SH-waves at a corrugated interface between a dry sandy half-space and an anisotropic elastic half-space S. K. Tomar and J. Kaur, Chandigarh, India Received June 13, 2006; revised September 22, 2006 Published online: December 21, 2006 Ó Springer-Verlag 2006 Summary. A problem of reflection and transmission of a plane SH-wave incident at a corrugated interface between a dry sandy half-space and an anisotropic elastic half-space is investigated. Rayleigh’s method of approximation is applied to derive the reflection and transmission coefficients for the first and second order approximation of the corrugation. The expressions for reflection and transmission coefficients for the first order approximation of the corrugation are obtained in closed form for a special type of interface, and the energy partition relation is derived. It is found that these coefficients are proportional to the amplitude of corrugation and are functions of elastic properties of the half-spaces and also of the angle of incidence. Numerical examples illustrating the effects of the sandiness, the anisotropy, the corrugation of the interface, the frequency, and the angle of the incidence on the coefficients are presented. 1 Introduction The theory of elastic waves finds numerous applications in seismology and geophysics. Seismic signals are applied to investigate the internal structure of the Earth, and they are used in the exploration of valuable materials, e.g., oils, water, minerals etc. The mathematical analysis of seismic waves is mainly devoted to the study of propagation, reflection/refraction and diffraction problems. Irregularities, such as mountains, basins, mountain roots and salt and ore deposits, affect the reflection and transmission of seismic waves. The interior boundaries of the Earth’s media are not planar but are of undulated nature. The roughness or undulation of interfaces do affect the energy partition between the reflected and transmitted waves. The problem of reflection and transmission of waves at irregular interfaces was studied by Asano [1]–[3], Abubakar [4]–[6], Dunkin and Eringen [7], Salvin and Wolf [8], Sumner and Deresiewicz [9], Gupta [10]–[12], Zhang and Shinozuka [13], Tomar and Saini [14], Tomar and Kaur [15] and Kaur et al. [16] among others. Earth is very complex in nature and contains various types of rocks and materials with amazing characteristics such as anisotropy, heterogeneity, sandiness etc. The effect of aniso- tropy on reflection and transmission of elastic waves at a plane interface between two elastic media was studied by Musgrave [17], Henneke [18], Daley and Hron [19], Saini and Singh [20], Keith and Crampin [21], Rokhlin et al. [22], Mandal [23], Ruger [24], among others. Acta Mechanica 190, 1–28 (2007) DOI 10.1007/s00707-006-0423-7 Printed in The Netherlands Acta Mechanica