next up previous contents
Next: Physical Interpretation Up: Waveform Inversion Algorithm Previous: Case 1: Prestack Migration.

Case 2: Postack Imaging.

Assuming a single source and a coincident receiver, equation 3.9 reduces to that for poststack imaging:

 
$\displaystyle \gamma (\bf {r})$ $\textstyle \cong$ $\displaystyle -\Delta \ddot{p}(\bf {r}_g,\bf {r}_g,\tau) \vert _{\tau = 2\tau_{ss} } ,$ (3.9)

where the subscript s denotes both the geophone and source position, which is now coincident with the geophone. For a homogeneous medium, this equations says that the reflection energy is smeared onto the family of circles $(x^2+z^2)^{1/2}/v_0 = 2 \tau_{ss}$ centered about the source point.



Gerard Schuster
1998-07-29