This chapter describes a quantitative approach that integrates data and results from mineral physics, petrological analyses, and geophysical inverse calculations to map geophysical data directly for mantle composition and thermal state. Seismic tomography has proved an important tool to image the inaccessible parts of the Earth. Computation of physical properties using thermodynamic models is described and discussed, and an application of the joint inverse methodology is illustrated in a case study where mantle composition and thermal state beneath continental Australia is determined directly from seismic data. There is a growing consensus that the cause of the imaged wavespeed anomalies not only relates to variations in temperature, but also bears a strong compositional component. However, separation of thermal and chemical effects from seismic wave speeds alone is difficult and is further complicated by the general insensitivity of seismic wave speeds to the density contrasts that are responsible for driving mantle convection.