On the gradient generated wave-paths in differential semblance velocity analysis

Differential semblance velocity analysis (“DSVA”, (Symes, 1986)) estimates velocity models<br>from waveform data, by means of prestack migration and its linearized adjoint state process.<br>Several authors have presented DSVA in its explicit differential forms for laterally<br>heterogeneous velocity models using various methods of prestack migration (Symes and<br>Versteeg, 1993; Kern and Symes, 1994; Chauris and Nobel, 2001;Mulder and ten Kroode,<br>2002). Shen et al. (2003) presented a version DSVA based on an objective of focusing the<br>image in subsurface offset. In this approach the wrong velocity is penalized by simply<br>multiplication of subsurface offset to the image volume. The name of “differential<br>semblance” is justified through its subsurface angle substitute (Shen, 2004), where an explicit<br>differential with respect to angle is formulated.