Abstract
This paper discusses the stochastic analysis of spatially complex, time‐dependent flows in spherical and cylindrical geometries where the reference states, internal heating rates, and boundary conditions are temporally invariant and rotationally symmetric. Snapshots of the aspherical temperature anomalies δT (r,Ω,t) from a single convection run are taken to be samples of a stationary, rotationally invariant random field, and the spatial two‐point correlation function CTT(r,r′,Δ) is constructed by averaging over rotational transformations of this ensemble. Three subfunctions are extracted: the rms variation, the radial correlation function, RT(r,r′) = CTT(r,r′,0)/ σT(r)σT(r′), and the angular correlation function All three are useful in assessing the structural differences among mantle convection simulations, but the diagnostic properties of RT and its robustness with respect to low‐pass filtering recommend it as a tool for testing stratification hypotheses against whole‐mantle tomographic models.
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