The Reflection of Elastic Waves From Transition Layers of Variable Velocity

Abstract

Elastic waves are reflected not only from discontinuities in the medium in which they are propagated, but also from transition layers in which the elastic constants are continuous functions of position; the coefficient of reflection is then a function of wave length. Section 1 of this paper gives explicit formulae for the coefficient of reflection of continuous waves from such a layer, at vertical incidence. In Section 2 the manner of variation of the coefficient of reflection with the angle of incidence is discussed qualitatively. Finally, in Section 3, the shape of a pulse reflected from a transition layer is determined.

Reflection characteristics of linear carbon dioxide transition layers

“…In this classic article, the analytical expression for the reflection coefficient of normal incidence P-waves was derived assuming constant density and a linear trend in velocity with depth. Later, Bortfeld (1960), under the same assumptions as Wolf (1937), derived the same result by considering the transition layer as the limit of a sequence of constant-velocity layers. The reflectivity and amplitude characteristics of reflections from sets of multiple transition layers have been treated theoretically in the work of Berryman et al (1958).…”

“…The reflectivity of transition layers was treated in the work of Wolf (1937). In this classic article, the analytical expression for the reflection coefficient of normal incidence P-waves was derived assuming constant density and a linear trend in velocity with depth.…”

The Caughey absorbing layer method - implementation and validation in Ansys software

“…Although some work has been done for linear variation (see Wolf (1937) and Liner and Bodmann (2010)), it is not directly applicable to the problem at hand. However, Oskooi (2008) has shown numerically that T R decreases as both d and L increase.…”

Seismic Reflectivity in Carbon Dioxide Accumulations: A Review

“…In those works, a comparative analysis of the results obtained with the layered saturation model and those obtained using the classic Wolf ramp [10], [11] was also presented.…”

“…However, low-saturation zones with dispersed CO 2 , or saturation transition zones may have an important role in the propagation of waves within the reservoir, giving rise to amplitude and phase changes of the seismic signals. Transition zones have been studied by different authors in the geophysical literature considering linear velocity trends with depth and constant density [10], [11]. Therefore, using the parameters of the Sleipner field, in Section 3.3 we model the reflectivity response of a CO 2 transition layer, defined by a given linear vertical CO 2 saturation profile, which results in a non-linear velocity trend with depth.…”