Geoid anomalies in a dynamic Earth

Abstract

In order to obtain a dynamically consistent relationship between the geoid and the earth's response to internal buoyancy forces, we have calculated potential and surface deformation Love numbers for internal loading. These quantities depend on the depth and harmonic degree of loading. They can be integrated as Green functions to obtain the dynamic response due to an arbitrary distribution of internal density contrasts. Spherically symmetric, self-gravitating flow models are constructed for a variety of radial Newtonian viscosity variations and flow configurations including both whole mantle and layered convection. We demonstrate that boundary deformation due to internal loading reaches its equilibrium value on the same time scale as postglacial rebound, much less than the time scale for significant change in the convective flow pattern, by calculating relaxation times for a series of spherically symmetric viscous earth models. For uniform mantle viscosity the geoid signature due to boundary deformations is larger than that due to internal loads, resulting in net negative geoid anomalies for positive density contrasts. Geoid anomalies from intermediate-wavelength density contrasts are amplified by up to an order of magnitude. Geoid anomalies are primarily the result of density contrasts in the interior of convecting layers; density contrasts near layer boundaries are almost completely compensated. Layered mantle convection results in smaller geoid anomalies than mantle-wide flow for a given density contrast. Viscosity stratification leads to more complicated spectral signatures. Because of the sensitivity of the dynamic response functions to model parameters, forward models for the geoid can be used to combine several sources of geophysical data (e.g., subducted slab locations, seismic velocity anomalies, surface topography) to constrain better the structure and viscosity of the mantle.

Towards a quantitative interpretation of global seismic tomography

“…Heterogeneity in the upper-mantle transition zone (between the seismic discontinuities near 410-and 660-km depth) and near the base of the mantle is manifest at very long wavelengths (Plate 2), with a predominance of fast wave propagation in the mantle beneath the circum-Pacific "Ring of Fire" and slow speeds beneath Africa and the central Pacific. This structure explains the long-wavelength variations in the gravity field [Richards and Hager, 1984;Hager et al, 1985;Cazenave et al, 1989] and correlates well with sites of post-Mesozoic subduction (recycling) of oceanic lithosphere [Richards and Engebretson, 1992;Ricard et al, 1993]. The shallow and lowermost mantles are marked by relatively strong heterogeneity, but the inferred magnitude of elastic heterogeneity decreases away from these boundary regions.…”

Postglacial variations in the level of the sea: Implications for climate dynamics and solid‐Earth geophysics

“…Section 4 will focus upon solidEarth geophysics, whereas section 5 will consider issues in climate dynamics. the convection timescale constraints provided by observed nonhydrostatic geoid anomalies [Hager, 1984;Richards and Hager, 1984]. This question is clearly related to the issue of whether the rheology of the mantle is Newtonian or non-Newtonian.…”

Geoid and topography over subduction zones: The effect of phase transformations

“…This includes density anomalies that drive mantle convection, such as dense slabs or buoyant plumes, and density anomalies that result from deformed boundaries as a result of convection. This problem was first addressed by Pekeris [1935] but has been expanded on by others [Morgan, 1965;McKenzie, 1977;Richards and Hager, 1984;Ricard et al, 1984]. Focusing on subduction zones for purposes of illustration, the mass excess due to the dense, sinking slab contributes a positive term to the total geoid while the mass deficit, due to the down warping of the surface above the slab, contributes a negative term to the total geoid.…”

“…Richards and Hager, 1984;Ricard et al, 1984]. (It should be noted that the boundary between the mantle and core is also deformed as a results of the flow driven by the sinking slab; however, at the wavelengths appropriate to subduction zone problems this is not a significant contribution, even though it is included in most geoid calculations [Richards and Hager, 1984]). …”

“…[3] In an isoviscous fluid the gravitational potential (or geoid) over a downwelling limb is negative [Richards and Hager, 1984]. While the density structure of a subducting slab is a complex function of temperature, chemical variations, and phase transformations, there is little doubt that subducting slabs are more dense than the surrounding mantle.…”