Linearly filtered estimation of the time-domain Green's function from measurements of ambient noise (L)

It is possible to estimate the time-domain Green's function of a channel based on measurements of ambient noise by sensors at either end of the channel. This paper presents theoretical results for the impact of filtering on this problem. These results lead to the development of two experimental rules-of-thumb. It is shown that there exists a relationship between system bandwidth and sensor separation, which determines the resolvability of the measurements. The relationship between high-pass filtering and differentiation is discussed, contributing to the debate about whether or not differentiation is required to estimate the time-domain Green's function.