Models for the Earth's geoid and dynamically supported topography usually account only for radial (vertical) variations in mantle rheology and flow structure. However, expected lateral variations in viscosity, due to temperature- or stress-dependent rheology, can degrade our ability to infer mantle structure from geoid models based on seismically determined density contrasts in the mantle. Theoretically, the main difficulty is that the harmonic components of the flow-stress-deformation field are no longer independent, and exact analytical methods cannot account for this ''mode coupling.'' For large thermal density contrasts of small lateral dimension (e.g., subducted slabs), it is difficult to form any general theory for these effects. However, we believe that the largest geoid anomalies which occur at the lowest harmonic degrees (l=2,3) are due to a global pattern of relatively mild temperature variations. For convection with mainly broadscale thermal and rheological changes, some relatively straightforward ideas can be developed.

Combining results from simple perturbation theory and numerical models for convective flow, we find the following: (1) If we are correct in inferring viscosity variations of less than one order of magnitude globally, the longest-wavelength geoid anomalies (l=2,3) are not seriously contaminated by lateral viscosity variations. (2) Contamination of the higher degrees (l≥4) is expected, and, in particular, self-coupling between l=2 heterogeneity and viscosity variations may be observable at degree 4; the most severe contamination occurs at the doubled harmonic (l=4) of the dominant heterogeneity harmonic (l=2). (3) Perturbation techniques are adequate to model global-scale lateral viscosity variations of an order of magnitude or less. (4) The steady state surface deformation problem at the heart of our geoid models may be more robust with respect to broadscale lateral viscosity variations than are models for transient deformations (e.g., postglacial rebound). (5) For loading by broadscale density heterogeneity, the effects of stress-dependent rheology are probably secondary to the effects of radial viscosity stratification. ¿ American Geophysical Union 1989