Reflection Amplitude

Vertical Incidence R = A r =  2 v 2 –  1 v 1 = Z 2 – Z 1 A i  2 v 2 +  1 v 1 Z 2 + Z 1 AiAi ArAr AtAt T = A t = 2  1 v 1 = 2 Z 1 A i  2 v 2 +  1 v 1 Z 2 + Z 1  v= acoustic impedance

Non-vertical incidence Zoeppritz’s Equations

Spherical Divergence Anstey (1977) A  1/r = 1/(Vt) >>> 1/(V 2 t)

Transmission Loss A 0 = 1 R1R1 (1-R 1 ) (1-R 1 ) (1-R 2 ) (1-R 1 ) R 2 (1-R 1 ) (1+R 1 ) R 2 = (1-R 1 2 )R 2 = (TL) R 2 R1R1 R2R2

Anelastic Attenuation A  e -  r  =  f Q V f = frequency Q = quality factor V = velocity  = attenuation coefficient

Amplitude Factors

Fresnel Zone R f = ( z/2) 1/2 = (V/2)(t/f) 1/2 S&D, 1995 KB&H, 2002

Amplitude and Reflector Curvature S = 1 S flat 1 - r w /r i S = 1 S flat 1 - r w /r i S = amplitude from curved reflector Sflat = amp from flat reflector r w = radius of curvature of wavefront r i = radius of curvature of reflector 3D 2D Anstey 77 “Brighten Up” Ratio “focussing”

Fresnel Zone in 3D

Sideswipe

More Focussing Gas “lens” Wedge

Waveform Interference (thin beds)

Amplitude and Tuning S&G 95

Amplitudes and Gradients Neidell