Scattering of plane SH waves by an isosceles trapezoidal hill

TM-Plane Wave Scattering from a Trapezoidal Cavity

“…The truncation depth of the open cavity is 𝑑 = ℎ 2 − ℎ 1 . We divide the analyzed region into three regions by introducing two semicircular auxiliary boundaries Γ 1 and Γ 2 [7]: sub-region 1 is an open region above semicircular Γ 1 whose radius is a; sub-region 2 is an enclosed area between two semicircular border Γ 1 and Γ 2 ; sub-region 3 is an enclosed area restricted with semicircular Γ 2 with radius b and the cavity bottom. The definitions of three Cartesian coordinate systems (x 1 , y 1 ), T (x 2 , y 2 ) and (x 3 , y 3 ) are taken as shown in Fig.…”

“…Accordingly, in the closed sub-region 2, the electric field 𝐸 𝑧 (2) (𝑍 1 , 𝑍 1 * ) for a wedge radial waveguide, satisfying the Helmholtz equation and the boundary condition at the cavity walls (i.e., 𝐸 𝑧 (2) = 0 at 𝜑 1 = 𝛽 + 2𝛼 and 𝜑 1 = −𝛽 where 𝛽 = 𝜋 2 − 𝛼) is given by [7] 𝐸 𝑧 (2)…”

“…However, most numerical methods use meshing techniques and consequently, the simulation time and the accuracy of computations are the significant challenge there. In this work, using the same manner as in [7] suggested for shear waves (SH-wave), we investigate the behavior of TM electromagnetic wave scattering from an isosceles trapezoidal cavity embedded in a PEC. Herein, the success of the solution procedure depends on the proper selection of auxiliary borders and wavefunctions.…”

Resonant amplified seismic response within a hill or mountain

“…The AGS's affected by seismic waves can be divided into two classes: i) a 'natural' AGS such as a hill [14,25,46,55,71,73,118,131,159,181,191,193,194,197,205,241,251,256,264,268,255,278,307,376,378,85,87,153,46,212,269,106,375,326,376,325,333,264], volcano [296,282,307,219,60,219,296], mountain [177,178,351,352,353,…”

A conservation law for testing methods of prediction of the seismic wave response of a protuberance emerging from flat ground

“…The seismic response of protuberances is an ongoing research theme in theoretical and applied seismology, mainly because of the variety of AGS's, the social and economic impact of the damage issue and a relatively-poor understanding of the empirical evidence that the seismic wave field is amplified on the stress-free boundary of the protuberance relative to this field on flat ground. For these reasons, a great variety of (mainly-numerical) solutions to specific AGS seismic response problems have been proposed [2,3,4,5,6,8,10,12,13,15,17,19,21,22,23,24,25,27,28,30,31,32,33,35,36,37,38,39,40,42,43,44], but the question that is often ignored or eluded is: how good are these solutions?…”