The viscosity structure of the mantle

During 1991–1994,the four year period covered by this report,there has been a shift in emphasis away from one‐dimensional (radial) mantle viscosity models and toward an understanding of the three‐dimensional (radial and lateral) structure of mantle viscosity. Our understanding of mantle viscosity comes primarily from two sources: studying the creep properties of mantle minerals under appropriate pressures and temperatures and using theoretical flow models to predict surface observables, such as: plate velocities, gravity, geoid, and heat flow. Laboratory measurements of deformation indicate that the rheology of upper mantle minerals such as olivine ((Mg,Fe) 2 SiO 4 ) is a strong function of temperatue, grain size, and stress [cf., Karato and Wu , 1993]. The deformation of minerals under mantle conditions generally follows a flow law of the form 1ε ˙ = A( σ μ ) n d − m exp ⁡ − Q ( − Q R T)where ϵ is the deformation rate,σ is the deviatoric stress, μ is the shear modulus,d is the grain size of the rock, Q is the activation energy for the deformation mechanism,T is the temperature in Kelvin,R is the gas constant and A is a constant. Viscosity is defined as 2η = ( σ ε ˙)therefore, deformation is directly related to viscosity. Substituting equation (1) into equation (2), an effective viscosity, 3η e f f = μ A( μ σ )n − 1d m exp ⁡ ( QR T ) ,can be defined.For temperature changes of 100 degrees K, the viscosity changes by an order of magnitude at constant stress [cf., Karato and Wu ,1993].Changes of deviatoric stress by a factor of 2 change the viscosity by an order of magnitude [cf., Karato and Wu ,1993]. Other factors, such as partial pressure of oxygen and water content may also have important effects.