|
|
|
| Target-oriented wave-equation inversion: regularization in the reflection angle | |
|
Next: Regularization in the reflection
Up: Target-oriented wave-equation inversion
Previous: Target-oriented wave-equation inversion
Tarantola (1987) formalizes the geophysical inverse problem. A linear version linking the reflectivity to the data has being discuss in the literature (Nemeth et al., 1999; Clapp, 2005; Kuhl and Sacchi, 2003). It provides a theoretical approach to compensate for experimental deficiencies (e.g., acquisition geometry, complex overburden), while being consistent with the acquired data.
This approach can be summarized as follows: given a linear modeling operator , compute synthetic data d using
where m is a reflectivity model. Given the recorded data , a quadratic cost function,
|
(1) |
is formed.
The reflectivity model that minimizes is given by the following:
|
(2) |
where (migration operator) is the adjoint of the linear modeling operator , is the migration image, and
is the Hessian of .
The main difficulty with this approach is the explicit calculation of the inverse Hessian. In practice, it is more feasible to compute the least-squares inverse image as the solution of the linear system,
|
(3) |
by using an iterative inversion algorithm.
|
|
|
| Target-oriented wave-equation inversion: regularization in the reflection angle | |
|
Next: Regularization in the reflection
Up: Target-oriented wave-equation inversion
Previous: Target-oriented wave-equation inversion
2007-09-18