1,721,002 research outputs found
A corrected finite-difference scheme for the flexure equation with abrupt changes in coefficient
No full textAbstract. The fourth-order differential equation describing elastic flexure of the lithosphere is one of the cornerstones of geodynamics that is key to understanding topography, gravity, glacial isostatic rebound, foreland basin evolution, and a host of other phenomena. Despite being fully formulated in the 1940s, a number of significant issues concerning the basic equation have remained overlooked to this day. We first explain the different fundamental forms the equation can take and their difference in meaning and solution procedures. We then show how numerical solutions to flexure problems as they are currently formulated are in general potentially unreliable in an unpredictable manner for cases in which the coefficient of rigidity varies in space due to variations of the elastic thickness parameter. This is due to fundamental issues related to the numerical discretisation scheme employed. We demonstrate an alternative discretisation that is stable and accurate across the broadest conceivable range of conditions and variations of elastic thickness, and we show how such a scheme can simulate conditions up to and including a completely broken lithosphere more usually modelled as an end-loaded, single, continuous plate. Importantly, our scheme will allow breaks in plate interiors, allowing, for instance, the creation of separate blocks of lithosphere which can also share the support of loads. The scheme we use has been known for many years but remains rarely applied or discussed. We show that it is generally the most suitable finite-difference discretisation of fourth-order, elliptic equations of the kind describing many phenomena in elasticity, including the problem of bending of elastic beams. We compare the earlier discretisation scheme to the new one in one-dimensional form and also give the two-dimensional discretisation based on the new scheme. We also describe a general issue concerning the numerical stability of any second-order finite-difference discretisation of a fourth-order differential equation like that describing flexure wherein contrasting magnitudes of coefficients of different summed terms lead to round-off problems, which in turn destroy matrix positivity. We explain the use of 128 bit floating-point storage for variables to mitigate this issue.Open-Access-Publikationsfonds 202
Current deformation rates and extrusion of the northwestern Okhotsk plate, northeast Russia
Full text linkNortheast Asia is a region of broad deformation resulting from the convergence of the Eurasian (EU) and North American (NA) plates. Part of this convergence has been suggested to be relieved by the extrusion and deformation of the Okhotsk plate (OK). Three models for the deformation of the seismically active northwestern corner of the Okhotsk plate, based on different modes of deformation partitioning, are calculated and compared to observations from GPS, seismicity, and geology. The results suggest that this region is being extruded southeastward and deforming internally by a mixture of pure contraction, “smooth” extrusion, and “rigid” extrusion. Calculated extrusion rates are ∼3–5.5 mm/yr, comparable to estimates from geologic data, and internal deformation rates are ∼3.0 × 10−9 yr −1. Internal deformation may be only partially accommodated by seismicity, but the short time span of seismic data leaves this subject to large uncertainty
The Subhercynian Basin: an example of an intraplate foreland basin due to a broken plate
Full text linkThe Late Cretaceous intraplate shortening event in central western Europe is associated with a number of marine basins of relatively high amplitude and short wavelength (2–3 km depth and 20–100 km width). In particular, the Harz Mountains, a basement uplift on a single, relatively steeply dipping basement thrust, have filled the adjacent Subhercynian Cretaceous Basin with their erosive product, proving that the two were related and synchronous. The problem of generating subsidence of this general style and geometry in an intraplate setting is dealt with here by using an elastic flexural model conditioned to take account of basement thrusts as weak zones in the lithosphere. Using a relatively simple configuration of this kind, we reproduce many of the basic features of the Subhercynian Cretaceous Basin and related basement thrusts. As a result, we suggest that overall, it shares many characteristics with larger-scale foreland basins associated with collisional orogens on plate boundaries.</p
Crustal balance and crustal flux from shortening estimates in the Central Andes
No full textAbstractThe Central Andes of South America form the second largest high elevation plateau on earth. Extreme elevations have formed on a noncollisional margin with abundant associated arc magmatism. It has long been thought that the crustal thickness necessary to support Andean topography was not accounted for by known crustal shortening alone. We show that this may in part be due to a two-dimensional treatment of the problem. A three-dimensional analysis of crustal shortening and crustal thickness shows that displacement of material towards the axis of the bend in the Central Andes has added a significant volume of crust not accounted for in previous comparisons. We find that present-day crustal thickness between 12°S and 25°S is accounted for (∼−10% to ∼+3%)with the same shortening estimates, and the same assumed initial crustal thickness as had previously led to the conclusion of a ∼25–35% deficit in shortening relative to volume of crustal material. We suggest that the present-day measured crustal thickness distribution may not match that predicted due to shortening, and substantial redistribution of crust may have occurred by both erosion and deposition at the surface and lower crustal flow in regions of the thermally weakened middle and lower crust
The Ulakhan fault surface rupture and the seismicity of the Okhotsk–North America plate boundary
Full text linkNew field work, combined with analysis of high-resolution aerial photographs, digital elevation models, and satellite imagery, has identified an
active fault that is traceable for ∼90 km across the Seymchan Basin
and is part of the Ulakhan fault system, which is believed to form the
Okhotsk–North America plate boundary. Age dating of alluvial fan sediments
in a channel system that is disturbed by fault activity suggests the current
scarp is a result of a series of large earthquakes (≥Mw 7.5)
that have occurred since 11.6±2.7 ka. A possible channel feature offset
by 62±4 m associated with these sediments yields a slip rate of 5.3±1.3 mm yr−1, in broad agreement with rates suggested from global
plate tectonics. Our results clearly identify the Ulakhan fault as the
Okhotsk–North America plate boundary and show that tectonic strain release
is strongly concentrated on the boundaries of Okhotsk. In light of our
results, the likelihood of recurrence of Mw 7.5 earthquakes is
high, suggesting a previously underestimated seismic hazard across the
region.</p
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