Characteristics of near surface crustal deformation associated with shield seismicity

The purpose of the present study is to understand the surface deformation associated with the Killari and Wadakkancheri earthquake and to examine if there are any evidence of occurrence of paleo-earthquakes in this region or its vicinity. The present study is an attempt to characterize active tectonic structures from two areas within penisular India: the sites of 1993 Killari (Latur) (Mb 6.3) and 1994 Wadakkancheri (M 4.3) earthquakes in the Precambrian shield. The main objectives of the study are to isolate structures related to active tectonism, constraint the style of near – surface deformation and identify previous events by interpreting the deformational features. The study indicates the existence of a NW-SE trending pre-existing fault, passing through the epicentral area of the 1993 Killari earthquake. It presents the salient features obtained during the field investigations in and around the rupture zone. Details of mapping of the scrap, trenching, and shallow drilling are discussed here. It presents the geologic and tectonic settings of the Wadakkancheri area and the local seismicity; interpretation of remote sensing data and a detailed geomorphic analysis. Quantitative geomorphic analysis around the epicenter of the Wadakkancheri earthquake indicates suitable neotectonic rejuvenation. Evaluation of remote sensing data shows distinct linear features including the presence of potentially active WNW-ESE trending fault within the Precambrian shear zone. The study concludes that the earthquakes in the shield area are mostly associated with discrete faults that are developed in association with the preexisting shear zones or structurally weak zones

A Variational Calculation of TE and TM Cutoff Wavenumbers in Circular Eccentric Guides by Conformal Mapping

The cutoff wavenumbers of higher order modes in circular eccentric guides are computed with the variational analysis combined with a conformal mapping. A conformal mapping is applied to the variational formulation, and the variational equation is solved by the finite-element method. Numerical results for TE and TM cutoff wavenumbers are presented for different distances between the centers and ratio of the radii. Comparisons with numerical results found in the literature validate the presented method

Invariant density for a class of initial distributions under quadratic mapping

For the discrete-time quadratic map xt+1=4xt(1-xt) the evolution equation for a class of non-uniform initial densities is obtained. It is shown that in the t to infinity limit all of them approach the invariant density for the map.