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Reflection seismology
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===Reflection and transmission at non-normal incidence=== [[File:Reflection at an interface.png|thumb|Diagram showing the mode conversions that occur when a P-wave reflects off an interface at non-normal incidence]] The situation becomes much more complicated in the case of non-normal incidence, due to mode conversion between [[P-waves]] and [[S-waves]], and is described by the [[Zoeppritz equations]]. In 1919, Karl Zoeppritz derived 4 equations that determine the amplitudes of [[Reflection (physics)|reflected]] and [[refraction|refracted]] waves at a planar interface for an incident P-wave as a function of the angle of incidence and six independent elastic parameters.<ref name="SheriffGeldart" /> These equations have 4 unknowns and can be solved but they do not give an intuitive understanding for how the reflection amplitudes vary with the rock properties involved.<ref>{{Cite journal | doi=10.1190/1.1441936| title=A simplification of the Zoeppritz equations| journal=Geophysics| volume=50| issue=4| pages=609β614| year=1985| last1=Shuey| first1=R. T.| bibcode=1985Geop...50..609S}}</ref> The reflection and transmission coefficients, which govern the amplitude of each reflection, vary with angle of incidence and can be used to obtain information about (among many other things) the fluid content of the rock. Practical use of non-normal incidence phenomena, known as AVO (see [[amplitude versus offset]]) has been facilitated by theoretical work to derive workable approximations to the [[Zoeppritz equations]] and by advances in computer processing capacity. AVO studies attempt with some success to predict the fluid content (oil, gas, or water) of potential reservoirs, to lower the risk of drilling unproductive wells and to identify new petroleum reservoirs. The 3-term simplification of the Zoeppritz equations that is most commonly used was developed in 1985 and is known as the "Shuey equation". A further 2-term simplification is known as the "Shuey approximation", is valid for angles of incidence less than 30 degrees (usually the case in seismic surveys) and is given below:<ref name="Avseth">Avseth, P, T Mukerji and [[Gary M. Mavko|G Mavko]] (2005). Quantitative seismic interpretation. Cambridge University Press, Cambridge, p. 183</ref> :<math>R(\theta ) = R(0) + G \sin^2 \theta </math> where <math>R(0)</math> = reflection coefficient at zero-offset (normal incidence); <math>G</math> = AVO gradient, describing reflection behaviour at intermediate offsets and <math>(\theta)</math> = angle of incidence. This equation reduces to that of normal incidence at <math>(\theta)</math>=0.
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