Admittance for a convection in a layered spherical shell

Lago, B.; Rabinowicz, M.

doi:10.1111/j.1365-246x.1984.tb01943.x

Cited by 20 publications

(4 citation statements)

References 17 publications

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“…The occurrence of thermally coupled plumes, in our calculations and those of Cserepes & Rabinowicz (1985), shows that the assumption of mechanical coupling for two-layer convection models (e.g . Hager 1984;Creager & Jordan 1984Lago & Rabinowicz 1984) is not always true. Thermal coupling under upper barren of radiogenic heat sources (Anderson 1982(Anderson , 1984, cooling of the Earth's core should provide enough energy to drive convection in the lower mantle.…”

Section: Discussion Implications For Mantle Convectionmentioning

confidence: 86%

Numerical models of thermally and mechanically coupled two-layer convection of highly viscous fluids

Ellsworth¹,

Schubert²

1988

Geophysical Journal International

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Numerical solutions for thermal convection of two superposed viscous fluid layers, with the same thicknesses as the Earth's upper and lower mantles and separated by a fixed horizontal interface, are obtained at the onset of convection and in the nonlinear regime. Several heating configurations and thermal boundary conditions are considered, including an isothermal bottom boundary, a prescribed heat flux bottom boundary, and internal heating with an insulated lower boundary. At the onset of convection and with the same material properties in each layer, the lower layer is more unstable than the upper layer and long horizontal wavelengths (proportional to the lower layer thickness) predominate. For layers with sufficiently different material properties, the upper layer can be more unstable and short horizontal wavelengths (proportional to the upper layer thickness) can predominate at the onset of convection. When the material properties are chosen to make the two layers equally unstable, there are two stability curve (Rayleigh number Ra versus wavelength) minima with the lower minimum at long wavelength. Linear stability results typify weakly nonlinear convection except when both layers are equally unstable. When the layers have unequal stability, the stable layer has a conductive temperature field and its flow is viscously driven by the convective flow in the unstable layer. When the two layers are equally unstable, both layers are separately convecting even at Rayleigh numbers of only twice the critical value for convection onset. At large enough supercritical Ra the lower layer convects with a long wavelength cell even when linear stability theory predicts short wavelength cells. The upper layer always begins convecting with short wavelength cells. However, the upper layer cell over the lower layer downwelling plume increases in size with increasing Ra. Thus, horizontal wavelength (plate dimension, for example) cannot be used to discriminate between whole mantle and layered mantle convection. Mechanical coupling of the layers (downwelling plume over upwelling plume) occurs for all cases with the same material properties in each layer and for the case with the same Ra in each layer. When the material properties of the layers are sufficiently different to produce short wavelength cells at the onset of convection, the upper layer has two thermally coupled cells (downwelling plume over downwelling plume and a shear zone at the interface) over both lower layer plumes. A large (50 per cent of total) temperature difference across the interface occurs in all cases examined, implying that two-layer mantle convection should also have a large temperature change across the 670 km discontinuity. However, temperature dependent viscosity may reduce the magnitude of this temperature difference. Interpretations of geoid anomalies over subduction zones and seismic traveltime anomalies of slabs should account for possible thermal coupling of separate upper and lower mantle convective systems.

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Section: Discussion Implications For Mantle Convectionmentioning

confidence: 86%

Numerical models of thermally and mechanically coupled two-layer convection of highly viscous fluids

Ellsworth¹,

Schubert²

1988

Geophysical Journal International

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“…The fact that cold subduction zones correspond to a relative geoid high suggests a factor !30 viscosity increase around the upper-lower mantle interface (Lago and Rabinowicz, 1984;Hager et al, 1985). The amount of deflection corresponds to the usual isostatic rule for a load close to an interface: the weight of the induced topography equals at first order the mass of the internal load.…”

Section: A Mantle Without Inertiamentioning

confidence: 99%

“…Before seismic imaging gave us a proxy of the 3-D density structure of the mantle, various theoretical attempts have tried to connect models of mantle convection to plate velocities O'Connell, 1979, 1981), to the Earth's gravity field (or to the geoid, proportional to ), to the lithospheric stress regime, or to the topography (Runcorn, 1964;Parsons and Daly, 1983;Lago and Rabinowicz, 1984;Richards and Hager, 1984;Ricard et al, 1984).…”

Section: A Mantle Without Inertiamentioning

confidence: 99%

Physics of Mantle Convection

Ricard

2007

Treatise on Geophysics

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“…We can gain further insight into the effects of compressibility by examining the admittance of the geoid anomaly with surface topography defined as •N(k) (32) which is a very sensitive signal since it involves the ratio between two different signatures with their own intrinsic depth resolution. This admittance function has been used previously by Lago and Rabinowicz [1984] and Ricard et ai.…”

Section: Effects From Variations In Wavelengthsmentioning

confidence: 99%

Dynamical effects from equation of state on topographies and geoid anomalies due to internal loading

Hong¹,

Yuen²

1990

J. Geophys. Res.

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The effects of mantle compressibility on geoid and topographic signatures caused by internal loading in the mantle are studied. For a Cartesian compressible model the Green's functions of these geophysical signatures are determined by solving a two-point boundary value problem with depth for each horizontal wave number associated with the density anomaly. Various types of equations of state have been considered, which include both constant and depth-dependent thermodynamic parameters. Surface topographies are not changed too much by the effects of mantle compressibility, even for long wavelengths. The deformation of bottom boundary is not seriously influenced by mantle compressibility, except for long wavelengths and large viscosity contrasts between the upper and lower mantles. Geoid signals with horizontal wavelengths, exceeding 10,000 km, can be greatly influenced by mantle compressibility. For large viscosity contrasts, differences of up to 100% between incompressible and compressible geoid responses can be found. The admittance function also shows great sensitivity to mantle compressibility at long wavelengths. There are significant differences in the geophysical signatures from the ways in parameterizing the viscosity stratification in the mantle. An exponentially dependent viscosity model produces smaller geoid and surface topographical signals than for a single step function viscosity model. INTRODUCTION In the past decade there have been growing efforts in using long-wavelength seismic anomalies in the mantle to interpret geoid signals on the basis of dynamical circulation models driven by internal density heterogeneities [Hager, 1984; Richards and Hager, 1984; Ricard et al., 1984; Hager et al., 1985; Forte and Peltlet 1987; Ricard et al., 1989; Ricard and Vigny, 1989]. It now appears possible to model and explain the long-wavelength portion of the geoid spectrum by using seismic tomographic results [Woodhouse and Dziewonski, 1984; Tanirnoto, 1987]. To a first approximation, a physical understanding of the relationship between seismic and geoid anomaly observables has now been derived. The paradox concerning the negative sign of the predicted long-wavelength geoid [Dziewonski, 1984] can be explained by taking into account the radial dependence of the viscosity structure in dynamical models with internal loading [Richards and Hager, 1984; Ricard et al., 1984; Lago and Rabinowicz, 1984]. However, there are many different ways in which a viscosity model can be parameterized [Hong and Yuen, 1986; Revenaugh and Parsons, 1987], and there exist invariably trade-offs between different viscosity structures, which can lead to nonunique solutions able to explain most of the data equally well [Ricard et al., 1989]. Calculations of geoid anomalies and topographies from internal heating have, up to now, been based on the incompressible (Boussinesq) approximation. However, the density in the mantle increases with depth because of compressibility. Hence it is necessary to evaluate the effects on surface signatures from ...

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Admittance for a convection in a layered spherical shell

Cited by 20 publications

References 17 publications

Numerical models of thermally and mechanically coupled two-layer convection of highly viscous fluids

Numerical models of thermally and mechanically coupled two-layer convection of highly viscous fluids

Physics of Mantle Convection

Dynamical effects from equation of state on topographies and geoid anomalies due to internal loading

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