d i u s ratio equal to the mean. In c o n t r a s t to the c o r r e l a t i o n o b s e r v e d b e t w e e n s u m m i t height a n d b a s a l r a d i u s n o such c o r r e l a tion exists b e t w e e n s u m m i t height a n d s u m m i t radius. T h e 85-point s a m p l e m e a n of the heightt o - s u m m i t - r a d i u s ratio is h/r t = 1.35 _+ 1.93; the m e d i a n is 0.64. As i n d i c a t e d b y the large s t a n d a r d d e v i a t i o n a n d the large difference b e t w e e n the
461
mean and median, the data are highly scattered: values of h / r t range between 0.18 and 12.7. The seamount with the lowest observed height-to-summit-radius ratio is a short flat-topped cone (h = 650 m, f = 0.60); the seamount with the highest height-to-summit-radius ratio is a tall pointy cone (h = 3500 m, f = 0.02). Flatness is plotted against summit height in Fig. 3. Values of f vary between 0 (a pointy cone) and 0.69 (a flat-topped cone). The 85-point sample mean is f = 0.31 _+ 0.18; the median is 0.32. These values are slightly higher than those obtained by Jordan et al. [26] whose 30-point sample mean is f = 0.21 _+ 0.03 and median is 0.18. The data points displayed in Fig. 3 are highly scattered. There is some evidence, however, that mean flatness decreases with summit height: seamounts with summit heights below 1000 m have a 56-point sample mean of f = 0.37 _+ 0.17; seamounts with summit heights in the range 1000-1800 m have a 17-point sample mean of f = 0.22_+ 0.11; and seamounts with summit heights above 2600 m have a 7-point sample mean of f = 0.08_+ 0.06. These values (plotted in Fig. 3 as triangles) suggest
14 12 10
iliili
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0.4
0.6
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1.0
flatness
Fig. 4. Number versus flatness plotted in bin widths of f = 0.05. The histogram shows a possible bimodal distribution with maxima occurring in the flatness ranges 0.10-0.20 and 0.35-0.50.
that the preferred shape of a large-size seamount may be that of a pointy cone. In addition, Fig. 3 suggests that there may be other groupings of
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height (m) Fig. 3. Flatness f versus summit height h. Flatness varies between 0 (a pointy cone) and 0.69 (a truncated cone). The greatest range in the values of flatness occurs for seamounts with summit heights below about 1000 m. Triangles correspond to the mean values of f obtained in the height ranges: 0-1000 m, 1000-1800 m, and 2600-3800 m. The mean flatness decreases as a function of summit height suggesting that the preferred shape of a large-sized seamount may be that of a pointy cone.
o~
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1000
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2000 height (m)
I
3000
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Fig. 5. Slope angle is plotted against summit height. Values of vary between 5 ° and 36 ° with a mean value of ~ = 1 8 °. The data points appear to fall into two groups. Most of the large-sized seamounts (h > 2600 m) have slope angles that cluster about their mean of #, = 15 o; seamounts with summit heights below 1800 m, however, form a somewhat diffuse group in which slope angle appears to be proportional to summit height.
462
points. For example, the histogram of number versus flatness displayed on Fig. 4 shows a possible bimodal distribution with maxima occurring at values of f which specify that the summit radius is 10-20% or 35 50% of the basal radius. Slope angle versus summit height is plotted in Fig. 5. Values of q~ vary between 5 ° (a small pointy seamount: h = 140 m, f = 0.14 and ~h = 0.08) and 36 ° (an intermediate-size flat-topped seamount with the largest observed height-toradius ratio: h = 1600 m, f = 0.35, and ~h = 0.46). The sample mean of the slope angle is q, = 18 o _+ 6°; the median is 17 °. The data points in Fig. 5 appear to fall into two groups. Seamounts with summit heights below 1800 m form a somewhat diffuse group in which the slope angle appears to be roughly proportional to summit height. Seamounts with summit heights above 2600 m form a second group in which most of the seamounts have slope angles that cluster closely about their mean of ep = 15 °.
3. Interdependence between seamount shape variables A multivariate principal component analysis was performed to determine which parameters account for most of the variance observed in the seamount shapes. The following five shape variables were used in the analysis: summit height, basal radius, summit radius, flatness, and slope. The first two eigenvectors of the normalized variance-covariance matrix account for approximately 82% of the variance in the data. It was found that the first eigenvector which accounts for about 42% of the total variance heavily weights the contributions from summit height and basal radius, and thus the first principal component primarily reflects differences in seamount size. Fig. 6 displays a few of the observed seamount shapes approximated as flat-topped cones and plotted at their respective positions on the first two principal components. An examination of Fig. 6 shows that along the first principal component seamounts are separated according to height: short seamounts plot at the left of the figure and tall seamounts plot at the right. (Because summit height and basal radius are highly correlated, either can be used to characterize the change in size; in this case summit height has been chosen.)
-3 -2
I 0
I 2
I 4
t 6
32
Fig. 6. Illustration o f some of the shapes of seamounts observed in this data set. The seamounts have been approximated as flat-topped cones and plotted at their respective position on the first two principal components of a five-variable principal component analysis. The horizontal axis is component one; the vertical axis is component two. Notice that the shapes of seamounts are sorted primarily according to summit height along the first component, and primarily according to flatness along the second component. The first two principal components account for more than 80% of the variance in the seamount shapes.
The second eigenvector which accounts for approximately 40% of the total variance heavily weights the contributions from flatness, summit radius, and slope; and Fig. 6 indicates that along the second principal component seamounts are sorted according to their shape. This variation is manifested primarily by the difference in seamount flatness: pointy seamounts plot at the bottom of the figure and flat-topped seamounts plot at the top. To check whether summit height and flatness are sufficient to express most of the variance in the shape data, an eyeball comparison was made between the position of a seamount on the plot in principal-component space and its position on the flatness height plane. Despite some exceptions the two plots are remarkably consistent. In order to explain these discrepancies and to recapture all the essential information about a seamount's shape the behavior of the other shape parameters (~h, 0, and h/r,) on the flatness height plane has been investigated. If h and r b were perfectly correlated (i.e., ~h is a constant) then lines of constant h / r t and q5 would follow lines of constant f. This is not the case, however, as seen in Fig. 7 which maps values of ~h onto the f - h
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(2a)
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(2b)
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20000
(m)
Fig. 8. Summit height versus basal radius for 85 cross-sectional profiles of Pacific seamounts. This figure is the same as Fig. 2 except that it displays as a dashed curve a least squares fit of a second-order polynomial (1) to the data points. The curve specifies that ~h increases systematically with height to approximately h = 1800 m than decreases slightly at larger sizes.
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plane. The plot is identical to Fig. 3 except that symbols have been used to represent values of ~hThere is some indication from Fig. 7 that there are different trends in the values of ~h between the group of seamounts with f < 0.25 (pointy) and the group of seamounts with f > 0.25 (flat-topped). For example, most of the pointy seamounts have values of ~h that are greater than the 85-point sample mean (~h = 0.21), and there are no obvious patterns within this group. In contrast, flat-topped seamounts have values of ~h that appear to be proportional to summit height. To determine whether some of the variation in h / r t and q, can be explained by assuming that ~h is n o t c o n s t a n t , l e t r b - - g ( h ) where g ( h ) is a p -
r b = g(h)
~i
(m)
Fig. 7. Values of ~h are displayed on the plot of flatness versus summit height. The range of ~h that each symbol represents is shown in the upper right comer of the plot. Solid circles and plusses correspond to seamounts with height-to-radius ratios that are below the mean of ~h = 0.21. Seamounts with f > 0.25 show more systematic variations in ~h than seamounts with f < 0.25.
proximated
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2000 height
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4000
(m)
Fig. 9. Values of h / r t are displayed on the flatness-height plane. The range of h / r t that each symbol represents is shown in the upper right corner of the plot. Model curves representing h / r t = 0.5, 1.4, 5, and 10 are plotted. These curves have been determined using equations (1) and (3) and the values of the coefficients given in (2). The observed variations of h / r t are well-approximated by the curves. Notice that except at the smallest sizes h / r t varies primarily with flatness: h / r t decreases as f increases.
464
primarily as a function of flatness (that is, h / r t decreases as f increases). Curves corresponding to constant slope angle (Fig. 10) do not describe the data as well although they approximate general trends. The model curves predict that slope angles increase primarily as a function of summit height below about h = 1000 m, and primarily as a function of flatness for seamounts with summit heights between 1000 and 4000 m. It is interesting to note that most of the seamounts with the steepest slope angles (q, >~ 25 ° ) also have large flatnesses ( f > 0.5).
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4. Summary and discussion
o.c
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3000
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4000
Fig. 10. Values of ep are displayed on the flatness-height plane. The range of ,h that each symbol represents is shown in the upper right corner of the plot. Curves representing ~ = 10 o, 15 °, 20 °, and 25 o have been calculated using equations (1) and (4) and the values of the coefficients given in (2) and are plotted on the figure. The model curves do not describe the data very well but they seem to approximate general trends; they indicate that slope angles increase primarily as function of summit height at small sizes (h < 1000 m) and primarily as a function of flatness at large sizes. Notice that most of the seamounts with the steepest slope angles (~ > 25 o) also have large flatnesses ( f > 0.5).
The theoretical curve specified by (1) and the coefficients given in (2) is dashed in Fig. 8. The results indicate that the height-to-radius ratio increases systematically with summit height from approximately ~h = 0.10 at h = 200 m to ~h = 0.26 at h = 1800 m; above this height ~h remains approximately constant (~h = 0.23 at h = 4000 m). Incorporating (1) into the flat-topped right-circular cone model for seamount shapes gives:
h / r t = h / [ fg( h)]
(3)
and: = arctan( h / [ g ( h ) ( 1 - f ) ] }
(4)
Model curves of constant h / r t and q, on the flatness-height plane are plotted in Figs. 9 and 10 respectively. (As mentioned a constant value of ~h would yield lines of constant h / r t and ~ that are horizontal on the f - h plane.) Fig. 9 shows that the observed variations of the height-to-summit-radius ratio are well approximated by the curves. For seamounts with heights above 500 m, h / r t varies
To the extent that a flat-topped right-circular cone is an appropriate model for average seamount shape the following conclusions can be drawn from the analysis of 70 Pacific seamounts: (1) Seamount height and basal radius are highly correlated (Fig. 2). The 85-point sample mean of ~h = 0.21 implies that a seamount's summit height is about one fifth of its basal radius. (2) Values of seamount flatness (ratio of summit radius to bottom radius) are highly scattered (Fig. 3). There is evidence, however, that the mean flatness decreases with increasing summit height so that the preferred shape of a large-sized seamount may be that of a pointy cone. In addition, the histogram of number versus flatness shown in Fig. 4 appears to be bimodally distributed. Assuming that the data set is not biased this distribution suggests that it is most c o m m o n for a seamount to have a summit radius that is either about 10-20% or 35-50% of the basal radius. (3) A multivariate principal component analysis using five shape parameters (summit height, basal radius, summit radius, flatness, and slope) indicates that most of the variance in the shapes of the seamounts is described by the flatness and summit height. Moreover, the observed variation of ~h about the mean can be used to explain most of the observed variation of the height-tosummit-radius ratio (Fig. 9) and part of the observed variation of the slope angle (Fig. 10) on the flatness-height plane. What controls seamount flatness? Until recently flat-topped shapes were associated with the truncation of a seamount at the sea surface [25]. It is now recognized, however, that this shape can be
465 a p r i m a r y c o n s t r u c t i o n a l form [9,10,12-16,19]. D e v e l o p m e n t of s u m m i t craters a n d calderas as well as infilling of s u m m i t depressions a n d b u i l d ing of s u m m i t p l a t e a u s p r o d u c e a shape which in cross-section a p p r o x i m a t e s a f l a t - t o p p e d cone [31]. It has b e e n suggested that the d e v e l o p m e n t of s u m m i t collapse features a n d their subsequent m o d i f i c a t i o n is c o n t r o l l e d b y geologic factors such as c o n d u i t geometry, m a g m a chemistry, a n d flow v o l u m e [13,16,21,32]. Because s e a m o u n t s with s u m m i t heights b e l o w a b o u t 1000 m exhibit the m o s t v a r i a t i o n in flatness, these factors m a y be highly variable for small-sized seamounts. In a d d i t i o n , s e a m o u n t s with different m o d e s of origin m a y a d d to the large scatter in flatness. F o r e x a m p l e , small d o m e - s h a p e d features (heights less t h a n a few h u n d r e d meters) also yield f l a t - t o p p e d profiles. These s e a m o u n t s , however, are p r o b a b l y f o r m e d b y a l a c c o l i t h - t y p e i n t r u s i o n into s e d i m e n t [13,14]. D o f l a t - t o p p e d s e a m o u n t s have m o r e regular shapes than p o i n t y seamounts? V a r i a t i o n in the o b s e r v e d values o f the shape p a r a m e t e r s ~h a n d 4~ o n the f l a t n e s s - h e i g h t p l a n e suggests t h a t s e a m o u n t s with s u m m i t heights below 1800 m can be d i v i d e d into two classes: p o i n t y cones ( f < 0.25) a n d f l a t - t o p p e d cones ( f > 0 . 2 5 ) . Flat-topped s e a m o u n t s show fairly systematic variations of the h e i g h t - t o - r a d i u s ratio ~h a n d the slope angle q~ on the flatness-height p l a n e while p o i n t y s e a m o u n t s d o not. V a r i a t i o n s of ~h a n d q, for f < 0.25 are p r i m a r i l y c o m p l i c a t e d b y small-sized s e a m o u n t s that have steeper t h a n expected slope angles a n d larger than expected h e i g h t - t o - r a d i u s ratios; it m a y be that the d a t a set c o m p r i s e s m o r e than one m o r p h o l o g i c a l t y p e of p o i n t y seamounts. W h y are there no large-sized s e a m o u n t s with large flatnesses? S e a m o u n t s without large collapse features, or s e a m o u n t s with s e c o n d a r y cones at the s u m m i t or resurgent calderas p r o d u c e cross-sectional profiles with m o r e p o i n t y shapes. F r o m the small subset of large-sized s e a m o u n t s it a p p e a r s that m e a n flatness decreases with increasing summit height, a n d thus the p r e f e r r e d shape of a large-sized s e a m o u n t is that of a p o i n t y cone. In a d d i t i o n , it is seen in Fig. 5 that all b u t one of the large-sized s e a m o u n t s have slope angles that are n e a r 15 o. W h y large-sized s e a m o u n t s exhibit these t r e n d s is n o t i m m e d i a t e l y clear; however, there m a y be a difference in the i m p o r t a n c e of various
geologic c o n t r o l s b e t w e e n large- a n d small-sized seamounts. Clearly there is m u c h to be l e a r n e d a b o u t the variations in s e a m o u n t shapes. D e v e l o p i n g m o r e s o p h i s t i c a t e d statistical techniques to c h a r a c t e r i z e s e a m o u n t shapes (for example, t a k i n g into a c c o u n t slope changes on a single feature) a n d a p p l y i n g these techniques to larger d a t a sets, as well as d a t a sets that d i f f e r e n t i a t e between different s e a m o u n t types, is likely to p r o v i d e f u n d a m e n t a l insights into the processes c o n t r o l l i n g their f o r m a t i o n .
Acknowledgements I t h a n k T. J o r d a n who p r o v i d e d m u c h of the m o t i v a t i o n for the study. This w o r k b e n e f i t t e d greatly f r o m n u m e r o u s lengthy discussions with J. Cann. P. Shaw, P. Meyer, K. Feigl, a n d G.P. L o h m a n p r o v i d e d constructive c o m m e n t s . I t h a n k D. F o r n a r i for his thoughtful review. I also t h a n k P. L o n s d a l e for the use of u n p u b l i s h e d Sea B e a m data. This research was s p o n s o r e d b y the N a t i o n a l Science F o u n d a t i o n u n d e r c o n t r a c t n u m b e r O C E 8800497. W H O I c o n t r i b u t i o n 6868.
References 1 S.C. Porter, Distribution, morphology, and size frequency of cinder cones on Mauna Kea Volcano, Hawaii, Geol. Soc. Am. Bull. 83, 3607-3612, 1972. 2 C.A. Wood, Morphometric evolution of composite volcanoes, Geophys. Res. Lett. 5, 437-439, 1978. 3 C.A. Wood, Morphometric evolution of cinder cones, J. Volcanol. Geotherm. Res. 7, 387-413, 1980. 4 C.A. Wood, Calderas: a planetary perspective, J. Geophys. Res. 89, 8391-8406, 1984. 5 R.J. Pike, Craters on Earth, Moon, and Mars: multivariate classification and mode of origin, Earth Planet. Sci. Lett. 22, 245-255, 1974. 6 R.J. Pike, Size-morphology relations of lunar craters: discussion, Mod. Geol. 5, 169-173, 1975. 7 R.J. Pike, Volcanoes on the inner planets: some preliminary comparisons of gross topography, Proc. 9th Lunar Planet. Sci. Conf., pp. 3239-3273, 1978. 8 D.H. Scott, Volcanoes and volcanic provinces: Martian western hemisphere, J. Geophys. Res. 87, 9839-9851, 1982. 9 C.D. Hollister, M.F. Glenn and P.F. Lonsdale, Morphology of seamounts in the western Pacific and Philippine Basin from multi-beam sonar data, Earth Planet. Sci. Lett. 41, 405-418, 1978. 10 P.F. Lonsdale and F.N. Spiess, A pair of young cratered volcanoes on the East Pacific Rise, J. Geol. 87, 157-173, 1979.
466 11 P.T. Taylor, C.A. Wood and T.J. O'Hearn, Morphological investigations of s u b m a r i n e volcanism: H e n d e r s o n seamount, Geology 8, 390-395, 1980. 12 P. Lonsdale, R. Batiza and T. Simkin, Metallogenesis at seamounts on the East Pacific Rise, Mar. Tech. Soc. J. 16, 54-60, 1982. 13 R. Batiza and D. Vanko, Volcanic development of small oceanic central volcanoes on the flanks of the East Pacific Rise inferred from narrow-beam echo-sounder surveys, Mar. Geol. 54, 53-90, 1983. 14 P.F. Lonsdale, Laccoliths (?) and small volcanoes on the flank of the East Pacific Rise, Geology, pp. 706-709, 1983. 15 R.C. Searle, Submarine central volcanoes on the Nazca p l a t e - - h i g h resolution sonar observations, Mar. Geol. 53, 77-102, 1983. 16 D.J. Fornari, W.B.F. Ryan and P.J. Fox, The evolution of craters and calderas on young seamounts: insights from Sea M A R C 1 and Sea Beam sonar surveys of a small seamount group near the axis of the East Pacific Rise at - 10 o N, J. Geophys. Res. 89, 11,069-11,083, 1984. 17 P.R. Vogt and N.C. Smoot, The Geisha Guyots: multibeam bathymetry and morphometric interpretation, J. Geophys. Res. 89, 11,085-11,107, 1984. 18 D.J. Fornari, R. Batiza and M.A. Luckman, Seamount abundances and distribution near the East Pacific Rise 0 - 2 4 ° N based on Sea Beam data, in: Seamounts, Islands and Atolls, B.H. Keating et al., eds., Am. Geophys. Union, Geophys. Monogr. 43, 13-21, 1987. 19 D.J. Fornari, R. Batiza and J.F. Allan, Irregularly shaped seamounts near the East Pacific Rise: implications for seamount origin and rise axis processes, in: Seamounts, Islands and Atolls, B.H. Keating et al., eds., Am. Geophys. Union, Geophys. Monogr. 43, 35-47, 1987. 20 G.A. Abers, B. Parsons and J.K. Weissel, Seamount abundances and distributions in the southeast Pacific, Earth Planet. Sci. Lett. 87, 137-151, 1988. 21 D.J. Fornari, M.R. Perfit, J.F. Allan, R. Batiza, R. Haymon,
22
23
24
25 26
27
28 29
30 31 32
A. Barone, W.B.F. Ryan, T. Smith and T. Simkin, Seamounts as windows into mantle processes: structural and geochemical studies of the Lamont seamounts, Earth Planet. Sci. Lett. 89, 63-83, 1988. L.S. Kong, R.S. Dietrich, P.J. Fox, L A . Mayer and W.B.F. Ryan, The morphology and tectonics of the M A R K area from Sea Beam and Sea M A R C I observations (MidAtlantic ridge 23 ° N), Mar. Geophys. Res., in press, 1988. A. Lacey, J.R. Ockendon and D.L. Turcotte, On the geometrical form of volcanoes, Earth Planet. Sci. Lett. 54, 139-143, 1981. C.L. Angevine, D.L. Turcotte and J.R. Ockendon, Geometrical form of aseismic ridges, volcanoes, and seamounts, J. Geophys. Res. 89, 11,287-11,292, 1984. H.W. Menard, Marine Geology of the Pacific, 271 pp., McGraw-Hill, New York, N.Y., 1964. T.H. Jordan, H.W. Menard and D.K. Smith, Density and size distribution of seamounts in the eastern Pacific inferred from wide-beam sounding data, J. Geophys. Res. 88, 10,508-10,518, 1983. D.K. Smith and T.H. Jordan, The size distribution of Pacific seamounts, Geophys. Res. Lett. 14, 1119-1122, 1987. D.K. Smith and T.H. Jordan, Seamount statistics in the Pacific Ocean, J. Geophys. Res. 93, 2899--2918, 1988. D.K. Smith, The Statistics of Seamount Populations in the Pacific Ocean, 212 pp., Ph.D. Thesis, University of California, San Diego, Calif., 1985. H.W. Menard, Origin of guyots, The "Beagle" to Sea Beam, J. Geophys. Res. 89, 11,117-11,123, 1984. T. Simkin, Origin of some flat-topped volcanoes and guyots, Mem. Geol. Soc. Am. 132, 183-193, 1972. P.F. Lonsdale, Structural patterns of the Pacific floor offshore of peninsular California, in: The Gulf and Peninsula Provinces of the Californias, Am. Assoc. Pet. Geol., Mere., submitted.
457
[51
Shape analysis of Pacific seamounts D e b o r a h K. Smith Department of Geology and Geophysics, Woods Hole Oceanographic Institution, Woods Hole, MA 02543 (U.S.A.) Received June 1, 1988; revised version received September 1, 1988 Shape statistics have been compiled from 85 profiles of well-surveyed Pacific seamounts in the height range 140-3800 m. A fiat-topped cone was fit to each seamount's cross-sectional profile maintaining the slopes of the sides as closely as possible. On each profile a basal width db, a s u m m i t width dr, and a m a x i m u m height h, were measured. The height-to-basal-radius ratio is ~h is estimated by the ratio 2 h / d b and flatness f by the ratio d t / d b. Slope angle ¢ = arctan(c) is estimated from c = 2 h / ( d b - dr). Summit height and basal radius are found to be highly correlated (r = 0.93). The 85-point sample mean of the height-to-basal-radius ratio is ~h = 0.21 + 0.08 implying that a seamount's summit height is typically one fifth its basal radius. Despite the high correlation, individual points show some scatter, and there may be groupings into different morphological types. For example, all but one of the seamounts with summit heights above 1000 m have values of ~h that are larger than the sample mean. The 85-point sample mean of flatness is f = 0.31 + 0.18. Data points show a large scatter with values of f varying between 0 (a pointy cone) and 0.69 (a fiat-topped cone). A histogram representation of flatness, however, indicates that certain values of f m a y be more common than others: the histogram shows a bimodal distribution with maxima occurring at values of f in the ranges 0.10-0.20 and 0.35-0.50. Moreover, there is some evidence that the m e a n flatness decreases with summit height so that the preferred shape of a large-sized seamount may be a pointy cone. Slope angle has an 85-point sample mean of q~= 18 _+ 6 ° ; individual values of ~ vary between 5 ° and 36 °. In addition to having a lower than average mean flatness seamounts with heights above 2600 m also have a lower than average mean slope angle (15 ° ). To determine which variables account for most of the observed variation in the seamount shapes, a multivariate principal component analysis was performed on the data using five shape variables (summit height, basal radius, s u m m i t radius, flatness, and slope). The analysis indicates that most of the variation is described by two variables: flatness and summit height.
1. Introduction
To date, quantitative and statistical studies of volcano morphology have been mostly restricted to subaerial volcanoes on Earth (e.g., [1-4]) and volcanoes imaged on the inner planets (e.g., [5-8]) because more high-quality topographic measurements are available for these volcanoes than those found in Earth's oceans. Recently, however, studies of submarine volcano morphology have been greatly benefitting from the rapid increase in the number of seamounts that have been surveyed by bathymetric instruments that provide high-resolution, two-dimensional coverage [9-22]; and emphasis is beginning to be placed on using the signals carried by a seamount's shape to better understand crustal and mantle processes. Wood [4] stated that the morphology of a subaerial volcano is a surface expression of: (1) the 0012-821X/88/$03.50
© 1988 Elsevier Science Publishers B.V.
chemical composition of the magma, (2) eruptive style, and (3) tectonic setting. In addition to these Batiza and Vanko [13] suggested that the following are some of the variables important in controlling seamount shapes: (1) age of the underlying lithosphere, (2) thickness of sediment cover, (3) initial and subsequent conduit geometries, and (4) fracture patterns in the crust and lithosphere. For example, irregular and elongated plan shapes of seamounts have been attributed to magma following existing fractures in the crust [13]; also it has been suggested that seamount slopes are inversely proportional to the rate of magma effusion during eruption [17]. It is obvious that many diverse factors play a role in controlling volcano formation; nonetheless, many volcanoes exhibit remarkable symmetry in their shapes suggesting a more universal control [23,24]. To this end, a number of workers have
458 addressed the problem of whether a seamount's gross topography may vary systematically with size. Menard [25] analyzed wide-beam profile data collected in the Pacific and observed that the cross-sectional profiles of seamounts (excluding those that reach the sea surface) appear to be approximately similar and independent of size. More recently, Batiza and Vanko [13] used Sea Beam surveys of approximately 30 seamounts located near the East Pacific Rise, and data from other well-surveyed seamounts in the literature, to measure seamount flatness (ratio of summit diameter to basal diameter) and median and m a x i m u m slopes. Their analysis, however, yielded no simple trends in these variables. Investigations of the areal statistics of seamount populations in the southern and eastern Pacific by Jordan et al. [26] and Smith and Jordan [27,28] also addressed the problem of modeling seamount shapes. The statistical formulation used in these investigations requires that the shape of a seamount be specified as a function of its size [26]. The specific shape model adopted by Jordan et al. [26] and Smith and Jordan [27,28] approximates seamounts as right-circular cones of constant slope ~, height-to-radius ratio ~h, and flatness f. F r o m a study of profiles constructed for 30 well-surveyed seamounts in the Pacific with summit heights varying from 200 to 4000 m, Jordan et al. [26] obtained mean values of ~h = 0.21, f = 0.21, and q, = 15 °. Although there is a lot of scatter in their data some trends are evident. For example, Jordan et al. [26] found that seamount height is roughly proportional to basal radius. Similar shape studies by Smith [29] and Abers et al. [20], using more extensive data sets, obtained mean values of ~h that differ by less than 5% from the value of Jordan et al. [26]. These results agree with the observations of Taylor et al. [11] who suggested that large seamounts typically have heights that are about 10% of their basal diameters (i.e., 20% of their basal radii). Jordan et al. [26] also noted that even though seamounts with heights less than about 1000 m have flatnesses more or less uniformly distributed between f = 0 (pointy cone) and f = 0.6, there is some suggestion that the mean flatness decreases with increasing height. To investigate the shapes of seamounts, and in particular, to investigate the relationship between seamount shape and size,
this report extends the shape analysis of Jordan et al. [26] to a more comprehensive data set comprising 85 profiles of seamounts in the Pacific Ocean.
2. Shape data Shape statistics have been compiled from 85 cross-sectional profiles representing 70 wellsurveyed Pacific seamounts in the height range 140-3800 m (Table 1). The data include published and unpublished bathymetric surveys as well as unpublished Sea Beam transit swaths (unpublished Sea Beam swaths were generously provided by P. Lonsdale). Seamounts from Sea Beam transit data were chosen as closed contour features greater than 100 m in relief whose summits were contained within the swath. All but nine of the seamounts in the data set are located in the eastern and southern Pacific. Of the 42 seamounts mapped by Sea Beam, 13 are located on the Cocos plate [13], two (Larson's seamounts) are located close to the East Pacific Rise at approximately 2 1 ° N [12], 19 are located between the Clarion and Murray fracture zones (Scripps Institution of Oceanography cruises Bonanza 2, Pascua 5, and Marathon 1), and eight are located along an essentially east-west transit between Tahiti and the East Pacific Rise (Scripps Institution of Oceanography cruise Ariadne 2). The data set also includes nine seamounts located on the Nazca plate that were surveyed using G L O R I A [15]. (The published profiles were derived from the acoustic shadows cast by the seamounts or, if the ship passed directly over the seamount summit, the profile was obtained from the narrow-beam echosounder.) Six additional profiles in the eastern Pacific were constructed from seamounts m a p p e d by the N O A A Pioneer Survey. Four profiles of oceanic volcanoes known to be active (Moua Pika and Rocard, Societies; Macdonald, Australs; Loihi, Hawaii) were obtained from Menard [30]. The final nine seamounts are located in the Western Pacific and Philippine Basin and were surveyed using the N A V O C E A N O multi-beam echosounding system [9]. High-resolution multi-beam swaths and sonar images of the seafloor are still too limited to provide a large inventory of large-size seamounts; therefore only 24 of the seamounts have summit heights above 1000 m, and only 7 have heights
TABLE 1 Seamount shape statistics No.
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 32 33
Height (m)
Basal diameter (103 m)
Summit diameter (103 m)
Flatness
Source/ location
No.
Height (m)
Basal diameter (103 m)
Summit diameter (103 m)
Flatness
Source/ location
1335 935 935 600 1465 1400 1600 1135 1065 935 935 935 800 800 535 535 535 535 1065 1200 1335 650 1400 700 1060 600 500 500 1250 750 390 320 220 330 300 315 370 190 760 700 790 700 730
10.8 8.9 10.2 7.3 9.5 8.1 6.9 7.9 7.7 6.0 8.1 7.9 6.1 6.9 8.8 5.5 5.3 4.5 7.9 9.3 10.0 12.0 12.7 8.8 9.6 6.8 7.7 7.5 8.7 6.5 7.2 5.0 5.3 3.8 7.0 4.0 3.5 5.6 6.5 5.9 6.5 7.5 7.4
1.6 5.3 5.1 1.0 1.6 1.6 2.4 2.5 0.5 0.8 3.3 3.6 2.1 2.5 5.5 2.4 0.3 0.5 1.3 3.8 0.8 7.2 3.7 3.5 3.9 3.4 4.5 4.9 2.6 3.1 3.0 2.6 2.1 1.9 2.9 1.6 0.6 1.9 4.0 1.9 3.4 3.2 2.6
0.15 0.60 0.50 0.14 0.17 0.20 0.35 0.32 0.07 0.13 0.39 0.46 0.34 0.36 0.62 0.44 0.06 0.12 0.16 0.41 0.08 0.60 0.29 0.40 0.41 0.50 0.59 0.65 0.30 0.48 0.41 0.53 0.39 0.50 0.42 0.41 0.17 0.34 0.62 0.32 0.52 0.42 0.35
[13] Cocos plate
34
565 620 650 210 380 560 1280 1360 900 900 925 925 150 345 430 495 880 905 150 165 320 220 185 180 145 140 155 175 190 170 180 440 1380 2780 2760 3800 3000 1760 2700 3500 2650 1600
8.6 7.9 7.2 3.7 4.0 4.0 7.6 7.1 5.8 9.8 13.8 9.2 2.3 4.9 5.8 4.3 7.2 6.8 2.0 1.2 2.1 2.9 2.1 3.3 2.9 3.5 3.4 1.4 2.1 0.9 3.4 2.2 8.9 22.6 21.8 35.7 25.1 15.3 23.2 27.4 15.0 13.7
5.8 5.4 3.3 0.3 2.0 0.8 1.1 1.5 1.7 3.8 5.1 1.5 0.7 2.0 2.2 1.7 4.4 3.8 0.4 0.2 0.4 1.4 0.4 0.7 0.4 0.5 1.6 0.3 0.9 0.1 0.6 0.2 1.7 0.9 0.6 6.4 3.5 3.7 2.1 0.6 0.8 0.0
0.67 0.69 0.46 0.07 0.51 0.12 0.19 0.21 0.29 0.39 0.37 0.16 0.30 0.42 0.37 0.40 0.61 0.56 0.20 0.16 0.19 0.49 0.21 0.20 0.15 0.14 0.47 0.22 0.42 0.11 0.16 0.09 0.19 0.04 0.03 0.18 0.14 0.24 0.09 0.02 0.05 0.00
[9] Phil. Basin
35 36 37 38 39 40 41 42 43 44 45 46 47 48 49
[15] Nazca plate
[Ariadne ~]
[12] Pac. plate 21 o N
50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70
[Bonanza a]
[9] Phil. Basin
[Pascua ~]
[Marathon a ]
[Pioneer Survey a]
Moua Pika b Macdonald b Loihi b Rocard b
[9] NW Pac. Basin
Two profiles were constructed for seamounts that were found to be significantly elongated. a SIO cruise Ariadne 2--transit between Tahiti and EPR; SIO cruises Pascua 5, Marathon 1, Bonanza 2 and NOAA Pioneer Survey --northeast Pacific between Clarion and Mendocino fracture zones. b Profiles of the last four seamounts in the table were obtained from Menard [30].
a b o v e 2600 m. There are no s e a m o u n t s in the data set w i t h s u m m i t heights b e t w e e n 1800 and 2600 m. A flat-topped c o n e was fit to each seamount's
cross-sectional
profile maintaining
the
slopes
of
t h e s i d e s a s c l o s e l y a s p o s s i b l e ( F i g . 1). T h e p r o files w e r e c o n s t r u c t e d
by hand;
on each a basal
460 dt
~
h,320
i
h
, ~ 0
m
%'2.9 km .
A)
B)
h:1 8 0 m
h
h,440 m (:1~ 2 . 2 krrt
'
db
1~0.20 '
l~dt~a h:145
m
1=0.15 ~l
d~
db
i
D)
c)
Fig. 1. Cross-sectional profiles constructed for some small seamounts mapped by Sea Beam on SIO cruises Marathon 1 and Pascua 5. Summit height is taken to be the height from the shallowest depth obtained to the average baseline. ~h is estimated by the ratio 2 h / d b, f by the ratio d t / d b , and c by the ratio 2 h / ( d b - dr). Two profiles were constructed for seamounts that were found to be significantly elongated.
w i d t h d b , a s u m m i t w i d t h d t, a n d a m a x i m u m height h, were m e a s u r e d . S u m m i t height is t a k e n to b e the height f r o m the shallowest d e p t h obt a i n e d to the average baseline. ~h is e s t i m a t e d b y the r a t i o 2h/db, f b y the ratio dJdb, a n d ~ b y 4000
350O 3000
/
2500
zooo ./ 1500 1000 5O0
%
S. I
"/ S%m
I
4000
~o
I
,
I
I
8000 basal
I
12000 radius
I
I
16000
I
20000
(m)
Fig. 2. Summit height versus basal radius for 85 cross-sectional profiles of Pacific seamounts. The solid line corresponds to the mean height-to-radius ratio ~h=0.21 obtained by equally weighting the ratios of all 85 profiles. Seamount height and basal radius are highly correlated ( r = 0.95). Notice that all but one of the seamounts with heights above 1000 m have higher than average values for ~w
2 h / ( d b - dr). T h e w i d t h - t o - l e n g t h r a t i o of each s e a m o u n t ' s p l a n s h a p e is less t h a n 2; w i t h i n this limit 15 s e a m o u n t s were f o u n d to b e significantly e l o n g a t e d a n d two profiles were c o n s t r u c t e d (Table 1). Fig. 2 is a p l o t of s u m m i t height versus b a s a l r a d i u s ( r b = d b / 2 ). T h e s a m p l e m e a n o b t a i n e d by equally weighting the values f r o m all 85 profiles is ~h = 0-21+-- 0.08 (shown on the p l o t as a solid line); the m e d i a n is 0.22. T h e m e a n height-tor a d i u s ratio d e t e r m i n e d b y this s t u d y is n e a r l y identical to the one d e t e r m i n e d b y J o r d a n et ai. [26] even t h o u g h the d a t a set used here is m o r e t h a n twice as large. Fig. 2 i n d i c a t e s that h a n d r b are s t r o n g l y c o r r e l a t e d ( r = 0.93); however, individual d a t a p o i n t s show s o m e scatter a n d there m a y be g r o u p i n g s into different m o r p h o l o g i c a l types. F o r example, all b u t one of the 24 s e a m o u n t s with s u m m i t heights a b o v e 1000 m have heightt o - r a d i u s ratios that are greater t h a n the s a m p l e mean; Fieberling Guyot (h=3800 m) has a h e i g h t - t o - r a d i u s ratio equal to the mean. In c o n t r a s t to the c o r r e l a t i o n o b s e r v e d b e t w e e n s u m m i t height a n d b a s a l r a d i u s n o such c o r r e l a tion exists b e t w e e n s u m m i t height a n d s u m m i t radius. T h e 85-point s a m p l e m e a n of the heightt o - s u m m i t - r a d i u s ratio is h/r t = 1.35 _+ 1.93; the m e d i a n is 0.64. As i n d i c a t e d b y the large s t a n d a r d d e v i a t i o n a n d the large difference b e t w e e n the
461
mean and median, the data are highly scattered: values of h / r t range between 0.18 and 12.7. The seamount with the lowest observed height-to-summit-radius ratio is a short flat-topped cone (h = 650 m, f = 0.60); the seamount with the highest height-to-summit-radius ratio is a tall pointy cone (h = 3500 m, f = 0.02). Flatness is plotted against summit height in Fig. 3. Values of f vary between 0 (a pointy cone) and 0.69 (a flat-topped cone). The 85-point sample mean is f = 0.31 _+ 0.18; the median is 0.32. These values are slightly higher than those obtained by Jordan et al. [26] whose 30-point sample mean is f = 0.21 _+ 0.03 and median is 0.18. The data points displayed in Fig. 3 are highly scattered. There is some evidence, however, that mean flatness decreases with summit height: seamounts with summit heights below 1000 m have a 56-point sample mean of f = 0.37 _+ 0.17; seamounts with summit heights in the range 1000-1800 m have a 17-point sample mean of f = 0.22_+ 0.11; and seamounts with summit heights above 2600 m have a 7-point sample mean of f = 0.08_+ 0.06. These values (plotted in Fig. 3 as triangles) suggest
14 12 10
iliili
ilililil
~ 8 6
•
0.4
0.6
o.a
1.0
flatness
Fig. 4. Number versus flatness plotted in bin widths of f = 0.05. The histogram shows a possible bimodal distribution with maxima occurring in the flatness ranges 0.10-0.20 and 0.35-0.50.
that the preferred shape of a large-size seamount may be that of a pointy cone. In addition, Fig. 3 suggests that there may be other groupings of
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2000
L
_o •
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3000
4000
height (m) Fig. 3. Flatness f versus summit height h. Flatness varies between 0 (a pointy cone) and 0.69 (a truncated cone). The greatest range in the values of flatness occurs for seamounts with summit heights below about 1000 m. Triangles correspond to the mean values of f obtained in the height ranges: 0-1000 m, 1000-1800 m, and 2600-3800 m. The mean flatness decreases as a function of summit height suggesting that the preferred shape of a large-sized seamount may be that of a pointy cone.
o~
I
I
1000
I
2000 height (m)
I
3000
I
4000
Fig. 5. Slope angle is plotted against summit height. Values of vary between 5 ° and 36 ° with a mean value of ~ = 1 8 °. The data points appear to fall into two groups. Most of the large-sized seamounts (h > 2600 m) have slope angles that cluster about their mean of #, = 15 o; seamounts with summit heights below 1800 m, however, form a somewhat diffuse group in which slope angle appears to be proportional to summit height.
462
points. For example, the histogram of number versus flatness displayed on Fig. 4 shows a possible bimodal distribution with maxima occurring at values of f which specify that the summit radius is 10-20% or 35 50% of the basal radius. Slope angle versus summit height is plotted in Fig. 5. Values of q~ vary between 5 ° (a small pointy seamount: h = 140 m, f = 0.14 and ~h = 0.08) and 36 ° (an intermediate-size flat-topped seamount with the largest observed height-toradius ratio: h = 1600 m, f = 0.35, and ~h = 0.46). The sample mean of the slope angle is q, = 18 o _+ 6°; the median is 17 °. The data points in Fig. 5 appear to fall into two groups. Seamounts with summit heights below 1800 m form a somewhat diffuse group in which the slope angle appears to be roughly proportional to summit height. Seamounts with summit heights above 2600 m form a second group in which most of the seamounts have slope angles that cluster closely about their mean of ep = 15 °.
3. Interdependence between seamount shape variables A multivariate principal component analysis was performed to determine which parameters account for most of the variance observed in the seamount shapes. The following five shape variables were used in the analysis: summit height, basal radius, summit radius, flatness, and slope. The first two eigenvectors of the normalized variance-covariance matrix account for approximately 82% of the variance in the data. It was found that the first eigenvector which accounts for about 42% of the total variance heavily weights the contributions from summit height and basal radius, and thus the first principal component primarily reflects differences in seamount size. Fig. 6 displays a few of the observed seamount shapes approximated as flat-topped cones and plotted at their respective positions on the first two principal components. An examination of Fig. 6 shows that along the first principal component seamounts are separated according to height: short seamounts plot at the left of the figure and tall seamounts plot at the right. (Because summit height and basal radius are highly correlated, either can be used to characterize the change in size; in this case summit height has been chosen.)
-3 -2
I 0
I 2
I 4
t 6
32
Fig. 6. Illustration o f some of the shapes of seamounts observed in this data set. The seamounts have been approximated as flat-topped cones and plotted at their respective position on the first two principal components of a five-variable principal component analysis. The horizontal axis is component one; the vertical axis is component two. Notice that the shapes of seamounts are sorted primarily according to summit height along the first component, and primarily according to flatness along the second component. The first two principal components account for more than 80% of the variance in the seamount shapes.
The second eigenvector which accounts for approximately 40% of the total variance heavily weights the contributions from flatness, summit radius, and slope; and Fig. 6 indicates that along the second principal component seamounts are sorted according to their shape. This variation is manifested primarily by the difference in seamount flatness: pointy seamounts plot at the bottom of the figure and flat-topped seamounts plot at the top. To check whether summit height and flatness are sufficient to express most of the variance in the shape data, an eyeball comparison was made between the position of a seamount on the plot in principal-component space and its position on the flatness height plane. Despite some exceptions the two plots are remarkably consistent. In order to explain these discrepancies and to recapture all the essential information about a seamount's shape the behavior of the other shape parameters (~h, 0, and h/r,) on the flatness height plane has been investigated. If h and r b were perfectly correlated (i.e., ~h is a constant) then lines of constant h / r t and q5 would follow lines of constant f. This is not the case, however, as seen in Fig. 7 which maps values of ~h onto the f - h
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radius
A least-squares fit of (1) to the data points plotted in Fig. 2 (regression was x (height) on y (radius)) yields the coefficients: c I = 0 . 5 m -1
(2a)
c 2 = 2.1
(2b)
c 3 = 1.5 X 10 3 m
(2c)
20000
(m)
Fig. 8. Summit height versus basal radius for 85 cross-sectional profiles of Pacific seamounts. This figure is the same as Fig. 2 except that it displays as a dashed curve a least squares fit of a second-order polynomial (1) to the data points. The curve specifies that ~h increases systematically with height to approximately h = 1800 m than decreases slightly at larger sizes.
1oI
• h / r t < 0.5 4- 0 5 -~ h / r t < L4 .)g. 1,4 "¢- h / r t < 5
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12000
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plane. The plot is identical to Fig. 3 except that symbols have been used to represent values of ~hThere is some indication from Fig. 7 that there are different trends in the values of ~h between the group of seamounts with f < 0.25 (pointy) and the group of seamounts with f > 0.25 (flat-topped). For example, most of the pointy seamounts have values of ~h that are greater than the 85-point sample mean (~h = 0.21), and there are no obvious patterns within this group. In contrast, flat-topped seamounts have values of ~h that appear to be proportional to summit height. To determine whether some of the variation in h / r t and q, can be explained by assuming that ~h is n o t c o n s t a n t , l e t r b - - g ( h ) where g ( h ) is a p -
r b = g(h)
~i
(m)
Fig. 7. Values of ~h are displayed on the plot of flatness versus summit height. The range of ~h that each symbol represents is shown in the upper right comer of the plot. Solid circles and plusses correspond to seamounts with height-to-radius ratios that are below the mean of ~h = 0.21. Seamounts with f > 0.25 show more systematic variations in ~h than seamounts with f < 0.25.
proximated
o~
I
I~
I
1000
2000 height
I 3000
¢
4000
(m)
Fig. 9. Values of h / r t are displayed on the flatness-height plane. The range of h / r t that each symbol represents is shown in the upper right corner of the plot. Model curves representing h / r t = 0.5, 1.4, 5, and 10 are plotted. These curves have been determined using equations (1) and (3) and the values of the coefficients given in (2). The observed variations of h / r t are well-approximated by the curves. Notice that except at the smallest sizes h / r t varies primarily with flatness: h / r t decreases as f increases.
464
primarily as a function of flatness (that is, h / r t decreases as f increases). Curves corresponding to constant slope angle (Fig. 10) do not describe the data as well although they approximate general trends. The model curves predict that slope angles increase primarily as a function of summit height below about h = 1000 m, and primarily as a function of flatness for seamounts with summit heights between 1000 and 4000 m. It is interesting to note that most of the seamounts with the steepest slope angles (q, >~ 25 ° ) also have large flatnesses ( f > 0.5).
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4. Summary and discussion
o.c
~ 2000 height (m)
3000
t
4000
Fig. 10. Values of ep are displayed on the flatness-height plane. The range of ,h that each symbol represents is shown in the upper right corner of the plot. Curves representing ~ = 10 o, 15 °, 20 °, and 25 o have been calculated using equations (1) and (4) and the values of the coefficients given in (2) and are plotted on the figure. The model curves do not describe the data very well but they seem to approximate general trends; they indicate that slope angles increase primarily as function of summit height at small sizes (h < 1000 m) and primarily as a function of flatness at large sizes. Notice that most of the seamounts with the steepest slope angles (~ > 25 o) also have large flatnesses ( f > 0.5).
The theoretical curve specified by (1) and the coefficients given in (2) is dashed in Fig. 8. The results indicate that the height-to-radius ratio increases systematically with summit height from approximately ~h = 0.10 at h = 200 m to ~h = 0.26 at h = 1800 m; above this height ~h remains approximately constant (~h = 0.23 at h = 4000 m). Incorporating (1) into the flat-topped right-circular cone model for seamount shapes gives:
h / r t = h / [ fg( h)]
(3)
and: = arctan( h / [ g ( h ) ( 1 - f ) ] }
(4)
Model curves of constant h / r t and q, on the flatness-height plane are plotted in Figs. 9 and 10 respectively. (As mentioned a constant value of ~h would yield lines of constant h / r t and ~ that are horizontal on the f - h plane.) Fig. 9 shows that the observed variations of the height-to-summit-radius ratio are well approximated by the curves. For seamounts with heights above 500 m, h / r t varies
To the extent that a flat-topped right-circular cone is an appropriate model for average seamount shape the following conclusions can be drawn from the analysis of 70 Pacific seamounts: (1) Seamount height and basal radius are highly correlated (Fig. 2). The 85-point sample mean of ~h = 0.21 implies that a seamount's summit height is about one fifth of its basal radius. (2) Values of seamount flatness (ratio of summit radius to bottom radius) are highly scattered (Fig. 3). There is evidence, however, that the mean flatness decreases with increasing summit height so that the preferred shape of a large-sized seamount may be that of a pointy cone. In addition, the histogram of number versus flatness shown in Fig. 4 appears to be bimodally distributed. Assuming that the data set is not biased this distribution suggests that it is most c o m m o n for a seamount to have a summit radius that is either about 10-20% or 35-50% of the basal radius. (3) A multivariate principal component analysis using five shape parameters (summit height, basal radius, summit radius, flatness, and slope) indicates that most of the variance in the shapes of the seamounts is described by the flatness and summit height. Moreover, the observed variation of ~h about the mean can be used to explain most of the observed variation of the height-tosummit-radius ratio (Fig. 9) and part of the observed variation of the slope angle (Fig. 10) on the flatness-height plane. What controls seamount flatness? Until recently flat-topped shapes were associated with the truncation of a seamount at the sea surface [25]. It is now recognized, however, that this shape can be
465 a p r i m a r y c o n s t r u c t i o n a l form [9,10,12-16,19]. D e v e l o p m e n t of s u m m i t craters a n d calderas as well as infilling of s u m m i t depressions a n d b u i l d ing of s u m m i t p l a t e a u s p r o d u c e a shape which in cross-section a p p r o x i m a t e s a f l a t - t o p p e d cone [31]. It has b e e n suggested that the d e v e l o p m e n t of s u m m i t collapse features a n d their subsequent m o d i f i c a t i o n is c o n t r o l l e d b y geologic factors such as c o n d u i t geometry, m a g m a chemistry, a n d flow v o l u m e [13,16,21,32]. Because s e a m o u n t s with s u m m i t heights b e l o w a b o u t 1000 m exhibit the m o s t v a r i a t i o n in flatness, these factors m a y be highly variable for small-sized seamounts. In a d d i t i o n , s e a m o u n t s with different m o d e s of origin m a y a d d to the large scatter in flatness. F o r e x a m p l e , small d o m e - s h a p e d features (heights less t h a n a few h u n d r e d meters) also yield f l a t - t o p p e d profiles. These s e a m o u n t s , however, are p r o b a b l y f o r m e d b y a l a c c o l i t h - t y p e i n t r u s i o n into s e d i m e n t [13,14]. D o f l a t - t o p p e d s e a m o u n t s have m o r e regular shapes than p o i n t y seamounts? V a r i a t i o n in the o b s e r v e d values o f the shape p a r a m e t e r s ~h a n d 4~ o n the f l a t n e s s - h e i g h t p l a n e suggests t h a t s e a m o u n t s with s u m m i t heights below 1800 m can be d i v i d e d into two classes: p o i n t y cones ( f < 0.25) a n d f l a t - t o p p e d cones ( f > 0 . 2 5 ) . Flat-topped s e a m o u n t s show fairly systematic variations of the h e i g h t - t o - r a d i u s ratio ~h a n d the slope angle q~ on the flatness-height p l a n e while p o i n t y s e a m o u n t s d o not. V a r i a t i o n s of ~h a n d q, for f < 0.25 are p r i m a r i l y c o m p l i c a t e d b y small-sized s e a m o u n t s that have steeper t h a n expected slope angles a n d larger than expected h e i g h t - t o - r a d i u s ratios; it m a y be that the d a t a set c o m p r i s e s m o r e than one m o r p h o l o g i c a l t y p e of p o i n t y seamounts. W h y are there no large-sized s e a m o u n t s with large flatnesses? S e a m o u n t s without large collapse features, or s e a m o u n t s with s e c o n d a r y cones at the s u m m i t or resurgent calderas p r o d u c e cross-sectional profiles with m o r e p o i n t y shapes. F r o m the small subset of large-sized s e a m o u n t s it a p p e a r s that m e a n flatness decreases with increasing summit height, a n d thus the p r e f e r r e d shape of a large-sized s e a m o u n t is that of a p o i n t y cone. In a d d i t i o n , it is seen in Fig. 5 that all b u t one of the large-sized s e a m o u n t s have slope angles that are n e a r 15 o. W h y large-sized s e a m o u n t s exhibit these t r e n d s is n o t i m m e d i a t e l y clear; however, there m a y be a difference in the i m p o r t a n c e of various
geologic c o n t r o l s b e t w e e n large- a n d small-sized seamounts. Clearly there is m u c h to be l e a r n e d a b o u t the variations in s e a m o u n t shapes. D e v e l o p i n g m o r e s o p h i s t i c a t e d statistical techniques to c h a r a c t e r i z e s e a m o u n t shapes (for example, t a k i n g into a c c o u n t slope changes on a single feature) a n d a p p l y i n g these techniques to larger d a t a sets, as well as d a t a sets that d i f f e r e n t i a t e between different s e a m o u n t types, is likely to p r o v i d e f u n d a m e n t a l insights into the processes c o n t r o l l i n g their f o r m a t i o n .
Acknowledgements I t h a n k T. J o r d a n who p r o v i d e d m u c h of the m o t i v a t i o n for the study. This w o r k b e n e f i t t e d greatly f r o m n u m e r o u s lengthy discussions with J. Cann. P. Shaw, P. Meyer, K. Feigl, a n d G.P. L o h m a n p r o v i d e d constructive c o m m e n t s . I t h a n k D. F o r n a r i for his thoughtful review. I also t h a n k P. L o n s d a l e for the use of u n p u b l i s h e d Sea B e a m data. This research was s p o n s o r e d b y the N a t i o n a l Science F o u n d a t i o n u n d e r c o n t r a c t n u m b e r O C E 8800497. W H O I c o n t r i b u t i o n 6868.
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466 11 P.T. Taylor, C.A. Wood and T.J. O'Hearn, Morphological investigations of s u b m a r i n e volcanism: H e n d e r s o n seamount, Geology 8, 390-395, 1980. 12 P. Lonsdale, R. Batiza and T. Simkin, Metallogenesis at seamounts on the East Pacific Rise, Mar. Tech. Soc. J. 16, 54-60, 1982. 13 R. Batiza and D. Vanko, Volcanic development of small oceanic central volcanoes on the flanks of the East Pacific Rise inferred from narrow-beam echo-sounder surveys, Mar. Geol. 54, 53-90, 1983. 14 P.F. Lonsdale, Laccoliths (?) and small volcanoes on the flank of the East Pacific Rise, Geology, pp. 706-709, 1983. 15 R.C. Searle, Submarine central volcanoes on the Nazca p l a t e - - h i g h resolution sonar observations, Mar. Geol. 53, 77-102, 1983. 16 D.J. Fornari, W.B.F. Ryan and P.J. Fox, The evolution of craters and calderas on young seamounts: insights from Sea M A R C 1 and Sea Beam sonar surveys of a small seamount group near the axis of the East Pacific Rise at - 10 o N, J. Geophys. Res. 89, 11,069-11,083, 1984. 17 P.R. Vogt and N.C. Smoot, The Geisha Guyots: multibeam bathymetry and morphometric interpretation, J. Geophys. Res. 89, 11,085-11,107, 1984. 18 D.J. Fornari, R. Batiza and M.A. Luckman, Seamount abundances and distribution near the East Pacific Rise 0 - 2 4 ° N based on Sea Beam data, in: Seamounts, Islands and Atolls, B.H. Keating et al., eds., Am. Geophys. Union, Geophys. Monogr. 43, 13-21, 1987. 19 D.J. Fornari, R. Batiza and J.F. Allan, Irregularly shaped seamounts near the East Pacific Rise: implications for seamount origin and rise axis processes, in: Seamounts, Islands and Atolls, B.H. Keating et al., eds., Am. Geophys. Union, Geophys. Monogr. 43, 35-47, 1987. 20 G.A. Abers, B. Parsons and J.K. Weissel, Seamount abundances and distributions in the southeast Pacific, Earth Planet. Sci. Lett. 87, 137-151, 1988. 21 D.J. Fornari, M.R. Perfit, J.F. Allan, R. Batiza, R. Haymon,
22
23
24
25 26
27
28 29
30 31 32
A. Barone, W.B.F. Ryan, T. Smith and T. Simkin, Seamounts as windows into mantle processes: structural and geochemical studies of the Lamont seamounts, Earth Planet. Sci. Lett. 89, 63-83, 1988. L.S. Kong, R.S. Dietrich, P.J. Fox, L A . Mayer and W.B.F. Ryan, The morphology and tectonics of the M A R K area from Sea Beam and Sea M A R C I observations (MidAtlantic ridge 23 ° N), Mar. Geophys. Res., in press, 1988. A. Lacey, J.R. Ockendon and D.L. Turcotte, On the geometrical form of volcanoes, Earth Planet. Sci. Lett. 54, 139-143, 1981. C.L. Angevine, D.L. Turcotte and J.R. Ockendon, Geometrical form of aseismic ridges, volcanoes, and seamounts, J. Geophys. Res. 89, 11,287-11,292, 1984. H.W. Menard, Marine Geology of the Pacific, 271 pp., McGraw-Hill, New York, N.Y., 1964. T.H. Jordan, H.W. Menard and D.K. Smith, Density and size distribution of seamounts in the eastern Pacific inferred from wide-beam sounding data, J. Geophys. Res. 88, 10,508-10,518, 1983. D.K. Smith and T.H. Jordan, The size distribution of Pacific seamounts, Geophys. Res. Lett. 14, 1119-1122, 1987. D.K. Smith and T.H. Jordan, Seamount statistics in the Pacific Ocean, J. Geophys. Res. 93, 2899--2918, 1988. D.K. Smith, The Statistics of Seamount Populations in the Pacific Ocean, 212 pp., Ph.D. Thesis, University of California, San Diego, Calif., 1985. H.W. Menard, Origin of guyots, The "Beagle" to Sea Beam, J. Geophys. Res. 89, 11,117-11,123, 1984. T. Simkin, Origin of some flat-topped volcanoes and guyots, Mem. Geol. Soc. Am. 132, 183-193, 1972. P.F. Lonsdale, Structural patterns of the Pacific floor offshore of peninsular California, in: The Gulf and Peninsula Provinces of the Californias, Am. Assoc. Pet. Geol., Mere., submitted.