JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 102, NO. B2, PAGES 2751-2769, FEBRUARY 10, 1997 Radial profile of mantle viscosity: Results from the joint inversion of convection and postglacial rebound observables Jerry X. Mitrovica Department of Physics, University of Toronto, Toronto, Ontario, Canada Alessandro M. Forte D6partement de Sismologie, Institut de Physique du Globe de Paris, Paris Abstract. We present new inferences of the radial profile of mantle viscosity that simultaneously fit long-wavelength free-air gravity harmonics associated with mantle convection and a large set of decay times estimated from the postglacial uplift of sites within previously glaciated regions (Hudson Bay,Arctic Canada, and Fennoscandia). The relativesea levelvariationat these latter sites is constrained by age-height pairs obtained by geological survey, rather than the subjective trendswhichare commonly used in glacial isostatic adjustment (GIA) studies. Our viscosity inferences are generated using two approaches. First, we adopt a relative viscosityprofile which is known to provide a good fit to the free-air gravity harmonics and determine an absolute scalingwhich yields a best fit to the GIA decay time constraints. Second,we perform an iterative, nonlinear, joint inversion of the two data sets. In both cases our inferred profiles are characterized by a significant increase of viscosity (-02 orders of magnitude), with depth, to values of -01022 Pa s in the bottomhalf of the lower mantle. The newviscosity profiles are shownto satisfy constraintsbased on the postglacialuplift of both Fennoscandia (the classic Haskell [1935] number) and Hudson Bay which have commonly been invoked to argue for an isoviscous mantle. Furthermore, the models are used to predict a set of long-wavelength signatures of the GIA process. These include predictions of GIA-induced variations in (1) the length-of-day over the late Holocene period; (2) the Earth's precession constant and obliquity over the last 2.6 Myr; and (3)the present-day zonal harmonics of the geopotential, j• (l _< 7). The predictions (1) and (3) bound the late Holocene (and ongoing) mass flux between the large polar ice sheets (Greenland and Antarctic) and the global oceans to smallvalues (<_ 0.4 mm/yr equivalent eustatic sea level rise). Introduction The fluid dynamics of the Earth's mantle is strongly influenced by the value and radial variation of vis- cosity within that region. For example, recent three- dimensional numerical simulations of mantle circula- tion indicate that a significant increase in viscosity, with depth, results in a convective planform dominated by long-wavelength, linear downwellings, akin to sub- ductionzones[Zhang and Yuen, 1995; Bunge et. el, 1996]. Furthermore, the dynamic topography of plates supportedby mantle convective flow is a strong' func- tion of the depth variation of mantlestrength [Gurnis, 1992]. Given this connection, it is not surprising that inferences of mantle viscosityhave commonlybeen de- Copyright 1997 by theAmerican Geophysical Union. Paper number 96JB03175. 0148-0227/97/96JB-03175509.00 rived from surface geophysical observables (e.g., long- wavelength gravityanomalies and plate motions) asso- ciatedwith the convection circulation [e.g., l-lager, 1984; Ricard et el., 1984; Richards and l-lager,1984; Forte and Peltlet, 1987, 1991; Ricard et el., 1989; Ricard and Vi- gny, 1989; l-lager and Clayton, 1989; Forte et el., 1991, 1993, 1994; King and Masters, 1992; Corrieu et el., 1994;King, 1995]. Historically, the first in situ inferencesof viscosity were obtained from analyses of data associated with glacial isostatic adjustment (GIA) [e.g., Haskell, 1935]. These analyseshave, to date, incorporated a globally distributedset of sea level variations[e.g., McConnell, 1968; Cathles, 1975; Peltier and Andrews, 1976; Wu and Peltier, 1983; Nakada and Lainbeck, 1987, 1989; Wolf, 1987; Lambeck et al., 1990; Tushingham and Peltlet, 1992; Mitrovica and Peltier, 1995; Han and Wahr, 1995; Davis and Mitrovica, 1996]and anomalies in both the Earth's gravity field [e.g., O'Connell, 1971; Cathles, 2751