TOMOGRAPHIC SYSTEMS OF EQUATIONS WITH IRREGULAR CELLS

How to implement seismic or any other type of ray-based tomography in a new class of cellular parameterization built from any chosen distrib ution of nodes in two or three dimensions is shown. The complete flexi bility of this novel approach allows one to introduce detail in a tomo graphic model only where desired, thereby reducing memory and computat ion time, or to impose complex a priori constraints on the inversion. Full details of powerful new algorithms are given to generate unequall y sized tetrahedral or polyhedral cells and to calculate the necessary Frechet derivatives required in linearized tomography. These algorith ms are efficient enough in three dimensions, to allow the parameteriza tion to be refined during an inversion. The methods are illustrated wi th numerical examples. It is concluded that in linear or nonlinear inv ersion the computational cost of the new algorithms will not be signif icantly higher than that incurred by using a regular Cartesian grid.