||Kirchhoff migration using eikonal-based computation of traveltime source-derivatives||
Next: Traveltime Source-derivative
Up: Li & Fomel: Kirchhoff
We consider the isotropic eikonal equation:
where is a point in space, is the traveltime and is the
velocity. For 2D models, is a vector containing the depth and the inline position.
For 3D models, also includes the crossline position. For conciseness, we define
as slowness-squared. Equation 1 can be derived by inserting the ray-theory series
into the wave-equation and setting the coefficient of the leading-order term to zero (Chapman, 2004).
We are interested in particular in point-source solutions of the eikonal equation, i.e. with the
where denotes the source location.