Refraction of seismic signals along a dipping layer Part I: Theory

In this investigation the method of generalized ray is applied to study the propagation of a cylindrical pulse in a dipping surface layer emitted from a buried line source of dilatation. According to the method, the displacements at the point of observation are represented by the sum of convolution integrals in which the appropriate time derivative of the function specifying the shape of the initial pulse is convoluted with the so-called “generalized ray"; each ray being associated with the particular path traversed by the disturbance. The generalized rays representing reflected cylindrical waves are obtained by superposing all of the reflected plane waves. The Cagniard method for inverting the Laplace-transformed displacements corresponding to the particular generalized ray is outlined. The arrival times of the direct and refracted generalized rays are discussed and the critical distances for the refracted waves to occur are given. \n In Part II, theoretical seismograms for the horizontal and vertical components of the displacement vector due to various groups of generalized rays will be presented.