Astronomical cycles recorded in stratigraphic sequences offer a powerful data source to estimate Earth’s axial precession frequency k, as well as the frequency of rotation of the planetary perihelia (gi) and of the ascending nodes of their orbital planes (si). Together, these frequencies control the insolation cycles (eccentricity, obliquity and climatic precession) that affect climate and sedimentation, providing a geologic record of ancient Solar system behavior spanning billions of years. Here we introduce two Bayesian methods that harness stratigraphic data to quantitatively estimate ancient astronomical frequencies and their uncertainties. The first method (TimeOptB) calculates the posterior probability density function (PDF) of the axial precession frequency k and of the sedimentation rate u for a given cyclostratigraphic data set, while setting the Solar system frequencies gi and si to fixed values. The second method (TimeOptBMCMC) applies an adaptive Markov chain Monte Carlo algorithm to efficiently sample the posterior PDF of all the parameters that affect astronomical cycles recorded in stratigraphy: five gi, five si, k, and u. We also include an approach to assess the significance of detecting astronomical cycles in cyclostratigraphic records. The methods provide an extension of current approaches that is computationally efficient and well suited to recover the history of astronomical cycles, Earth-Moon history, and the evolution of the Solar system from geological records. As case studies, data from the Xiamaling Formation (N. China, 1.4 Ga) and ODP Site 1262 (S. Atlantic, 55 Ma) are evaluated, providing updated estimates of astronomical frequencies, Earth-Moon history, and secular resonance terms.

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.

The subduction of carbon and recycling to volcanoes affects planetary scale processes that set the composition of Earth’s surface and mantle environments. The largest flux of surficial carbon that subducts at trenches globally is sedimentary. This is paradoxical, as most carbonate dissolves and organic carbon oxidizes in the ocean before reaching the deep seafloor. Nonetheless, different events conspire to deliver variable fluxes of carbon, some of them large, to different trench sectors. Thus, sedimentary carbon subduction is not a global phenomenon – it is a regional one where heterogeneity rules. Here we have calculated the flux and isotopic composition of both incoming sediment and trench fill for organic and inorganic carbon at the world’s trenches. Our calculations are at the scale of kms along the trench, and so make predictions relevant to individual volcanoes as well as entire arc segments. A useful comparative metric is the carbon flux delivered by altered oceanic crust (AOC), which is a less variable input of largely inorganic carbon to all subduction zones. In some regions, subducting sedimentary carbon is much less than in the AOC unit subducts, for example, along the ~ 2000-km Tonga-Kermadec trench. Given the very high convergence rate, this region constitutes a large flux of carbonate with δ13C heavier than the mantle. At the other extreme, downgoing plates with km-thick turbidites deliver terrestrial organic carbon with δ13C lighter than the mantle. Trench segments that subduct >4X AOC carbon in sediments include the Nicobar Fan off Sumatra and the Aleutian and South Chile trenches. Regions with high biological productivity (Central America) and shallow seafloor (Hikurangi) supply large sedimentary carbonate fluxes with δ13C heavier than mantle. In addition to enormous isotopic heterogeneity (spanning from –25 to +1 per mil δ13C), bulk sediments also span a wide range in oxidation capacity, from carbonate to organic carbon. These highly heterogeneous point- and regional-sources of carbon fluxes, isotopes and oxidiation states provide natural laboratories to study recycling efficiencies at subduction zones and the creation of diamonds, carbonated melts and other carbon heterogeneities in the mantle.

Magnetic anomalies over mid-ocean ridge flanks record the history of geomagnetic field reversals, and the width of magnetized crustal blocks can be combined with absolute dates to generate a Geomagnetic Polarity Time Scale (GPTS). We update here the current GPTS for the Late Cretaceous-Eocene (chrons C33-C13, ~84-33 Ma) by extending to several spreading centers the analysis that originally assumed smoothly varying spreading rates in the South Atlantic. We assembled magnetic anomaly tracks from the southern Pacific (23 ship tracks), the northern Pacific (35), the southern Atlantic (33), and the Indian Ocean (55). Tracks were projected onto plate tectonic flow line, and distances to magnetic polarity block boundaries were estimated by fitting measured magnetic anomalies with a Monte Carlo algorithm that iteratively changed block model distances and anomaly skewness angles. Distance data from each track were then assembled in summary sets of block model distances over 13 ridge flank regions. We obtained a final MQSD20 GPTS with another Monte Carlo algorithm that iteratively perturbs ages of polarity chron boundaries to minimize the variability of spreading rates over all ridge flanks and fit an up-to-date set of radioisotopic dates. The MQSD20 GPTS highlights a major plate motion change at ~47 Ma, when spreading rates decreased in the Indian Ocean as India collided with Eurasia while spreading rates increased in the South Atlantic and Northern Pacific and the Hawaii-Emperor seamount chain changed its orientation.