A simplification of the Zoeppritz equations

TLDR: In this paper, the compressional wave reflection coefficient R(θ) given by the Zoeppritz equations is simplified to the following: R0+[A0R0+Δσ(1-σ)2]sin2θ+1/2ΔVpVp(tan 2θ-sin2

Abstract: The compressional wave reflection coefficient R(θ) given by the Zoeppritz equations is simplified to the following: R(θ)=R0+[A0R0+Δσ(1-σ)2]sin2θ+1/2ΔVpVp(tan2θ-sin2θ). The first term gives the amplitude at normal incidence (θ = 0), the second term characterizes R(θ) at intermediate angles, and the third term describes the approach to critical angle. The coefficient of the second term is that combination of elastic properties which can be determined by analyzing the offset dependence of event amplitude in conventional multichannel reflection data. If the event amplitude is normalized to its value for normal incidence, then the quantity determined is A=A0+1(1-σ)2ΔσR0. A0 specifies the normal, gradual decrease of amplitude with offset; its value is constrained well enough that the main information conveyed is Δσ/R0, where Δσ is the contrast in Poisson’s ratio at the reflecting interface and R0 is the amplitude at normal incidence. This simplified formula for R(θ) accounts for all of the relations between R(θ...