Finite-Frequency Inversion of Cross-Correlation Amplitudes for Ambient Noise Source Directivity Estimation

We present a new method for determining the azimuthal variation of ambient noise sources, which combines the computational speed and simplicity of traditional approaches with the rigor of waveform-inversion-based approaches to noise source estimation. This method is based on a previously developed theoretical framework of sensitivity kernels for cross-correlation amplitudes. It performs a tomographic inversion for ambient noise sources on the Earth's surface and is suitable for small- (local-) scale studies. We apply the method to passive seismic data acquired in an exploration context and account for azimuth-dependent uncertainties in observed cross-correlation amplitudes. Our inversion results correlate well with the azimuthal distribution of noise sources suggested by signal-to-noise ratio analysis of noise cross-correlation functions.