Major‐element composition of sediments in terms of weathering and provenance: Implications for crustal recycling

The elemental composition of a sediment is set by the composition of its protolith and modified by weathering, sorting, and diagenesis. An important problem is deconvolving these contributions to a sediment's composition to arrive at information about processes that operate on the Earth's surface. We approach this problem by developing a predictive and invertible model of sedimentary major‐element composition. We compile a dataset of sedimentary rock, river sediment, soil, and igneous rock compositions. Principal component analysis of the dataset shows that most variation can be simplified to a small number of variables. We thus show that any sediment's composition can be described with just two vectors of igneous evolution and weathering. We hence define a model for sedimentary composition as a combination of these processes. A 1:1 correspondence is observed between predictions and independent data. The log‐ratios ln(K2O/MgO) and ln(Al2O3/Na2O) are found to be simple proxies for, respectively, the model's protolith and weathering indices. Significant deviations from the model can be explained by sodium‐calcium exchange. Using this approach, we show that the major‐element composition of the upper continental crust has been modified by weathering and we calculate the amount of each element that it must have lost to modify it to its present composition. By extrapolating modern weathering rates over the age of the crust we conclude that it has not retained a significant amount of the necessarily produced weathering restite. This restite has likely been subducted into the mantle, indicating a crust‐to‐mantle recycling rate of 1.33 ± 0.89×1013 kg yr‐1

Reciprocity and sensitivity kernels for sea level fingerprints

Reciprocity theorems are established for the elastic sea level fingerprint problem including rotational feedbacks. In their simplest form, these results show that the sea level change at a location x due to melting a unit point mass of ice at x' is equal to the sea level change at x' due to melting a unit point mass of ice at x. This identity holds irrespective of the shoreline geometry or of lateral variations in elastic Earth structure. Using the reciprocity theorems, sensitivity kernels for sea level and related observables with respect to the ice load can be readily derived. It is notable that calculation of the sensitivity kernels is possible using standard fingerprint codes, though for some types of observable a slight generalisation to the fingerprint problem must be considered. These results are of use within coastal hazard assessment and have a range of potential applications within studies of modern-day sea level change.Comment: Paper submitted to Geophysical Journal Internationa

GIA imaging of 3D mantle viscosity based on palaeo sea-level observations - Part I: Sensitivity kernels for an Earth with laterally varying viscosity

Summary A key initial step in geophysical imaging is to devise an effective means of mapping the sensitivity of an observation to the model parameters, that is to compute its Fréchet derivatives or sensitivity kernel. In the absence of any simplifying assumptions and when faced with a large number of free parameters, the adjoint method can be an effective and efficient approach to calculating Fréchet derivatives and requires just two numerical simulations. In the Glacial Isostatic Adjustment (GIA) problem, these consist of a forward simulation driven by changes in ice mass and an adjoint simulation driven by fictitious loads that are applied at the observation sites. The theoretical basis for this approach has seen considerable development over the last decade. Here, we present the final elements needed to image 3D mantle viscosity using a dataset of palaeo sea-level observations. Developments include the calculation of viscosity Fréchet derivatives (i.e., sensitivity kernels) for relative sea-level observations, a modification to the numerical implementation of the forward and adjoint problem that permits application to 3D viscosity structure, and a recalibration of initial sea level that ensures the forward simulation honors present-day topography. In the process of addressing these items, we build intuition concerning how absolute sea-level and relative sea-level observations sense Earth’s viscosity structure and the physical processes involved. We discuss examples for potential observations located in the near field (Andenes, Norway), far field (Seychelles), and edge of the forebulge of the Laurentide ice sheet (Barbados). Examination of these kernels: (1) reveals why 1D estimates of mantle viscosity from far-field relative sea-level observations can be biased; (2) hints at why an appropriate differential relative sea-level observation can provide a better constraint on local mantle viscosity; and (3) demonstrates that sea-level observations have non-negligible 3D sensitivity to deep mantle viscosity structure, which is counter to the intuition gained from 1D radial viscosity Fréchet derivatives. Finally, we explore the influence of lateral variations in viscosity on relative sea-level observations in the Amundsen Sea Embayment and at Barbados. These predictions are based on a new global 3D viscosity inference derived from the shear-wave speeds of GLAD-M25 and an inverse calibration scheme that ensures compatibility with certain fundamental geophysical observations. Use of the 3D viscosity inference leads to: (1) generally greater complexity within the kernel; (2) an increase in sensitivity and presence of shorter length-scale features within lower viscosity regions; (3) a zeroing out of the sensitivity kernel within high-viscosity regions where elastic deformation dominates; and (4) shifting of sensitivity at a given depth towards distal regions of weaker viscosity. The tools and intuition built here provide the necessary framework to explore inversions for 3D mantle viscosity based on palaeo sea-level data.</jats:p