Receiver-pair Seismic Interferometry and the Cosine Method

In this paper we consider ambient seismicity with an a priori unknown, but strong, directionality. We develop methods to use the recorded Rayleigh waves for estimating an average dispersion curve and for estimating the directionality of the (noise) field. With the first method: receiver-pair seismic interferometry, a well-sampled circular array of receivers is used. The method consists of two steps. In the first step the recordings are crosscorrelated for opposite receiver pairs. From these crosscorrelations, the backazimuth of the source(s) are found with a stationary-phase analysis. In the second step, the crosscorrelations are stacked, yielding the actual surface-wave response between two positions on the circle. From the retrieved response, the dispersion curve is extracted. With the second method: the cosine method, there are only a few receivers on the circle. The backazimuth of the source is found from the crosscorrelations through an inversion scheme. A minimum of 4 receivers is required. Subsequently, we generalize the cosine method for non-circular arrays of receivers. For the generalized case a minimum of 3 receivers is required. In both latter cases, the dispersion curve can be found directly from the crosscorrelations after estimating the backazimuth of the source.