Abstract. We present a simple time-progressive model for the Hawaiian Island chain bathy-metry and the associated flexural response of the elastic oceanic lithosphere. The model is used to study the vertical tectonic history of Cross seamount, a Cretaceous guyot brought close to the Hawaiian hot spot by plate motion. Geological evidence indicates that Cross was truncated at sea level, but its flat top is presently 400 m below sea level. Our reconstruction suggests the seamount was elevated on the Hawaiian Swell and truncated about 3.2 m.y. ago. The post-truncation subsidence is attributed to the flexural moat that developed around the growing Hawaiian Islands. Flexural isostatic adjustment explains the current depth of Cross seamount provided the elastic plate thickness is in the 30-35 km range.
Introduction
Cross seamount is a Cretaceous guyot, situated only 250 km west of the island of Hawaii, in the Central Pacific Ocean. Plate motion has brought the ~85 m.y. old seamount close to the Hawaiian hot spot. The seamount now sits on the inner flank of the bathymetric arch which surrounds the Hawaiian Island chain. The formation of the Hawaiian swell apparently uplifted the seamount to sea level within the last few million years, resulting in truncation of the seamount summit followed by flexurally controlled subsidence which eventually drowned the seamount. Thus Cross seamount has acted as a geologic "dipstick," meaning that its elevation reflects the vertical motion. We present geological arguments that the summit of the Cretaceous seamount was uplifted to sea level and truncated as plate motion brought it onto the Hawaiian swell. Geological observations on the timing of the uplift and subsidence are summarized, and constraints are placed on the amount of uplift and subsidence.
A simple time-progressive model for the evolution of the Hawaiian Islands and the associated flexural compensation were used to estimate the plate thickness and flexural deformation and to estimate the time-dependent vertical tectonism affecting Cross. Thermal rejuvenation and/or plume buoyancy have caused the seafloor to shallow by as much as 1 km in the vicinity of the hot spot [Detrick and Crough, 1978; Olson, 1990]. The uplift history along a transect through Cross seamount, parallel to plate motion, was approximated by a cosine ramp, between 3 and 8 Ma. The vertical motion, which is a combination of swell uplift and subsequent flexural deformation, was calculated for a variety of elastic plate thicknesses. According to these models, uplift took place between 3 and 8 Ma. Subsequently, subsidence of nearly 400 m has taken place during the last 2.8 m.y. We show that the geological observations and results from previous flexural modeling are consistent with the flexural models presented here.
Background
Cross seamount is one of 38 seamounts situated southwest of the Hawaiian Islands Chain. This seamount group, extending from 153W to 164W, between 16 and 22N, consists of (1) several widely dispersed seamounts south of the island of Hawaii, (2) a cluster of seamounts south of Oahu, Molokai and Maui, and (3) isolated seamounts south of Nihoa and Necker Island (Figure 1). Cross lies on the northern arm of a V-shaped ridge, approximately 250 km south of Oahu. Cross seamount sits on the inner slope between the Hawaiian Arch, a bathymetric arch surrounding the island of Hawaii, and the Hawaiian Deep, a trough which lies inward of the flexural arch. The Hawaiian Deep is well developed on the northeast of the island of Hawaii. Southwest of the island chain, the trough is poorly preserved, since most of the trough is filled with material shed from the island as massive land slides and ash layers derived from the active Hawaiian volcanoes [Moore et al., 1989].
Figure 1. Location map showing Cross and other seamounts in one of the Geologist Seamounts clusters west of the Hawaiian Seamount Group. Despite their proximity, the two seamount groups are of vastly different ages. Radiometric dating suggests a Cretaceous age for the Geologist Seamounts. Volcanoes on the Hawaiian Islands Chain from Hawaii through Kauai range in age from 0 to 5 Ma. The contours represent depth in kilometers.
Radiometric dating of Cross seamount is based upon K/Ar studies by Dymond and Windom [1968] and 40Ar/39Ar determinations reported by Sager and Pringle [1987]. Sager and Pringle [1987] combined the results of previous studies and reported a weighted average age of 84.6 ± 3.8 Ma on trachyte and hawaiite samples. The seafloor northwest of Cross seamount was recently dated as Cretaceous with an age of 110 ± 2 Ma based upon fossils overlying basaltic basement [Waggoner, 1993]. Manganese crust dredged from Cross contain Santonian or lower Campanian nannofossils (D. Bukry, personal communication, 1985).
Seismic reflection profiles across several seamounts in this seamount cluster indicate that the seamounts generally are characterized by rough topography and an absence of sediments. Cross seamount and one seamount nearer the Hawaiian Islands are exceptions. These seamounts have flat summits. Side scan sonar images of the other seamounts in this cluster confirm the rough topography and general lack of low reflectivity sediments [Kroenke and Campbell, 1985].
A side scan sonar survey of Cross seamount was completed using the SeaMARC II mapping system; the side scan image is reproduced in a separate publication (Keating, B. H., Evidence for uplift and truncation of Cross seamount in response to Hawaiian hot spot lithospheric deformation, submitted to Geol. Soc. Am. Bull., 1993). The bathymetric map produced in that survey was merged with a Preusag map of Cross seamount made using a Seabeam mapping system. A three-dimensional view based upon the merged bathymetric data of Cross seamount is illustrated in Figure 2. The bathymetric surveys indicate that Cross seamount has a flattened summit with low mounds and small pinnacles that can be identified in the side scan images. Because (1) the observed mounds display the distinctive mound or bulbous shape commonly observed for subaerial trachyte bodies and (2) most of the summit rocks radiogenically dated are trachytes, we suggest the mounds are associated with trachyte bodies such as those sampled by dredging [Dymond and Windom, 1968; Sager and Pringle, 1987]. We correlate the mounds observed in the side scan images with the trachyte mounds observed on other Pacific islands. Submersible observations indicate the pinnacles are erosional remnants of heavily jointed dike rock (K. Kelly, personal communications, 1992).
Figure 2. Contour map and three-dimensional relief map of Cross Seamount derived from available Seabeam and SeaMARC II data. The flat top indicates truncation at sea level. Contour interval is 0.25 km.
The side scan sonar images show that low-reflectivity material blankets the seamount summit and flanks. Submersible studies prove that carbonate debris buries approximately 70% of the flanks of the seamount to depths of 2000 m. Below 2000 m the flanks are characterized by high backscatter and high acoustic reflectivity, interpreted to be volcanics, lava flows, and debris flows. Acoustic profiles across the summit of Cross seamount indicate that the sediment thickness varies over the summit of the seamount. A layered acoustic unit 75 m thick is present. Sampling of the sediments using a small piston corer on the Pisces submersible yielded carbonate sands. Micropaleontologic study of these sediments revealed shallow bank deposits containing young microfossils. No Cretaceous fossils are present in the sediment sample (J. Resig, personal communications, 1992).
Geological Constraints
The summit of Cross seamount is truncated. In order to estimate the degree of truncation, we have graphically estimated the preerosion height of the seamount by projecting the truncated cone upward. We have accomplished this by projecting a cross section of the adjacent seamount to the west, Swordfish (plotted to the same scale), onto a bathymetric cross section of Cross seamount, using the bathymetry of Wilde et al. [1980]. This graphic reconstruction (Figure 3) shows the projected summit of Cross seamount approximately 300 m higher than the current summit. Thus an estimate of the minimum uplift of the summit of Cross seamount is 300 m.
Figure 3. Bathymetric model (contour map and perspective view) showing the current bathymetry of Swordfish and Cross seamounts. Contour interval is 0.25 km. This model is based upon the regional bathymetry published by Wilde et al. [1980] and the new bathymetric database for Cross presented in Figure 2. Above, a graphical reconstruction of the preerosional morphology of Cross seamount based on the projection of the summit shape of the nearest seamount to the west (Swordfish) onto the truncated summit of Cross seamount. The reconstruction implies a truncation of approximately 300 m.
The seamounts adjacent to Cross have irregular summits and lack sediment caps. On the basis of the lack of evidence of erosion and truncation at sea level and the lack of sediment caps, we conclude these seamounts did not reach sea level. The summit of Washington seamount (the adjacent seamount to the east) rises to a depth of ~900 m, whereas the flattened summit of Cross seamount reaches a depth of approximately 400 m; the current difference in height is approximately 500 m. Assuming that sea level remained constant, these considerations suggest that Cross seamount was at least 400 m above its current depth but not more than 900 m to reach sea level, otherwise the summits of adjacent seamounts would also be truncated. Therefore the uplift and truncation of Cross at sea level was apparently followed by 400-900 m of subsidence.
Flexural Modeling
In order to model the tectonic uplift of Cross seamount, all available ship-survey bathymetry and land topography were compiled. The database was sampled on a uniform (5 arc min by 5 arc min) grid employing a continuous curvature splines in tension algorithm [Smith and Wessel, 1990], using the U.S. Navy's SYNBABS data set [Van Wyckhouse, 1973] to constrain areas with no ship surveys. Figure 4 is a perspective view of the gridded topography and bathymetry, with land areas shown in white. In the foreground is the Geologists Seamount Group (also called the South West Hawaii Group), which includes Cross seamount.
Figure 4. Perspective view of the gridded bathymetry and topography data for the Hawaiian Islands based upon ship measurements and the SYNBAPS data set (see text). The growth of the volcanic ridge from left to right in this illustration depressed the oceanic lithosphere and caused subsidence of Cross seamount following its truncation at sea level. Contour interval is 1 km.
In most flexural modeling cases the topography data, above a base level, are used directly to load the elastic plate, and the flexural deformation is calculated [Watts and ten Brink, 1989]. The Pacific plate is moving Cross seamount at 9 cm/yr to the WNW with respect to the hot spot. Because Cross seamount experienced a time-dependent vertical tectonism resulting from flexural deformation caused by the hot spot volcanism, it is necessary to examine the Hawaiian Islands as a function of time. Simply taking the final load (i.e., the current shape) will not reveal anything about the time history of uplift and subsidence. The complexity of seamount formation and subsequent modification by erosion and landslides makes this a formidable problem. Fortunately, the thick elastic lithosphere acts as a strong low-pass filter, making the details of volcanic construction irrelevant to the flexure problem. Therefore we need only attempt to make a first-order model describing the evolution of the Hawaiian seamount chain.
Observational [Walker, 1988] and theoretical [Lacey et al., 1981] studies suggest that volcanoes tend to build up and outward. To model this growth, we approximated the shape of a volcano at different stages by a series of cones. For simplicity, we require the growth rate of the volcano to be constant during its active life, which results in constant volume conical sheets that decrease in thickness but increase in radius (Figure 5a). To simplify the flexural calculations further, we approximate the conical sheets by discs of the same volume and thickness. The stacked discs represent a loading history that is equivalent to that of the conical sheets (Figure 5b). The advantage here is that the axisymmetrical deflection of an elastic plate of thickness Te in response to a disc load of radius r0 and height h can be obtained analytically using Kelvin-Bessel functions [Lambeck and Nakiboglu, 1980] and is given by
The constants a-d are determined to be
where the primes denote differentiation with respect to r. Other symbols are defined in Table 1. The flexural parameter g is given by
The deformation of the seafloor caused by one volcano is then given by the sum of the deformation caused by all the discs that make up the volcano.
Figure 5. (a) Simple conical model for volcano construction. Assuming a constant volume-rate source, the volcano will grow up and out and produce conical sheets of equal volume. (b) The pressure on the base caused by the sheets can be approximated by a disk of the same volume and radius. Thus the loading history can be represented by a stack of disks with increasing radii and decreasing thickness.
The density of the cones was set to 2.8 Mg/m3, as suggested by other flexural studies [Watts and ten Brink, 1989] and actual density measurements [Daly et al., 1966; Hyndman et al., 1979]. The infill density was set equal to the load density which makes the flexural calculations particularly simple as only the seamounts' height (h) above the base level prior to subsidence is required [Lambeck and Nakiboglu, 1980]. While the infill density used is somewhat high, the load density may be slightly underestimated (gravity modeling of seamounts often include dense (2.9 Mg/m3) vertical feeder pipes or volcanic conduits [Kellogg et al., 1987]). Taken together, we estimate the error in deflection amplitude and wavelength caused by uncertainties in density structure to be less than 10%.
Using the gridded topography as constraints, we approximated the Hawaiian seamount chain from Nihoa to Loihi by 15 major and 10 minor cones. The radii and heights of the cones were chosen such that the sum of all the cones was as close to the observed shape and volume as possible. The cone model presented here comes within 5% of the observed volume shown in Figure 4. To provide a self-consistent model, we assigned to each individual conical volcano an age given by its current distance from the hot spot divided by the plate velocity. We allowed for a finite construction time by letting each volcano begin forming 0.5 m.y. before its assigned age and terminate 0.5 m.y. after, effectively giving most volcanoes a life span of 1 m.y. The flexural calculations were run from 9 Ma to present in steps of 0.2 m.y. For each stage the load geometry was updated and the elastic deformation was recalculated. Figure 6 shows the geometry of the load at five stages, each 1 m.y. apart. The shape of the final (present) stage is visually very similar to the real data (Figure 4) and within 5% of the observed volume. The bull's-eye in Figure 6 marks the location of Cross seamount where we monitored the vertical motion as a function of time. In this reference frame the plate is fixed while the hotspot is moving to the ESE. However, prior to the flexural deformation, Cross seamount will experience uplift by "riding" the Hawaiian hot spot swell.
Figure 6. A simple time-progressive model for the construction of the Hawaiian Islands. We approximated the present topography from the locations of known volcanoes and the topography shown in Figure 4 by 15 major and 10 minor cones. Each cone was assigned an age according to its distance from the hotspot and given a growing period of 1 m.y. Shown here are the model topography at five stages in the evolution of the chain. The final stage (at 0 Ma) is visually very similar to Figure 4 and comes within 5% of the correct volume. Contour interval is 1 km.
Thermal rejuvenation [Detrick and Crough, 1978] and/or plume head buoyancy [Olson, 1990] have caused the seafloor to shallow by as much as 1 km in the vicinity of the hot spot. We approximated this uplift history by analyzing the present bathymetry variation along a transect through Cross seamount, parallel to the direction of plate motion. The uplift at this distance from the center of the swell was then approximated by a cosine ramp between 7.8 Ma and 2.8 Ma. Our approach therefore implicitly assumes that the swell has been a steady state phenomenon over this time interval. The validity of this assumption is difficult to address. There is no clear evidence that the swell was any smaller at 3.2 Ma when Cross reached its highest point; observations suggest instead that the plume buoyancy flux (and hence swell height) was probably less at 25 Ma [Davies, 1992]. As a consequence of the ascent the base of Cross seamount was elevated from -5500 m to -4700 m for a total of 800 m uplift. The total absolute vertical motion is therefore the sum of the swell uplift and subsequent flexural deformation.
Figure 7. Time-dependent flexure of an elastic lithosphere calculated using the time-dependent loading model presented in Figure 6. The vertical deflection at Cross seamount was monitored for several choices of elastic thickness Te. In addition, we accounted for the hotspot swell uplift by approximating its effect based on the present swell shape (see text). Assuming constant sea level, Cross was truncated at 3.2 Ma and has subsided ~400 m since then. This subsidence is consistent with a 35-km-thick elastic plate.
This combined signal is plotted in Figure 7 for a variety of elastic plate thicknesses ranging from 25 km to 45 km. Assuming Cross seamount was truncated at sea level at the time the combined swell and flexural signal was at a maximum, we find that a relative subsidence of 375 m is predicted by the 35-km-thick elastic plate. According to this model, the truncation took place at 3.2 Ma. Since then, the truncated top of Cross seamount has subsided approximately 400 m from flexural deformation. The posttruncation subsidence for the entire area is outlined in Figure 8. We note that the general pattern of subsidence compares well with that shown by Moore et al. [1990] (their Figure 1), although the times frames are somewhat different. Furthermore, it is evident from the predictions in Figure 8 that Washington seamount may have subsided as much as 200 m more than Cross, suggesting that the depth difference between the two seamounts after uplift but prior to subsidence was probably closer to 300 m. Thus the upper limit on subsidence from geological constraints (900 m) is therefore probably too high.
Figure 8. Plan view of the flexural subsidence (in meters) experienced in the area since the time of truncation (3.2 Ma) assuming Te = 35 km. The location of Cross seamount is indicated by the bull's-eye.
Discussion
While the model outlined here is capable of explaining the observed subsidence at Cross seamount, there are several factors that may influence our results. The most obvious is our assumption that sea level at 3.2 Ma was the same as today's level; in fact, it could have been lower than present by maybe as much as 100 m [Haq et al., 1987]. This uncertainty translates into a slightly thinner plate thickness (32 km for 275 m subsidence).
We have attempted to account for swell uplift, but we have not tried to approximate any thermal subsidence as Cross seamount is carried away from the hot spot. Crough [1978] studied the depth anomalies associated with hot spot swells and found that their anomalous depths could be explained if the oceanic lithosphere had been thermally reset to an age of 25 Ma. This would imply a thermal subsidence of about 100 m since 2.8 Ma (when Cross was at the shallowest point of the swell). However, the exact shape of the swell is more complicated. A recent analysis of the swell shape [Wessel, 1993a] shows that the swell remains shallow until it approaches the Murray Fracture Zone, after which it falls off rapidly. A more appropriate thermal reset age for the youngest part of the chain may be 45 Ma, yielding 60 m thermal subsidence as a maximum value. The uncertainties related to sea level changes and thermal subsidence are of comparable magnitude; the maximum combined effect is thus probably less than 200 m. In this extreme case, we find that only 200 m of flexural deformation may be necessary to accommodate geological observations. Even this endmember value requires only a slightly thinner elastic plate (Te = 30 km), testifying to the robustness of the present modeling technique.
In our model, the age of the individual volcanoes depends only on distance from the hot spot. Age information exists for all the volcanoes in question and could be used to improve the timing of construction. There may also be evidence for a somewhat shorter (600 k.y. versus 1 m.y.) average construction time for the shield volcanoes [Moore and Clague, 1992]. The slightly different ages and durations will lead to a modified time history but would not affect the values of D in Figure 7 significantly (D corresponds to an elastic plate thickness of 30 km.) The sea level and thermal subsidence uncertainties fall in the bracketed area in Figure 7, indicating that the elastic thickness may be in the 30-35 km range. The best fitting elastic thickness (Te = 30-35 km) is in the range (25-40 km) of estimates based on flexural calculation with data constraints of a different nature [McNutt and Shure, 1986; Watts and ten Brink, 1989; Wessel, 1993b]. Most of these studies determined Te indirectly by comparing observed gravity anomalies to predictions based on the flexural modeling. It is reassuring that the new approach presented here gives comparable results, with low internal uncertainty.
The cone model was designed after the present topography. This approach neglects the effects of erosion and landslides that are known to have taken place [Moore et al., 1989]. The exact effect of our simplification is difficult to assess, but we believe it to be only a second-order perturbation to the vertical history curve in Figure 7. Much of the uncertainty related to sea level change and thermal subsidence could be eliminated if detailed studies of other flat-topped Cretaceous seamounts surrounding the Hawaiian chain were made. Such data could arguably provide the strongest constraints on the thermomechanical properties of the oceanic lithosphere in this area.
Acknowledgments. We thank J. L. Davis, J. N. Kellogg, and J. G. Moore for thorough and helpful reviews. This is School of Ocean and Earth Science and Technology contribution 3472.
References
Crough, S. T., Thermal origin of mid-plate hot-spot swells, Geophys. J. R. Astron. Soc., 55, 451-469, 1978.
Daly, R. A., G. E. Manger, and S. P. Clark, Density of rocks, Geol. Soc. Am. Bull., 97, 19-40, 1966.
Davies, G. F., Temporal variation of the Hawaiian plume flux, Earth Planet. Sci. Lett., 113, 277-286, 1992.
Detrick, R. S., and S. T. Crough, Island subsidence, hot spots, and lithospheric thinning, J. Geophys. Res., 83, 1236-1244, 1978.
Dymond, J., and H. L. Windom, Cretaceous K-Ar ages from Pacific ocean seamounts, Earth Planet. Sci. Lett., 4, 47-52, 1968.
Haq, B. U., J. Hardenbol, and P. R. Vail, Chronology of fluctuating sea levels since the Triassic, Science, 235, 1156-1167, 1987.
Hyndman, R. D., N. I. Christensen, and M. J. Drury, Velocities, densities, electrical resistivities, porosities and thermal conductivities of core samples from boreholes in the islands of Bermuda and the Azores, in Deep Drilling Results in the Atlantic Ocean: Oceanic Crust, Maurice Ewing Ser., vol. 2, edited by M. Talwani, C. G. Harrison, and D. E. Hayes, pp. 94-112, AGU, Washington, D. C., 1979.
Kellogg, J. N., B. S. Wedgeworth, and J. Freymueller, Isostatic compensation and conduit structures of western Pacific seamounts: Results of three-dimensional gravity modeling, in Seamounts, Islands, and Atolls, Geophys. Monogr. Ser., vol. 43, edited by B. H. Keating, P. Fryer, R. Batiza, and G. W. Boehlert, pp. 85-96, AGU, Washington, D. C., 1987.
Kroenke, L. W., and F. Campbell, Resource assessment of cobalt rich ferromanganese crusts within the Hawaiian exclusive economic zone, U.S. Dep. of the Inter., Washington, D. C., 1985.
Lacey, A., J. R. Ockendon, and D. L. Turcotte, On the geometrical form of volcanoes, Earth Planet. Sci. Lett., 54, 139-143, 1981.
Lambeck, K., and S. M. Nakiboglu, Seamount loading and stress in the ocean lithosphere, J. Geophys. Res., 85, 6403-6418, 1980.
McNutt, M. K., and L. Shure, Estimating the compensation depth of the Hawaiian swell with linear filters, J. Geophys. Res., 91, 13,915-13,923, 1986.
Moore, J. G., and D. A. Clague, Volcano growth and evolution of the island of Hawaii, Geol. Soc. Am. Bull., 104, 1471-1484, 1992.
Moore, J. G., D. A. Clague, R. T. Holcomb, P. W. Lipman, W. R. Normark, and M. E. Torresan, Prodigious submarine landslides on the Hawaiian ridge, J. Geophys. Res., 94, 17,465-17,484, 1989.
Moore, J. G., D. A. Clague, K. R. Ludwig, and R. K. Mark, Subsidence and volcanism of the Haleakala Ridge, J. Volcanol. Geotherm. Res., 42, 273-284, 1990.
Olson, P., Hot spots, swells and mantle plumes, in Magma Transport and Storage, edited by M. P. Ryan, pp. 33-51, John Wiley, New York, 1990.
Sager, W. W., and M. S. Pringle, Paleomagnetic Constraints on the Origin and Evolution of the Musicians and South Hawaiian Seamounts, Central Pacific Ocean, in Seamounts, Islands, and Atolls, Geophys. Monogr. Ser., vol. 43, edited by B. H. Keating, P. Fryer, R. Batiza, and G. W. Boehlert, pp. 133-162, AGU, Washington, D. C., 1987.
Smith, W. H. F., and P. Wessel, Gridding with continous curvature splines in tension, Geophysics, 55, 293-305, 1990.
Van Wyckhouse, R., SYNBAPS, Tech. Rep. TR-233, U.S. Natl. Oceanogr. Office, Stennis Space Center, Miss., 1973.
Waggoner, D. G., The age and alteration of central Pacific oceanic crust near Hawaii, Site 843, Proc. Ocean Drill. Program, in press, 1993.
Walker, G. P. L., "Coherent intrusion complexes" in large basaltic volcanoes - A new structural model, in Essays on Magmas and Other Earth Fluids, edited by K. G. Cox and P. Baker, J. Volcanol. Geotherm. Res., 50, 41-54, 1988.
Watts, A. B., and U. S. ten Brink, Crustal structure, flexure, and subsidence history of the Hawaiian islands, J. Geophys. Res., 94, 10,473-10,500, 1989.
Wessel, P., Observational constraints on models of the Hawaiian hot spot swell, J. Geophys. Res., 98, 16,095-16,104, 1993a.
Wessel, P., A reexamination of the flexural deformation beneath the Hawaiian islands, J. Geophys. Res., 98, 12,177-12,190, 1993b.
Wilde, P., T. E. Chase, W. R. Normark, J. A. Thomas, and J. D. Young, Oceanographic Data off Southern Hawaiian Islands, University of California, Berkeley, 1980.