Relationship Between Integrated Bottom Scattering Strength and Modal Backscattering Matrix

The integrated bottom scattering strength (ISS) and the modal backscattering matrix (MBSM) have been used to describe the bottom backscattering in shallow-water reverberation modeling, and both can be extracted from the reverberation data. The relationship between the ISS and the MBSM based on the same reverberation data in shallow water is discussed. It is shown that the ISS is an angular weighting average of the MBSM in mode space. The weighting factors are range–depth–frequency-dependent and also depend on the sound-speed profile (SSP) in the water column. Thus, the ISS has a complex variation. This complexity of the ISS causes it to be so variable that it provides little basic understanding of the scattering. Numerical examples are conducted to show this complexity.