I. On the reflection of plane waves by stratified systems (normal incidence). II. The determination of seismic velocities in layers with non-parallel interfaces

Abstract

Listen

Translate article

The purpose of this study is to establish that the reflection of a plane wave (at normal incidence) by a nonhomogeneous layer with properties varying only in the direction of wave propagation may be deduced by a limiting process from the formulae which are valid in the case of discrete homogeneous layers. In this limiting process the number of layers is made to increase without bounds while the thickness of each layer tends to zero in such a way that the total thickness remain constant. This is done by using the matrix relation which binds the up and down-going wave amplitudes in two layers of a pile of homogeneous layers on top of a semi-infinite homogeneous medium. Then the number of layers is increased as described above and the limit of the matrix relation obtained. It is then verified that the result thus gotten is identical to the quantity obtained by solving the differential equation for the disturbance in a nonhomogeneous layer whose properties are the ones which the discrete case is made to tend to. A method for calculating velocities in homogeneous isotropic layers and the position of their interfaces from surface reflection seismic measurements is described. The problem is discussed only in the case of parallel strikes. Conditions of applicability are plane interfaces and good lateral correlations. Also the accuracy of the determination of the velocities and the position of the interfaces depends very much on the velocity, the dip and a distance which gives the position of the interface. One should be careful to estimate in each particular case whether the method may safely be used.