Tests of inversion for temperature

The inversion is based on a normal mode asymptotic coupling mechanism (NACT, Li and Romanowicz, 1996). The seismic data used for the inversion are long period fundamental and overtone spheroidal modes selected on the vertical component of the seismograms included in the existing collection. Including higher modes provide resolution in the transition zone. No crustal correction has been used at this point. The direct inversion of the seismic waveforms for temperature requires $\partial$lnV/$\partial$lnT (anelastic effects included) as a function of pressure (depth) and temperature and a starting thermal model as well. We choose an adiabat with a potential temperature of 1300$^{\circ}$C overlaid by the geotherm for 60 m.y. old oceanic lithosphere.

To test the results of the inversion and assess the best way to address the non-linearities, we test our temperature inversion by performing in parallel an inversion for a physical reference model. The chosen model is one of the best-fit adiabatic pyrolitic models (PREF) for traveltime and fundamental mode data from Cammarano et al., 2005. The models tested span the range of elastic properties for each mineral as inferred from mineral physics and applying different anelasticity models that cover the range of 1-D seismic attenuation models. Note that the thermal structure is exactly the same. An example of how a temperature slice may be obtained by inverting with respect to a reference model is given in Figure 13.52

Figure 13.52: Example of horizontal tomographic slice for temperature at 300 km depth. Composition is pyrolitic. Note that the extremely low temperature beneath the African Craton is consistent with a contribution from compositional heterogeneity.
Figure 13.53: Examples of non linearity effects at 300km. Triangles represent variation of V$_S$ with T by including anelasticity effects, squares are without it. Black line indicates the reference T at this depth.
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The sensitivity kernels of the seismogram with respect to velocity are translated into temperature by using the partial derivatives. The kernels should be recomputed after each iteration of the inversion because of the non linearity introduced by attenuation. However, knowing how the effect changes as a function of temperature and depth, we will try to correct the model after each iteration. In figure 13.53, we show at a given depth (300 km) how the kernels change around the thermal reference temperature. Note that the kernels (the derivatives of Figure 13.53) change both towards high and low temperature.

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