Bending of spherical lithosphere–axisymmetric case

Effects of sphericity are commonly ignored in the lithospheric bending problem. In order to examine its effects, I solve a simple axisymmetric spherical-shell model. The full solution and the asymptotic solution are derived from the basic equations, and their relationship to the flat-plate solution is examined. For displacement, effects of sphericity are small, and use of the flat-plate solution produces results that are numerically indistinguishable from those of the spherical solution. The most significant effect of sphericity appears in the stress, in particular the normal stress along the strike direction of the trench. This stress is approximately given by Eu_r/R , where E is Young's modulus, u_r is the vertical deformation of the shell and R is its radius of curvature. If the shell (lithosphere) is bent downwards and reaches 30 km, this stress can become about 5 kbar in the Earth. While plastic behaviour may set in under such high pressure conditions and analysis beyond elasticity theory may be required, sphericity may be a cause of large compressive stress in the trench strike direction. This stress may play an important role in forming the overall shape of the Earth's subduction zones.     

Models of crustal flow in the India–Asia collision zone

Surface velocities in parts of the India–Asia collision zone are compared to velocities calculated from equations describing fluid flow driven by topographically produced pressure gradients. A good agreement is found if the viscosity of the crust is ∼10²⁰ Pa s in southern Tibet and ∼10²² Pa s in the area between the Eastern Syntaxis and the Szechwan Basin. The lower boundary condition of the flow changes between these two areas, with a stress-free lower boundary in the area between the Szechwan basin and the Eastern Syntaxis, and a horizontally rigid but vertically deformable boundary where strong Indian lithospheric material underlies southern Tibet. Deformation maps for olivine, diopside and anorthite show our findings to be consistent with laboratory measurements of the rheology of minerals. Gravitationally driven flow is also suggested to be taking place in the Indo–Burman Ranges, with a viscosity of ∼10¹⁹–10²⁰ Pa s. Flow in both southern Tibet and the Indo–Burman Ranges provides an explanation for the formation of the geometry of the Eastern Himalayan Syntaxis. The majority of the normal faulting earthquakes in the Tibetan Plateau occur in the area of southern Tibet which we model as gravitationally spreading over the Indian shield.     

Peat layer accumulation and post‐burial deformation during the mid‐late Holocene in the Po coastal plain (Northern Italy)

Peat horizons are characteristic features of delta plains worldwide. In this study, we tested the use of peat‐based correlations to assess the deformation of Holocene strata in the Po coastal plain (Northern Italy). The Holocene stratigraphy, about 30 km inland from the modern coastline consists of a peat‐bearing, estuarine and deltaic succession, up to 23 m thick. Through the analysis of 31 core data and 100 piezocone penetration tests, we identified and mapped three 10–40 cm‐thick peat layers (T1–T3) dated to 6.6–5.8, 5.5–5.0 and 3.3–2.7 cal kyr BP respectively. These peat horizons were found to be suitable stratigraphic markers within the Holocene succession over an area of about 200 km². The mid‐late Holocene palaeogeography, reconstructed through high‐resolution peat correlation, supported by 72 radiocarbon dates, highlights a typical upper delta plain environment, with ribbon‐shaped distributary channels and swamp interdistributary areas. Peat layers are inclined towards E‐NE with gradients that increase downsection from ~0.016% (T3) to 0.021% (T1). The gradient of the oldest peat horizon is one order of magnitude larger than the slope of the modern delta plain (~0.0025%). We infer that peat horizons accumulated during periods of low sediment supply mainly controlled by autogenic processes and were deformed after deposition. Differential compaction of underlying sedimentary strata and recent tectonic activity of the buried Apenninic thrust systems are the most likely drivers of strata deformation. Based on isochore maps, we document that higher sedimentation rates in topographically depressed areas compensated, in part at least, the ongoing deformation, keeping unaltered the topographic gradient and the depositional environment. This study demonstrates that peat‐based correlation and mapping can shed lights on the mechanisms of strata accumulation and deformation in deltaic settings, constituting a robust basis for reconstructing delta evolution.     

Post-seismic rebound of a spherical Earth: new insights from the application of the Post–Widder inversion formula

The post-seismic response of a viscoelastic Earth to a seismic dislocation can be computed analytically within the framework of normal-modes, based on the application of propagator methods. This technique, widely documented in the literature, suffers from several shortcomings; the main drawback is related to the numerical solution of the secular equation, whose degree increases linearly with the number of viscoelastic layers so that only coarse-layered models are practically solvable. Recently, a viable alternative to the standard normal-mode approach, based on the Post–Widder Laplace inversion formula, has been proposed in the realm of postglacial rebound models. The main advantage of this method is to bypass the explicit solution of the secular equation, while retaining the analytical structure of the propagator formalism. At the same time, the numerical computation is much simplified so that additional features such as linear non-Maxwell rheologies can be simply implemented. In this work, for the first time, we apply the Post–Widder Laplace inversion formula to a post-seismic rebound model. We test the method against the standard normal-mode solution and we perform various benchmarks aimed to tune the algorithm and to optimize computation performance while ensuring the stability of the solution. As an application, we address the issue of finding the minimum number of layers with distinct elastic properties needed to accurately describe the post-seismic relaxation of a realistic Earth model. Finally, we demonstrate the potentialities of our code by modelling the post-seismic relaxation after the 2004 Sumatra–Andaman earthquake comparing results based upon Maxwell and Burgers rheologies.     

Geodetic inversion for space–time distribution of fault slip with time-varying smoothing regularization

We have developed a new geodetic inversion method for space–time distribution of fault slip velocity with time-varying smoothing regularization in order to reconstruct accurate time histories of aseismic fault slip transients. We introduce a temporal smoothing regularization on slip and slip velocity through a Bayesian state space approach in which the strength of regularization (temporal smoothness of slip velocity) is controlled by a hyperparameter. The time-varying smoothing regularization is realized by treating the hyperparameter as a time-dependent stochastic variable and adopting a hierarchical Bayesian state space model, in which a prior distribution on the hyperparameter is introduced in addition to a conventional Bayesian state space model. We have tested this inversion method on two synthetic data sets generated by simulated aseismic slip transients. Results show that our method reproduces well both rapid changes of slip velocity and steady-state velocity without significant oversmoothing and undersmoothing, which has been hard to overcome by the conventional Bayesian approach with time-independent smoothing regularization. Application of this method to transient deformation in 2002 caused by a silent earthquake off the Boso peninsula, Japan, also shows similar advantages of this method over the conventional approach.