Earrh and Planetary Science Letters, 87 (1988) 137-151 Elsevier Science Publishers B.V., Amsterdam - Printed 137 in The Netherlands Seamount abundances and distributions Geoffrey ’ Department A. Abers ofEarth,Atmospheric, ’ Lumont-Doherty ‘, Barry Parsons in the southeast Pacific ‘,* and Jeffrey K. Weissel 2 and Planetary Science, Massachusetts Institute of Technology, Cambridge MA 02139 (U.S.A.) Geological Observatory of Columbia University, Palisades NY 10964 (U.S.A.) Received March 25, 1987; revised version received August 19, 1987 Sea Beam bathymetry was recorded for 17,277 km of ship track in the southeast Pacific and has been analyzed for seamount population characteristics. All the ship tracks are over the Pacific plate and most fall along 7 lines parallel to the East Pacific Rise between 7 o S and 22O S. The lines fall into three age categories: one line is over 0.5-2 Ma crust, three are over S-10 Ma crust, and three are over 30-40 Ma crust. Seamount locations were recorded, diameters were manually estimated, and heights were measured if the swath crossed the seamount center. Over 382 features were counted along the entire ship track with heights ranging from 50 m to over 2500 m, with sampling most consistent at heights between 100 m and 1000 m. Height-to-radius ratios vary considerably, suggesting that seamount shapes do not scale to a single parameter. The observed variety of morphological forms demonstrates that there is a wide range of seamount shapes for small features. The distribution of sizes for the population was approximated by exponential dependence and by power-law dependence using methods developed by Smith and Jordan [17]. The power-law distribution overestimates abundances at the smallest size ranges and both distributions fail to predict abundances of large seamounts determined from wide-beam data [17]. Size distributions were also determined for seamounts in each seafloor age category. Almost all small seamounts appear to be produced on crust younger than 0.5-2 Ma, while the number of larger seamounts increases to 5-10 Ma. For all size ranges observed here the number of seamounts at 5-10 Ma and at 30-40 Ma is roughly identical. These observations suggest that most small seamounts are formed on very young, thin lithosphere that permits the passage of small volumes of magma. Small volumes would cool in older, thicker lithosphere before reaching the surface although larger magma bodies might not. Numerous small sources of melt must exist near the ridge crest to supply the small seamounts, probably trapped remnants of the large-scale upwelling. 1. Introduction cated top sometimes containing craters (e.g. [9]). Small or young volcanoes may form as fairly simple cones or elongated domes, but as volcanoes grow larger circumferential feeders and flank eruptive centers become common [1,3]. Flat tops are often observed to develop, presumably by the filling in of a central depression built by caldera collapse and circumferential growth along ringfracture conduits [1,3,10]. Larger and older seamounts show a wide variety of morphologies, including both flat and domed tops [4], multiple summits and flank rift zones [S], and possible coalescing of adjacent volcanic centers [3]. Craters may form intermittently on the flat or bulging top as eruptions occur. It is possible that large seamounts are active over periods of millions of years [ll]. The presence of numerous seamounts near the ridge crest suggests that smaller features In the past twenty years much attention has been given to features which are obviously related to first-order plate-tectonic processes, such as mid-ocean ridges, fracture zones, and hot-spot volcanoes. Only recently have high-resolution mapping instruments become available to allow smaller features such as seamounts to be studied in detail (e.g. [l-S]). The advent of these technologies has allowed small-scale submarine volcanism and other second-order marine processes to be understood as well as more fundamental features. Seamounts are usually defined as roughly circular steep-sided features, with a conical or trun* Present address: Department of Earth Sciences, of Oxford, Parks Road, Oxford OX1 3PR, U.K. 0012-821X/88/$03.50 University 0 1988 Elsevier Science Publishers B.V. 138 can grow over time scales of hundreds of thousands of years (e.g. [1,3]). However, few seamounts have well-documented histories. Estimates for total abundance of seamounts vary over an order of magnitude from study to study [9,12-18]. Most of this uncertainty results from basing abundance estimates on map counts in regions of irregularly and often poorly sampled seafloor bathymetry; for example the region investigated in this study has areas of several hundred square kilometers with no bathymetric information at all. Also, when a seamount is located by only a single track of wide-beam data it is not known whether or not the true top of the seamount is observed, so sizes are frequently underestimated. Rather than counting features off maps to estimate abundances [12-15] an alternative approach is to treat seamounts identified on individual depth profiles as samples from a random distribution on the seafloor and to statistically derive areal distributions [16-18]. Statistical studies based on wide-beam echo-sounder records ]16,17] assumed that each seamount was a truncated cone with a fixed flatness and height-toradius ratio. These assumptions were necessary to relate the statistical distribution of apparent volcano heights on sonar records to the distribution of true volcano height abundances. These studies indicated that in the east Pacific seamounts cover 6% of the seafloor and comprise 0.4% of the total crustal volume [16]. Hence, seamount volcanism is a significant contributor to the oceanic crust. It is well known that large seamounts are more numerous on older seafloor (e.g. [11-14]). Smaller seamounts, however, do not seem to increase much in abundance with crustal age and may in fact decrease in number [13-17]. The increase in the total number of seamounts is easily explained by the existence of off-ridge volcanism, but the change in size distribution is harder to understand. Increasing plate thickness is often hypothesized as causing the size of seamounts produced to increase (e.g. [13,14]) but few mechanisms have been proposed. Menard [9] suggested the increase in average volcano size is simply due to continued growth as the seamount moves away from the ridge. Vogt [19] and Gorodnitskiy et al. [14] used isostatic mass balance to argue for seamount height increasing as the square-root of crustal age, proportional to lithospheric thickness. Increasing sediment thickness with age could cause burial of smaller seamounts in such a way that the observed ratio of large to small seamounts would increase [13]. Temporal variability in seamount production at mid-ocean ridges could also explain the observed abundance variations. There is much evidence for a mid-late Cretaceous episode of extensive intrusive igneous activity and increased seamount production, especially for larger seamounts [9,20]. This evidence consists of extensive 115-70 Ma sills and extrusive basalts in the central Pacific [20], flexural signatures for 90-120 My crust indicative of anomalously high ridge-crest volume [21,22], anomalous seamount abundances in this age range [17], and abnormally thick crust in Cretaceous volcanic plateaus. Other peaks in global magma productivity have been suggested as well, such as during the mid-Miocene [23] or Eocene [13], but these are not easily seen in seamount abundance variations (e.g. [17]). The proposed mechanisms for control of seamount locations and distributions generally fall into two classes: crustal variations that constrain magma migration paths, and source variations that control where magma is produced (e.g. mantle plumes). Many workers suggest the distribution of seamounts is non-random (e.g. [1,6,14,15]) and is controlled by features like fracture zones [1,24], overlapping spreading centers [5], and other mid-ocean ridge irregularities (e.g. [3,25]). However. such an observation is hard to quantify as correlations and lineations are often identifiable in any random areal distribution. Furthermore, many near-ridge seamounts cannot be obviously associated with any such feature. Many small seamounts are found near ridge crests so that magma processes associated with seafloor spreading are probably important for seamount production. Magnetic and geochemical evidence suggests that some small seamounts form away from the ridge crest [26], but the volcanoes studied were still on fairly young ( < 10 Ma) crust. Mechanisms for lithospheric control of off-ridge seamount locations are somewhat more enigmatic, although pre-existing fractures in the crust have been suggested as primary conduits [1,24,27]. Heavily fractured crust south of the Eltanin frac- 139 ture zone has been associated with anomalously high seamount abundances [17] possibly indicating that crustal fractures provide easy pathways for magma to ascend. At some scale it seems likely that the mantle thermal regime controls intraplate seamount production. Hot-spot traces are certainly well documented sources of seafloor volcanism but are usually associated with chains of ocean islands or large guyots. It is not clear that the concept of mantle plumes is relevant to the more numerous smaller seamounts. It is not the aim of this paper to discuss the origin of large volcanoes possibly of hotspot origin; rather, we wish to characterize the population of smaller seamounts that are probably not associated with isolated, individual upwellings. This study takes advantage of the high resolution of modem bottom-mapping technology (Sea Beam) to characterize many seamounts in one part of the Pacific. Most of the data (45667 km* of Sea Beam swath) is confined to a relatively homogeneous region of the crust distributed over several age ranges, allowing for good resolution of population variations with age. The coverage of highresolution bathymetry is well suited for constraining the gross properties of smaller seamounts (< 500 m in height) that conventional echo-sounders cannot resolve. Accurate estimation of basal diameters, heights, slopes, and volumes are made. It is almost always possible to tell if the summit of a seamount was ensonified by Sea Beam, unlike wide-beam sonar, so that population statistics can be generated without relying on an a priori assumed shape for the features. A primary goal of this study is to determine whether or not small seamounts form away from the ridge crest. 2. Observations Over 17,000 km of multi-narrow-beam sonar (Sea Beam) was recorded in the eastern Pacific on R/V “Robert D. Conrad” cruise RC2608 in 1985 (Fig. 1). Height resolution for Sea Beam is nominally about 10 m [28] although scatter between successive soundings can be somewhat greater. Systematic artifacts can be quite large, especially in regions of rough topography, but most are easy to identify since they produce distinctive patterns in the bathymetry [29]. To reduce the random fluctuations depths for each beam were averaged over several (usually 5) soundings during postprocessing. Averaging produced a set of depth values that were roughly evenly spaced every 100-200 m both along-track and across-track. After the data was collected, it was remerged with corrected navigation (Global Positioning System for 6-8 hours/day, transit satellite fixes, and dead reckoning between fixes), providing an approximate grid of ocean depth values 17,277 km long and averaging 2.6 km wide. Total swath width, approximately 75% of the water depth, varied from 2000 m near the ridge to 3000 m over older seafloor. Seamounts were located and their sizes were measured interactively with computer-generated swath charts (Fig. 2). The charts were created so that the ship track is straight and passes horizontally from left to right, with depths calculated by linearly interpolating between recorded Sea Beam depth values. Actual cross-track distances determined by the Sea Beam system were retained, as were the locations of data gaps, to minimize distortions and extrapolations. The diameter of each seamount was estimated by visually fitting a circle to its base, defined to be the contour where the feature becomes indistinguishable from the surrounding terrain. A height was calculated for all seamounts whose centers were crossed by the Sea Beam swath by subtracting the minimum water depth in the central half of the circle from a basal depth at a point picked on the perimeter. The radius and height comprise the basic size parameterization of each seamount. Diameters were estimated for 523 features, of which 382 had centers which fell on the swaths. Parameters for all the seamounts crossed are summarized in Table 1. Cross-sectional profiles were constructed for all seamounts whose centers were crossed by averaging the depth values recorded by Sea Beam in each of a series of concentric annuli around the center of the seamount. Volumes were estimated for the seamounts by integrating the cross-sections around the assumed center, assuming the seamounts possessed axial symmetry. Other variables were tabulated to describe the morphology of the seamount such as a top radius (for flattopped features) and existence of lineations, satellite cones, and craters. Since it is not always clear whether or not a feature is a seamount (i.e. a ,% ~":~ 160 ,-'~ o -.~,'<'° <;',:~- 160 ~,~ L 150 "+ C i P -: . . . . 150 .... P ::' 140 .~%3u ~ ~I . I~0 L~0 , ." ;.~ F o j p ~ G o S 140 r.z. ° \ I.~- , :~ i °. . _ - ~ . 120 120 ~ " + °' \ ) I10 ~ II0 o /o / ~ ' ° I00 . I00 . 30 ,o qg. 1. Bathymetric map for the ,study area. Ship-tracks used in the Sea Beam data set (dashed lines) are also shown. Pacific plate motion in the hot-spot frame of reference is hown by large one-headed arrows, and relative plate motion is shown by the two-headed arrows. Small squares are earthquake epicenters. 5C ,o I0 ~0 141 Fig. 2. Some examples of seamounts on the Sea Beam data. Color contours change every 40 m. Horizontal scale bar has tics every 5 km; horizontal and vertical scales are the same. The ship-track passes from left to right across the center of each figure. A. Large regular, conical seamount with a flat top, estimated height = 912 m and radius = 2973 m. B. Small conical seamount, height = 330 m, radius = 1316 m, and h / r = 0.251. C. Small seamount similar in area to B but much flatter, height = 231 m, radius = 1490 m, and h / r = 0.155. D. Seamount elongated parallel to the structural trends, estimated height = 475 m and radius = 1978 m. E. Irregular structure assumed to be volcanic, with approximated height = 502 m and radius = 2280 m. B and C illustrate typical variation in h/r for small seamounts. D and E are examples of non-conical morphologies. TABLE 1 Summary of study regions Region All data All data b On ridge 0 - 2 M a crust 5 - 1 0 M a crust 3 0 - 4 0 M a crust Track Area Number of seamounts: Total length (km) covered (km2) total identified center on swath volume (km3) 17277 17277 - 800 1508 4964 4526 45667 45667 - 2000 3330 12577 14055 523 324 0 45 143 129 382 233 0 35 95 99 1082.0 534.5 0 66.1 434.9 298.4 a For seamounts with centers on the Sea Beam swath. b Regular edifices only, assigned highest-quality rating. a Radius a Height a Seamounts min. (m) max. (m) min. (m) max. (m) with craters a 292 332 . 423 342 292 10790 9052 . . 5363 9052 10790 49 64 . 70 49 64 2394 2394 . 1382 2394 1325 40 35 14 11 4 142 volcanic edifice) levels of certainty were also attached to the identifications. Axially symmetric cones with simple, regular shape were assigned to the highest confidence level (e.g. Fig. 2A-C), while more irregular features or elongate features associated with seafloor lineations were given a lower confidence rating (e.g. Fig. 2D, E). Often the largest features were assigned low confidences because these features were rarely simple cones and it was difficult to tell if the center was crossed. A tabulation describing all the seamounts is available from the authors. The technique for fitting radii assumes all seamounts are circular in plan view, which was not always true. For elliptical features (Fig. 2D) or irregular features (Fig. 2E) we attempted to fit a circle to the base of the seamount such that it covered approximately the same area as the actual feature. The radius then should provide a robust estimate of the seamount size. Diameters were extrapolated for larger features that extend off the Sea Beam swath. Although the base picked for the seamount circumference is used in the height determination, the actual diameter has little influence on relative depth values (if slopes near the base are small) so the height and radius measurements have been treated as being independent. For most features the basal depth is fairly clear from the regional bathymetry and a reference height is easily established. Heights were only estimated for features whose centers clearly lie on the swath so that no extrapolations were necessary to define the shape of seamounts. Minimum water depth is then usually adequate to estimate height for most seamounts, which have a well-defined peak or are flat-topped. A problem exists in estimating height for irregular features (Fig. 2E), where it is difficult to be sure that the true summit was crossed and not just some flank peak. Sediment thicknesses, determined from the 3.5 kHz echo-sounder, were almost always less than 100 m and should not significantly affect the height distributions. 3. Height-to-radius ratios The homogeneity of the region surveyed allows systematic properties of the shapes of seamounts to be investigated. It has been suggested (e.g. height vs. radius 2000 1500 l A E 1000 500 .~,~%,~~ 0 ' 40'00 80'00 rad;us (m) Fig. 3. Scatter plot of height vs. base radius. Only the seamounts whose centers were crossed and which were designated regular, conical volcanoes are plotted. [10,16,30]) that the height-to-radius ratio is constant for most submarine volcanoes, implying that constructional processes are fairly uniform. For wide-beam parameter estimation, it is necessary to assume values for some of these relationships to relate apparent height observations to areal abundances [16,17]. In order to see if this parameter is useful for describing the shapes of small seamounts measurements were compared using only the 233 features described as regularly shaped seamounts and whose centers were crossed. Sample size is less important here than measurement quality since the inferences concern shapes, not abundances. Plotting height (h) against radius (r) for the volcanoes shows that there is a wide range in seamount shapes for the smaller features (also compare Fig. 2B and 2C), but for larger seamounts height increases roughly with radius (Fig. 3). The average value for h/r is 0.221 +_ 0.091 for 233 seamounts smaller than h = 2400 m, compared to a value of 0.214_+ 0.006 obtained by Smith [18] for 85 Pacific seamounts smaller than h = 3800 m. Smith's estimate of h/r is based on many features that are larger than those from our study and has less scatter. Comparing her results with ours suggests that larger seamounts are more regular in shape than small ones. There appears to be an upper limit on the h/r values (Fig. 3), with many measurements bunching up near the maximum observed slope. 143 4. Size distributions their notation to facilitate comparison with their results. All seamounts with a basal radius in the range r k + A r / 2 were counted to obtain the number n k of seamounts in radius interval k, where rk = (k - 1 / 2 ) A r for k = 1, 2 . . . . , N. The n k form a set of differential abundances. The cumulative abundance ~k of all seamounts with radius greater The variation in abundances of seamounts with height and radius was calculated by making histograms of the seamount size measurements, following the methodology of Jordan et al. [16] and Smith and Jordan [17]. We will attempt to follow ( XPONENTIAL Height range 100- lO00m Radius range 5 0 0 - 6 0 0 0 m 10 3 103 x. x b~ 102 102 ©.(3 0 bOO. 101 I00 O', o 10-1 i i I i 400 0,,(3 ,,x ",O "O 0 "ocoXXo 0 (30 I 0o 10-1 i i I o 800 ' 2000 (m) height .. o %0, %~ C~ "x 6 o ,~X~x O" O c "q. o o~-~. .x %, 101 "'~,x o-. • o "~.x o "~.x "© x'x O-.O O" "O ~ 40'00 radius ' 60'00 ' (m) POWER-LAW Height Radius range 500-6000m 100- lO00m range 10 3 10 3 "x-x 10 2 x~ x-. x -x 10 2 0'.0 °.% 0 o 101 Oo (3OO OO', 06"oo 101 oo © ©(1N~ 10 0 "Q o ~ ".0 '-OO I 0o 10-I I0-1 10 2 height 10 3 (m) 10 2 103 radius (m) 10 4 Fig. 4. Semi-log (top) and log-log (bottom) abundance histograms for height (left) and radius (right) measurements. The circles are the observed number of seamounts in each size interval, and " × " designates the cumulative number of all seamounts with sizes greater than the height or radius of the × . Only seamounts whose centers were crossed are used in all the abundance diagrams. The dashed lines show the best-fitting exponential (top) and power-law (bottom) population models. The size ranges used in the maximum-likelihood estimation are shown above each figure. 144 than rk - Ar/2 was counted from the differential abundances, and similar statistics were generated f o r t h e h e i g h t m e a s u r e m e n t s a t sizes h j + A h / 2 , j = 1, 2 . . . . . M . Size r a n g e s A r a n d A h w e r e t a k e n t o b e 250 m a n d 5 0 m , r e s p e c t i v e l y , f o r r a d i i f r o m 500 t o 6 0 0 0 m a n d h e i g h t s f r o m 100 t o 1000 m. Abundance histograms were generated for the 382 s e a m o u n t s w h o s e c e n t e r s w e r e c r o s s e d a n d f o r t h e s u b s e t o f 233 f e a t u r e s t h a t w e r e a s s i g n e d t h e h i g h e s t q u a l i t y level. O t h e r t h a n i n t o t a l n u m b e r s no obvious distinction was found between the distributions of the two groupings. Thus the larger set o f o b s e r v a t i o n s , w h i c h i n c l u d e s i r r e g u l a r l y shaped seamounts, was used in making comparisons. The abundance of seamounts increases drastic a l l y w i t h d e c r e a s i n g size in a m a n n e r t h a t h a s b e e n d e s c r i b e d as e i t h e r e x p o n e n t i a l o r p o w e r - l a w d e c a y [17]. T h e c u m u l a t i v e e x p o n e n t i a l tion has the form: distribu- p(r) =Uo e-~r w h e r e t h e p a r a m e t e r s v0 a n d a a r e ber of seamounts and the rate of crease with radius, respectively. power-law cumulative distribution, b y Pl a n d y, h a s t h e f o r m : u(r) = the total numabundance deSimilarly, the parameterized t,'lr "r Both descriptions predict far fewer large s e a m o u n t s t h a n s m a l l o n e s . T h e e x p o n e n t i a l distribution predicts a finite number of small seamounts while the power-law distribution has an infinite total number. In order to compare these two distribution models the differential and cumulative abundances are shown on both semi- TABLE 2 Population parameters for height data A. Exponential model: ~,(h) = u0e-~h Size range (m) fl ~ (kin 1) % a Number per 106 km 2 a ( × 1 0 - 3 km-2) h > 300 m All data All data All data 0-2 Ma 5-10 Ma 30-40 Ma 100-1000 100- 700 300-1000 100- 600 100- 800 100- 800 5,44+-0.27 5,76+-0.25 4,86 +-0.36 12.85 + 2.48 5.51 +-0.52 4.72 + 0.39 12.66 + 0.76 12.83 + 0.76 10.22 + 1.43 27.18+-8.62 10.71 + 1.32 9.83 + 1.11 2473 + 193 2278 __178 2379 + 233 575+-309 2052 + 328 2387 +- 336 55 __14 40 +- 10 79 + 22 0+- 1 43 + 21 88 +- 33 Smith and Jordan [17], all areas b Jordan et al. [16] ~ Batiza [13] 400-2500 300-1500 3.47 + 0.21 2.95 +-0.36 5.44+-0.65 3.96+-1.12 1920+- 116 1633+-416 117 169+- 17 207+-62 Region - h >1000 m B. Power-law model: ~,(h) = ulh - ~ a ul (my-2) " Number per h > 300 m h > 1000 m 0.68 + 0.02 0.56+-0.01 0.97 + 0.03 1.54 +-0.07 1.34-+0.14 2.48+-0.47 0.83+-0.04 0.64 +-0.02 2.08+0.17×10 7 1.36_+0.01×10 7 8.73 + 1.34 × 10- 7 1,80 + 0.75 × 10- 5 4A5 +2.70x 10 5 1,12+2.62x10 3 4.07 + 0.88 x 10- v 1.80 + 0.28 × 10 7 4391+ 375 5744_+ 376 3411 +_ 523 2724 + 1140 1987+1293 792_+1850 3600 + 774 4763 + 726 1944±162 2943_+193 1058 + 162 426 ± 178 396_+258 40+ 93 1326 + 800 2206 + 337 2.37 + 0.00 2.28+0.09x10 -3 3016+ Region Size range (m) Y All data All data All data All data 0-2 Ma 0-2 Ma 5-10 Ma 30-40 Ma 100-1000 100- 700 200- 800 300-1000 100- 450 150- 500 150 700 150- 700 Smith [18], all areas b 400-2500 a Errors are lo uncertainties from maximum-likelihood estimates. b Flatness ( r t / r ) = 0.3. c Flatness = 0.2. 91 10 6 km 2 a 173+- 5 145 TABLE 3 Population parameters for radius data A. Exponential model: p ( r ) = u0e-~r Region All data 0 - 2 Ma 5-10 Ma 30-40 Ma B. Power-law model: Region Number per 106 km 2 a Size range (m) a a ( k m - l) ()<10 -3 km - 2 ) 500-6000 500-1750 500-4000 500-4000 1.01 + 0.05 3.02 _+0.50 0.87 + 0.07 1.11 _+0.10 12.76 _+ 0.75 33.32 _+10.37 10.59 _+ 1.19 11.26 _+ 1.28 PO a r > 5000 m 2799 -+ 208 362 _+200 2858 _+392 2130 _+316 81-+19 0-+ 1 135_+46 43 _+20 u(r) = vlr -r Size range 3' a Pl ( m r - 2 ) a 0.71+0.02 1.35_+0.06 0.77_+0.02 2.53+0.44 0.55+0.02 0.81_+0.04 7.54_+ 0.87×10 7 5.37_+ 2.27)<10 5 10.5 _+ 1.5 ×10 -7 81.9 _+235.2 )<10 -3 3.36_+ 0.53)<10 -7 14.23_+ 3.63×10 7 (m) Alldata All data Alldata 0-2Ma 5-10Ma 30-40Ma r > 1500 m 500-6000 1000-7500 500-7500 750-2000 750-4000 750-4000 Number per 106 km 2 a r >1500m r > 5000 m 4253_+ 489 2854_+1205 3812_+ 531 736_+2111 5816_+ 926 3699_+ 943 1814_+208 565_+238 1513_+211 35_+100 2982_+475 1388_+354 a Errors are lo uncertainties from maximum-likelihood estimates. log plots (Fig. 4, top) and log-log plots (Fig. 4, bottom). Both abundance diagrams are consistent with a linear trend suggesting that both decay functions can describe the observed abundances. There is some indication on the abundance-radius diagrams that the semi-log plot is linear to smaller sizes than the log-log plot, implying that the exponential function has a wider range of validity. Smith and Jordan [17] found the exponential distribution described observed abundances far better than the power-law distribution over large size intervals. Parameters for the decay laws 0'0 and a or ul and 3') were fit to the measurements using a maximum-likelihood estimation procedure developed by Smith and Jordan [17]. Parameters for the exponential function are determined for seamount sizes from 500 to 6000 m in radius and from 100 to 1000 m in height (Tables 2 and 3). Calculations were made for a number of other size ranges to investigate the dependence of the parameters on the maximum and minimum sizes used. For all distribution curves (Fig. 4) the large-size limit of the observed cumulative distribution is set to the predicted value since the actual number of seamounts at larger sizes is poorly constrained by the observations. Therefore, the estimated abundance inherently matches the total observed num- ber of seamounts exactly [17] and the predicted and observed cumulative curves will always agree at the smallest and largest size range in which data is taken. The parameters are being fit to the incremental abundances, not the cumulative abundances, so that adjusting the cumulative curve in this way does not affect the parameter estimates. Because the counted incremental abundances are plotted out to larger sizes than were actually fit to the decay relations, some of the outlying points appear greater than the cumulative distributions allow. The total number of seamounts (e.g. h > 300 m in Table 2) predicted by both distributions roughly agrees with wide-beam estimates. For large seamounts (h > 1000 m in Table 2), however, the exponential distribution function under-predicts the wide-beam counts by a factor of 2 - 4 and the power-law distribution over-predicts the same counts by nearly an order of magnitude. Observed abundances at the large sizes are low (Fig. 4), so that the estimates for h > 1000 m are mostly based on extrapolation from smaller sizes. Seamount observations from wide-beam echo-sounders are plentiful to heights of 1000-2000 m and should provide more accurate abundance estimates for these sizes. The large differences between data sets may suggest that the slopes of the distribution 146 curves ( - / 3 or - "¢) change between the small-size seamounts sampled in this study and the larger volcanoes sampled by the wide-beam data set, for either distribution model. Alternatively, they could reflect differences in the regions sampled or some sort of measurement bias. Some differences between wide-beam and Sea Beam seamount counts were found by Smith and Jordan [17]. From the histograms the resolution limits of this study can be estimated. At the smallest size ranges (r < 500 m and h < 100 m), the number of seamounts is much lower than would be expected from the rate of abundance increase predicted by larger seamounts. In part the accuracy of the Sea Beam instrument (at best + 10 m in depth and + 100 m in location) limits the resolution, but more often the background "noise" level of topographic variation interferes with identification of small seamounts. Features such as linear ridges, abyssal hills, and relic ridge-crest structures frequently have heights of 100 m in the Pacific and tend to obscure identification of volcanic edifices of the same size or smaller. Existent topography and structure also significantly affect the morphology associated with seafloor volcanism so that simple conical seamounts are less common in more rugged regions. 5. Variations with crustal age The main advantage of studying seamount distribution with this data set is that the region sampled is fairly homogeneous with respect to tectonic history, although a range of ages are covered. Therefore, the distribution should be controlled by relatively few variables. As a first estimate of heterogeneity in the seamount population, the locations of all features whose centers were crossed are marked on a map with symbols scaled to the seamount diameters (Fig. 5, top). The portion of the East Pacific Rise in the study area and the major fracture zones crossed by the ship are shown for reference and indicate possible controls on population segmentation. The distribution of seamounts appears uneven but other than a near absence of volcanoes near the equator where there is a thick sediment layer there are no obvious large-scale variations parallel to the ridge. At smaller scales seamounts and seamount-free areas occur in clumps, and some of these clumps 1~$C°W O°S 150°~¢ 120°W 110°W 100°W o 10°S .'..~ ~,]e g 20°S I I GjI seamounts i 50°S [ 140°'h , i ' 30°W .20o,~i 110°W 100°7, iI I 1 C,% l / / i 4 i j y, :argo seamounts { r - ~-O00m}, ! 50°S ] Fig. 5. Map showing locations of seamounts whose centers were crossed, south of the equator. Top: all the seamounts observed. Bottom: all seamounts with radii measured larger than r = 4000 m. The circle size is scaled to the seamount diameter, exaggerated 5 times relative to map scale. Also shown are the East Pacific Rise north of Easter Island, and the major fracture zones. appear continuous from one line of data to the next, but it is difficult to be sure that these are not within the expected range of random fluctuations. By separating the large seamounts (r > 4000 m) from the rest some patterns emerge (Fig. 5). Only one large seamount is found at the ridge-crest while more than twice as many by area occur on the lines away from the ridge. By contrast, there seems to be very little difference in the number of smaller seamounts near and far from the East Pacific Rise. Away from the ridge the number of both large and small seamounts is roughly constant with seafloor age. A more quantitative evaluation of the changes in size distribution with crustal age is made by comparing abundance-size relations for subsets of the data (Fig. 6). Semi-log abundance histograms 147 All data. h:100 0-2 1 -j _- r.~ ~la. t-100-60C, m 10 3 % % 102 x. x o o 0.0 10 ~ o o'~ o ~ × Oo O..O O-© E c x 8o o "~.x "0. 0 O O [0 o 0 ado ~.x 0~ o 0o 0 L' c 0 10-1 10-1 , 400 5-10 height (m) height , 400 800 ~ 8 0 (rn) 3 0 - 4 0 Mo. h : 1 0 0 - 8 0 0 m Ma, h : 1 0 0 - 8 0 0 m 103 '~E 102 10 2 o o O0 101 E c x. x x.,x o O ~. x bO C~x"-. •" x'. x-. dO 100 o • o Sex. q o 10 ~ 10 -1 ~X ":~"~ "-~ x ( 3 ° o ° Q - Q D "" %~'~-x "-..o x~- ;~.~ do..o dO Odd- c 10 ° 0 "000 10 ~ 6 400 height 800 (rn) 4 0 8 0 height (m) Fig. 6. Semi-log abundance histograms for the different age regions. Exponential model fits are also shown for the entire data set, for the line on 0 - 2 M a crust, for the lines on 5 - 1 0 M a crust, and for the lines on 3 0 - 4 0 M a crust• All abundances are normalized by the area ensonified by Sea Beam in the sample for comparison. Symbols are the same as in Fig. 3. were generated and maximum-likelihood estimates of the exponential-decay population parameters were made for: (1) data just west of the East Pacific Rise between 9 °S and 22 ° S, with 560 km of track over 1.5-2 Ma crust and 1000 km over 0.3-0.7 Ma crust, (2) the three parallel lines and two short segments connecting them between l 1 5 ° W and 1 2 5 ° W on 5 - 1 0 Ma crust, and (3) the three lines and two connecting segments between 1 2 8 ° W and 1 3 8 ° W on 30-40 Ma crust. In order to compare different subsets, abundances in each histogram were normalized by the seafloor area sampled. Significant differences between normal- ized plots should directly correspond to differences in frequency-size relationships, since for any stationary population the abundances should scale directly to the area covered (so long as only seamounts whose centers were crossed are included). A direct comparison of the normalized distribution histograms for the oldest two age regions reveals an almost identical size distribution. At the largest sizes differences exist, but since only one or two seamounts are in any size range the sampling may not be significant. In other studies [12-14,17] it is observed that the number of very large 148 seamounts in the Pacific increases steadily with crustal age, but the Sea Beam data presented here show that below some moderate size (4000-6000 m in radius and 800-1000 m in height) there are no more seamounts on 5-10 Ma crust than on 30-40 Ma crust. Repeated tests with different size ranges showed that the minimum and maximum sizes listed in Tables 2 and 3 are approximately the largest ranges for which estimates were consistent with the observations, and are assumed to represent the resolution limits of the study. By contrast, the distribution of sizes for seamounts on the youngest seafloor falls off significantly faster than for seamounts on older crust (Fig. 6). The largest size resolved for seamounts on 0.5-2 Ma crust, about 400-500 m in height, is much smaller than for the other subsets because only one line was available instead of three. There is 4-5 times less area covered in this sample than in each of the older subsets (taking into account the increase in swath width with water depth) so the fits to the 0.5-2 Ma counts are somewhat poor, reflecting the lack of coverage. The differences between the youngest-age subset and the others is therefore marginally substantial. Twosigma error bars for the abundance estimates in Fig. 7 would not overlap between the 0.5-2 Ma sample and the other age samples. The accuracy of the large relative uncertainty estimates predicted for the young-age sample is difficult to assess, since the values are critically dependent on the assumed form of the probability distribution and the size range used. The inference of a low number of large seamounts on zero-age crust is also supported by the distribution maps discussed earlier (Fig. 5). An added constraint is provided by examining Sea Beam data directly along the East Pacific Rise. We examined Sea Beam bathymetry recorded on the PASCUA-2 cruise along 800 km of ridge-crest between 10°S and 25°S and did not find any features that could be considered seamounts on zero-age crust. Therefore, all of the seamounts observed on the 0 - 2 Ma sample must have formed away from the ridge, but not more that 20-50 km distant. The number of smallest (height < 250 m) seamounts appears to be 50-100% greater for the youngest age group than the others (Fig. 6), and is reflected in a larger value of the zero-value u0 oh seomounts 40,30 35O0 5000 2500 E 2000 o a 1500 c 1000 Smith ond Jordon: z~ This Study: [ ] 500 .El ' 1'0 2'0 3'0 4'0 5~0 6~0 5'0 6J0 oge (My) [orge s e o m o u n t s 400 55O 300 250 oE 200 o A 150 100 + 50 l:m i Jo 2'0 3'0 4'0 age (My) Fig. 7. Predicted abundances for all seamounts (h > 300 m) and for large seamounts (h > 1000 m), using the fits to the exponential distribution. Points with boxes are from the data presented in this study, and those with triangles are from the wide-beam study by Smith and Jordan [17]. Vertical error bars are 1o and horizontal bars show age ranges. Note change in vertical scale between the plots. (Tables 2 and 3). Some possible explanations for the apparent decrease in the number of small seamounts with a g e are insufficient near-ridge sampling, sampling bias due to increased background "noise" with age, and recent changes in near-ridge seamount production rates. Alternatively, the number of smallest seamounts may actually decrease with crustal age as clusters of small volcanoes grow and merge into large single seamounts. Sedimentary burial may cause a decrease in the number of small seamounts [13], but 149 the observed sediment thickness on all lines was generally less than 50-100 m. 6. Discussion The abundance estimates presented here predict that there are over 7000 seamounts with heights of 100 m or more and over 800 seamounts with heights greater than 500 m per 10 6 k m 2. These estimates are similar to those of previous statistical sampling studies [16,17] but are over an order of magnitude more than estimated from map counts (Table 2) [13]. The decrease in the number of seamounts with increasing size can be described as either an exponential decay (%e -~r) or a power-law decay (~,lr-V). Seamount counts seem to fit the exponential distribution function better at small sizes than the power-law, but this is only marginally apparent from our data (Fig. 4). Neither distribution, when fit to the populations counted here, predicts the abundances of large seamounts determined from wide-beam echo-sounder records (Table 2) [17]. These simple two-parameter distributions may be inadequate to describe the distribution of seamounts over large size ranges. The number of seamounts increases dramatically between the ridge-crest and 5-10 Ma crust but changes little after that (Fig. 7). The maps of seamount locations (Fig. 5) and the abundance histograms (Fig. 6) show that the increase in numbers is most rapid for small seamounts which do not show any significant change in abundance after 0.5-2 Ma. The number of larger seamounts increases until 5-10 Ma, and previous studies of more the extensive sets of wide-beam sonar records [17] indicate that the number of even larger features may increase on older crust. The numbers of small seamounts counted at 5-10 Ma and 30-40 Ma are essentially identical to those determined from wide-beam data in other parts of the Pacific (Fig. 7, top). The agreement is somewhat surprising since large along-strike regional variations in abundance have been observed [17]. It is possible that the observed age variations are due to temporal changes in magma production, and that there are less large seamounts being produced now than 10 Ma ago. There has been a reorganization of the Pacific-Nazca spreading system in the last 10 Ma [31] so that changes in seamount production would not be surprising. However, observations of similar abundance changes in other parts of the Pacific (Fig. 7, top) suggest that the change observed here is related to processes that depend predominantly on lithospheric age. We can speculate as to the origin of these seamounts which (unlike hot-spot volcanoes) are probably a byproduct of upwelling and accretion at a normal mid-ocean ridge. Partial melt produced by large-scale upwelling under the ridgecrest is likely to be the dominant source of magma for the seamounts observed here, because nearly all the growth in seamount population occurs near the ridge. Much of the basaltic melt forming at depth probably reaches the surface at the ridge crest since only - 0.4% of the total crustal volume is necessary to produce the volume of seamounts observed (Table 1). The heterogeneous petrology of near-ridge seamounts suggests that they do not tap directly the voluminous and well-mixed magma bodies just below the ridge crest but rather receive magma from deeper levels, where there is less mixing [2]. As melt ascends towards the ridge it is likely that small quantities of magma (not necessarily well mixed) would not reach the ridge axis but would be trapped beneath the lithosphere. Concentrations of trapped melt could and sometimes penetrate the lithosphere to form seamounts. These small volumes of melt, which would produce small seamounts, could ascend through the thin lithosphere near the ridge but probably are unable to penetrate older and thicker lithosphere because they would solidify before reaching the surface. The amount of available melt would decrease with time as the lithosphere moves farther from ascending magma beneath the ridge crest, and as remaining trapped melt reaches the surface or crystallizes in place. Production of small seamounts would stop as the lithosphere becomes too thick to permit passage of magma and as the volume of available melt decreases. Larger volumes of melt would be more likely than small volumes to pass through thick lithosphere without completely solidifying. Probably almost all large concentrations of melt formed near the ridge crest come out as new seafloor so that there are few sources for large volcanoes on very young crust (excluding hot-spot sources such as Iceland). Small melt pockets could coalesce to 150 b e c o m e b o d i e s b i g e n o u g h to f o r m l a r g e r s e a m o u n t s , b u t t h e m i g r a t i o n w o u l d t a k e time. T h u s , l a r g e r m a g m a sources m i g h t b e d i s t r i b u t e d f u r t h e r f r o m the ridge t h a n s m a l l sources. C o n t i n u e d g r o w t h at the s u r f a c e of s m a l l e r s e a m o u n t s m a y p r o d u c e larger o n e s if a d d i t i o n a l m e l t passes through lithosphere heated by earlier magma. Also, isostatic b a l a n c e suggests taller v o l c a n o e s can f o r m o n o l d e r crust as the m a g m a c o n d u i t s b e c o m e longer through thicker lithosphere. Continued prod u c t i o n of large s e a m o u n t s is likely d u e to a c o m b i n a t i o n o f these causes, a n d is f a v o r e d relative to p r o d u c t i o n o f s m a l l e r s e a m o u n t s p r i m a r i l y b e c a u s e of a g r e a t e r a b i l i t y of l a r g e r m a g m a b o d ies to m i g r a t e t h r o u g h the l i t h o s p h e r e a n d p o s s i b l y b e c a u s e o f an i n c r e a s i n g a v e r a g e size for m a g m a sources. Acknowledgements G e o f f r e y A b e r s g r a t e f u l l y a c k n o w l e d g e s support from a National Science Foundation graduate fellowship. T h i s s t u d y is b a s e d o n o b s e r v a t i o n s m a d e d u r i n g leg R C 2 6 0 8 of R / V " R o b e r t D. C o n r a d " w h i c h was f u n d e d b y N a t i o n a l S c i e n c e F o u n d a t i o n g r a n t s O C E - 8 4 1 8 3 7 1 to M I T a n d OCE-8418119 to C o l u m b i a University. Tom J o r d a n a n d D e b b i e S m i t h s p e n t m u c h t i m e disc u s s i n g their w o r k a n d p r o v i d i n g advice. W e w o u l d like to t h a n k t h e N E C O R Sea B e a m p e r s o n n e l o n this leg for their efforts: J o y c e Miller, J o h n F r e i tag, a n d N i c k Kallas. J o h n M a d s e n k i n d l y let us use s o m e p r o g r a m s he h a d w r i t t e n to d i s p l a y Sea B e a m s w a t h profiles, a n d J e f f F o x p r o v i d e d a t a p e o f P A S C U A - 2 Sea B e a m r e c o r d s a l o n g the ridgecrest. A d d i t i o n a l s u p p o r t for this analysis c a m e from Office of Naval Research contract N001486-K-0325. References 1 R. 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