next up previous [pdf]

Next: Bibliography Up: Gradient of image-space wave-equation Previous: Numerical example

conclusion

I showed a detailed derivation of the gradient of the objective function for the image-space wave-equation tomography by means of the adjoint-state method. I used the augmented Lagrangian methodology, which clarifies the action of the different operators that compose the image-space wave-equation tomography operator. The derivation is valid whether one considers migration of shot-profiles or generalized sources. Image-space phase-encoded gathers significantly accelerate image-space wave-equation tomography. In addition to decreasing the computational cost, the numerical example shows that image-space phase-encoded gathers can be used to generate sufficiently accurate optimized slowness.




2009-10-16