Differential Geometric Spreading  

To correct peglegs for the effects of greater geometric spreading losses, I follow previous authors (, ) and write offset-dependent geometric spreading corrections for a primary ($g_{\rm prim}$) and its pegleg multiples ($g_{\rm mult}$) in the following notation:

$$\begin{eqnarray} g_{\rm prim} &=& v^*t_{\rm prim}(x) = \sqrt{(\tau v^*)^2 + \l... ...[(\tau+j\tau^*) v^*]^2 + \left(\frac{xv^*}{V_{\rm eff}}\right)^2}.\end{eqnarray}$$ (23) (24)

v^* is the velocity at the surface. After scaling by $g_{\rm mult}/g_{\rm prim}$ and Snell resampling, the amplitudes of an imaged pegleg multiple and its associated primary are consistent, to within a reflection coefficient.