Mitigating array-induced bias in ambient noise beamforming

We show that the geometry of a seismic array affects estimates of velocity and propagation direction of ambient seismic noise wavefields measured with beamforming techniques. We demonstrate how this results in apparent anisotropy estimates and present first approaches to mitigate the effect. Beamforming is an array technique originating from earthquake seismology that has become increasingly popular to analyse the ambient noise wavefield with the goal to characterise ambient noise sources (e.g., regions of origin of Love and Rayleigh waves) as well as subsurface structures (shear-velocity profiles, fracture orientation). Beamforming techniques estimate the dominant velocity, direction of propagation, and (in case of three-component data) the polarisation of a wavefield recorded within a limited time window at a seismic array. An important parameter in beamforming is the array response function, which shows the response of an array to a wave that is arriving directly from below. It can be thought of as the fingerprint of the array and depends on the array geometry, i.e., number of stations, station spacing, and orientation of station pairs. A biased array can lead to oversampling of certain directions and, thus, prioritising them in the beamform heatmap.The first attempt to mitigate the influence of the array focuses on analysing the orientation of station pairs in an array and applying a weighting matrix in order to enhance contributions from orientations that are underrepresented. This approach leads to a modified array response function, that looks more regular and has the fingerprint of the array partly removed. Using synthetic data and different array geometries we demonstrate the effect on the estimated anisotropy. The second approach is based on simulating synthetic, isotropic wavefield recordings at an array of choice and measuring their dominant velocities and propagation directions using beamforming. Comparing expected and observed values shows that the effect of the array can be significant, in particular when multiple sources act simultaneously (as is often the case for ambient noise): both measured velocities and propagation directions are affected by the design of the array, leading to erroneous anisotropy estimates. Once we have an estimate of array-induced anisotropy, however, we can subtract it from the anisotropy measured in real data and thereby reduce the effect. Examples for different array geometries are presented and compared.