Seismic Tomography with Irregular Meshes

The current state of seismic tomography using irregular parameterizations is described. A review is given of previous work in the area covering local, regional and global seismic applications. The potential advantage of an irregular parameterization over a regular (uniform) one is that, by introducing higher resolution grids in particular parts of the model, one can maximize the information extracted from the data. Although irregular parameterizations have only recently been used in 3-D mantle tomography, their origins can be traced back more than twenty years. The use of irregular meshes in two and three dimensional tomographic imaging creates a number of 'implementation' issues, not seen with uniform grids. An outline of algorithms for solving all of these bookkeeping problems arising in cubic, tetrahedral or polygonal meshes is included, and references given to more detailed descriptions. Some recent implementations of tomography are discussed where the parameterization is refined during the course of the inversion process. Two examples of adaptive tomography in non-seismic problems suggest that the gradual refinement of the parameterization may be an effective way to regularize the inverse problem. The intention here is to point out the potential advantages and pitfalls of using an irregular parameterization in tomography. At present experience with seismic problems is rather limited (especially in 3-D) and an optimal approach is yet to emerge.