REFLECTIONS FROM MULTIPLE TRANSITION LAYERS PART I—THEORETICAL RESULTS

Abstract

Continuous velocity logs may be approximated by a series of zones in which the velocity is a linear function of the depth. The reflection response of a series of transition layers may be calculated from an iterative type formula, developed in this paper, which is well suited to digital computer use. This solution takes into account multiple reflections between layers. The reflection output for any input wave shape may be calculated. In this paper a Gram Charlier series pulse having a spectrum peaked at 40 cps is used throughout to facilitate comparison of results. The dependence of the reflection response of single and double layers on frequency and the reflections for the standard input pulse are illustrated. It is shown that 1. Symmetrical double transition layers give an appreciable reflection output even for a base thickness as low as 10 ft. 2. The upper layers of a multilayer group may influence considerably the reflection character from the lower layers.