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.

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[1] Orbital tuning, the process of fitting sedimentary cycles to orbital periodicities, can estimate with high resolution the timing and duration of key events in the geological record. We formulate here orbital tuning as the inverse problem of finding the variation in sedimentation rate that matches sediment cycles with orbital periodicities. Instead of obtaining a single best estimate, we apply a Bayesian formulation and define a probability distribution of sedimentation rate variations that result in powerful orbital periodicities. By sampling this distribution with a Monte Carlo method, we quantify the uncertainty in the inferred sedimentation rates due to uncertainties in the tuning periods and to components of the sedimentary signal that are unrelated to orbital cycles. The method is applied to the chronology of a 30 m interval in the Cismon APTICORE borehole (Southern Alps, Italy) that includes the early Aptian oceanic anoxic event 1a (Selli Level), estimated to last 1.11 ± 0.11 Ma (95% interval). The d 13 C record shows a sudden negative shift of about −1‰ at the base of the Selli Level (22-47 ka) followed by a recovery to preshift values in ∼240 ka, consistent with a scenario where light carbon is quickly added and then flushed out of the oceanatmosphere system.

The geologic record of Milankovitch climate cycles provides a rich conceptual and temporal framework for evaluating Earth system evolution, bestowing a sharp lens through which to view our planet's history. However, the utility of these cycles for constraining the early Earth system is hindered by seemingly insurmountable uncertainties in our knowledge of solar system behavior (including Earth-Moon history), and poor temporal control for validation of cycle periods (e.g., from radioisotopic dates). Here we address these problems using a Bayesian inversion approach to quantitatively link astronomical theory with geologic observation, allowing a reconstruction of Proterozoic astronomical cycles, fundamental frequencies of the solar system, the precession constant, and the underlying geologic timescale, directly from stratigraphic data. Application of the approach to 1.4-billion-year-old rhythmites indicates a precession constant of 85.79 ± 2.72 arcsec/year (2σ), an Earth-Moon distance of 340,900 ± 2,600 km (2σ), and length of day of 18.68 ± 0.25 hours (2σ), with dominant climatic precession cycles of ∼14 ky and eccentricity cycles of ∼131 ky. The results confirm reduced tidal dissipation in the Proterozoic. A complementary analysis of Eocene rhythmites (∼55 Ma) illustrates how the approach offers a means to map out ancient solar system behavior and Earth-Moon history using the geologic archive. The method also provides robust quantitative uncertainties on the eccentricity and climatic precession periods, and derived astronomical timescales. As a consequence, the temporal resolution of ancient Earth system processes is enhanced, and our knowledge of early solar system dynamics is greatly improved.

The contribution of extensional faulting to seafloor spreading along the East Pacific Rise (EPR) axis near 3°S and between 13°N and 15°N is calculated using data on the displacement and length distributions of faults obtained from side scan sonar and bathymetric data. It is found that faulting may account for of the order of 5–10% of the total spreading rate, which is comparable to a previous estimate from the EPR near 19°S. Given the paucity of normal faulting earthquakes on the EPR axis, a maximum estimate of the seismic moment release shows that seismicity can account for only 1% of the strain due to faulting. This result leads us to conclude that most of the slip on active faults must be occurring by stable sliding. Laboratory observations of the stability of frictional sliding show that increasing normal stress promotes unstable sliding, while increasing temperature promotes stable sliding. By applying a simple frictional model to mid‐ocean ridge faults it is shown that at fast spreading ridges (≥90 mm/yr) the seismic portion of a fault (Ws) is a small proportion of the total downdip width of the fault (Wƒ). The ratio Ws/ Wƒ interpreted as the seismic coupling coefficient X, and in this case X≈ 0. In contrast, at slow spreading rates (≤40 mm/yr), Ws≈Wƒ, and therefore X≈ 1, which is consistent with the occurrence of large‐magnitude earthquakes (mb= 5.0 to 6.0) occurring, for example, along the Mid‐Atlantic Ridge axis.