Velocity-measurement bias of the ambient noise method due to source directivity: a case study for the Swedish National Seismic Network

The bias of velocity measurements from ambient-noise covariograms due to an anisotropic distribution of noise sources is studied assuming that the noise field consists of planar surface waves from large distance. First, general characteristics of the bias are described in terms of their dependence on wavelength, source-anomaly amplitude and width. Second, the expected bias of measurements in Sweden based on a noise-source model for the adjacent regions is analysed. The bias is conceptually explained and described in terms of two regimes, namely a high-frequency and a finite-frequency regime and their parameter domains quantified. Basic scaling laws are established for the bias. It is generally found to be small compared to lateral heterogeneity, except in the finite-frequency regime when interstation distance is small compared to a wavelength and in regions of low levels of heterogeneity. The potential bias, that is, its peak-to-peak variation, is generally higher for group-velocity than phase-velocity measurements. The strongly varying noise-source distribution as seen from Sweden results in predictions of relatively strong bias in the area at relevant frequencies and interstation distances. Levels of heterogeneity in the Baltic shield are relatively low, rendering the potential bias significant. This highlights the need for detailed studies of source anisotropy before application of ambient-noise tomography, particularly in regions with weak velocity heterogeneity. Predicted bias only partially explains deviations of phase-velocity measurements from a regional average for individual station pairs. Restricting measurements to station pairs with interstation distance exceeding five wavelengths limits the potential velocity bias in the area to within 1 per cent. This rather dramatic restriction can be relaxed by directional analysis of the noise-source field and application of azimuthal restrictions to the selected station pairs for measurement.