Direct Sequential Simulation for spherical linear inverse problems

We present a method for obtaining efficient probabilistic solutions to geostatistical and linear inverse problems in spherical geometry. Our Spherical Direct Sequential Simulation (SDSSIM) framework combines information from possibly noisy observations, that provide either point on the model or are related by averaging kernel, statistics derived a-priori information. It generates realizations marginal posterior probability distributions of parameters not limited be Gaussian. avoid restriction Cartesian geometry built into many existing simulation codes, work instead with grids relevant Earth Space sciences. demonstrate our scheme using synthetic example, showing it produces realistic consistent known solution while fitting observations within their uncertainty reproducing distribution covariance models. Secondly, we an application real satellite estimating geomagnetic field at core–mantle boundary. results reproduce well-known features boundary magnetic field, also allow investigations morphology. Small-length scale determined but match extracted geodynamo simulations. The presented here represents step towards more general approaches inversion