The spherical harmonic spectra of plate velocities, gravity, topography, and heat flow are closely approximated by forms Ml-n, where l is harmonic degree. The magnitudes M and slopes n of heat flow and gravity, compared to those of the poloidal velocity, imply a lithospheric viscosity of ~1023 g/cm/s, similar to stress/strain rate ratios inferred from studies of flexure at subduction zones. The correlations among the field as functions of degree also appear explicable as the consequence of properties of the lithosphere (including its subducted extension). Applying boundary layer theory to plate velocities implies a Rayleigh number (based on observed heat flux) of ~108 for whole mantle convection and ~107 for convection confined to the upper mantle. To estimate the constraints on thermal and theological parameters therefrom, a temperature curve consistent with phase transition data is constructed. The effective thermal expansivity is increased by phase transitions at depths of 400--700 km, but this effect is less important than a marked decrease from ~3¿10-5 to 10-5/¿K at the bottom of the mantle. The Rayleigh number for upper mantle convection then is approximated rather well by viscosities corresponding to standard nonlinear strain rate stress laws below 60 km. The Rayleigh number for whole mantle convection requires a moderate increase in viscosity with depth, such as could plausibly arise from a decrease with depth in the activation volume for creep partially counteracting the effect of pressure. Hence constraints on the depth and other properties of mantle convection will require more detailed modeling utilizing relationships between the harmonic coefficients, as well as relative spectral magnitudes, of the surface fields.