Inferring Equations of State of the Lower Mantle Minerals Using Artificial Neural Networks (ANNs)

Interpretation of information available from seismic data requires an understanding of the seismic properties of minerals at different pressure and temperature environments. With the help of high pressure-temperature-volume (P-T-V) experiment data and by applying equations of state (EOSs), seismic/elastic properties of minerals can be determined. However, uncertainties in the measurements and choice of pressure scale, as well as different functional forms of EOSs all contribute to the uncertainties in mineral seismic properties. A specific choice of pressure scale and/or functional form of EOS has potential to produce biased results. In this study, we collate experimental data for the lower mantle minerals together with reported uncertainties, regardless of pressure scale or functional form used. By applying artificial neural network (ANN) techniques, P-T-V relationships (or EOSs) are implicitly learned from data without imposing any explicit thermodynamic assumptions or ad-hoc relationships. The problem of inferring EOSs using ANNs involves prediction of a continuous relationship between input (P and/or T) and output (V), but the conditional average provided by conventional neural networks only gives a limited information on that relationship. This is because we need to deal with multi-valued target data, and a probabilistic treatment is necessary to model the uncertainties. Hence, we combine a conventional neural network with Gaussian Mixture Model to compute the uncertainties in EOSs. Moreover, we compute the Jacobian of the mapping (i.e. derivatives of V with respect to P and T) which are then used to extract additional mineral properties such as bulk modulus and thermal expansivity. We first demonstrate the feasibility of this methodology using periclase (MgO), with a view to extend the application to other major lower mantle minerals.

Keywords: lower mantle, periclase, MgO, equations of state, artificial neural networks