On the linearity of cross-correlation delay times in finite-frequency tomography

We explore the validity of the linear relation between cross-correlation delay times and velocity model perturbations that is required for linearized finite-frequency tomography. We estimate delay times from a large number of 'ground truth' seismograms computed with the spectral element method in 3-D models. We find that the observed cross-correlation delays remain sufficiently linear, depending on frequency, for sharp velocity contrasts of up to 10 per cent in a checkerboard model. This significantly extends the domain of linearity beyond that of inversions based on direct waveform differences. A small deviation from linearity can be attributed to the Wielandt effect (i.e. the asymmetry in the effect of positive and negative anomalies on the traveltime). Smoother Gaussian covariance models can have velocity variations twice as large and cross-correlation delay times still remain sufficiently linear for tomographic interpretations.