Abstract
Several lines of evidence imply that hotspots are embedded within shallow, kinematically rigid layers in the outer mesosphere. The existence of such “mesoplates” in motion relative to one another is enhanced with recognition of stationarity of the Eastern Caribbean island arc relative to the Atlantic-Indian hotspot frame (Tristan mesoplate) over the past ~70 m.y. In addition, inception of volcanism along the East African Rift over the past ~60 m.y. occurred at the same north-to-south rate as African motion in the Tristan frame. Embedding of hotspots in mesoplates is consistent with a top-down origin of the “plumes” inferred to produce hotspots, especially in light of recent tomographic evidence for variable depth of origin of plumes.
Introduction
What is the kinematic and dynamic significance of plate reconstruction models relative to hotspots? This question is a bit different from those more commonly expressed: Do plumes exist? Are plumes responsible for hotspots? Do hotspots form an “absolute” reference frame? If not plumes, then what mechanism is responsible for hotspots?
Plate reconstructions are key tools in tectonic and paleogeographic analysis of the Earth. The significance of relative reconstructions of lithospheric plates is intuitively clear on several levels. The constraints on the reconstructions (magnetic isochrons and fracture zone offsets) and the reconstructions themselves provide discrete “snapshots” of plate positions and, by interpolation, insight into regional and global plate kinematics and the evolution of the boundaries. Reconstructions and derivative kinematics have further implications for, e.g., inferred paleooceanography, continental margin basin evolution, and development of mountain belts. And, as a matter of geoscientific faith, reconstructions and derivative kinematics manifest the driving mechanism of plate tectonics: mantle convection.
The meaning of plate reconstructions relative to hotspots is less clear. Part of the reason for this uncertainty is the coupling of the hypothesis of “fixed” hotspots with the more fundamental “plume” hypothesis for their origin. Additionally, there is doubt concerning whether hotspots do, indeed, form a fixed frame of reference: fixed relative to one another, fixed relative to the geomagnetic poles, and/or fixed relative to the Earth’s spin axis. Finally, should any sort of reference frame (or frames) defined by hotspots be demonstrable, its significance could still be uncertain.
At present, there are, indeed, three apparent hotspot reference frames defined by plate reconstructions over the past 130 to 150 m.y. Pilger (2003) has termed these reference frames the Tristan, Hawaiian, and Icelandic mesoplates (Fig. 1). For much of the Atlantic and Indian Oceans (underlain by the Tristan mesoplate), Müller et al. [1993] have produced a remarkable model that “fits” the physiographic expression of inferred hotspot traces quite well, although questions regarding the dating of the traces have been raised. Several similar models (to each other) of Pacific plate motion relative to underlying hotspots (within the Hawaiian mesoplate) have been advanced [e.g., in Richards and Van der Hilst., 2000], again fitting the inferred traces, but also with some age uncertainty. Relative plate reconstructions imply that the two sets of hotspots are incompatible and form largely independent reference frames [e.g. Raymond et al., 2000; Gaina et al., 2000]. The third hotspot reference frame (Icelandic mesoplate) is less well constrained in its motion (Norton, 2000) due to recognition of only one significant hotspot trace (Iceland). Paleomagnetic data also imply that the hotspot reference frames are independent of the geomagnetic poles [e.g., Tarduno et al., 1999; Duncan and Richards, 1991].
Figure 1. Mesoplate boundaries (dotted), modified from Pilger (2003a, b).
As a prerequisite to addressing the significance of mesoplates, the relation of hotspots to the surrounding mantle needs to be constrained. That is, do hotspots “move” relative to adjacent “normal” mantle, or are they embedded? These questions are largely overlooked in the ongoing debate concerning the origin of hotspots and the potential existence of deep mantle plumes. Yet, they are critical at least insofar as mesoplates have any significance at all. This contribution, building upon previous work (Pilger, 2003a, b), examines two lines of evidence that support the idea that hotspots are indeed embedded in the mesosphere, within a distinct mesoplate. Hotspot Reconstructions
Before considering the new evidence, a basic assumption needs to be examined. How good are plate-hotspot reconstruction models? Unfortunately, the answer to this question is not easily achieved.
For the Atlantic-Indian Oceans Müller et al.’s [1993] reconstruction parameters and hotspot locations have been judged by several workers as remarkable. Their physiographic fit to inferred hotspot traces, especially Kerguelen-Ninetyeast, Reunion-Chagos-Laccadive, Tasman, Great Meteor-New England-White Mountain, and Tristan-Walvis-Rio Grande is a significant advance over previous models. However, close examination of predicted and analytical isotopic ages produces several apparent discrepancies [e.g., Pilger, 2003a]. Given a plate moving over a hotspot, measured volcanic ages from the surface of the plate should provide a minimum estimate of the age of encounter of a point on the plate with the hotspot, to allowing penetration and extrusion, prolonged volcanism from a residual magma chamber, and cooling. Thus ages younger than the predicted encounter age are to be expected. Conversely, measured ages older than predicted could imply some defect in the reconstruction model or “fixity” of the hotspot.
“Too old” dates are apparent from Ninetyeast, Chagos, and New England traces when compared with Müller et al.’s model [Pilger, 2003a]. Baksi [1999] has reexamined the analytical data for many of the Ar/Ar dates from these traces, has rejected some, and recalculated others. He thereby concluded that the plate-hotspot model is inapplicable, on the assumption that most of the dates are questionable. However, when only his filtered and recalculated dates are considered, very few discrepancies between predicted ages and recalculated dates remain for the three traces [Pilger, 2003]; actually, Baksi’s analysis increases confidence in the plate-hotspot parameters produced by Müller et al.
Three recent models for Pacific plate motion relative to hotspots have been advanced [Harada and Hamano, 2000; Norton, 2000; Raymond et al., 2000], based on physiography and isotopic age dates. While varying in details, the models produce similar fits to the long-lived Hawaiian-Emperor and Louisville traces, plus a number of Pacific traces of shorter duration. Pilger [2003] has extended the model of Raymond et al. [2000] to three traces on the Nazca plate. Very few dates appear to be “too old”, at least in terms of internal consistency. However, there is emerging evidence for some Ar/Ar dates being “too young”; the bend in the Hawaiian-Emperor chain may be as old as 47-48 Ma, instead of the commonly accepted 43 Ma [Sharp and Clague, 1999; Clague, 2003]. Further, three recent reconstruction models do not imply prolonged fixity of stage poles and rates describing Pacific plate motion relative to hotspot, key assumptions in some work that attempts to test hotspot fixity [e.g., Koppers et al., 2001].
Hotspot Traces and Plumes
The ideas of a fixed hotspot reference frame and deep mantle plumes are tightly linked in much contemporary thought, due largely to their coupling in Morgan’s [1971, 1972] primary contributions. There is a Gedankenexperiment one could undertake that would provide a rationale for coupling fixed hotspots with deep mantle plumes (although it is not contained in Morgan’s papers). If hotspots formed a global reference frame, and, therefore, did not move relative to one another over a time scale of tens, even a hundred million years, this would imply that hotspots would not be fixed relative to the surrounding shallow mantle -- somehow the hotspot material would probably need to displace adjacent shallow mesosphere in order to maintain fixity relative to other hotspots. Why? Because expansion of the Atlantic and Indian Oceans requires contraction of the Pacific and Tethys Oceans (assuming an Earth of fixed radius). Thereby, shallow sublithospheric mantle beneath the Pacific and Tethys would be displaced relative to sublithospheric mantle beneath the surrounding plates, a geometric requirement recognized (in a different context) by Alvarez [1982]. This displacement would be a consequence of the asymmetric convergence of convergence zones between the plates of the Pacific and Tethys and the Atlantic-Indian Ocean continental plates. If hotspots were embedded in the sublithospheric mantle, Pacific hotspots would be displaced with the mantle relative to Atlantic-Indian Ocean hotspots. If, on the other hand, hotspots maintained their positions relative to one another, plumes, vertically penetrating shallower mantle, and maintaining a vertical trajectory would seem to be required as the source of the hotspots.
The plume-fixed hotspot argument above is largely academic as abundant evidence now indicates a single global, fixed hotspot reference frame does not exist (although it still has its advocates, e.g., Gordon [2004]). Nevertheless, the apparent non-existence of a global fixed hotspot reference frame does not preclude the existence of deep mantle plumes (despite the assertions of some that it does); plumes could still move relative to one another. The absence of a fixed hotspot frame merely removes one argument for plumes.
Neither does the existence of two or three distinct hotspot reference frames require or preclude deep mantle plumes. The plume model does imply some degree of lateral displacement of shallow mantle, at least with initial penetration of an inferred plume head. Is there evidence of movement of hotspots relative to surrounding mantle? Or, conversely, are hotspots fixed or embedded within the upper mesosphere? These questions are largely hidden in much of the literature concerning hotspots and plumes, but their answers could provide important constraints on the nature of shallow mantle convection, as well as the nature of hotspots.
Evidence for Embedded Hotspots
Is there evidence that hotspots are embedded – that is, whatever their origin, are hotspots surrounded by “normal” mantle that is not moving laterally, relative to the hotspot? While hotspots produce “tracks”, the movement of plates relative to normal upper mantle (upper mesosphere) is, perhaps, more difficult to determine. Nevertheless, there are a couple of lines of evidence that point to an answer to the question.
Intraplate Stresses
Zoback et al. [1989] have shown that contemporary stress fields within continental plates – especially North and South America and Africa – are consistent with plate motions in the hotspot reference frame. For example, the contemporary motion of western North America is to the southwest, as implied by the orientation of the youngest part of the Yellowstone hotspot track (the Snake River plain); similarly maximum principal horizontal compressive stresses are oriented to the southwest over much of the mid-continent, from Alberta to Texas to New York.
Pilger [2003] has shown that paleostress field orientations within North America (130 Ma to present) and Africa (80 Ma to present) are also consistent with inferred plate motions relative to the hotspot model of Müller et al. [1993]. The origin of the stress fields includes interaction of plates with the underlying asthenosphere/mesosphere. If the sublithospheric mantle resists plate motion, it could very well introduce stress fields with maximum principal horizontal compressive stress components parallel to the direction of plate motion relative to the underlying mantle.
Unfortunately, stress field orientations within oceanic plates are largely unknown, so that orientation consistency as observed within continental crust cannot be inferred in the oceans. Further, the probable greater thickness of partially molten asthenosphere beneath oceanic plates than continental plates may inhibit the development of consistent stress orientations, if they could be observed.
If (1) hotspots are embedded within the sublithospheric mantle, (2) the upper mantle is not deforming significantly on a smaller than plate-scale, and (3) drag of continental plates against underlying asthenosphere/mesosphere controls the intraplate stress fields, then hotspots would produce tracks consistent with the stress orientations. If, on the other hand, mantle convection is significant and small scale, one might not expect consistent intraplate stress orientations over large areas of a plate. Or, if hotspots are not embedded (and are moving semi-independently of “normal” mantle), hotspot trace orientations should not parallel intraplate stresses.
Minor Hotspots and Gravity Lineations
Oceanic plate thickness is a function of age; plates are thinnest near ridges and thicken progressively as the square-root of age [Parker and Oldenburg, 1973]. As plates move over the underlying asthenosphere and mesosphere, isostasy affects sublithospheric mantle. Older, thicker plate depresses underlying mantle, while passage of thinner plate results in uplift of the mantle. With uplift, depressurization melting can occur, possibly producing plate-penetrating volcanism, manifested in minor hotspot traces and cross-grain gravity lineations [e.g., Raddick et al., 2002]. Indeed, the older portions of virtually all young (<45 Ma) hotspot traces on the Pacific plate occur to the southwest of a fracture zone separating older lithosphere on the north from younger on the south (Pilger, 2003a). Similarly, most cross-grain gravity lineations appear in a similar structural position.
Consistency of orientation of young hotspot traces and gravity lineations with the orientation of the two major hotspot traces (Hawaiian and Louisville) implies that the source of the lineations and young hotspot traces represent essentially the same reference frame as the major hotspots. The minor hotspots appear, from the structural evidence, to have a shallow, isostatically-controlled origin, while the two major traces are at least embedded within stable shallow mesosphere/asthenosphere, even if they owe their origins to deep mantle plumes.
Evidence from Subduction Zones and Marginal Basins
In the same volume in which Morgan [1972] elaborated the hotspot-plume hypothesis, Moberly [1972] discussed the origin of marginal basins behind subduction zones. Moberly suggested that there are basically two types of subduction, controlled by the motion of the upper plate of the subduction zone. That is, relative to the mesosphere, motion of the upper plate towards the subduction zone results in mountain belt formation on Andean type. Conversely, motion of the upper plate away from the subduction zone produces back-arc extension.
Morgan [1972] showed that his contemporary instantaneous plate kinematic model in a global hotspot frame was consistent with the Moberly proposal. Subsequent refinements of the contemporary plate-hotspot model (most recently, Gripp and Gordon [2002]), are still consistent with Moberly’s proposal – including the back-arcs of the Tonga-Kermadec, Philippine, and Lesser Antilles subduction zones. Contemporary models are certainly suggestive, while reconstructions going back in time could provide even more insight.
Pindell and colleagues have provided a series of analyses of the tectonic evolution of the Caribbean region which are particularly relevant. Pindell and Kennan’s [2002] recent reconstructions include inferences of the positions of Caribbean region plate boundaries and volcanic arcs relative to North America for discrete times extending from the Jurassic to the Present. The reconstructions incorporate plate positions of South American relative to North America via combination of conventional magnetic-isochron and fracture zone reconstructions via the African plate. They also include the relative positions of “microplates”, crustal blocks, and their boundaries.
From Pindell and Kennan’s [2001, 2002] map reconstructions, the major plate and microplate boundaries were digitized along with inferred magmatic arc centers for discrete ages (9.5, 19, 33, 46, 56, and 72 Ma; Fig. 2). They were then restored to calculated positions at each appropriate time in the Tristan hotspot reference frame (using Müller et al.’s [1993] Africa-hotspot parameters, extended to North America: Pilger [2003a]) (Fig. 3-4).
Figure 2. Magmatic centers of the Caribbean . Present-day (0) centers are active volcanoes. Other centers are as interpreted and reconstructed by Pindell and Kendall, 2002, relative to a fixed North America . Ages in m.y.
What is particularly remarkable about the Caribbean reconstructions relative to the Tristan frame is the clustering of the restored magmatic centers along a narrow zone close to the current Lesser Antilles volcanic arc (Figure 3). Volcanic arcs above subduction zones are above the zone of melting that demarcates first contact of subducting lithosphere with asthenosphere. The relative stability of the restored magmatic centers in Fig. 3 implies that the locus of asthenosphere-subducting slab contact has remained fairly stationary in the Atlantic-Indian Ocean hotspot reference frame over the past ~70 Ma.
Figure 3. Interpreted major plate boundaries of the Caribbean, based on interpretation and reconstructions of Pindell and Kendall (2002), restored to “original” location relative to Atlantic-Indian Ocean
Figure 4. Interpreted magmatic centers of the Caribbean (original interpreted locations relative to North America shown in Figure 1, based on Pindell and Kendall, 2002), restored to position relative to Atlantic-Indian Ocean (Tristan) hotspot reference frame. Methods of data point digitization are described in the Appendix. Reconstruction methods are described in the text. Note clustering of magmatic loci along a narrow zone close to the contemporary volcanic arc of the Lesser Antilles.
If hotspots and an island arc are fixed relative to one another over tens of millions of years, what might this mean? Consider the location of the volcanic arc relative to the underlying subduction zone. Since early in the development of plate tectonics, the volcanic arc has been inferred to overly the zone of first contact between the descending oceanic plate and the asthenosphere (immediately below the upper plate of the subduction zone). Whether the magmatism represents partial melting of oceanic crust, dewatering of the crust and anatexis of the asthenospheric wedge or of the base of the overlying plate, the location of the arc appears to represent that zone of joint contact of the base of the upper plate, the upper surface of the descending plate, and the asthenospheric wedge.
Significance of East Caribbean Arc Reconstructions
The geometry and kinematics of subduction boundaries, if combined with relative stationarity of the volcanic arc implies fixity in the reference frame of the subduction zone plus that part of the upper plate between the trench and the arc, regardless of the motion of the back-arc. Mechanically and geometrically, relative stationarity of subduction zones and hotspots could imply that the mesosphere beneath the subducting plate and incorporating a set of hotspots is not significantly deforming to the depth at which the subduction zones and hotspots extend. Thus Moberly’s [1972] idea of stationarity of marginal basin subduction zones relative to sublithospheric mantle is supported. Further, the hypothetical existence of a shallow mesospheric reference frame with embedded hotspots is further supported.
Evidence from East Africa
The volcanism associated with the East African Rift was not incorporated into the initial hotspot-plume model [Morgan, 1971, 1972]. Subsequently, a number of workers suggested that the rift system is underlain by one or more plumes. Unlike typical island/seamount chains and aseismic ridges of oceanic regions, the volcanics of East Africa are not readily interpreted in terms of distinct traces.
Turcotte and Oxburgh [1974] undertook an analysis of available isotopic ages of volcanics from East Africa, and noticed a north-to-south pattern of inception of activity, with continuation of activity into the Recent. The pattern is similar to that of volcanism along the Snake River Plain in the western United States [e.g., Suppe et al., 1975], where inception of activity was oldest to the west and persisted almost to the present.
Pilger [2003a] produced a compilation of isotopic ages (mostly K/Ar) from East Africa, including the sources used by Turcotte and Oxburgh [1974], with ages converted to a common base, using contemporary standards [Steiger and Jäger, 1977]. After filtering (accepting only the oldest date from each sample location), plots demonstrate north-to-south inception of activity (Fig. 5a). Further, when hotspot loci are constructed, based on Müller et al.’s [1993] Africa-hotspot model, the age data show north-to-south inception of volcanism consistent with motion of Africa in the hotspot reference frame (Fig 5a).
However, when the three-dimensional distribution of dates is considered, a single hotspot locus does not fit all of the data (Fig 5b). Fig. 5 and 6 are stereographic projections of the data and two loci. The two loci roughly fit two clusters of isotopic ages, but at least two more would seem to be required to fit additional clusters.
Figure 5a. East African volcanics: latitude versus age, <= 60 Ma , with hypothetical hotspot loci at 5 m.y. restored according to model of Müller et al. [1993] with interpolation by Pilger [2003].
Figure 5b. African volcanics: longitude versus age, <= 60 as in Fig. 5a.
Figure 6. Stereo view: filtered isotopic ages of East African Volcanics, <= 60 Ma , with hypothetical hotspot loci at 5 m.y. according to model of Müller et al. [1993] with interpolation by Pilger [2003]. Younger data points closer to viewer.
Figure 7. Stereo view, filtered East African volcanic isotopic ages (<= 60 Ma), restored to cooling location, according to model of Müller et al. [1993] with interpolation by Pilger [2003]. Younger data points closer to viewer.
The data points in Fig. 5-6 are restored to their hypothetical position relative to the African hotspot reference frame for their cooling age, according to the hotspot model of Müller et al. [1993], as interpolated by Pilger [2003], and shown in Fig. 7. The clusters imply a minimum of four or five hotspots, located at approximately 3ºS, 30ºE; 4ºS, 35ºE; and 4ºN, 33ºE; plus 1ºS, 34ºE; and/or 2ºN, 36ºE. Whether the volcanics of the East African Rift represent distinct hotspots, the age-migration patterns are consistent with motion of Africa relative to the same mantle reference frame as the principal hotspots of the Atlantic and Indian Oceans. Conceivable, the volcanics could be an indirect effect of the crustal extension responsible for the Rift. Mapped faults, including active normal faults, extend well to the south of known volcanics. Thus fracturing alone may not be adequate for volcanism. Rather, significant extensional thinning of the African plate may be required, in order for partial melting to occur beneath the lithosphere.
Migration patterns imply that the zones of partial melting are fixed, at least in part, within sublithospheric mantle. Thus, crustal extension may facilitate partial melting, but the zones of anatexis remain within mantle beneath the African plate. The patterns further imply the existence of a kinematically rigid, sublithospheric mantle.Uncertainty
Reconstructions
A natural question to consider in assessing the significance of the reconstructions (especially Fig. 4) is what level of confidence to place in the reconstructions. Müller et al. [1993] did not assign uncertainties to their reconstruction parameters for Africa in the hotspot reference frame. Similarly, uncertainty estimates are not available for the relative reconstructions of the African and North American plates used [Pilger, 2003].
Pindell and Kendall [2001] have not explicitly quantified uncertainties in their Caribbean reconstructions (which depend on African and South American reconstructions as well as African and North American). Additionally, while their reconstructions correspond with distinct magnetic isochrons, magnetic isochrons recording the relative motion of the Caribbean plates and microplates relative to North and South America are largely absent (except for young lineations in the Cayman Trough).
Even if uncertainty estimates for the major plates’ reconstructions were incorporated, a more fundamental issue would require addressing. There is no physically justified mechanism for interpolation between reconstructions and, thereby, attaching uncertainty estimates to such interpolations.
Conceivably, the restored magmatic centers in Fig. 4, with slight revision in age and/or reconstruction parameters, might be even more closely clustered. Or, the clustering of the calculated restorations might be a remarkable coincidence. The latter possibility seems improbable if only because Pindell and Kendall did not utilize Müller et al.’s [1993] hotspot framework to constrain their reconstructions.
Isotopic Ages
The accuracy and precision of isotopic ages is ultimately critical to the validation of plate reconstructions relative to hotspots, as well as to other plates. The dates used in the East African Rift study are all K/Ar, some acquired more than forty years ago. Similarly, questions have been raised, as noted above, concerning certain, more recent Ar/Ar analyses of submarine volcanic samples.
Precise and accurate redating of the rocks referred to in this and so many other studies is clearly desirable. However, this contribution points out patterns in dates and reconstructions which in all probability cannot be attributable to analytical error. The age migration patterns appear to be real, even if precise and accurate dates are yet unavailable. Improved analyses will go far in testing the ideas advanced here, and, if validated, better parameterize the inferred reconstruction parameters.
Summary and Conclusions
Left unaddressed in much of the debate concerning the origin of hotspots and the possible existence of plumes is the nature of the shallow mesosphere. Is it freely convecting at rates comparable to or greater than rates of plate motion? Or, is the shallow mesosphere kinematically rigid, on comparable scales to the rigid of lithospheric plates.
The following implies that the shallow mesosphere behaves in a plate-like manner:
(1) The two hotspot reference frames of the Atlantic-Indian Ocean and the Pacific Ocean appear to be distinct, at least over much of the past 70 m.y.
(2) Intraplate stress fields within continental terranes of moderate elevation are consistent with the local hotspot reference frame.
(3) The motion of North and South America in the Tristan hotspot reference frame, during the Laramide period, is consistent with displacement of the Hawaiian hotspot reference frame relative to Tristan.
(4) The eastern Caribbean magmatic arcs remained fixed in the Tristan hotspot frame for at least 70 m.y.
(5) Volcanic inception patterns along the East African Rift are consistent with African plate motion in the Tristan hotspot frame.
Additional evidence implies that hotspots are embedded within the shallow mesosphere:
(1) Most of the minor hotspot chains of the Pacific Ocean appear to owe their origin to age-controlled thickness variations in the Pacific plate.
(2) Cross-grain gravity lineations in the Pacific Ocean occur in similar structural positions to minor hotspot traces, and parallel the direction of plate motion in the Hawaiian hotspot reference frame.
Mesoplates, kinematically rigid layers within the outer mesosphere, appear to be the habitat of hotspots. Interaction of the lithosphere with mesoplates is apparent in hotspot traces, continental stress fields, and stationarity of island arcs.
At least three mesoplates exist: Tristan, Hawaiian, and Icelandic. Their relative motions are largely controlled by subduction zones and the relative motions of the upper plates of the subduction zones.
Evidence for mesoplates has further implications for mantle convection. The upper surface of mesoplates is the deep solidus (the base of lithoplates is the shallow solidus – the region between the two soliduses is the asthenosphere; Pilger [2003b]). As new plate is created at spreading centers, mesosphere beneath the spreading center rises isostatically, partially melts, and is converted to asthenosphere. Thus, convection within the upper mesosphere is largely radial, and focused beneath spreading centers.
When rapid lithospheric thinning occurs above a region of the mesoplate (either by intraplate extension or by passage of thinner plate), isostasy produces rising asthenosphere and shallow mesosphere (e.g., Raddick et al. [2002]). The top of the mesosphere, if fertile, partially melts, producing a hotspot. Recent tomographic results imply that hotspots (“plumes”) extend vertically to varying depths (varying from hotspot to hotspot) in the mesosphere [Montelli et al., 2003]. Thus plumes appear to have a top-down origin, which is consistent with the mesoplate model and evidence assembled here for the embedding of hotspots in mesoplates.
Acknowledgements
The following software applications were used in data digitization, manipulation, and display: GeoGraphix Discovery (by Landmark Graphics), JASC Paintshop Pro, Microsoft Internet Explorer, Visual C++, Word, and Excel.
Appendix
Data Digitization, Transformation, and Display
Original locations of plate boundary components and magmatic centers in Fig. 2 and transformed in Fig. 3-4, were generated from graphics (jpegs: *.jpg’s) posted at the web link for Pindell and Kendall (2002). Each jpeg were opened in JASC’s Paintshop Pro, in which pixel locations for equivalent longitudinal and latitudinal indices were recorded. From these parameters, individual ESRI World File parameters were calculated, and a corresponding parameter file constructed to accompany each jpeg. Each jpeg image was then imported into Landmark’s GeoGraphix Discovery mapping application, GeoAtlas, as a distinct map layer, assuming a simple Mercator mapping projection. Contours (polylines) and magmatic center data points were digitized onto a transparent overlay. The resulting contours and data points were then exported as simple ASCII files in latitude and longitude. The resulting contours and data points were restored to calculated positions in the Tristan hotspot reference frame (Müller et al., 1993, as modified by and using the spline interpolation methodology of Pilger, 2003). Restored contours and magmatic centers were then imported as distinct layers into GeoAtlas, as displayed in Fig. 3-4.
Stereo View Construction
The stereo views in Figs. 7-9 were constructed by the application of the following formulas:
Left Image: xleft = x - (age [Ma]/10) tan 3º
Right Image: xright = x + (age[Ma]/10) tan 3º
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Manuscript originally prepared in 2007.
© 2010 Rex H. Pilger, Jr.
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