Transdimensional inference in the geosciences

Seismologists construct images of the Earth's interior structure using observations, derived from seismograms, collected at the surface. A common approach to such inverse problems is to build a single 'best' Earth model, in some sense. This is despite the fact that the observations by themselves often do not require, or even allow, a single best-fit Earth model to exist. Interpretation of optimal models can be fraught with difficulties, particularly when formal uncertainty estimates become heavily dependent on the regularization imposed. Similar issues occur across the physical sciences with model construction in ill-posed problems. An alternative approach is to embrace the non-uniqueness directly and employ an inference process based on parameter space sampling. Instead of seeking a best model within an optimization framework, one seeks an ensemble of solutions and derives properties of that ensemble for inspection. While this idea has itself been employed for more than 30 years, it is now receiving increasing attention in the geosciences. Recently, it has been shown that transdimensional and hierarchical sampling methods have some considerable benefits for problems involving multiple parameter types, uncertain data errors and/or uncertain model parametrizations, as are common in seismology. Rather than being forced to make decisions on parametrization, the level of data noise and the weights between data types in advance, as is often the case in an optimization framework, the choice can be informed by the data themselves. Despite the relatively high computational burden involved, the number of areas where sampling methods are now feasible is growing rapidly. The intention of this article is to introduce concepts of transdimensional inference to a general readership and illustrate with particular seismological examples. A growing body of references provide necessary detail.

Global azimuthal seismic anisotropy and the unique plate-motion deformation of Australia

Differences in the thickness of the high-velocity lid underlying continents as imaged by seismic tomography, have fuelled a long debate on the origin of the 'roots' of continents. Some of these differences may be reconciled by observations of radial anisotropy between 250 and 300 km depth, with horizontally polarized shear waves travelling faster than vertically polarized ones. This azimuthally averaged anisotropy could arise from present-day deformation at the base of the plate, as has been found for shallower depths beneath ocean basins. Such deformation would also produce significant azimuthal variation, owing to the preferred alignment of highly anisotropic minerals. Here we report global observations of surface-wave azimuthal anisotropy, which indicate that only the continental portion of the Australian plate displays significant azimuthal anisotropy and strong correlation with present-day plate motion in the depth range 175-300 km. Beneath other continents, azimuthal anisotropy is only weakly correlated with plate motion and its depth location is similar to that found beneath oceans. We infer that the fast-moving Australian plate contains the only continental region with a sufficiently large deformation at its base to be transformed into azimuthal anisotropy. Simple shear leading to anisotropy with a plunging axis of symmetry may explain the smaller azimuthal anisotropy beneath other continents.