  A series of numerical simulations of thermal convection of Boussinesq fluid
with infinite Prandtl number, with Rayleigh number $10^7$, and with the
strongly temperature- and depth- dependent viscosity in a three-dimensional
spherical shell is carried out to study the mantle convection of single-plate
terrestrial planets like Venus or Mars without an Earth-like plate tectonics.
The strongly temperature-dependent viscosity (the viscosity contrast across the
shell is $\geq 10^5$) make the convection under stagnant-lid short-wavelength
structures. Numerous, cylindrical upwelling plumes are developed because of the
secondary downwelling plumes arising from the bottom of lid. This convection
pattern is inconsistent with that inferred from the geodesic observation of the
Venus or Mars. Additional effect of the stratified viscosity at the upper/lower
mantle (the viscosity contrast is varied from 30 to 300) are investigated. It
is found that the combination of the strongly temperature- and depth-dependent
viscosity causes long-wavelength structures of convection in which the
spherical harmonic degree $\ell$ is dominant at 1--4. The geoid anomaly
calculated by the simulated convections shows a long-wavelength structure,
which is compared with observations. The degree-one ($\ell = 1$) convection
like the Martian mantle is realized in the wide range of viscosity contrast
from 30 to 100 when the viscosity is continuously increased with depth at the
lower mantle.
