Bleistein Born DMO and its inverse

Starting from a different argument, Bleistein 1990 proposed a DMO operator that he derived from a Born approximation for modeling wave propagation. This new operator, named Born DMO (BDMO), is kinematically equivalent to Hale's (1984) DMO and Zhang's (1988) DMO and only differs from each of them by a simple amplitude factor. This new Jacobian is defined as

$${J_1} =\frac {\partial{(t_0,{\bf x}_0)}} {\partial{(t_2,{\bf x}_2)}}=\frac {2A_2^2-1} {A_2}\; . \EQNLABEL{Bleistein.jacob}$$ (36)

Similar to the previous analysis, and recognizing that this Born DMO is kinematically equivalent to Hale's DMO, the weights for its inverse are then,

$${J_2}=\frac {1} {2\pi A_2^2}\; . \EQNLABEL{Bleistein_inv}$$ (37)