3D Stereotomography in Tetrahedral Models

Stereotomography is a distinctive tomographic method. It is capable of estimating the reflector position, the local dip of reflector and the macro velocity simultaneously. In the previous work, we extend the 2D stereotomography from the B-spline based model representation to triangulated-mesh based model representation In this abstract, we further extend 2D stereotomography in triangulated model to 3D Stereotomography in Tetrahedral model. Firstly we construct the 3D stereotomography (frechet) matrix for Tetrahedral model in the 3D Cartesian coordinate. All the first-order derivatives of the data components with respect to the model components needed by 3D stereotomography in Tetrahedral model are derived based on the ray perturbation theory for interfaces. Then a sensitivity test is implemented to verify the correctness of the frechet derivatives. Finally, we present two synthetic data examples to demonstrate the correctness of the presented algorithm. It provides a solid foundation for its later real applications.