Lateral temperature variations in the Earth have been inferred since the first tomography studies began to reconstruct 3-D seismic velocity structure (*Dziewonski et al.*, 1977, *Woodhouse and Dziewonski*, 1984). However, in spite of the ever-improving resolution of seismic velocity models and a general agreement of different models on at least the large-scale structure (e.g. *Ritsema*, 2004, *Su et al.*, 1994, *Li and Romanowicz*, 1995), interpretation is still challenging.

An important issue for seismic interpretation concerns the non-physical nature of any seismic model. Typically, the physical interpretation of a given seismic dataset is performed in two steps. First, a seismic model that fits satisfactorily the data is constructed. Second, the model is interpreted for the physical parameters based on the knowledge of the elastic and anelastic properties of mantle minerals plus constraints on plausible composition and temperature ranges from geochemistry - i.e. the signature of outcropping rocks (orogenic peridotites) and mantle inclusions (xenoliths and xenocrysts) -, heat flow measurements at surface and conditions for melting mantle materials. The second part of the process is commonly regarded as the critical one for the interpretation. Instead, it is often forgotten that the seismic models are already an interpretation of the data. The seismic models are non-unique and depend on the parametrization and distribution, quality and type of data used. More important, it is not ensured that a given best-fit seismic model corresponds to a physical model. For example, the non-clear physical meaning of the seismic reference models (PREM *Dziewonski and Anderson*,1981, AK135 *Kennett et al.*, 1995) has been elucidated by the previous work of one of us (*Cammarano et al.*, 2003). The same problems are transferred to 3-D tomography models that are obtained by perturbing the starting average model.

Here we invert long-period seismic waveforms, which are mainly sensitive to shear velocity, with respect to a physical reference model instead than common seismic reference models (e.g., PREM). Velocity variations will thus correspond to thermal (or compositional) variations and a consistent three-dimensional density and structure may be determined. We start assuming purely thermal variations because in the upper mantle composition plays a secondary role. We compare the thermal features constrained by the seismic data against expected thermal variations and estimated geotherms in various tectonic regions. The average velocity model extracted from the physically constrained tomography provides insights on the nature of the transition zone. In order to assess the uncertainties in the thermal model and estimate how well average velocity and velocity gradient with depth in the upper mantle are constrained by long-period seismic data, we perform a series of inversions starting with various models.

We test our inversion by using some of the PREF models from *Cammarano et al.* (2005a,b). These are pyrolitic, adiabatic models that fit global seismic data (i.e. travel times and fundamental modes). We select three PREF models that represent well the differences in seismic and mineral physics properties within the family of PREF models. The use of different starting PREF models, characterized by their own sensitivities of seismic velocities to temperature, will help to assess the effects of the mineral physics uncertainties on the physically-constrained inversion. At the same time, this will test how good is the assumption of non-dependence of the outcome from the starting model. To further investigate this point, we also invert the seismic data starting with a model that has a much smaller jump at 410km and different velocity gradients above and below this discontinuity (Figure 3).

The data used are long-period fundamental and higher-order mode surface waveforms from the existing Berkeley compilation. Events with moment magnitude larger than six and at teleseismic distance (epicentral distance between 15and 165) have been selected. The original seismograms have been deconvolved for the instrument response and filtered between 60 s and a variable maximum period, typically between 220 s and one hour, which is chosen according to the event magnitude. Wave-packets for both fundamental and overtones are extracted from the seismograms.
The seismic waveform tomographic method is based on the Non-linear Asymptotic Coupling Theory method (NACT, *Li and Romanowicz*, 1995).

We start the inversion with a low-resolution version of a recent anisotropic model (SAW642AN, *Panning and Romanowicz*, 2006), but replacing the background seismic reference model with a physical reference model (i.e., PREF). We invert for the isotropic part down to 1000 km, while we keep fixed the radially anisotropic part of the model, represented by (
). Radial anisotropy is required to simultaneously fit spheroidal and toroidal fundamental modes. We correct for crustal structure assuming the model CRUST2.0 (*Bassin et al.*, 2000). We solve iteratively the inversion procedure following, for each step, the classical least-squares approach.

The upper-mantle geotherms constrained by long-period seismic data are able to reproduce the range of expected geotherms beneath oceans
and cratons (Figure 26.2). We compare the seismic geotherms with geotherms for different oceanic age, based on the plate
cooling model (*Turcotte and Schubert*, 1982), and continental geotherms, purely conductive, computed at steady-state and based on
surface heat flow and radiogenic heat production in the crust (*Chapman*, 1986). Extremely low temperatures are found, sometimes, in
cratons (Figure 26.2), that are likely to be related to the secondary compositional effect.

The capacity of inferring absolute temperatures and thermal gradients depends on how precisely we can determine absolute seismic velocity and gradients. To this end, we should point out that our results rely on assumed crustal and anisotropy structure.

In figure 3, we show the inverted average structure obtained by the 3-D tomographic model. Absolute velocities and gradients are well constrained from long period data, except in proximity of the 410 km discontinuity (Figure 26.3). The velocity structure below 300 km is very similar in those different tectonic regions indicating the global character of the inverted average model in the transition zone.

The inverted model tends toward PREM, which is confirmed to be a very good average seismic model. The differences are due to the different starting parametrization. For example, because PREF does not have a 220 km discontinuity as PREM, the final model does not have this feature either. Instead, a higher velocity gradient than the starting model is required by the seismic data around this depth (Figure 26.3). Long-period seismic waveforms are not directly sensitive to the mantle discontinuities, and therefore, the gradients nearby a discontinuity are not well constrained by those data. This can be clearly seen when we compare the gradients nearby the 410 km discontinuity between the PREF inverted model and the model with the small jump at 410 km (see Figure 26.3).

The velocity jump imposed in the starting model at the olivine-wadsleyite transition dictates the gradients around it (Figure 3). Pyrolitic models, which have 60 vol % of olivine, do have a larger jump than seismic reference models for this discontinuity ( 6-10%, 6-12% (*Cammarano et al.*, 2005a) vs 2.5% and 3.5%, respectively, for PREM and 3.5% and 4% for AK135). If we assume in our starting model the large jump inferred from mineral physics, long period seismic waveforms require the changes in gradients above and below the 410 km discontinuity shown in Figure 3. A thermal interpretation of this structure is not feasible as we obtain temperatures 1250 K at 350 km, 1750 K around 500 km and geodynamically unrealistic thermal gradients throughout the upper mantle. We conclude that dry pyrolite can not be reconciled with seismic data. This conclusion has a global character as the similarity of the velocity profiles below 300 km beneath oceans and cratons show (Figure 26.3).

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