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Zoeppritz equations
In geophysics and reflection seismology, the Zoeppritz equations are a set of equations that describe the partitioning of seismic wave energy at an interface, typically a boundary between two different layers of rock. They are named after their author, the German geophysicist Karl Bernhard Zoeppritz, who died before they were published in 1919.〔Zoeppritz, Karl (1919). Erdbebenwellen VII. VIIb. Über Reflexion und Durchgang seismischer Wellen durch Unstetigkeitsflächen. Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen, Mathematisch-physikalische Klasse, 66-84.〕
The equations are important in geophysics because they relate the amplitude of P-wave, incident upon a plane interface, and the amplitude of reflected and refracted P- and S-waves to the angle of incidence.〔Sheriff, R. E., Geldart, L. P., (1995), 2nd Edition. Exploration Seismology. Cambridge University Press.〕 They are the basis for investigating the factors affecting the amplitude of a returning seismic wave when the angle of incidence is altered - also known as amplitude versus offset analysis - which is a helpful technique in the detection of petroleum reservoirs.
The Zoeppritz equations were not the first to describe the amplitudes of reflected and refracted waves at a plane interface. Cargill Gilston Knott used an approach in terms of potentials almost 30 years earlier, in 1899, to derive Knott's equations. Both approaches are valid and Zoeppritz's approach is more easily understood.〔
==Equations==
There are 4 equations with 4 unknowns and although they can be solved, they do not give an intuitive understanding for how the reflection amplitudes vary with the rock properties involved (density, velocity etc.). Several attempts have been made to develop approximations to the Zoeppritz Equations, such as Bortfeld’s (1961) and Aki & Richards’ (1980),〔Aki, K. and Richards, P. G., 1980, Quantitative seismology: Theory and methods, v.1 : W.H. Freeman and Co.〕 but the most successful of these is the Shuey's, which assumes Poisson's ratio to be the elastic property most directly related to the angular dependence of the reflection coefficient.
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