Extrapolating Oceanic Age Distributions

Rowley (2008) (get the paper here) discusses Extrpolation of Oceanic Lithosphere Age Distributions.

Abstract:Extrapolation of the age distribution of oceanic lithosphere has played a significant role in assessments of variations in global mean spreading rate, global mean ocean basin depth, and implications for global mean sea level. Subduction has already removed 50% of oceanic lithosphere younger than 55.7 Ma, making some level of extrapolation a necessary part of global plate reconstructions. An area equal in size to the Pacific Basin oceanic lithosphere must be extrapolated for ages older than 29.1 Ma. Three modes of extrapolation are identified. Mode 1 extrapolation uses the preserved history as recorded on one plate to infer the history of the previously adjacent plate. This mode of extrapolation is exemplified by the inferred history of the Farallon, Vancouver, Nazca, and Cocos plates relative to the Pacific Plate, on which this record is preserved. Mode 2 involves extrapolation beyond the preserved age extent of a given ridge system. No observable data exist that directly constrain the motions beyond the youngest magnetic reversal–dated oceanic lithosphere along such a boundary. This mode has, for example, been employed to extrapolate the age distribution resulting from spreading along the Izanagi-Pacific ridge system for as much as 60 m.yr. beyond the last directly determined record preserved on the Pacific Plate. Mode 3 is extrapolation of age distributions of entirely subducted ocean basins where no information explicitly constrains the relative-motion history of such basins. The age distri-butions in various neo-Tethyan basins require mode 3 extrapolation. This article examines extrapolations specifically using modes 2 and 3, employing the known spreading histories of the Pacific-Farallon/Vancouver and Pacific-Phoenix plate systems and the Tasman Sea as case studies. These tests demonstrate that extrapolated distributions of ages do not match preserved ages. Important events recorded in the preserved oceanic lithosphere, including both initiation and extinction of spreading ridges, cannot be inferred from the extrapolations and yet constitute important events that control aspects of the preserved oceanic lithosphere age distribution. Hence, reconstructed age distributions that require significant mode 2 and 3 extrapolations cannot provide a rigorous basis for testing hypotheses related to global histories of ridge production, mean age, mean depth, or other potentially correlated phenomena. This may appear to be an obvious result, and hence not worth publishing, but the persistent use of extrapolated age distributions in the published literature suggests that problems with extrapolation have not been appreciated by all. (Figure Captions provided below)

Figure 1. Fractional area of preserved oceanic lithosphere as a function of age (Ma), based on the Müller et al. (2008) Age Grid 2.6 data set: non-Pacific (Atlantic, Indian, circum-Antarctic, and small ocean basins) in lighter gray, Pacific (Pacific, Nazca, Cocos, Rivera, and Juan de Fuca plates) in medium gray. The dashed curve shows a polynomial fit to this distribution and correlation coefficient. This is the relationship expected of nearly constant ridge production and subduction of equal areas of all ages per unit time (Parsons 1982; Rowley 2002). The solid curve shows area of extrapolated oceanic lithosphere as a multiple of the Pacific oceanic lithosphere area of that age and older.

Figure 2. Reconstructed age grid from Müller et al. (2008; downloaded from www.earthbyte.org as file age_depth_bath_70.xyadb.bz2 on April 9, 2008). Three modes of extrapolation are highlighted on this map as translucent gray overlays. Testing of extrapolation modes 2 and mode 3 is the focus of this article.

Figure 3. Age structure of the Pacific and adjacent areas based on the Age Grid 2.6 data set of Müller et al. (2008). Isochrons derived by contouring the age grid for reversals M5y and C34no are shown as thicker lines, as are the modern mid-oceanic ridges. EB indicates the Ellice Basin region, where Taylor (2006) has described sea-floor fracture zone fabric that parallels the 120-Ma Pacific-Phoenix isochron orthogonal to the trends in older lithosphere immediately to the north. Imaginary subduction zones (A, B) and a suture zone (C) are highlighted as white lines, with triangles representing the equivalent of the extrapolations used, for example, by Müller et al. (2008) along the Pacific-Izanagi ridge and neo-Tethyan basins. Figures 4A, 5A, and 6A correspond to extrapolations related to imaginary subduction zones A, B, and C, respectively

Figure 4. A, Extrapolation of isochron M5y (126.7 Ma) to present (solid gray lines) at 10-m.yr. intervals, based on the M5y-to-C34no rotation parameters of Müller et al. (2008). Contours of the Müller et al. age grid at every 10 m.yr. (dashed gray lines) are also shown. Horizontal labels refer to model age isochrons and tilted labels to the extrapolated isochrons. Closely spaced (0.5-m.yr.) isochrons were extrapolated about this fixed pole and used as the basis for creating an extrapolated age grid using the GMT “surface” routine (Smith and Wessel 1990). Color shading shows the difference between extrapolated and modeled ages. B, Extrapolated age versus the median age difference between extrapolated age and the modeled age at each 0.1° cell for the Pacific-Farallon system. Black dots represent the median age difference as a function of extrapolated age. The gray background shows the 95% range of differences between the extrapolated age and model ages about the median. This range can reasonably be considered as representing the 95% confidence interval of the extrapolated ages. Upward-pointing triangles represent the maximum age difference and downward-pointing triangles the minimum value among all model ages along a given extrapolated isochron.

Figure 5. A, Comparison of extrapolated (solid gray lines) and modeled ages (Müller et al. 2008; dashed gray lines) for the Phoenix-Pacific ridge system (contours at 10-m.yr. intervals). Horizontal labels refer to model age isochrons and tilted labels to the extrapolated isochrons. The modern southwest Pacific extension of the East Pacific Rise defines the southeast boundary of the color-shaded region. Color shading represents the difference between extrapolated and modeled ages in each 0.1° cell. Note the symmetric disposition of the 90-Ma model age contours marking the vicinity in the model of the extinction of the Phoenix-Pacific ridge, corresponding to the Osbourn Trough (Billen and Stock 2000; Taylor 2006; Müller et al. 2008). B, Comparison of the extrapolated and modeled ages for the Phoenix-Pacific system shown in A. Symbols and shading as in figure 4B. Note that no extrapolated ages younger than 44 Ma are on the Pacific Plate. The decreasing extent of the vertical lines at younger ages simply reflects the truncation at the modern plate boundary.

Figure 6. A, Comparison of extrapolated (solid gray lines) and modeled ages (Müller et al. 2008; dashed gray lines) for the Tasman Sea region between eastern Australia and the Lord Howe Rise (contours at 10-m.yr. intervals). Horizontal labels refer to model age isochrons and tilted labels to the extrapolated isochrons. Note the symmetric disposition of the 60-Ma contours of the modeled ages, reflecting the extinction of the Tasman Ridge at about 52 Ma. Color shading highlights the difference between the extrapolated and modeled ages at each 0.1° cell. The extrapolated area of the Tasman Sea is about eight times its actual size. The plot in B compares only the fraction of the extrapolated ages with the modeled ages that actually exist within the Tasman Sea (i.e., the color-shaded region of this figure). B, Comparison of the extrapolated and modeled ages for the region shown in A. Symbols and shading as in figure 4B. The decreasing extent of the vertical lines at younger ages simply reflects the truncation at the Lord Howe Rise margin of the Tasman Sea. This comparison includes only grid cells with ages specified in the modeled age grid within the Tasman Sea region; hence, it excludes the regions shown as black in A as well as younger oceanic lithosphere in the Fiji and adjacent basins to the north and east of the Norfolk Rise, unrelated to the Tasman Sea.