Previously proposed models for the evolution of the Tyrrhenian basin‐Apenninic arc system do not seem to satisfactorily explain the dynamic relationship between extension in the Tyrrhenian and compression in the Apennines. The most important regional plate kinematic constraints that any model has to satisfy in this case are: (1) the timing of extension in the Tyrrhenian and compression in the Apennines, (2) the amount of shortening in the Apennines, (3) the amount of extension in the Tyrrhenian, and (4) Africa‐Europe relative motion. The estimated contemporaneous (post‐middle Miocene) amounts of extension in the Tyrrhenian and of shortening in the Apennines appear to be very similar. The extension in the Tyrrhenian Sea is mostly accomplished in an E‐W direction, and cannot be straightforwardly related to the calculated N‐S Africa‐Europe convergence. A model of outward arc migration fits all these constraints. In a subducting system, the subduction zone is expected to migrate outward due to the sinking of the underthrusting plate into the mantle. The formation of a back‐arc or internal basin, i.e. of a basin internal to the surrounding belt of compression, (in this case the Tyrrhenian Sea) is then expected to take place if the motion of the overriding plate does not compensate for the retreat of the subduction zone. The sediment cover will be stripped from the underthrusting plate by the outward migrating arc of the overriding plate, and will accumulate to form an accretionary wedge. This accretionary body will grow outward in time, and will eventually become an orogenic belt, (in this case the present Apennines) when the migrating arc collides with the stable continental foreland on the subducting plate. An arc migration model satisfactorily accounts for the basic features of the Tyrrhenian‐Apennine system and for its evolution from 17 Ma to the present, and appears to be analogous to the tectonic evolution of other back‐arc settings both inside and outside the Mediterranean region. An interesting implication of the proposed accretionary origin of the Apennines is that the problematic “Argille Scagliose” (scaly clays) melange units might have been emplaced as overpressured mud diapirs, as observed in other accretionary prisms, and not by gravity slides from the internal zones.

Summary A key element in the solution of a geophysical inverse problem is the quantification of non‐uniqueness, that is, how much parameters of an inferred earth model can vary while fitting a set of measurements. A widely used approach is that of Bayesian inference, where Bayes' rule is used to determine the uncertainty of the earth model parameters a posteriori given the data. I describe here, a natural extension of Bayesian parameter estimation that accounts for the posterior probability of how complex an earth model is (specifically, how many layers it contains). This approach has a built‐in parsimony criterion: among all earth models that fit the data, those with fewer parameters (fewer layers) have higher posterior probabilities. To implement this approach in practice, I use a Markov chain Monte Carlo (MCMC) algorithm applied to the nonlinear problem of inverting DC resistivity sounding data to infer characteristics of a 1‐D earth model. The earth model is parametrized as a layered medium, where the number of layers and their resistivities and thicknesses are poorly known a priori. The algorithm obtains a sample of layered media from the posterior distribution; this sample measures non‐uniqueness in terms of how many layers are effectively resolved by the data and of the range of layer thicknesses and resistivities consistent with the data. Because the complexity of the model is effectively determined by the data, the solution does not need to be regularized. This is a desirable feature, because requiring the solution to be smooth beyond what is implied by prior information can lead to underestimating posterior uncertainty. Letting the number of layers be a free parameter, as done here, broadens the space of earth models possible a priori and makes the determination of posterior uncertainty less dependent on the parametrization.

Atmospheric carbon dioxide concentrations and climate are regulated on geological timescales by the balance between carbon input from volcanic and metamorphic outgassing and its removal by weathering feedbacks; these feedbacks involve the erosion of silicate rocks and organic-carbon-bearing rocks. The integrated effect of these processes is reflected in the calcium carbonate compensation depth, which is the oceanic depth at which calcium carbonate is dissolved. Here we present a carbonate accumulation record that covers the past 53 million years from a depth transect in the equatorial Pacific Ocean. The carbonate compensation depth tracks long-term ocean cooling, deepening from 3.0-3.5 kilometres during the early Cenozoic (approximately 55 million years ago) to 4.6 kilometres at present, consistent with an overall Cenozoic increase in weathering. We find large superimposed fluctuations in carbonate compensation depth during the middle and late Eocene. Using Earth system models, we identify changes in weathering and the mode of organic-carbon delivery as two key processes to explain these large-scale Eocene fluctuations of the carbonate compensation depth.

A common way to account for uncertainty in inverse problems is to apply Bayes' rule and obtain a posterior distribution of the quantities of interest given a set of measurements. A conventional Bayesian treatment, however, requires assuming specific values for parameters of the prior distribution and of the distribution of the measurement errors (e.g., the standard deviation of the errors). In practice, these parameters are often poorly known a priori, and choosing a particular value is often problematic. Moreover, the posterior uncertainty is computed assuming that these parameters are fixed; if they are not well known a priori, the posterior uncertainties have dubious value. This paper describes extensions to the conventional Bayesian treatment that assign uncertainty to the parameters defining the prior distribution and the distribution of the measurement errors. These extensions are known in the statistical literature as “empirical Bayes” and “hierarchical Bayes.” We demonstrate the practical application of these approaches to a simple linear inverse problem: using seismic traveltimes measured by a receiver in a well to infer compressional wave slowness in a 1D earth model. These procedures do not require choosing fixed values for poorly known parameters and, at most, need a realistic range (e.g., a minimum and maximum value for the standard deviation of the measurement errors). Inversion is thus made easier for general users, who are not required to set parameters they know little about.