SeisTeC: A neural network tool to constrain mantle thermal and chemical properties from seismic observables

Abstract

Three-dimensional variations of wave speeds and density have identified the presence of seismically distinct structures in the Earth's mantle. To determine the thermochemical properties and dynamic relevance of these structures, it is crucial to understand the relationship between seismic properties and temperature and composition. However, multiple thermochemical parameters influence seismic wave speeds simultaneously. A given wave speed pair (compressional and shear) and density can be generated by many possible combinations of thermochemical parameters, which makes the inversion of wave speeds and density for thermochemical parameters a non-unique problem. We have developed a tool which efficiently captures the mapping between seismic wave speeds (and density) and thermochemical properties, with the capacity to represent both the inherent trade-offs between parameters as well as data uncertainties. These trade-offs and uncertainties are represented by the posterior probability density function provided by a neural network. We demonstrate the concept for seismic wave speeds and density, but the same tool can also be adapted for other parameters such as attenuation or properties of seismic discontinuities. SeisTeC is available to the wider community and is intended to facilitate interpretations of seismic structures inside the Earth, or in general, any planetary bodies.

Our tool is based on a neural network, which implicitly learns the non-linear mapping between temperature and bulk composition. We chose the example of the lower mantle and expressed composition in terms of six end-member oxides (${\mathrm{SiO}}_2,\mathrm{MgO},{\mathrm{Al}}_2{O}_3,\mathrm{FeO},{\mathrm{Na}}_{2}O,\mathrm{CaO}$) and modelled seismic wave speeds and density at appropriate temperature and pressure conditions. Wave speeds and density are calculated for 750,000 thermochemical models, whose temperature and composition are selected at random from pre-defined ranges, using thermodynamic modelling. We train neural networks with wave speeds plus or minus density as the input, and temperature and bulk composition as target outputs. The networks then approximate a probability density function for each output, which allows us to interpret seismic observables in terms of physical parameters, crucially, with uncertainties. When working with wave speeds ($V_P$ and $V_S$) only, we find trade-offs between pairs of parameters such as temperature - $\mathrm{FeO}$, ${\mathrm{SiO}}_2$ - $\mathrm{MgO}$, ${\mathrm{SiO}}_2$ - ${\mathrm{Na}}_{2}O$, and ${\mathrm{SiO}}_2$ - ${\mathrm{Al}}_2{O}_3$ which limits the constraints one can place on mantle temperature and chemistry using these observables. We also emphasise the importance of combining $V_P$ and $V_S$ for constraining ${\mathrm{SiO}}_2$ content. The main advantage of including density with wave speeds is that it helps to better constrain the temperature and the most abundant and dynamically relevant compositional end-members, namely, the ${\mathrm{SiO}}_2$, $\mathrm{MgO}$ and $\mathrm{FeO}$ by breaking down the trade-offs between them. Some trade-offs between pairs of parameters involving minor compositional end-members still remain, namely temperature - $\mathrm{CaO}$, ${\mathrm{SiO}}_2$ - ${\mathrm{Na}}_{2}O$, ${\mathrm{SiO}}_2$ - ${\mathrm{Al}}_2{O}_3$. In general, except mid-ocean ridge basalt, most rocks only have a small fraction of ${\mathrm{Na}}_{2}O$ and ${\mathrm{Al}}_2{O}_3$. By excluding mid-ocean ridge basalt in the training data most of the apparent trade-offs will disappear when considering more average mantle compositional ranges.