Improving Bayesian analysis for LISA Pathfinder using an efficient Markov Chain Monte Carlo method

We present a parameter estimation procedure based on a Bayesian framework by applying a Markov Chain Monte Carlo algorithm to the calibration of the dynamical parameters of the LISA Pathfinder satellite. The method is based on the Metropolis-Hastings algorithm and a two-stage annealing treatment in order to ensure an effective exploration of the parameter space at the beginning of the chain. We compare two versions of the algorithm with an application to a LISA Pathfinder data analysis problem. The two algorithms share the same heating strategy but with one moving in coordinate directions using proposals from a multivariate Gaussian distribution, while the other uses the natural logarithm of some parameters and proposes jumps in the eigen-space of the Fisher Information matrix. The algorithm proposing jumps in the eigen-space of the Fisher Information matrix demonstrates a higher acceptance rate and a slightly better convergence towards the equilibrium parameter distributions in the application to LISA Pathfinder data. For this experiment, we return parameter values that are all within ～1σ of the injected values. When we analyse the accuracy of our parameter estimation in terms of the effect they have on the force-per-unit of mass noise, we find that the induced errors are three orders of magnitude less than the expected experimental uncertainty in the power spectral density.     

Fossil flat-slab subduction beneath the Illinois basin, USA

The Illinois basin is one of several well-studied intracratonic sedimentary basins within the North American craton whose formational mechanisms and subcrustal structure are not well understood. We study the S-velocity structure of the upper mantle beneath the Illinois basin and its surrounding area through seismic tomography. We utilize continental scale waveform data of seismic S and surface waves, enhanced by regional earthquakes located near the Illinois basin. Our 3D tomographic model, IL05, confirms the existence of a slow S-velocity structure in the uppermost mantle beneath the Illinois basin region. This anomalously slow region exists from the base of the crust to depths of  90 km, and is slower than the North American cratonic average by about 200 m/s. This anomalous uppermost mantle beneath the Illinois basin is underlain by a faster lithosphere, typical of the surrounding craton, to depths of  200 km. Excluding the formation of the Reelfoot Rift, this area of North American has been stable for over 1.0 Gy. Thus, we do not expect thermal anomalies from before that time to persist into present day S-velocity anomalies and we consider a delamination origin as an explanation of Illinois basin subsidence unlikely. We cannot rule out that the slow mid-lithosphere beneath the Illinois basin is caused by an uppermost mantle enriched by a deep, but weak plume. We attribute the slow mid-lithosphere to the presence of either oceanic, hydrous crust, or, a relatively cool mantle wedge with preserved hydrous minerals in the Illinois basin's uppermost mantle, related to a fossilized flat subduction zone.     

Barium partitioning in coccoliths of Emiliania huxleyi

The coccolithophore Emiliania huxleyi was grown in seawater under different Ba concentrations. The relationship of coccolith Ba/Ca ratio and seawater Ba/Ca ratio was found to be linear. The linear regression yields the apparent Ba exchange coefficient of 0.10. Our data support a recently proposed generic model (Langer G., Gussone N., Nehrke G., Riebesell U., Eisenhauer A., Kuhnert H., Rost B., Trimborn S., and Thoms S. (2006) Coccolith strontium to calcium ratios in Emiliania huxleyi: the dependence on seawater strontium and calcium concentrations. Limnol. Oceanogr.51, 310-320.) developed for explaining apparent exchange coefficients of metabolically inert divalent trace metals, such as Sr, in E. huxleyi. This model represents the first approach combining cell physiological processes and data from inorganic precipitation experiments, which quantitatively explains coccolith apparent Sr and Ba exchange coefficients.