Bayesian Inversion for Layered Spherical Symmetric Earth Conductivity Model from Global Magnetic Data

Abstract

In the Bayesian perspective, inference on model parameters from observed data is performed by calculating the likelihood of the data given prior model parameters, i.e. to estimate the posterior probability of model parameters. With the advent of computational resources, there are increasing interests in resolving full non-linear inverse problems using global approach. Although the current trends are geared towards algorithms to efficiently explore the model space, we employed the classical “pure” Monte Carlo method to resolve the inverse problem in the global scale induction study. Observatory and satellite magnetic data are used to provide insight on the deep mantle conductivity. In this case, layered (1D) spherical symmetric conductivity model can be considered as adequate to represent the Earth’s conductivity variation with depth. Model parameters (resistivities and thicknesses) with uniform probabilities over predefined intervals are drawn as samples of the model space. Reliable posterior estimates are derived from a large number of samples which are still manageable with the current PC technology. Relatively small uncertainties of the posterior estimates suggest that the Monte Carlo method is adequately sampled the model space with a small number of model parameters. Our results are consistent with a monotonic increase of conductivity with depth with a marked inflexion at about 700-900 km, while discontinuities at 410 km and 660 km known from seismic and petrology data seem unresovable directly from EM data.