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SUMMARY Presence of electrical anisotropy in the lithosphere can provide useful constraints on regional structure patterns and dynamics of tectonic processes, and they can be imaged by magnetotelluric (MT) data. However, Inversion of MT data for anisotropic structures using standard gradient-based approaches requires subjective choices of model regularization for constraining structure and anisotropy complexity. Furthermore, the ubiquitous presence of galvanic distortion due to small-scale near-surface conductivity inhomogeneities prevents accurate imaging of subsurface structures if ignored or not properly removed. Here, we present a transdimensional Bayesian approach for inverting MT data in layered anisotropic media. The algorithm allows flexible model parametrization, in which both the number of layers and model parameters of each layer are treated as unknowns. In this manner, the presence or absence of anisotropy within the layers, as well as the level of model complexity, is determined adaptively by the data. In addition, to account for the effects of galvanic distortion, three frequency-independent distortion parameters resulting from the distortion decomposition are treated as additional variables during the inversion. We demonstrate the efficiency of the algorithm to resolve both isotropic and anisotropic structures with synthetic and field MT data sets affected by galvanic distortion effects. The transdimensional inversion results for the field data are compatible with results from previous studies, and our results improve the constraints on the magnitude and the azimuth (i.e. most conductive direction) of electrically anisotropic structures. For practical applications, the validity of 1-D anisotropic approximation should be first tested prior to the use of our approach. Otherwise it may produce spurious anisotropic structures due to the inapplicability of the anisotropic 1-D inversion for MT data affected by 2-D or 3-D electrical resistivity structures.

SUMMARY To understand earth processes, geoscientists infer subsurface earth properties such as electromagnetic resistivity or seismic velocity from surface observations of electromagnetic or seismic data. These properties are used to populate an earth model vector, and the spatial variation of properties across this vector sheds light on the underlying earth structure or physical phenomenon of interest, from groundwater aquifers to plate tectonics. However, to infer these properties the spatial characteristics of these properties need to be known in advance. Typically, assumptions are made about the length scales of earth properties, which are encoded a priori in a Bayesian probabilistic setting. In an optimization setting, appeals are made to promote model simplicity together with constraints which keep models close to a preferred model. All of these approaches are valid, though they can lead to unintended features in the resulting inferred geophysical models owing to inappropriate prior assumptions, constraints or even the nature of the solution basis functions. In this work it will be shown that in order to make accurate inferences about earth properties, inferences can first be made about the underlying length scales of these properties in a very general solution basis. From a mathematical point of view, these spatial characteristics of earth properties can be conveniently thought of as ‘properties’ of the earth properties. Thus, the same machinery used to infer earth properties can be used to infer their length scales. This can be thought of as an ‘infer to infer’ paradigm analogous to the ‘learning to learn’ paradigm which is now commonplace in the machine learning literature. However, it must be noted that (geophysical) inference is not the same as (machine) learning, though there are many common elements which allow for cross-pollination of useful ideas from one field to the other, as is shown here. A non-stationary trans-dimensional Gaussian Process (TDGP) is used to parametrize earth properties, and a multichannel stationary TDGP is used to parametrize the length scales associated with the earth property in question. Using non-stationary kernels, that is kernels with spatially variable length scales, models with sharp discontinuities can be represented within this framework. As GPs are multidimensional interpolators, the same theory and computer code can be used to solve geophysical problems in 1-D, 2-D and 3-D. This is demonstrated through a combination of 1-D and 2-D non-linear regression examples and a controlled source electromagnetic field example. The key difference between this and previous work using TDGP is generalized nested inference and the marginalization of prior length scales for better posterior subsurface property characterization.

SUMMARY Bayesian inversion of magnetotelluric (MT) data is a powerful but computationally expensive approach to estimate the subsurface electrical conductivity distribution and associated uncertainty. Approximating the Earth subsurface with 1-D physics considerably speeds-up calculation of the forward problem, making the Bayesian approach tractable, but can lead to biased results when the assumption is violated. We propose a methodology to quantitatively compensate for the bias caused by the 1-D Earth assumption within a 1-D trans-dimensional Markov chain Monte Carlo sampler. Our approach determines site-specific likelihood functions which are calculated using a dimensionality discrepancy error model derived by a machine learning algorithm trained on a set of synthetic 3-D conductivity training images. This is achieved by exploiting known geometrical dimensional properties of the MT phase tensor. A complex synthetic model which mimics a sedimentary basin environment is used to illustrate the ability of our workflow to reliably estimate uncertainty in the inversion results, even in presence of strong 2-D and 3-D effects. Using this dimensionality discrepancy error model we demonstrate that on this synthetic data set the use of our workflow performs better in 80 per cent of the cases compared to the existing practice of using constant errors. Finally, our workflow is benchmarked against real data acquired in Queensland, Australia, and shows its ability to detect the depth to basement accurately.

SUMMARY Surface heat flow has been widely used to constrain the thermal structure of subduction zones. However, the forward modelling approaches in previous geodynamic studies have only provided limited information on the model parameters controlling the thermal structure, which makes model validation difficult. Here we apply a probabilistic inversion technique based on Bayes’ theorem to surface heat flow data from Tohoku in Japan and Cascadia to simultaneously infer five model parameters that appear to have the greatest influence on the thermal structure of subduction zones. The surface heat flow is predicted via 2-D steady-state thermomechanical modelling. The Metropolis algorithm is used to obtain the posterior probability distributions. A comparison of our results with previous estimates indicates that our activation energy for the shear viscosity of dislocation creep is lower in both regions, and our radiogenic heat production rate in the upper continental crust is lower in Cascadia. These findings suggest that our geodynamic models cannot explain the surface heat flow observations with the acceptable ranges of model parameter values. We therefore need to refine the models by including, for example, the effects of recent backarc extension, vigorous thermal convection beneath the overriding plate and fluid circulation in the uppermost part of the oceanic crust. The approach presented here also allows us to determine trade-offs between the parameters. This study provides a framework to validate and refine geodynamic models based on various types of observations.

SummaryWe present a methodology for 1-D imaging of upper-mantle structure using a Bayesian approach that incorporates a novel combination of seismic data types and an adaptive parametrization based on piecewise discontinuous splines. Our inversion algorithm lays the groundwork for improved seismic velocity models of the lithosphere and asthenosphere by harnessing the recent expansion of large seismic arrays and computational power alongside sophisticated data analysis. Careful processing of P- and S-wave arrivals isolates converted phases generated at velocity gradients between the mid-crust and 300 km depth. This data is allied with ambient noise and earthquake Rayleigh wave phase velocities to obtain detailed V S and V P velocity models. Synthetic tests demonstrate that converted phases are necessary to accurately constrain velocity gradients, and S–p phases are particularly important for resolving mantle structure, while surface waves are necessary for capturing absolute velocities. We apply the method to several stations in the northwest and north-central United States, finding that the imaged structure improves upon existing models by sharpening the vertical resolution of absolute velocity profiles, offering robust uncertainty estimates, and revealing mid-lithospheric velocity gradients indicative of thermochemical cratonic layering. This flexible method holds promise for increasingly detailed understanding of the upper mantle.

International audience; Azimuthal anisotropy is a powerful tool to reveal information about both the present structure and past evolution of the mantle. Anisotropic images of the upper mantle are usually obtained by analysing various types of seismic observables, such as surface wave dispersion curves or waveforms, SKS splitting data, or receiver functions. These different data types sample different volumes of the earth, they are sensitive to different length scales, and hence are associated with different levels of uncertainties. They are traditionally interpreted separately, and often result in incompatible models. We present a Bayesian inversion approach to jointly invert these different data types. Seismograms for SKS and P phases are directly inverted using a cross-convolution approach, thus avoiding intermediate processing steps, such as numerical deconvolution or computation of splitting parameters. Probabilistic 1-D profiles are obtained with a transdimensional Markov chain Monte Carlo scheme, in which the number of layers, as well as the presence or absence of anisotropy in each layer, are treated as unknown parameters. In this way, seismic anisotropy is only introduced if required by the data. The algorithm is used to resolve both isotropic and anisotropic layering down to a depth of 350 km beneath two seismic stations in North America in two different tectonic settings: the stable Canadian shield (station FFC) and the tectonically active southern Basin and Range Province (station TA-214A). In both cases, the lithosphere-asthenosphere boundary is clearly visible, and marked by a change in direction of the fast axis of anisotropy. Our study confirms that azimuthal anisotropy is a powerful tool for detecting layering in the upper mantle.

SUMMARY We present an inversion of nutation observations in terms of parameters characterizing the Earth’s interior properties. We use a Bayesian inversion in the time-domain, allowing us to take fully into account non-linearities in the nutation model and to reduce the loss of information occurring in frequency-domain inversions. Among the parameters we retrieve are two complex parameters, K CMB and K ICB, referred to as ‘coupling constants’, characterizing the mechanical coupling at the core–mantle boundary (CMB) and the inner core boundary (ICB), respectively. Based on a joint inversion of nutation observations provided by different analysis centres, we find Im(K CMB) = (−1.78 ± 0.02) 10 −5 ,R e(K ICB) = (1.01 ± 0.02) 10 −3 and Im(K ICB) = (−1.09 ± 0.03) 10 −3 (where the errors correspond to 99.7 per cent confidence intervals). While our value of Im(K CMB) is similar to previous estimates, our new values of Re(K ICB) and Im(K ICB) are significantly different. This is mainly because of the different inversion strategy that we use and also because of the lengthier record of observation available. We show that, based on existing coupling models, neither viscous nor electromagnetic coupling alone can explain our new values of Re(K ICB) and Im(K ICB). A combination of these two mechanisms is required and necessitates a radial magnetic field at the ICB of total rms strength between 6 and 7 mT and a kinematic viscosity of the fluid core at the ICB should be between 10 and 30 m 2 s −1 , depending on the exact partition between viscous and electromagnetic coupling.