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We conduct an experiment to investigate whether linearity in the observed velocity gradient in the volume of the inner core sampled by the PKP ray paths beneath Central America is a robust approximation. Instead of solving an optimization problem, we approach it within the Bayesian inference. This is an ensemble approach, where model specification is relaxed so that instead of only one solution, groups of reasonable models are acceptable. Furthermore, in transdimensional Bayesian inference used here, the number of basis functions needed to model observations is by itself an unknown. Our modeling reveals that in the ensemble of models, the most likely are those containing only 2 nodes (linear trend). Thus our result justifies the assumption used for the determination of inner core rotation with respect to the rest of the mantle that the observed gradient is constant in its nature (linear). Recent observations in seismology suggest that it is likely that the spatial variability in elastic parameters is a widespread phenomenon in the inner core. Future array observations will further constrain spatial extent and magnitude of velocity changes and show whether there is a significant difference between these observations in the two quasi-hemispheres of the inner core. [ABSTRACT FROM AUTHOR]

Geodynamical models and seismic observations suggest that the Earth's solid inner core rotates at a different rate than the mantle. However, discrepancies exist in rotation rate estimates based on seismic waves produced by earthquakes. Here we investigate the inherent assumption of a constant rotation rate using earthquake doublets-repeating earthquakes that produce similar waveforms. We detect that the rotation rate of the Earth's inner core with respect to the mantle varies with time. We perform an inverse analysis of 7 doublets observed at the College station, Alaska, as well as 17 previously reported doublets, and reconstruct a history of differential inner-core rotation between 1961 and 2007. We find that the observed doublets are consistent with a model of an inner core with an average differential rotation rate of 0.25-0.48° yr−1 and decadal fluctuations of the order of 1° yr−1 around the mean. The decadal fluctuations explain discrepancies between previous core rotation models and are in concordance with recent geodynamical simulations. [ABSTRACT FROM AUTHOR]

Describes a numerical method for solving partial differential equations in problems where traditional eulerian and lagrangian techniques fail. Use of the geometrical concept of natural neighbors; `Natural-element method' (NEM); Example of NEM. INSET: A new method to calculate natural-neighbour...

Working with a large temporal dataset spanning several decades often represents a challenging task, especially when the record is heterogeneous and incomplete. The use of statistical laws could potentially overcome these problems. Here we apply Benford's Law (also called the 'First-Digit Law') to the traveled distances of tropical cyclones since 1842. The record of tropical cyclones has been extensively impacted by improvements in detection capabilities over the past decades. We have found that, while the first-digit distribution for the entire record follows Benford's Law prediction, specific changes such as satellite detection have had serious impacts on the dataset. The least-square misfit measure is used as a proxy to observe temporal variations, allowing us to assess data quality and homogeneity over the entire record, and at the same time over specific periods. Such information is crucial when running climatic models and Benford's Law could potentially be used to overcome and correct for data heterogeneity and/or to select the most appropriate part of the record for detailed studies. [ABSTRACT FROM AUTHOR]