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Reflection Amplitude

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					Reflection Amplitude
          Vertical Incidence
              Ai          Ar       rv= acoustic impedance




                         At


R = Ar    =        r2v2 – r1v1 = Z2 – Z1
    Ai             r2v2 +r1v1    Z2 + Z1

 T = At   =      2 r1v1        =    2 Z1
     Ai        r2v2 + r1v1         Z2 + Z1
Non-vertical incidence
            Spherical Divergence
                               Anstey (1977)




A a 1/r = 1/(Vt) >>> 1/(V2t)
          Transmission Loss
          A0 = 1
                     R1
                            (1-R1) (1+R1) R2 = (1-R12)R2 = (TL) R2
R1
                          (1-R1) R2
           (1-R1)


            (1-R1)        (1-R1) R2

R2
     (1-R1) (1-R2)
               Anelastic Attenuation

      A a e - ar


      a = pf
          QV

a = attenuation coefficient
f = frequency
Q = quality factor
V = velocity
Amplitude Factors
                       Fresnel Zone




KB&H, 2002



   Rf = (lz/2)1/2 = (V/2)(t/f)1/2

                                      S&D, 1995
  Amplitude and Reflector Curvature
                          “Brighten Up” Ratio

                               S =              1
                    3D
                               Sflat          1 - rw/ri



                               S =              1
                    2D         Sflat          1 - rw/ri


                         S = amplitude from curved reflector
                         Sflat = amp from flat reflector
                         rw = radius of curvature of wavefront
                         ri = radius of curvature of reflector

“focussing”                                              Anstey 77
Fresnel Zone in 3D
Sideswipe
        More Focussing




Gas “lens”         Wedge
Waveform Interference
     (thin beds)
Amplitude and Tuning




                       S&G 95
  Amplitudes and Gradients




Neidell

				
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posted:10/21/2011
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