Cross-Spectral Analysis of Midfrequency Acoustic Waves Reflected by the Seafloor

Direct path measurements of a single-bottom interacting path on a vertical array are used to probe the seabed structure. The phase of the cross-spectrum, commonly used in engineering acoustics, permits examination of the importance of subbottom paths. When the cross-spectral phase is linear with frequency it implies that source to receiver propagation is dominated by a single path. A linear cross-spectral phase would also satisfy the linear seabed reflection coefficient phase approximation sometimes employed in forward modeling and geoacoustic inversion approaches. Shallow water measurements of the cross-spectrum, however, evidence a strongly nonlinear phase, below about 1500 Hz at one site, and 600 Hz at another site, implying that: 1) the subbottom structure plays an important role (i.e., a seabed half-space approximation would be inappropriate); and 2) the linear reflection phase approximation would be violated at those frequencies.