MINIMUM‐PHASE AND RELATED PROPERTIES OF THE RESPONSE OF A HORIZONTALLY STRATIFIED ABSORPTIVE EARTH TO PLANE ACOUSTIC WAVES

Abstract

In a horizontally stratified absorptive earth with vertically traveling plane compressional waves, denote the Fourier transforms of the reflectivity, delayed transmissivity, and the acoustic impedance by R, T, and Z, respectively. It is shown that both Z and 1±R are positive real (p‐r) functions. Although R, in general, is neither p‐r nor minimum phase, |R|