Toward quantifying uncertainty in travel time tomography using the null-space shuttle

The solution of large linear tomographic inverse problems is fundamentally non-unique. We suggest to explore the non-uniqueness explicitly by examining the null-space of the forward operator. We show that with the null-space shuttle it is possible to assess robustness in tomographic models, and we illustrate the concept for the global P-wave model MIT-P08. We found a broad range of acceptable solutions compatible with the travel time data. The root mean square (RMS) velocity perturbations vary from 0.2 to 0.6% in the lowermost mantle and from 0.3 to 1.3% in the upper mantle. Such large variations in average amplitudes prohibit meaningful inferences on temperature or chemical variations in the Earth from tomographic models alone. On a global scale much short wavelength structure resides in the null-space of the forward operator, suggesting that the data do not everywhere resolve structure on the smallest length scale (