Simple Topographic Parameter Reveals the Along-Trench Distribution of Frictional Properties on a Shallow Plate Boundary Fault

The critical taper model of a sedimentary wedge best describes the first-order mechanics of a subduction zone wedge. The tapered wedge geometry, which is conventionally defined by two parameters, the slope angle and the basal dip angle, is responsible for the strength of a megathrust. By applying this theoretical model to subduction zones, fault frictional properties and earthquake occurrences can be compared among subduction zones, and within a single subduction zone, the spatial distribution or temporal change of fault strength can be investigated. The slope angle can be accurately estimated from bathymetry data, but the basal dip angle must be inferred from the subsurface structure, and it requires highly accurate depth-converted seismic reflection profiles. Thus, application of the critical taper model is often limited by a lack of a sufficient number of highly accurate profiles, and the spatial distribution of frictional coefficients must be inferred from relatively few data, generally less than a dozen points. To improve this situation, we revisited the theoretical formula of the critical taper model. We found that the effect of the décollement dip angle β on the critical taper model of a sedimentary wedge is negligible when the pore fluid pressure ratio is high or internal friction is small, conditions which are met in many subduction zones. Therefore, this finding allows frictional variation to be approximated by using only the slope angle variation obtained from the bathymetry. We applied this approximation to the Japan Trench as an example of this approximation, and were able to estimate the friction coefficient distribution on the shallow plate boundary fault from 71 data points. We found that the area where the friction coefficient was smaller than the mean corresponded to the segment where a large coseismic shallow rupture occurred during the 2011 Tohoku-oki earthquake (Mw 9.0). This result shows that by approximating tapered wedge geometry using a simple topographic parameter that can be obtained from existing global bathymetry, we can quickly estimate the distribution of frictional properties on a plate boundary fault along a trench and related seismic activity.

Corneal Parameters in Patients with Multiple Sclerosis: A Pilot Study

Objective To evaluate the corneal topographic parameter values measured with the Pentacam Scheimpflug system in patients with multiple sclerosis (MS). Methods A total of 108 eyes of 62 MS patients were studied. In addition to a complete examination of anterior and posterior segments, all patients were scanned using the Pentacam Scheimpflug camera. The diagnosis of MS was made according to the McDonald criteria. All MS patients were clinically assessed using the Multiple Sclerosis Severity Score (MSSS). Results The mean age was 38.89 ± 10.18 years (36.16 – 41.30) for MS patients and 40.94 ± 9.44 years (38.49 – 43.11) for the controls (p = 0.26). Only central corneal thickness (CCT) and corneal volume (CV) values were significantly lower in MS patients (p < 0.001). The other corneal parameters were not significantly different between the study eyes and control eyes (p > 0.05 for all). Pachymetric measurements at the corneal apex were 525.69 ± 29.35 (518.29 – 533.67) µm for the study eyes versus 563.13 ± 23.70 (562.13 – 576.36) µm for the control eyes. CV were 59.22 ± 4.11(58.18 – 60.20) mm3 for the study eyes versus 62.78 ± 3.09 (62.38 – 64.00) mm3 for the control eyes. Conclusion This is the first study that has reported lower CCT and CV measurements in MS patients than healthy subjects of a similar age. These results should be supported by further studies.

Steep Shelf Stabilization of the Coastal Bransfield Current: Linear Stability Analysis

In situ measurements obtained during the 2010 COUPLING cruise were analyzed in order to fully characterize the velocity structure of the coastal Bransfield Current. An idealized two-layer shallow-water model was used to investigate the various instability processes of the realistic current along the coastal shelf. Particularly studied is how the topographic parameter To (ratio between the shelf slope and the isopycnal slope of the surface current) impacts the growth and the wavelength of the unstable perturbations. For small bottom slopes, when the evolution of the coastal current is controlled by the baroclinic instability, the increase of the topographic parameter To yields a selection of smaller unstable wavelengths. The growth rates increase with small values of To. For larger values of To (To ≳ 10, which is relevant for the coastal Bransfield Current), the baroclinic instability is strongly dampened and the horizontal shear instability becomes the dominant one. In this steep shelf regime, the unstable growth rate and the wavelength selection of the baroclinic coastal current remains almost constant and weakly affected by the amplitude of the bottom velocity or the exact value of the shelf slope. Hence, the linear stability analysis of an idealized Bransfield Current predicts a typical growth time of 7.7 days and an alongshore scale of 47 km all along the South Shetland Island shelf. The fact that these large growth times are identical to the typical transit time of water parcels along the shelf may explain why the current does not exhibit any unstable meanders.

3D Multi-Scale Topography Analysis in Specifying Quality of Honed Surfaces

The quality of the surface texture on cylinder liners of engines has an important influence on oil consumption and running performance. This texture is generated with a succession of three honing operations (rough, finishing and plateau honing). These honing steps are difficult to optimize due to the large number of process variables (Velocity of the rotational motion, velocity of the axial motion ...) and their complex interrelation. This paper discusses the use of the multiscale topographic parameter of the honing process as a new concept to identify the relation between the process variables and the resulting performances in terms of form and surface finish. To achieve this objective, a multi-scale decomposition method of surface topography based on 2D continuous wavelets transform was performed to analyze the evolution of the topographic honing. This approach also shows a good indication of the dependence between the honing steps and the roughness scales. Finally, it provides an efficient tool to predict the surface characteristics corresponding to given process variables and can be extended to optimize other multi-stage abrasive machining processes.

The Quasi-Nondispersive Regimes of Long Extratropical Baroclinic Rossby Waves over (Slowly Varying) Topography

Actual energy paths of long, extratropical baroclinic Rossby waves in the ocean are difficult to describe simply because they depend on the meridional-wavenumber-to-zonal-wavenumber ratio τ, a quantity that is difficult to estimate both observationally and theoretically. This paper shows, however, that this dependence is actually weak over any interval in which the zonal phase speed varies approximately linearly with τ, in which case the propagation becomes quasi-nondispersive (QND) and describable at leading order in terms of environmental conditions (i.e., topography and stratification) alone. As an example, the purely topographic case is shown to possess three main kinds of QND ray paths. The first is a topographic regime in which the rays follow approximately the contours f /hαc = a constant (αc is a near constant fixed by the strength of the stratification, f is the Coriolis parameter, and h is the ocean depth). The second and third are, respectively, “fast” and “slow” westward regimes little affected by topography and associated with the first and second bottom-pressure-compensated normal modes studied in previous work by Tailleux and McWilliams. Idealized examples show that actual rays can often be reproduced with reasonable accuracy by replacing the actual dispersion relation by its QND approximation. The topographic regime provides an upper bound (in general a large overestimate) of the maximum latitudinal excursions of actual rays. The method presented in this paper is interesting for enabling an optimal classification of purely azimuthally dispersive wave systems into simpler idealized QND wave regimes, which helps to rationalize previous empirical findings that the ray paths of long Rossby waves in the presence of mean flow and topography often seem to be independent of the wavenumber orientation. Two important side results are to establish that the baroclinic string function regime of Tyler and Käse is only valid over a tiny range of the topographic parameter and that long baroclinic Rossby waves propagating over topography do not obey any two-dimensional potential vorticity conservation principle. Given the importance of the latter principle in geophysical fluid dynamics, the lack of it in this case makes the concept of the QND regimes all the more important, for they are probably the only alternative to provide a simple and economical description of general purely azimuthally dispersive wave systems.