Geology 5660/6660 Applied Geophysics 27 Jan 2016 © A.R. Lowry 2016 Read for Fri 29 Jan: Burger (Ch 3-3.2) Last time: Seismic Amplitude depends on Source amplitude Geometrical Spreading (spread of energy in increasing volume). Uniform halfspace spherical spreading : For refracted head wave, cylindrical spreading : Anelastic Attenuation depends on Quality Factor Q :

Important: V P, V S, Q P, Q S seismic properties are four independent pieces of information that can be used to separate effects of lithology, porosity, fluids, cementation and temperature… Much of the emphasis in industry seismic is on imaging “geometry” (structure) of velocity contrasts, but characterizing the physical properties is becoming increasingly important!

incoming P reflected P refracted P refracted S  1,  1,    2,  2,   A0A0 B1B1 A1A1 B2B2 A2A2 Mode Conversions: i2i2 j2j2 j1j1 i1i1 i0i0 Snell’s Law predicts ray angles: For i 0  i c, (For i 0 > i c, rules change a bit.) However Snell’s law gives no information about amplitudes ! reflected S

incoming P reflected P reflected S refracted P refracted S  1,  1,    2,  2,   A0A0 B1B1 A1A1 B2B2 A2A2 Mode Conversions: i2i2 j2j2 j1j1 i1i1 i0i0 Consider particle displacements & stress at the interface: u 1, u 3 are nonzero ( u 2 = 0) and must be continuous across the boundary: Also stress must be continuous: x1x1 x3x3

We also require that energy is conserved: Sum of energy in wave amplitudes leaving the boundary must equal the energy in the incident wave. After lots of algebra & trig:

These four equations in five unknowns are called Zoeppritz’ Equations. If we fix the amplitude for the incident wave (e.g., A 0 = 1 ), we can solve for the other four algebraically. Model from: ResearchLinks/ ExplorerPrograms/ZE/ ZEcrewes.html  1 = 2000,  2 = 2200 kg/m 3  1 = 3000,  2 = 4000 m/s  1 = 1500,  2 = 2000 m/s RpRp TpTp RsRs TsTs Crewes Zoeppritz Explorer (T = “Transmitted”)

water shale gas sand shale Example for a synthetic seismogram

water shale gas sand shale RpRp TpTp RsRs TsTs Water/ShaleShale/Gas Sand

4D: imaging changes in impedance: From Osdal et al., The Leading Edge, Model w/out seismic Model with seismic Red = gas cap over oil (neutral colors); blue = water