## 1 Introduction

[2] The knowledge of material properties at high pressures (P) and temperatures (T) is fundamental for understanding the evolution and the current physical conditions inside the Earth and other planetary bodies. Steady advances in experimental techniques and ab initio computations [*Manghnani and Syono*, 2013; *Wentzcovitch and Stixrude*, 2010] are contributing to augment the amount of information we have on material properties at high pressure and temperature. The different pieces of information are modeled together in a thermodynamical self-consistent manner to obtain the stable mineralogical phases and the properties of rock assemblages at P-T typical of the Earth's deep interior [*Connolly*, 2005; *Holland and Powell*, 1998, 2011; *Matas et al.*, 2007; *Stixrude and Lithgow-Bertelloni*, 2005, 2011]. The material databases can be incorporated in geodynamic modeling tools [e.g., *Afonso et al.*, 2013; *Baumann et al.*, 2010; *Bunge et al.*, 2007; *Nakagawa et al.*, 2009; *Tackley et al.*, 2005] and are increasingly used to interpret geophysical observations [*Afonso et al.*, 2013; *Cammarano et al.*, 2003, 2009; *Forte et al.*, 2010; *Khan et al.*, 2009; *Steinberger and Calderwood*, 2006, and many others].

[3] A straightforward implementation of the P-T and composition databases in numerical simulations can be done since it is possible to have direct control on pressure, both in space than in time (for example, this is done in the mantle convection code STAGYY) [*Nakagawa et al.*, 2009]. However, all geophysical models involve depth. Therefore, a pressure-to-depth conversion is required to use the material properties databases.

[4] This is usually done by using a scaling relation given by a 1-D pressure profile of our planet. In most of the cases, using the preliminary reference Earth model (PREM) pressure profile [*Dziewonski and Anderson*, 1981] is sufficiently accurate, but it must be recognized that we are thus introducing an unnecessary bias in our interpretation. It is desirable, and certainly more rigorous, to use directly the experimentally determined P-dependent density to compute the correct pressure profile. The goal of this paper is to quantify accurately, for the first time, what are the effects of assuming the PREM pressure profile on geophysical interpretation. Note that we do not aim to refine the physical interpretation of existing seismic models or data.

[5] The (static) pressure profile is simply given by:

that can be discretized in small steps in which the density can be assumed to be constant. Both the density, *ρ*, than the gravity acceleration, *g*, are a function of depth (*z*). We choose not to invert for the *g* profile, which requires tedious iteration because of the feedback with the density profile. Instead, we approximate the gravity profile by using the PREM profile. Note that *g* does not vary much throughout the Earth's mantle, slightly increasing when approaching the dense core. Not inverting for *g* does not introduce any observable variations in our results. We also use the *P*(*z*) profile of PREM as starting one. The density distribution associated to the PREM pressure profile for a given thermal and compositional structure is then inferred from the material-property database and the pressure profile updated. We continue iteratively this procedure up to convergence that takes place very rapidly, usually in few steps, for a tolerance given by a normalized root-mean-squared-error of 10^{−6}. Note that the steps in depth should be very small and should be chosen according to the rate of density variation. Care should be taken to the drastic jumps in density that are associated with mineralogical phase transitions.

[6] In what follows, we present two examples. A first one referring to the 1-D interpretation of seismic models and a second to the interpretation of a 2-D thermal structure of oceanic lithosphere, as predicted by a half-space cooling model.