2.4 Geodynamic models

rum:

Our spherical harmonic expansion of slabs in the upper mantle obtained from the RUM seismicity contours [ Gudmundsson and Sambridge, 1998] which are in turn based on the Engdahl et al. [1998] catalog. We integrate along the RUM contours at each layer using them as $\delta$-functions such that the effective width of the slabs is determined by $\ell_{\mathrm{max}}$ and the $\cos^2$-taper that we apply for $\ell>0.75\ell_{\mathrm{max}}$.

lrr98d:

Density model by Lithgow-Bertelloni and Richards [1998] on spherical harmonics laterally ( $\ell_{\mathrm{max}}=25$) and layers with depth. lrr98d is based on ``slablets'', i.e. negative buoyancy anomalies, that sink at different speeds in the upper and lower mantle after starting at estimated past trench locations which are based on Mesozoic and Cenozoic plate reconstructions [ Ricard et al., 1993; Lithgow-Bertelloni et al., 1993]. The sinking rate was adjusted to fit geopotential fields, tomography, and plate motions.

stb00d:

Density model by Steinberger [2000] on spherical harmonics ( $\ell_{\mathrm{max}}=31$) and radial layers. stb00d is also based on past plate motions and subduction; Lithgow-Bertelloni et al.'s [1993] sets of plate boundaries were, however, interpolated at 2 Ma intervals while Lithgow-Bertelloni and Richards [1998] held boundaries fixed during individual plate-tectonic stages. stb00d is furthermore different from lrr98d in that it allows for lateral advection of slablets once they are below 380 km, due to the flow that is generated by plate motion and slab buoyancy. stb00d can be considered more realistic than lrr98d with respect to the treatment of convective flow.

zmg00t:

Temperature snapshot from a 3-D spherical convection calculation by Zhong et al. [2000]. We use the residual (RMS) temperature from their case 7 at time $9.25\cdot 10^{-4}$. Case 7 is an incompressible, temperature and depth-dependent viscosity calculation without phase transitions that allowed for plate-like flow through the inclusion of fixed weak zones [plates 2a and b of Zhong et al., 2000]. Assuming constant thermal expansivity, $\alpha$, variations in non-dimensional temperature, $\bar{T}$, relate to density, $\rho$, as $d\ln \rho = - \alpha \Delta T \ d \bar{T}$. With $\Delta T=1800^\circ$ K for the non-adiabatic mantle gradient and $\alpha=1.4\cdot 10^{-5}$ K$^{-1}$, we scale with $\alpha \Delta T \approx 0.025$.

All quantitative measures used to characterize and compare different mantle models are explained in the G-Cubed article .