Thomas Bodin

Transdimensional inversion of receiver functions and surface wave dispersion

[1] We present a novel method for joint inversion of receiver functions and surface wave dispersion data, using a transdimensional Bayesian formulation. This class of algorithm treats the number of model parameters (e.g. number of layers) as an unknown in the problem. The dimension of the model space is variable and a Markov chain Monte Carlo (McMC) scheme is used to provide a parsimonious solution that fully quantifies the degree of knowledge one has about seismic structure (i.e constraints on the model, resolution, and trade-offs). The level of data noise (i.e. the covariance matrix of data errors) effectively controls the information recoverable from the data and here it naturally determines the complexity of the model (i.e. the number of model parameters). However, it is often difficult to quantify the data noise appropriately, particularly in the case of seismic waveform inversion where data errors are correlated. Here we address the issue of noise estimation using an extended Hierarchical Bayesian formulation, which allows both the variance and covariance of data noise to be treated as unknowns in the inversion. In this way it is possible to let the data infer the appropriate level of data fit. In the context of joint inversions, assessment of uncertainty for different data types becomes crucial in the evaluation of the misfit function. We show that the Hierarchical Bayes procedure is a powerful tool in this situation, because it is able to evaluate the level of information brought by different data types in the misfit, thus removing the arbitrary choice of weighting factors. After illustrating the method with synthetic tests, a real data application is shown where teleseismic receiver functions and ambient noise surface wave dispersion measurements from the WOMBAT array (South-East Australia) are jointly inverted to provide a probabilistic 1D model of shear-wave velocity beneath a given station.

Reconstructing plate-motion changes in the presence of finite-rotations noise

Understanding lithospheric plate motions is of paramount importance to geodynamicists. Much effort is going into kinematic reconstructions featuring progressively finer temporal resolution. However, the challenge of precisely identifying ocean-floor magnetic lineations, and uncertainties in geomagnetic reversal timescales result in substantial finite-rotations noise. Unless some type of temporal smoothing is applied, the scenario arising at the native temporal resolution is puzzling, as plate motions vary erratically and significantly over short periods (<1 Myr). This undermines our ability to make geodynamic inferences, as the rates at which forces need to be built upon plates to explain these kinematics far exceed the most optimistic estimates. Here we show that the largest kinematic changes reconstructed across the Atlantic, Indian and South Pacific ridges arise from data noise. We overcome this limitation using a trans-dimensional hierarchical Bayesian framework. We find that plate-motion changes occur on timescales no shorter than a few million years, yielding simpler kinematic patterns and more plausible dynamics.

A self-parametrizing partition model approach to tomographic inverse problems

Partition modelling is a statistical method for nonlinear regression and classification, and is particularly suited to dealing with spatially variable parameters. Previous applications include disease mapping in medical statistics. Here we extend this method to the seismic tomography problem. The procedure involves a dynamic parametrization for the model which is able to adapt to an uneven spatial distribution of the information on the model parameters contained in the observed data. The approach provides a stable solution with no need for explicit regularization, i.e. there is neither user supplied damping term nor tuning of trade-off parameters. The method is an ensemble inference approach within a Bayesian framework. Many potential solutions are generated, and information is extracted from the ensemble as a whole. In terms of choosing a single model, it is straightforward to perform Monte Carlo integration to produce the expected Earth model. The inherent model averaging process naturally smooths out unwarranted structure in the Earth model, but maintains local discontinuities if well constrained by the data. Calculation of uncertainty estimates is also possible using the ensemble of models, and experiments with synthetic data suggest that they are good representations of the true uncertainty.

REDBACK: Open‐source software for efficient noise‐reduction in plate kinematic reconstructions

Knowledge of past plate motions derived from ocean-floor finite rotations is an important asset of the Earth Sciences, because it allows linking a variety of shallow-rooted and deep-rooted geological processes. Efforts have recently been taken toward inferring finite rotations at the unprecedented temporal resolution of 1 Myr or less, and more data are anticipated in the near future. These reconstructions, like any data set, feature a degree of noise that compromises significantly our ability to make geodynamical inferences. Bayesian Inference has been recently shown to be effective in reducing the impact of noise on plate kinematics inferred from high-temporal-resolution finite-rotation data sets. We describe REDBACK, an open-source software that implements transdimensional hierarchical Bayesian Inference for efficient noise-reduction in plate kinematic reconstructions. Algorithm details are described and illustrated by means of a synthetic test.

Three billion years of crustal evolution in eastern Canada: constraints from receiver functions

The geological record of SE Canada spans more than 2.5 Ga, making it a natural laboratory for the study of crustal formation and evolution over time. We estimate the crustal thickness, Poissons ratio, a proxy for bulk crustal composition, and shear velocity (Vs) structure from receiver functions at a network of seismograph stations recently deployed across the Archean Superior Craton, the Proterozoic Grenville, and the Phanerozoic Appalachian provinces. The bulk seismic crustal properties and shear velocity structure reveal a correlation with tectonic provinces of different ages: the post-Archean crust becomes thicker, faster, more heterogeneous, and more compositionally evolved. This secular variation pattern is consistent with a growing consensus that crustal growth efficiency increased at the end of the Archean. A lack of correlation among elevation, Moho topography, and gravity anomalies within the Proterozoic belt is better explained by buoyant mantle support rather than by compositional variations driven by lower crustal metamorphic reactions. A ubiquitous ∼20 km thick high-Vs lower crustal layer is imaged beneath the Proterozoic belt. The strong discontinuity at 20 km may represent the signature of extensional collapse of an orogenic plateau, accommodated by lateral crustal flow. Wide anorthosite massifs inferred to fractionate from a mafic mantle source are abundant in Proterozoic geology and are underlain by high-Vs lower crust and a gradational Moho. Mafic underplating may have provided a source for these intrusions and could have been an important post-Archean process stimulating mafic crustal growth in a vertical sense.

Evidence of micro-continent entrainment during crustal accretion

Simple models involving the gradual outboard accretion of material along curvilinear subduction zones are often inconsistent with field-based evidence. A recent study using 3-D geodynamic modelling has shown that the entrainment of an exotic continental fragment within a simple subduction system can result in a complex phase of growth. Although kinematic models based on structural mapping and high-resolution gravity and magnetic maps indicate that the pre-Carboniferous Tasmanides in southeastern Australia may have been subjected to this process, to date there has been little corroboration from crustal scale geophysical imaging. Here, we apply Bayesian transdimensional tomography to ambient noise data recorded by the WOMBAT transportable seismic array to constrain a detailed (20 km resolution in some areas) 3-D shear velocity model of the crust beneath southeast Australia. We find that many of the velocity variations that emerge from our inversion support the recently developed geodynamic and kinematic models. In particular, the full thickness of the exotic continental block, responsible for orocline formation and the tectonic escape of the back arc region, is imaged here for the first time. Our seismic results provide the first direct evidence that exotic continental fragments may profoundly affect the development of an accretionary orogen.

Decomposition of the laboratory gamma irradiation component of angular ESR spectra of fossil tooth enamel fragments

Spectrum decomposition of the angular measurements of fossil tooth enamel fragments using an automated simulated annealing (SA) procedure shows that the mix CO(2)(-) radicals generated by laboratory irradiation is significantly different to that of the natural sample. The naturally irradiated sample contains about 10% of non-oriented CO(2)(-) radicals and a mix of 35:65 orthorhombic to axial CO(2)(-) radicals. In contrast, laboratory irradiation generated about 40% of non-oriented radicals and a large amount of orthorhombic CO(2)(-) radicals, while we failed to detect any axial CO(2)(-) radicals. The results indicate that geological aging of the sample incurs various annealing and transfer processes; their precise nature is yet unknown. Nevertheless, the understanding of the formation and transfer processes that leads to the observed mix of CO(2)(-) radicals in fossil tooth enamel is essential for the reliable application of ESR dating.

Probabilistic surface reconstruction of coastal sea level rise during the twentieth century

We present a new surface reconstruction procedure based on the Bayesian inference method for coastal relative sea level variation during the twentieth century. Average rates are computed from tide gauge records. Models based on a Voronoi tessellation adapt to the level of information which proves well suited to the strong heterogeneity of data. Each point of the reconstructed surface is defined through a probability density function, a format particularly well adapted to this climate-related datum. The resolution of reconstructed surfaces strongly varies among the six large regions considered and within a given region. Anomalous sea level variations recorded locally are shown to reflect either anthropogenic effects or well-identified fast tectonics. For a poor data coverage, these can cause a problematic distortion of the reconstructed surface. Europe, North America, Australia, and Africa present a single trend with a decreasing precision of the reconstructed surface as a function of resolution of the tide gauge record. The most prominent feature in Europe is the pronounced uplift of Fennoscandia. Coasts of United States have the best resolution in North America and present stronger rates of sea level rise on the Atlantic than their European counterparts. Australia (especially in the North) and Africa are poorly resolved. Asia and South America depart clearly from this trend: a relatively uniform rise is obtained for Asia in spite of a good tide gauge record. Conversely, the reconstructed surface for South America presents an exceptional degree of roughness, at odds with a relatively poor record. Overall, this method not only offers a new assessment of sea level change (validating earlier results) but also quantifies the reliability of estimates.

On the Nature of the P-Wave Velocity Gradient in the Inner Core beneath Central America

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.

Cascadia subduction slab heterogeneity revealed by three-dimensional receiver function Kirchhoff migration

We present a 3-D model of upper mantle seismic discontinuity structure below Cascadia using a receiver function Kirchhoff migration method. A careful analysis of the primary and multiple reverberated phases allows imaging of the Juan de Fuca plate dipping below the North American continent. The subducting slab is observed as an eastward dipping signal at all latitudes. We associate this signal with a thermal gradient between the slab and surrounding mantle, rather than a sharp chemical discontinuity. Our model also shows along-strike variations in the dipping angle and strength of this signal. To the southern and northern ends of the subduction system, the signal is clearly observed down to ~300 km. However, beneath central Oregon, this structure is missing below ~150 km depth. We propose that this gap is due to weakening of the slab beneath central Oregon possibly caused by deformation and hydration combined with plume-slab interaction processes after subduction.