Tarantola (1987) formalizes the geophysical inverse problem by giving a theoretical approach to compensate for experiment deficiencies (e.g., acquisition geometry, obstacles), while being consistent with the acquired data.
His approach can be summarized as follows: given a linear modeling operator compute synthetic data, **d**, using,

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The main difficulty with this approach is the explicit calculation of the Hessian inverse. In practice, it is more feasible to compute the least-squares inverse image as the solution of the linear system of equations

(5) |

Another difficulty with this approach is that the explicit calculation of the Hessian for the entire model space is impractical. Valenciano and Biondi (2004) and Valenciano et al. (2005) discuss a way to make this problem more tractable.

10/31/2005