Wave spreads over a larger surface as it travels through the medium. For a spherical wave, the wave energy falls off as the square of the distance. Its effect is to weaken the later arrivals in the seismic section. We correct this effect by multiplying the amplitude by the distance (if known) or traveltime. Medium effects on waves Geometrical spreading

A part of wave energy is dissipated into the earth as heat. Wave energy falls off exponentially with distance. In seismic exploration, its effect is usually very small compared to that of geometrical spreading. It is usually neglected. Medium effects on waves Absorption

r GS  1/r 2 A  exp(-  r)  = m -1 A: absorption GS: geometrical spreading S: source position r: distance from source  : absorption coefficient S Geometrical spreading versus absorption Medium effects on waves Geometrical spreading versus absorption

Amplitude GS A Geometrical spreading versus absorption Medium effects on waves Geometrical spreading versus absorption

Reflection/refraction Medium effects on waves Reflection/refraction When a wave encounters an interface between two layers, part of its energy is reflected back. The other part is refracted (transmitted) into the other medium. Snell’s law governs reflection and refraction angles.

Snell’s law Medium effects on waves Snell’s law PtPt PiPi PrPr SrSr StSt ii rr rr tt tt         Sin  i Sin  r Sin  t Sin  r Sin  t  1  1  2  1  2

occurs when wave encounters sharp discontinuities in the medium important in defining faults generally considered as noise in seismic sections seismic migration usually corrects for this effect Diffraction Medium effects on waves Diffraction

X Z Earth model X T Seismic Section Diffraction Medium effects on waves Diffraction

Reflection coefficients PtPt PiPi PrPr SrSr StSt ii rr rr tt tt         Sin  i Sin  r Sin  t Sin  r Sin  t  1  1  2  1  2

 1 : density in incident medium  2 : density in refraction medium V 1 : seismic velocity in incident medium V 2 : seismic velocity in refraction medium Reflection coefficients  i ≈ 0  VV VV RC   + - =

very slight deviation from the normal-incidence case For most seismic exploration purposes,  i ≤ 15  is a good assumption. Therefore, normal-incidence RC is used in general. Reflection coefficients  i ≤ 15 

Reflection coefficients  i > 15  high deviation from the normal-incidence case Therefore, normal-incidence is NOT a good assumption. Full Zoeppritz equations have to be used. Zoeppritz equations are very complicated algebraically. If  i ≤ 30 , approximations of Zoeppritz equations are used. Studies involving amplitude variation with offset (AVO) use these approximations.

Reflection coefficients Magnitude Rock-rock RC < |0.3| Rock-soil RC ~ |0.7| Rock-water RC ~ |0.7| Rock-air RC ~ |1.0| Water-deep-sea sediments RC ~ |0.3| Water-air RC ~ |1.0|