Optimization of cell parameterizations for tomographic inverse problems

We develop algorithms for the construction of irregular cell (block) models for parameterization of tomographic inverse problems. The forward problem is defined on a regular basic grid of non-overlapping cells. The basic cell s are used as building blocks for construction of nonoverlapping irregular cells. The construction algorithms are not computationally intensive and no t particularly complex, and, in general, allow for grid optimization where cell size is determined from scalar functions, e.g., measures of model samp ling or a priori estimates of model resolution. The link between a particul ar cell j in the regular basic grid and its host cell k in the irregular gr id is provided by a pointer array which implicitly defines the irregular ce ll model. The complex geometrical aspects of irregular cell models are not needed in the forward or in the inverse problem. The matrix system of tomog raphic equations is computed once on the regular basic cell model. After gr id construction, the basic matrix equation is mapped using the pointer arra y on a new matrix equation in which the model vector relates directly to ce lls in the irregular model, Next, the mapped system can be solved on the ir regular grid. This approach avoids forward computation on the complex geome try of irregular grids. Generally, grid optimization can aim at reducing th e number of model parameters in volumes poorly sampled by the data while el sewhere retaining the power to resolve the smallest scales warranted by the data. Unnecessary overparameterization of the model space can be avoided a nd grid construction can aim at improving the conditioning of the inverse p roblem. We present simple theory and optimization algorithms in the context of seismic tomography and apply the methods to Rayleigh-wave group velocit y inversion and global travel-time tomography.