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Differential Geometrical Spreading for Pegleg Multiples

The Snell resampling transformation derived in the previous section renders pegleg multiples and primaries invariant with respect to AVO and attenuation. However, because of their longer raypaths, multiples suffer greater geometric spreading losses than the corresponding primary. Following previous authors Lu et al. (1999); Ursin (1990), I write offset-dependent geometric spreading corrections for a primary (gprim) and its pegleg multiples (gmult), respectively:
      \begin{eqnarray}
g_{prim} &=& v^*t_{prim}(x) 
 = \sqrt{(\tau v^*)^2 + \left(\fra...
 ...qrt{[(\tau+j\tau^*) v^*]^2 + \left(\frac{xv^*}{V_{eff}}\right)^2}.\end{eqnarray} (4)
(5)
Veff is defined in equation (2). After scaling by the ratio gmult/gprim and Snell resampling, a pegleg multiple should be an exact copy of its associated primary, to within a scaling by the appropriate reflection coefficient.
next up previous print clean
Next: Estimation of Seabed Reflection Up: Brown: Pegleg amplitudes Previous: Snell Resampling Removes AVO/Attenuation
Stanford Exploration Project
7/8/2003