The response of a point source in a liquid layer overlying a liquid half space

Abstract

The response to a harmonic point source in a liquid layer overlying a liquid half space is computed as a function of frequency. Included are the contributions form all normal modes that occur, and the branch-line integral representing the refraction arrival. The value of the refraction arrival is given in terms of the complex error function. The effect of different velocity and density contrasts are considered, and the effect of source depth and the distance to the receiver are investigated. The results giving the behavior of the magnitude of the branch line show that it is much larger at the mode cutoffs than at other values of frequency. The total amplitude of the response shows a regular oscillation in the frequency range in which two modes are present, and somewhat irregular high and low values over the range in which three modes are present. This behavior reflects the difference in amplitude at frequencies for which modes reinforce or interfere with each other.