Mathematical modelling and parameter studies of torsional surface wave

Abstract

In seismological studies, torsional surface wave is important in predicting earthquake. Torsional surface wave is restricted to propagate in the upper crustal earth, and it can only exist in the solid materials. The studies of torsional surface waves are limited in the public domain as compared to Rayleigh, Love, and Stoneley waves, although the research of torsional surface wave in the elastic medium is very impactful in seismology. The focus of this thesis is to determine the effects of sandy level, gravity field, homogeneous and initial stress parameters on the torsional surface waves propagation in stress-free and rigid surfaces. The derivative of the phase velocity of torsional surface waves is derived by using dynamical equations of motion in a cylindrical coordinate system with displacement characteristic, where ??=0 ;??=0 ;??=??(??,??,??). The solution is found through the separation of variable method in the form of expanded linear Whittaker function. Hence, the phase velocity of torsional surface wave can be obtained. The graphical analysis of the solution indicates the relationship between phase velocity of torsional surface wave with sandy level, gravity field, initial stress, homogeneous and rigidity parameters respectively. The results show that in the presence of the gravity field, torsional surface waves can propagate in elastic and sandy media. However, in the absence of gravity field, the torsional surface waves cannot propagate in the sandy medium but can propagate in elastic medium. In addition, homogenous, initial stress and rigidity parameters also play important roles in influencing the phase velocity of the torsional surface waves.