Implementing spectral leakage corrections in global surface wave tomography

We analyse the effect of uneven ray coverage in global surface wave tomography. An inhomogeneous distribution of seismic rays may bias tomographic models because certain areas are better sampled than others. It is possible to suppress this bias, known as the spectral leakage, by using a linear inversion technique with a specific data weighting. We use finite-frequency sensitivity kernels to calculate the appropriate data weightings which suppress spectral leakage. Exact calculations are very computer intensive and approximations are needed. We give a rule-of-thumb for the parameters entering the approximation. We show that a low-degree phase velocity model constructed from real data, without special precaution, suffers from noticeable spectral leakage. This leakage effect is stronger than any contamination of the solution by data errors. Model damping cannot correct for spectral leakage unless the inverse problem is overparametrized. Model damping implies varying resolution of retrieved features and makes a precise geodynamic interpretation of the images difficult. Increasing computer power makes spectral leakage corrections possible, allowing tomographic images with perfect resolution.