Gradient of image-space wave-equation tomography by the adjoint-state method |

**Claudio Guerra**

Optimization with gradient-descent techniques requires computing the gradient of the objective function. The gradient can be determined by using the Frech
t derivatives, but, for practical problems, this can be very expensive. The gradient can be more efficiently computed by the adjoint-state method, which does not require the use of the Frech
t derivatives. Here, I derive the gradient of the image-space wave-equation tomography using the adjoint-state method. I also show its application with a numerical example using image-space phase-encoded gathers.

- introduction
- Image-space phase-encoded gathers
- Gradient of ISWET by the adjoint-state method
- Numerical example
- conclusion
- Bibliography
- About this document ...

2009-10-16