In geophysical inversion, inferences of Earth's properties from sparse data involve a trade-off between model complexity and the spatial resolving power. A recent Markov chain Monte Carlo (McMC) technique formalized by Green, the so-called trans-dimensional samplers, allows us to sample between these trade-offs and to parsimoniously arbitrate between the varying complexity of candidate models. Here we present a novel framework using trans-dimensional sampling over tree structures. This new class of McMC sampler can be applied to 1-D, 2-D and 3-D Cartesian and spherical geometries. In addition, the basis functions used by the algorithm are flexible and can include more advanced parametrizations such as wavelets, both in Cartesian and Spherical geometries, to permit Bayesian multiscale analysis. This new framework offers greater flexibility, performance and efficiency for geophysical imaging problems than previous sampling algorithms. Thereby increasing the range of applications and in particular allowing extension to trans-dimensional imaging in 3-D. Examples are presented of its application to 2-D seismic and 3-D teleseismic tomography including estimation of uncertainty.
In order to characterize the subsurface structure of the Jakarta Basin, Indonesia, a dense portable seismic broad-band network was operated by The Australian National University (ANU) and the Indonesian Agency for Meteorology, Climatology and Geophysics (BMKG) between October 2013 and February 2014. Overall 96 locations were sampled through successive deployments of 52 seismic broad-band sensors at different parts of the city. Oceanic and anthropogenic noises were recorded as well as regional and teleseismic earthquakes. We apply regularized deconvolution to the recorded ambient noise of the vertical components of available station pairs, and over 3000 Green's functions were retrieved in total. Waveforms from interstation deconvolutions show clear arrivals of Rayleigh fundamental and higher order modes. The traveltimes that were extracted from group velocity filtering of fundamental mode Rayleigh wave arrivals, are used in a 2-stage Transdimensional Bayesian method to map shear wave structure of subsurface. The images of S wave speed show very low velocities and a thick basin covering most of the city with depths up to 1.5 km. These low seismic velocities and the thick basin beneath the city potentially cause seismic amplification during a subduction megathrust or other large earthquake close to the city of Jakarta.
The use of Bayesian trans‐dimensional sampling in 2‐D and 3‐D imaging problems has recently become widespread in geophysical inversion. Its benefits include its spatial adaptability to the level of information present in the data and the ability to produce uncertainty estimates. The most used parameterization in Bayesian trans‐dimensional inversions is Voronoi cells. Here we introduce a general software, TransTessellate2D, that allows 2‐D trans‐dimensional inference with Voronoi cells and two alternative underlying parameterizations, Delaunay triangulation with linear interpolation and Clough‐Tocher interpolation, which utilize the same algorithm but result in either C0 or C1 continuity. We demonstrate that these alternatives are better suited to the recovery of smooth models, and show that the posterior probability solution is less susceptible to multimodalities which can complicate the interpretation of model parameter uncertainties.
Over the last 25 years, several studies have tested for a link between geomagnetic field intensity and reversal frequency. However, despite a large increase in the number of absolute paleointensity determinations, and improved methods for obtaining such data, two competing models have arisen. Here we employ a new tool for objectively analyzing paleomagnetic time series to investigate the possibility of a link between reversal frequency and paleointensity. Transdimensional Markov chain Monte Carlo techniques are applied to a quality-filtered version of the global paleointensity (PINT) database for the last 202 Myr to model long-term paleointensity behavior. A large ensemble of models is sampled, from which a final representative mean model is extracted. The resulting paleointensity model confirms published conclusions that the single-silicate crystal method gives significantly different results from more conventional whole rock paleointensity methods; this makes it difficult to jointly model the two data types in the same analysis. When the much larger whole rock data set is considered, a stable paleointensity of 5.46 ± 0.28 × 10 22 A/m 2 for the last 202 Myr is consistent with the 95% confidence interval of the paleointensity model. Statistical tests indicate no significant correlation between reversal frequency and field intensity at the 0.05 level. However, this result is likely due to the characteristics of the PINT database rather than being a genuine, physically representative conclusion. Given the paucity of data and general state of the global paleointensity database, concerted efforts to increase the number of high-quality, well-dated paleointensity data are required before conclusions about a link between geomagnetic field intensity and reversal frequency can be confidently drawn.
The S3-3, POLAR, and FAST satellite auroral observations of parallel and perpendicular electric field structures have been identified as belonging to a large "U"-shaped potential structure that supports oblique electric double layers. This interpretation is verified by terrestrial laboratory measurements of a self-consistently supported three-dimensional oblique current-free double layer. Its width is a few tens of Debye lengths, its oblicity (with respect to the magnetic field) varies from 0 up to 30 degrees, and its strength is a few times the electron temperature.
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