3‐D multiobservable probabilistic inversion for the compositional and thermal structure of the lithosphere and upper mantle. I:a prioripetrological information and geophysical observables

Abstract

[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.

High resolution 3-D crustal structure beneath NE China from joint inversion of ambient noise and receiver functions using NECESSArray data

“…We thus used a Markov chain Monte Carlo (MCMC) method to invert for S wave velocity by only using surface wave data, and roughly estimated model uncertainties (Afonso et al, 2013;Shen et al, 2013b). This non-linear inversion method generates an ensemble of acceptable models to represent the posterior probability distribution function (PDF) of the earth structure reflected by the observations (Afonso et al, 2013;Bodin et al, 2012;Shen et al, 2013b). We used 4 b-splines and 5 b-splines to represent crustal and mantle layers, respectively.…”

The thermochemical structure of the lithosphere and upper mantle beneath south China: Results from multiobservable probabilistic inversion

“…In this work, we follow the method described by Afonso et al . [, ], focusing on the 1‐D structure of nine distinct lithospheric columns within south China for which reliable surface wave data exist (section ).…”

“…This PDF summarizes all the information we have on both the model parameters and the observable data and represents our best “state of knowledge.” Likewise, all prior information about the parameter space that is independent from the actual observational data is typically represented by another PDF, known as the prior PDF [cf. Tarantola , ; Afonso et al ., ]. When no closed forms exist for these PDFs and the parameter space is large (as in the present case), Monte Carlo sampling methods are commonly used to solve the inversion problem [cf.…”

Comparing gravity-based to seismic-derived lithosphere densities: a case study of the British Isles and surrounding areas

“…Another study proposed to include electrical conductivity in the joint lithosphere studies, due to its different sensitivity to temperature and composition (Khan et al 2015). The most advanced joint inversion studies are characterizing the thermochemical structure of the lithosphere using seismic data, gravity observations, and surface heat flow, together with geochemical information of the rock composition (Afonso et al 2013a(Afonso et al ,b, 2016b.…”