Geophysical imaging using trans-dimensional trees.

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

Bayesian noise-reduction in Arabia/Somalia and Nubia/Arabia finite rotations since ~20 Ma: Implications for Nubia/Somalia relative motion

Knowledge of Nubia/Somalia relative motion since the Early Neogene is of particular importance in the Earth Sciences, because it (i) impacts on inferences on African dynamic topography; and (ii) allows us to link plate kinematics within the Indian realm with those within the Atlantic basin. The contemporary Nubia/Somalia motion is well known from geodetic observations. Precise estimates of the past-3.2-Myr average motion are also available from paleo-magnetic observations. However, little is known of the Nubia/Somalia motion prior to ∼3.2 Ma, chiefly because the Southwest Indian Ridge spread slowly, posing a challenge to precisely identify magnetic lineations. This also makes the few observations available particularly prone to noise. Here we reconstruct Nubia/Somalia relative motions since ∼20 Ma from the alternative plate-circuit Nubia-Arabia-Somalia. We resort to trans-dimensional hierarchical Bayesian Inference, which has proved effective in reducing finite-rotation noise, to unravel the Arabia/Somalia and Arabia/Nubia motions. We combine the resulting kinematics to reconstruct the Nubia/Somalia relative motion since ∼20 Ma. We verify the validity of the approach by comparing our reconstruction with the available record for the past ∼3.2 Myr, obtained through Antarctica. Results indicate that prior to ∼11 Ma the total motion between Nubia and Somalia was faster than today. Furthermore, it featured a significant strike-slip component along the Nubia/Somalia boundary. It is only since ∼11 Ma that Nubia diverges away from Somalia at slower rates, comparable to the present-day one. Kinematic changes of some 20% might have occurred in the period leading to the present-day, but plate-motion steadiness is also warranted within the uncertainties. Key Points Bayesian inference to reduce finite-rotation noise Reconstruction of Nubia/Somalia motion since ∼20 Ma Nubia/Somalia relative motion changed at ∼11 M

A statistical simulation of magnetic particle alignment in sediments

Sedimentary magnetizations are fundamental to palaeomagnetism, but the mechanisms that control remanence acquisition remain poorly constrained. Observed sedimentary natural remanent magnetizations are often orders of magnitude smaller than the saturatio

Rethinking lifestyle and middle-class migration in “left behind” regions

So-called “left behind” regions have gained infamy for working-class discontent. Yet a concurrent phenomenon has gone unremarked: middle-class lifestyles in peripheral places. This article examines how middle-class migrants (defined by economic, social, and cultural capital) to peripheral regions envisage and enact their aspirations. Against presumed migration trajectories to growing urban centres or for better-paid employment, we argue that seeming moves down the “escalator” reveal how inequalities between regions offer some migrants opportunities to enact middle-class lifestyles affordably. We present a qualitative case study of West Wales and the Valleys, predominantly rural and post-industrial and statistically among Europe's most deprived regions. Drawing from interviews with EU and UK in-migrants alongside long-term residents, we illustrate how three dimensions of quality of life—material, relational, subjective—are mobilised in middle-class placemaking amidst peripherality. We demonstrate how spatial inequalities and career trade-offs offer affordable material access to lifestyle and how middle-class aspirations enable migrants to subjectively transform peripherality into enchantment

Advances in Trans-dimensional Geophysical Inference

This research presents a series of novel Bayesian trans-dimensional methods for geophysical inversion. A first example illustrates how Bayesian prior information obtained from theory and numerical experiments can be used to better inform a difficult multi-modal inversion of dispersion information from empirical Greens functions obtained from ambient noise cross-correlation. This approach is an extension of existing partition modeling schemes. An entirely new class of trans-dimensional algorithm, called the trans-dimensional tree method is introduced. This new method is shown to be more efficient at coupling to a forward model, more efficient at convergence, and more adaptable to different dimensions and geometries than existing approaches. The efficiency and flexibility of the trans-dimensional tree method is demonstrated in two different examples: (1) airborne electromagnetic tomography (AEM) in a 2D transect inversion, and (2) a fully non-linear inversion of ambient noise tomography. In this latter example the resolution at depth has been significantly improved by inverting a contiguous band of frequencies jointly rather than as independent phase velocity maps, allowing new insights into crustal architecture beneath Iceland. In a first test case for even larger scale problems, an application of the trans-dimensional tree approach to large global data set is presented. A global database of nearly 5 million multi-model path average Rayleigh wave phase velocity observations has been used to construct global phase velocity maps. Results are comparable to existing published phase velocity maps, however, as the trans-dimensional approach adapts the resolution appropriate to the data, rather than imposing damping or smoothing constraints to stabilize the inversion, the recovered anomaly magnitudes are generally higher with low uncertainties. While further investigation is needed, this early test case shows that trans-dimensional sampling can be applied to global scale seismology problems and that previous analyses may, in some locales, under estimate the heterogeneity of the Earth. Finally, in a further advancement of partition modelling with variable order polynomials, a new method has been developed called trans-dimensional spectral elements. Previous applications involving variable order polynomials have used polynomials that are both difficult to work with in a Bayesian framework and unstable at higher orders. By using the orthogonal polynomials typically used in modern full-waveform solvers, the useful properties of this type of polynomial and its application in trans-dimensional inversion are demonstrated. Additionally, these polynomials can be directly used in complex differential solvers and an example of this for 1D inversion of surface wave dispersion curves is given

Transdimensional Bayesian Attenuation Tomography of the Upper Inner Core

Following the linearized attenuation tomography from our previous study (Pejić et al., 2017, https://doi.org/10.1002/2016JB013692), we perform hierarchical transdimensional Bayesian tomography of the upper ≈400 km of the inner core, using 398 globally distributed t∗ estimates. The results are in good agreement with the ones obtained through linearized tomography: they show more complex attenuation pattern than the purely hemispherical one, and the noise estimated from the hierarchical inversion is in good agreement with estimates obtained from the Discrepancy Principle in the previous study. The attenuation pattern we observe gives more weight to the geodynamical models that couple the thermal anomalies of the lowermost mantle to the inner core boundary.Pejic and Hawkins thank the Australian National University for IPRS and APA scholarships that made this research possible

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