Tarantola (1987) formalizes the geophysical inverse problem by giving a theoretical approach to compensate for experimental deficiency (e.g., acquisition geometry, complex overburden), while being consistent with the acquired data.
His 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) |

(2) |

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,

(3) |

4/5/2006