Kirchhoff migration using eikonal-based computation of traveltime source-derivatives

Next: Traveltime Source-derivative Up: Li & Fomel: Kirchhoff Previous: Introduction

# Theory and Implementation

We consider the isotropic eikonal equation:

 (1)

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 initial condition where denotes the source location.

Subsections

2013-07-26