This paper aims to study the dispersion of torsional surface waves in a crustal layer being sandwiched between a rigid boundary plane and a sandy mantle. In the mantle, rigidity and initial stress vary linearly while density remains constant. Dispersion relation has been deduced in a closed form by means of variable separable method in the form of Whittaker function. The velocity equation for isotropic layer over a homogeneous half-space has been obtained which coincides with the standard result of Love wave under the effect of rigid boundary.

Subsidence has been adversely affecting Jharia Coalfield (JCF) for the last few decades. This study attempts to show the feasibility of the modified Persistent Scatterer Interferometric Synthetic Aperture Radar (PS-InSAR) technique with C-band SAR data to investigate the slow surface deformation caused by coal mine fire and underground mining activities in JCF. Also, a multi-temporal analysis of SAR images of ENVISAT ASAR has been carried out for monitoring and mapping of temporal land subsidence of the area under study. The modified PSI technique has proven its ability to detect land subsidence over the vegetated and rural areas. It also resolves low spatial density of permanent scatterers by considering partially correlated scatterers as permanent scatterers (PSs) and extracting information from these PSs. The study has been concentrated towards detecting continuous slow rate subsidence of five major sites of JCF. The maximum rate of slow deformation among all sites is recorded as 29 mm/year with a cumulative subsidence value of 90 mm. Field validation of subsidence results obtained through PS-InSAR is correlated with the previously published report and the master plan of JCF, showing subsidence locations. Conclusively, the adopted methodology is practically feasible for detection, monitoring and mapping of slow deformation using C-band SAR data in coal mine area.