Performance and limitations of spectral factorization for ambient noise sub-bottom profiling

Abstract

Using a drifting vertical array as a means to measure noise directionality one can infer reflection coefficient vs angle and frequency. This can be converted to a time-varying impulse response, i.e., a sub-bottom profile, by using spectral factorization to recover the phase. Limitations of the technique are discussed with simulations and experiment. First, spectral factorization provides a minimum phase realization of the impulse response for the given spectrum, whereas the true reflection coefficient may not actually be minimum phase. Second, the beam width, determined by array length, slightly smudges the interference fringes that are characteristic of the reflection coefficient. This reduction in frequency resolution reduces the maximum depth to which layers can be detected. Consideration of the detailed mechanism leads to a way of improving frequency resolution and hence maximum depth. Spectral factorization tends to function well unless the impedance contrast between water and upper layers is very small. The depth limitations due to beam width will usually be more important than those of spectral factorization even with the proposed recovery of frequency resolution. At 4kHz design frequency the layer structure thus determined during a 6km drift compares well with a seismic boomer down to 15m.