The Martian surface composition appears mainly mafic but recent observations have revealed the presence of differentiated rocks, only in the Highlands. Here, we demonstrate that differentiated melts can form during the construction of thick crustal regions on Mars by fractional crystallisation of a mafic protolith, without plate tectonics. On a stagnant-lid planet, regions of thicker crusts contain more heat-producing elements and are associated to thinner lithospheres and to higher mantle melt fractions. This induces larger crustal extraction rates where the crust is thicker. This positive feedback mechanism is favoured at large wavelengths and can explain the formation of the Martian dichotomy. We further develop an asymmetric parameterised thermal evolution model accounting for crustal extraction, where the well-mixed convective mantle is topped by two lithospheres (North/South) characterised by specific thermal and crustal structures. We use this model in a Bayesian inversion to investigate the conditions that allow crustal temperatures to be maintained above the basalt solidus during crustal growth, resulting in the formation of evolved melts. Among the thermal evolution models matching constraints on the structure of the Martian crust and mantle provided by the InSight NASA mission, a non-negligible fraction allows partial melting and differentiation of the crust in the south, which can occur very early (<100 Myr) as well as during the Hesperian ; partial melting in the north appears unlikely. Although crustal differentiation may occur on a hemispheric scale on Mars, its vertical extent is limited to less than a third of the crustal thickness.

The frequency/magnitude distribution of earthquakes can be approximated by an exponential law whose exponent (the so-called b-value) is routinely used for probabilistic seismic hazard assessment. The b-value is commonly measured using Aki’s maximum likelihood estimation, although biases can arise from the choice of completeness magnitude (i.e. the magnitude below which the exponential law is no longer valid). In this work, we introduce the b-Bayesian method, where the full frequency-magnitude distribution of earthquakes is modelled by the product of an exponential law and a detection law. The detection law is characterized by two parameters, which we jointly estimate with the b-value within a Bayesian framework. All available data are used to recover the joint probability distribution. The b-Bayesian approach recovers temporal variations of the b-value and the detectability using a transdimensional Markov chain Monte Carlo (McMC) algorithm to explore numerous configurations of their time variations. An application to a seismic catalog of far-western Nepal shows that detectability decreases significantly during the monsoon period, while the b-value remains stable, albeit with larger uncertainties. This confirms that variations in the b-value can be estimated independently of variations in detectability (i.e. completeness). Our results are compared with those obtained using the maximum likelihood estimation, and using the b-positive approach, showing that our method avoids dependence on arbitrary choices such as window length or completeness thresholds.

In geophysical inverse problems, the distribution of physical properties in an Earth model is inferred from a set of measured data. A necessary step is to select data that are best suited to the problem at hand. This step is performed ahead of solving the inverse problem, generally on the basis of expert knowledge. However, expert-opinion can introduce bias based on pre-conceptions. Here we apply a trans-dimensional algorithm to automatically weigh data on the basis of how consistent they are with the fundamental assumptions made to solve the inverse problem. We demonstrate this approach by inverting arrival times for the location of a seismic source in an elastic half space, under the assumptions of a point source and constant velocities. The key advantage is that the data do no longer need to be selected by an expert, but they are assigned varying weights during the inversion procedure.

Seismic hazard assessment in active fault zones can benefit of strain rate measurements derived from geodetic data. Producing a continuous strain rate map from discrete data is an inverse problem traditionally tackled with standard interpolation schemes. Most algorithms require user-defined regression parameters that determine the smoothness of the recovered velocity field, and the amplitude of its spatial derivatives. This may lead to biases in the strain rates estimation which could eventually impact studies on earthquake hazard. Here we propose a transdimensional Bayesian method to estimate surface strain rates from GNSS velocities. We parameterize the velocity field with a variable number of Delaunay triangles, and use a reversible jump Monte-Carlo Markov Chain algorithm to sample the probability distribution of surface velocities and spatial derivatives. The solution is a complete probability distribution function for each component of the strain rate field. We conduct synthetic tests and compare our approach to a standard b-spline interpolation scheme. Our method is more resilient to data errors and uneven data distribution, while providing uncertainties associated with recovered velocities and strain rates. We apply our method to the Southwestern US, an extensively studied and monitored area and infer probabilistic strain rates along the main fault systems, including the San Andreas one, from the inversion of interseismic GNSS velocities. Our approach provide a full description of the strain rate tensor for zones where strain rates are highly contrasted, with no need to manually tune user-defined parameters. We recover sharp velocity gradients, without systematic artifacts.

The seismic low-velocity zone (LVZ) of the upper mantle is generally associated with a low-viscosity asthenosphere that has a key role in decoupling tectonic plates from the mantle. However, the origin of the LVZ remains unclear. Some studies attribute its low seismic velocities to a small amount of partial melt of minerals in the mantle, whereas others attribute them to solid-state mechanisms near the solidus, or the effect of its volatile contents. Observations of shear attenuation provide additional constraints on the origin of the LVZ. On the basis of the interpretation of global three-dimensional shear attenuation and velocity models, here we report partial melt occurring within the LVZ. We observe that partial melting down to 150–200 kilometres beneath mid-ocean ridges, major hotspots and back-arc regions feeds the asthenosphere. A small part of this melt (less than 0.30 per cent) remains trapped within the oceanic LVZ. Melt is mostly absent under continental regions. The amount of melt increases with plate velocity, increasing substantially for plate velocities of between 3 centimetres per year and 5 centimetres per year. This finding is consistent with previous observations of mantle crystal alignment underneath tectonic plates. Our observations suggest that by reducing viscosity, melt facilitates plate motion and large-scale crystal alignment in the asthenosphere.

Seismic anisotropy in the Earth’s mantle inferred from seismic observations is usually interpreted either in terms of intrinsic anisotropy due to Crystallographic Preferred Orientation (CPO) of minerals, or extrinsic anisotropy due to rock-scale Shape Preferred Orientation (SPO). The coexistence of both contributions misconstrues the origins of seismic anisotropy observed in seismic tomography models. It is thus essential to discriminate CPO from SPO. Homogenization/upscaling theory provides means to achieve this goal. This theory enables to compute the effective elastic properties of a heterogeneous medium, as seen by long-period waves. In this work, we investigate the effects of upscaling an intrinsically anisotropic and highly heterogeneous Earth’s mantle. We show analytically in 1-D that the full effective radial anisotropy ξ * is approximately the product of the effective intrinsic radial anisotropy ξ * CPO and the extrinsic radial anisotropy ξ * SPO : ξ * ≈ ξ * CPO x ξ * SPO. This law is verified numerically in the case of a 2-D marble cake model of the mantle with a binary composition, and in the presence of CPO obtained from a micro-mechanical model of olivine deformation. We compute the long-wavelength effective equivalent of this mantle model using the 3-D non-periodic elastic homogenization technique. Our numerical findings predict that for wavelenghts smaller than the scale of deformation patterns, tomography may overestimate the true anisotropy (i.e. intrinsic anisotropy due to CPO) due to significant SPO-induced extrinsic anisotropy. However, at wavelenghts larger than deformation patterns, intrinsic anisotropy is always underestimated in tomographic models due to the spatial averaging of the preferred orientation of anisotropic minerals. Thus, we show that it is imperative to homogenize a CPO evolution model first before drawing comparisons with tomographic models. As a demonstration, we use our composite law with a homogenized CPO model of a plate-driven flow underneath a mid-ocean ridge, to estimate the SPO contibution to an existing tomographic model of radial anisotropy.