[1] Traditional inversion techniques applied to the problem of characterizing the thermal and compositional structure of the upper mantle are not well suited to deal with the nonlinearity of the problem, the trade-off between temperature and compositional effects on wave velocities, the nonuniqueness of the compositional space, and the dissimilar sensitivities of physical parameters to temperature and composition. Probabilistic inversions, on the other hand, offer a powerful formalism to cope with all these difficulties, while allowing for an adequate treatment of the intrinsic uncertainties associated with both data and physical theories. This paper presents a detailed analysis of the two most important elements controlling the outputs of probabilistic (Bayesian) inversions for temperature and composition of the Earth's mantle, namely the a priori information on model parameters, (m), and the likelihood function, L(m). The former is mainly controlled by our current understanding of lithosphere and mantle composition, while the latter conveys information on the observed data, their uncertainties, and the physical theories used to relate model parameters to observed data.[2] The benefits of combining specific geophysical datasets (Rayleigh and Love dispersion curves, body wave tomography, magnetotelluric, geothermal, petrological, gravity, elevation, and geoid), and their effects on L(m), are demonstrated by analyzing their individual and combined sensitivities to composition and temperature as well as their observational uncertainties. The dependence of bulk density, electrical conductivity, and seismic velocities to major-element composition is systematically explored using Monte Carlo simulations. We show that the dominant source of uncertainty in the identification of compositional anomalies within the lithosphere is the intrinsic nonuniqueness in compositional space. A general strategy for defining (m) is proposed based on statistical analyses of a large database of natural mantle samples collected from different tectonic settings (xenoliths, abyssal peridotites, ophiolite samples, etc.). This strategy relaxes more typical and restrictive assumptions such as the use of local/limited xenolith data or compositional regionalizations based on age-composition relations. We demonstrate that the combination of our (m) with a L(m) that exploits the differential sensitivities of specific geophysical observables provides a general and robust inference platform to address the thermochemical structure of the lithosphere and sublithospheric upper mantle. An accompanying paper deals with the integration of these two functions into a general 3-D multiobservable Bayesian inversion method and its computational implementation.

We apply a novel 3‐D multiobservable probabilistic tomography method that we have recently developed and benchmarked, to directly image the thermochemical structure of the Colorado Plateau and surrounding areas by jointly inverting P wave and S wave teleseismic arrival times, Rayleigh wave dispersion data, Bouguer anomalies, satellite‐derived gravity gradients, geoid height, absolute (local and dynamic) elevation, and surface heat flow data. The temperature and compositional structures recovered by our inversion reveal a high level of correlation between recent basaltic magmatism and zones of high temperature and low Mg# (i.e., refertilized mantle) in the lithosphere, consistent with independent geochemical data. However, the lithospheric mantle is overall characterized by a highly heterogeneous thermochemical structure, with only some features correlating well with either Proterozoic and/or Cenozoic crustal structures. This suggests that most of the present‐day deep lithospheric architecture reflects the superposition of numerous geodynamic events of different scale and nature to those that created major crustal structures. This is consistent with the complex lithosphere‐asthenosphere system that we image, which exhibits a variety of multiscale feedback mechanisms (e.g., small‐scale convection, magmatic intrusion, delamination, etc.) driving surface processes. Our results also suggest that most of the present‐day elevation in the Colorado Plateau and surrounding regions is the result of thermochemical buoyancy sources within the lithosphere, with dynamic effects (from sublithospheric mantle flow) contributing only locally up to ∼15–35%.

No abstract

1] Here we present a 3-D multi-observable probabilistic inversion method, particularly designed for high-resolution (regional) thermal and compositional mapping of the lithosphere and sub-lithospheric upper mantle that circumvents the problems associated with traditional inversion methods. The key aspects of the method are as follows: (a) it exploits the increasing amount and quality of geophysical datasets; (b) it combines multiple geophysical observables (Rayleigh and Love dispersion curves, body-wave tomography, magnetotelluric, geothermal, petrological, gravity, elevation, and geoid) with different sensitivities to deep/shallow, thermal/compositional anomalies into a single thermodynamic-geophysical framework; (c) it uses a general probabilistic (Bayesian) formulation to appraise the data; (d) no initial model is needed; (e) compositional a priori information relies on robust statistical analyses of a large database of natural mantle samples; and (f) it provides a natural platform to estimate realistic uncertainties. In addition, the modular nature of the method/algorithm allows for incorporating or isolating specific forward operators according to available data. The strengths and limitations of the method are thoroughly explored with synthetic models. It is shown that the a posteriori probability density function (i.e., solution to the inverse problem) satisfactorily captures spatial variations in bulk composition and temperature with high resolution, as well as sharp discontinuities in these fields. Our results indicate that only temperature anomalies of T & 150°C and large compositional anomalies of Mg# > 3 (or bulk Al 2 O 3 > 1.5) can be expected to be resolved simultaneously when combining high-quality geophysical data. This resolving power is sufficient to explore some long-standing problems regarding the nature and evolution of the lithosphere (e.g., vertical stratification of cratonic mantle, compositional versus temperature signatures in seismic velocities, etc) and offers new opportunities for joint studies of the structure of the upper mantle with unprecedented resolution. (2013), 3-D multi-observable probabilistic inversion for the compositional and thermal structure of the lithosphere and upper mantle. II: general methodology and resolution analysis,

[1] We present an interactive 3-D computer program (LitMod3D) developed to perform combined geophysical-petrological modeling of the lithosphere and sublithospheric upper mantle. In contrast to other available modeling software, LitMod3D is built within an internally consistent thermodynamicgeophysical framework, where all relevant properties are functions of temperature, pressure, and composition. By simultaneously solving the heat transfer, thermodynamic, rheological, geopotential, and isostasy (local and flexural) equations, the program outputs temperature, pressure, surface heat flow, density (bulk and single phase), seismic wave velocities, geoid and gravity anomalies, elevation, and lithospheric strength for any given model. These outputs can be used to obtain thermal and compositional models of the lithosphere and sublithospheric upper mantle that simultaneously fit all available geophysical and petrological observables. We illustrate some of the advantages and limitations of LitMod3D using synthetic models and comparing our predictions with those from other modeling methods. In particular, we show that (1) temperature at midlithosphere depths may be overestimated by as much as 200 K when compositional heterogeneities in the mantle and T-P effects are not considered in lithospheric models and (2) the neglect of mantle phase transformations on gravity-based models in thin-crust settings can result in a significant overestimation and underestimation of the derived crustal thickness and its internal density distribution, respectively.

No abstract

[1] The electrical conductivity of mantle minerals is highly sensitive to parameters that characterize the structure and state of the lithosphere and sublithospheric mantle, and mapping its lateral and vertical variations gives insights into formation and deformation processes. We review state-of-the-art conductivity models based on laboratory studies for the most relevant upper mantle minerals and define a bulk conductivity model for the upper mantle that accounts for temperature, pressure, and compositional variations. The bulk electrical conductivity model has been integrated into the software package LitMod, which allows for petrological and geophysical modeling of the lithosphere and sublithospheric upper mantle within an internally consistent thermodynamic-geophysical framework. We apply our methodology to model the upper mantle thermal structure and hydrous state of the western block of the Archean Kaapvaal Craton and the Proterozoic Rehoboth Terrane, in southern Africa, integrating different geophysical and petrological observables: namely, elevation, surface heat flow, and magnetotelluric and xenolith data. We find that to fit the measured magnetotelluric responses in both the Kaapvaal and Rehoboth terranes, the uppermost depleted part of the lithosphere has to be wetter than the lowermost melt-metasomatized and refertilized lithospheric mantle. We estimate present-day thermal lithosphere-asthenosphere boundary (LAB) depths of 230-260 and 150 ± 10 km for the western block of the Kaapvaal and Rehoboth terranes, respectively. For the Kaapvaal, the depth of the present-day thermal LAB differs significantly from the chemical LAB, as defined by the base of a depleted mantle, which might represent an upper level of melt percolation and accumulation within the lower lithosphere.

[1] Measurements of electrical conductivity of "slightly damp" mantle minerals from different laboratories are inconsistent, requiring geophysicists to make choices between them when interpreting their electrical observations. These choices lead to dramatically different conclusions about the amount of water in the mantle, resulting in conflicting conclusions regarding rheological conditions; this impacts on our understanding of mantle convection, among other processes. To attempt to reconcile these differences, we test the laboratory-derived proton conduction models by choosing the simplest petrological scenario possiblecratonic lithosphere -from two locations in southern Africa where we have the most complete knowledge. We compare and contrast the models with field observations of electrical conductivity and of the amount of water in olivine and show that none of the models for proton conduction in olivine proposed by three laboratories are consistent with the field observations. We derive statistically model parameters of the general proton conduction equation that satisfy the observations. The pre-exponent dry proton conduction term (s 0 ) and the activation enthalpy (DH wet ) are derived with tight bounds, and are both within the broader 2s errors of the different laboratory measurements. The two other terms used by the experimentalists, one to describe proton hopping (exponent r on pre-exponent water content C w ) and the other to describe H 2 O concentration-dependent activation enthalpy (term aC w 1/3 added to the activation energy), are less well defined and further field geophysical and petrological observations are required, especially in regions of higher temperature and higher water content. Calibrating laboratory-determined models of electrical conductivity of mantle minerals using geophysical and petrological observations, Geochem. Geophys. Geosyst., 13, Q06010,