Sensitivity kernels for interstation cross-correlations

For regional surface wave tomography the interstation method is often used. This method relies on the cross-correlation between two seismograms, recorded at two stations. In case of wave propagation from the event to both stations along a single great-circle, the average (frequency dependent) phase velocity between the stations can be estimated from the cross-correlation. For a simple Earth model such as PREM (Dziewonski and Anderson, 1981), it is likely that small velocity perturbations, that are located slightly off the great-circle, can influence the arrival times at both stations. The effect that a known perturbation at a certain location would have on the seismograms should therefore be quantified. Because of the similarity of the ray paths between the source and the nearest receiver, perturbations in that area are not expected to significantly influence the travel time between the stations; the interstation method would therefore be useful to investigate the interstation area. However, hardly any research has been done to check whether this is true and to what extent of complexity the method is still valid. The first step of this research is to use the adjoint method (Fichtner et al., 2006) to create sensitivity kernels for a simple Earth model (PREM), based on the travel time of the maximum of the interstation cross-correlations. The misfit is defined as the (frequency dependent) traveltime difference between two stations, which results in an adjoint wavefield that is independent on observed data. Synthetic results are obtained by modelling a spherical section of the earth in the SES3D programme package (Fichtner, 2009), which is based on a spectral element method. In the case of a single source and two receivers, the travel time cross-correlation kernels do not only have the expected interstation contribution, but there is also a significant contribution from the source to the nearest receiver. However, combining two sources, by adding their sensitivity kernels, increases the interstation sensitivity significantly, whereas the values in surrounding areas partly cancel out. So interstation structure cannot reliably be obtained from the interstation travel time cross-correlation of a single event, but the method gives better results when multiple events (along the great-circle) are used.