Direct solution of the backscatter equation for ABS instruments through a Riccati reformulation

• Published in: Continental shelf research Vol. 46; pp. 83 - 86
• Main Authors: Hamilton, L.J., Hall, M.V.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.09.2012
• Subjects: ABS; Acoustic backscatter; Suspended sediment; Suspended sediment; ABS; Acoustic backscatter
• ISSN: 0278-4343; 1873-6955
• DOI: 10.1016/j.csr.2011.07.006

Measurements of suspended sediment concentration profiles in aquatic environments may be made by remote sensing acoustic backscatter (ABS) instruments. These typically operate at MHz frequencies and narrow beamwidths (1–2°). The backscatter equation for these instruments is not in a closed form. It may be solved by iteration. A direct general solution has previously been presented by recasting into the form of a Bernoulli equation [Thosteson, E.D., Hanes, D.M., 1998. Journal of the Acoustical Society of America 104 (2), 820–830 (Pt. 1)]. It is shown that the direct solution is also enabled by recasting as a Riccati equation. The direct solution obtained by the Riccati formulation has the same form as given previously, but its derivation clarifies inconsistencies in previous work which have disguised its potential usefulness. ► The direct solution for the backscatter equation for mono-frequency ABS instruments is derived by a Riccati formulation. ► Discrepancies are noted in a previous derivation which have disguised the usefulness of the direct solution. ► An integration constant may be evaluated at multiple points through the water column, not just one. ► This potentially allows the form of the sediment distribution with range to be calculated for mono-frequency ABS.