![]() |
![]() |
![]() |
![]() | Wave-equation migration velocity analysis by residual moveout fitting | ![]() |
![]() |
In this appendix I present the analytical development needed to compute all the terms in equation 16. Equations 14 and 15 provide the expression for computing the derivatives of the moveout parameters with respect to slowness as:
![]() |
The derivative of the image vector with respect to slowness,
are evaluated by applying
the conventional wave-equation tomography operator
that links perturbations in the slowness model
to perturbations in the propagated wavefields
by a first-order Born linearization
of the wave equation.
Applying the chain rule to equation 1,
and taking into account the offset-to-angle transformation 2,
we can write
In more compact matrix notation the previous expression can be written as
Almomin and Tang (2010) present an equivalent, but different,
derivation of an algorithm to compute the application of the operator
,
(or its adjoint)
to a vector of slowness perturbations (or image perturbations).
![]() |
![]() |
![]() |
![]() | Wave-equation migration velocity analysis by residual moveout fitting | ![]() |
![]() |