Seismic methods at the long wavelength limit detect the total seismic velocity anomaly Xoff ?c where ?c is the change of the velocity of the recorded wave. If seismic velocity varies linearly with temperature over this range, the total velocity anomaly is proportional to ?TdownXdown. As a caveat, trace amounts of partial melt may well affect seismic velocity in the asthenosphere, so the coefficient to convert temperature variation to seismic velocity variation is not obvious. Linearization may even be inappropriate and the proportionality coefficient may vary with depth as the phase assemblage changes. Till et al. review these issuesplicated relationships between temperature and seismic velocity are beyond the scope of this paper.
van Wijk et al. presented models of downwellings at the edge of rifted thin lithosphere. Their models had T? of ?57 and ?107 K within the range where stagnant-lid formalism is applicable. Their viscosity increased with depth along an adiabat, increasing by a factor of e per scale depth D? of 83 km. Their downwellings widened with depth and then ponded ?300 km beneath the top of the asthenosphere. Their viscosity increased by a factor of 37 over that interval to approximately 10 20 Pa s, consistent with the results of Lee et al. and Harig et al. . From (15) the model heat move in equilibrium with thin lithosphere in the model of van Wijk et al. is about 2.5 times that in my models, so the anomaly from (15) is 2.5 times mine, 1750 K km.
van Hunen and Zhong discussed the effective length scale for flow in isoviscous asthenosphere. In agreement with my approach, they concluded that the depth beneath the base of the lithosphere provides a length scale and that the actual length scale varies modestly due to the vagaries of the spacing of downwellings http://datingranking.net/es/sitios-de-citas-para-agricultores/. Read more “step 3.3. Total Downwelling Anomaly Resolved from the Seismology”