The relationship between surface topography, gravity anomalies, and temperature structure of convection

Abstract

Normal stresses associated with convection in a fluid layer, whose boundaries can deform, produce topography on those boundaries. When the equations of motion are linear, integral relations between topography on the boundaries and the temperature structure can be found as a function of wavelength. Expressions of this kind have been derived for the case of convection in a constant viscosity fluid when inertial effects are negligible. The total gravity anomaly is the sum of contributions due to the topography on the two boundaries and to temperature variations within the fluid, and similar integral relations between gravity and the temperature structure can also be derived. At wavelengths large compared to the depth the shape of the kernels in the integrals, particularly that for gravity, is sensitive to the boundary conditions used. The transfer function between gravity and topography is also characteristic of the boundary conditions at long wavelengths. In all the cases considered, there is a transition between short‐and long‐wavelength behavior which occurs at wavelengths proportional to the layer depth. If the bottom boundary can deform as well as the upper boundary, the gravity anomaly tends to zero at long wave‐lengths as the gravity kernel tends to zero everywhere. The surface topography kernel is always zero at the bottom boundary. The lack of any significant surface expression produced by temperature variations near the bottom of the layer provides an explanation of the similar relationships between gravity and topography associated with the dissimilar temperature structures produced by different modes of heating. At least for cellular convection, surface topography and gravity anomalies largely reflect temperature variations in the vicinity of the upper thermal boundary layer. This is consistent with an explanation of geoid anomalies over mid‐ocean swells in terms of convection beneath the lithosphere, where the lower part of the thermally defined plate acts as the upper thermal boundary layer of the convection.

LitMod3D: An interactive 3‐D software to model the thermal, compositional, density, seismological, and rheological structure of the lithosphere and sublithospheric upper mantle

“…[42] Several authors have demonstrated that the topography of the outer surface in mantle-like fluids is primarily controlled by the physical conditions within the uppermost thermal boundary layer [McKenzie, 1977;Parsons and Daly, 1983;Marquart and Schmeling, 1989]. Although ''dynamic'' loads associated with sublithospheric flow can influence the surface topography to some extent, this effect seems to be important only in regions of large upwellings or downwellings [e.g., Marquart and Schmeling, 1989].…”

Crustal structure of rifted and convergent margins : the U.S. East Coast and Aleutian margins

“…In the convective mantle beneath the thermal lid, the effective depth of compensation may be limited by viscous stresses of convection that tend to balance thermal buoyancy forces [Parsons and Daly, 1983]. Studies of hotspot swells suggest compensation depths of 70 to 200 krn [e.g.…”

Lithosphere structure and upper mantle characteristics below the Bay of Bengal

“…(2) ……… (3) Here, k | and z | represent non-dimensional wavenumber and depth of the convecting layer respectively. It is noticeable that model-2 produces higher amplitudes for theoretical admittance, and according to Parsons and Daly (1983) as the largest temperature variation occurs closer to the bottom boundary, the amplitude of transfer increases. The analytical expressions for the calculation of theoretical admittance curves for the above temperature distributions (after Parsons and Daly, 1983) and for different convective layer thicknesses (640 km and 400 km)…”

“…We compare the observed admittance values with the theoretical admittance curves computed for a simplified mantle convection model assuming Newtonian convection in a uniformly viscous mantle layer, and neglecting the effect of inertia, self-gravitation and sphericity (Parsons and Daly, 1983). It is known that the observed geoid can be defined as a function of the deformation of the upper and lower surfaces of the convective layer and density structure imposed by the temperature distribution (T) within the convective layer (Black and models 1 and 2.…”