Optimal spherical spline filters for the analysis and comparison of regional-scale tomographic models

Advances in seismic tomography lead to increasingly detailed models of the Earth that are often represented on irregular and resolution-adaptive grids. To take full advantage of such models, their assessment must progress beyond a purely visual analysis, and tools must become available for their quantitative comparison.We present a method for the spectral analysis and comparison of multi-scale tomographic models. The method is applicable to irregular grids on the sphere, and is more efficient that filters based on spherical-harmonic expansions or convolution integrals. The combination of a spherical spline representation of tomographic information with Abel-Poisson scaling enables the construction of targetted spatial filters by solving a nonlinear inverse problem for appropriate weighting coefficients. This can be readily achieved with a simulated annealing approach for the limited number of weights. Once suitable filters have been generated they can be employed to address issues such as the patterns of small-scale heterogeneity, transitional structures and comparison of independent models from a region.We illustrate our method in a series of applications where we use different bandpass filters to detect differences in the distribution of small-scale heterogeneity beneath central and eastern Europe, and to compare several recent tomographic models of the Australian region.