


 Targetoriented waveequation inversion: regularization in the reflection angle  

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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 leastsquares inverse image as the solution of the linear system,

(3) 
by using an iterative inversion algorithm.



 Targetoriented waveequation inversion: regularization in the reflection angle  

Next: Regularization in the reflection
Up: Targetoriented waveequation inversion
Previous: Targetoriented waveequation inversion
20070918