A concept for the global assessment of tomographic resolution and uncertainty

Abstract

A major challenge in seismic tomography consists in quantifying and representing model resolution and uncertainty, particularly at global scales. This information is crucial for interpretations of tomographic images and their technical application in geodynamics. However, due to large computational costs, there have been only few attempts so far to coherently analyse the spatially varying resolving power for a complete set of model parameters. Here, we present a concept for an effective evaluation and global representation of the 3-D resolution information contained in a full set of averaging kernels. In our case, these kernels are constructed using the ‘Subtractive Optimally Localized Averages’ (SOLA) method, a variant of classic Backus-Gilbert inversion suitable for global tomography. Our assessment strategy incorporates the following steps: 1) a 3-D Gaussian function is fitted to each averaging kernel to measure resolution lengths in different directions; 2) we define a classification scheme for the quality of the averaging kernels based on their focus with respect to the estimated 3-D Gaussian, allowing us to reliably identify whether the inferred resolution lengths are robust. This strategy is not restricted to SOLA inversions, but can, for example, be applied in all cases where point-spread functions are computed in other tomographic frameworks. Together with model uncertainty estimates that are derived from error propagation in the SOLA method, our concept reveals at which locations, resolution lengths and interpretations of model values are actually meaningful. We finally illustrate how the complete information from our analysis can be used to calibrate the SOLA inversion parameters —locally tunable target resolution kernels and trade-off parameters— without the need for visual inspection of the individual resulting averaging kernels. Instead, our global representations provide a tool for designing tomographic models with specific resolution-uncertainty properties that are useful in geodynamic applications, especially for linking seismic inversions to models of mantle flow.