Rayleigh wave dispersion in an irregular sandy Earth's crust over orthotropic mantle

The present paper presents a study of Rayleigh wave propagation in a sandy crustal layer of the Earth lying over an orthotropic mantle with irregular boundary surfaces under the influence of initial stress, gravity field and rigid boundary plane. An attempt has been made to study the dynamics of the individual medium and derive the displacement of the wave for both the media separately. Suitable boundary conditions have been imposed to derive the dispersion equation in closed form. In general, the obtained dispersion equation is complex, which on separating into real and imaginary parts, leads to two different dispersion equations, of which we are neglecting the imaginary part being damping in nature. The real part contains complete information regarding corrugation parameter, wave number, phase velocity, sandy parameter, initial stress and gravity field. The results for irregular boundaries have been obtained in three cases and presented using graphs. It has been found that the initial stress and sandy parameter have a significant effect and remarkable bearing on the phase velocity of Rayleigh surface wave. Corrugation parameters also have a dominant impact on the propagation of Rayleigh wave. This study may be of great help in the field of industrial engineering, submarine structures, civil engineering, aerospace, chemical pipe and metallurgy as well as geophysics.