Method for tomographic inversion by matrix transformation

G - Physics – 01 – V

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G01V 1/28 (2006.01)

Patent

CA 2616379

Method for reducing instability and increasing computational efficiency in tomographic inversion for velocity model building. A system of tomographic equations is developed for a uniform grid. A non-uniform parameterization is found for which a linear mapping exists between the space of the uniform grid and the space of the non-uniform grid. The matrix that relates velocity to the tomographic data in the non-uniform representation is then given by the matrix product of the corresponding matrix in the uniform grid representation and the mapping matrix. Inversion can then be performed for the non-uniform parameterization on a smaller, more stable matrix.

La présente invention concerne un procédé pour réduire une instabilité et augmenter une efficacité de calcul dans le cadre d'une inversion tomographique pour établir un modèle de vitesse. Un système d'équations tomographiques est mis au point pour une grille uniforme. Il s'agit ensuite de trouver un paramétrage non uniforme pour lequel il existe une application linéaire entre l'espace de la grille uniforme et l'espace de la grille non uniforme. La matrice qui relie la vitesse aux données tomographiques dans la représentation non uniforme est ensuite donnée par le produit matriciel de la matrice correspondante dans la représentation de grille uniforme et la matrice d'application. L'inversion peut ensuite être effectuée pour le paramétrage non uniforme sur une matrice plus petite et plus stable.

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