Published in EOS Trans. AGU 74(43):80, October 26, 1993, presented as Poster U32A-08
Degree-one Mantle Convection
The geoid is a constraint on models of the convection of the Earth's interior, except at degree one. The frame of reference is adjusted so that the center of coordinates is at the center of mass, and the degree-one components are zero, by definition. The distributions of mass in the interior may have degree-one components. Observational support for degree-one convection is missing, but could be a result of the way degree-one components have been treated.
The measurements of degree-one components have been neglected in the past (Mentock, Phys. Earth Planet. Inter., 73:77-84, 1991) and may have been understated. Degree-one components are called "forbidden" or "inadmissable" harmonics of the geoid, and are sometimes ignored in other contexts. It is possible to reduce the magnitude of the degree-one components by adjusting the frame of reference even for measurements other than the geoid. The toroidal degree-one component can be adjusted by allowing for a rotation of the hotspot reference frame. The degree-one component of seismic tomography is sensitive to the source and station corrections. The first technique used to study the lateral heterogeneity of Earth's interior is insensitive to odd-degree harmonics.
Strong statements against degree-one convection can be shown to be unsupported. Hess (History of Ocean Basins, Petrologic Studies, 599-620, 1962) asserted that Chandrasekhar had shown that degree-one convection was impossible in the modern Earth, but is not supported by a close reading of Chandrasekhar. Other arguments are applications of Occam's razor, pointing out that there is no need to assume degree-one convection. The modern view of super-continent supercycles supports the possiblity of ongoing degree one convection. The analogy of continents to "bouyant scum" is no longer apt and degree-two convection might be sufficient for dispersal, but a degree-one convection current (or net transport) is more likely to sweep all the continents back into a single super continent.