Cross-correlation in band-limited ocean ambient noise fields.

Observations of ambient noise in the ocean are generally band limited, because of the natural spectral shape of the noise or the restricted bandwidth of the detection system. Either way, the noise may be regarded as white noise to which a band-limiting filter has been applied. An analysis of the two-point cross-correlation function of such filtered noise is presented for two cases, isotropic and surface-generated noise. The most pronounced effects occur with high-pass and bandpass filters when the low-frequency cut-off falls well above the first few zeros in the coherence function. In this situation, the sensor separation is very many times the longest acoustic wavelength (associated with the lowest frequency) in the passband. The filtering then produces sharp pulses at correlation delays equal to the numerical value of the acoustic travel time between the sensors. Although these pulses are narrow, they have a finite width, within which a fine structure appears in the form of multiple rapid oscillations, due to the differentiating action of the filter. The number of such oscillations increases as the low-frequency roll-off of the filter becomes steeper. This fine structure is evident in several recently published experimental determinations of the cross-correlation function of band-limited ocean ambient noise.