Mathematics – Dynamical Systems
Scientific paper
Dec 2006
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006agufm.v23e0689a&link_type=abstract
American Geophysical Union, Fall Meeting 2006, abstract #V23E-0689
Mathematics
Dynamical Systems
1032 Mid-Oceanic Ridge Processes (3614, 8416), 1040 Radiogenic Isotope Geochemistry, 3270 Time Series Analysis (1872, 4277, 4475), 8121 Dynamics: Convection Currents, And Mantle Plumes
Scientific paper
Heterogeneities of the asthenospheric mantle along mid-ocean ridges have been documented as the ultimate effect of complex processes dominated by temperature, pressure and composition of the shallow mantle, in a convective regime that involves mass transfer from the deep mantle, occasionally disturbed by the occurrence of hot spots (e.g. Graham et al., 2001; Agranier et al., 2005; Debaille et al., 2006). Alternatively, upper mantle heterogeneity is seen as the natural result of basically athermal processes that are intrinsic to plate tectonics, such as delamination and recycling of continental crust and of subducted aseismic ridges (Meibom and Anderson, 2003; Anderson, 2006). Here we discuss whether the theory of chaotic dynamical systems applied to isotopic space series along the Mid-Atlantic Ridge (MAR) and the East Pacific Rise (EPR) can delimit the length-scale of upper mantle heterogeneities, then if the model of marble-cake mantle (Allègre and Turcotte, 1986) is consistent with a fractal distribution of such heterogeneity. The correlations between the isotopic (Sr, Nd, Hf, Pb) composition of MORB were parameterized as a function of the ridge length. We found that the distribution of isotopic heterogenity along both the MAR and EPR is self- similar in the range of 7000-9000 km. Self-similarity is the imprint of chaotic mantle processes. The existence of strange attractors in the distribution of isotopic composition of the asthenosphere sampled at ridge crests reveals recursion of the same mantle process(es), endured over long periods of time, up to a stationary state. The occurrence of the same fractal dimension for both the MAR and EPR implies independency of contingent events, suggesting common mantle processes, on a planetary scale. We envisage the cyclic route of "melting, melt extraction and recycling" as the main mantle process which could be able to induce scale invariance. It should have happened for a significant number of times over the Earth's mantle history before it acquired a chaotic structure, thus calling for ancient mantle events. The dimension of 7000 km might be related to the common size of the mantle region which has been affected by these processes.
Armienti Pietro
Gasperini Daniela
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