Distortion of the Frequency Dependence of Bottom Attenuation $\alpha(f)$ Inverted From Modal Attenuation $\beta_{m}$ due to Bottom Model Mismatching

The geoacoustic (GA) parameters (sound speed $c$ , density $\rho$ , and attenuation $\alpha$ ) of the bottom play crucial roles in broadband acoustical propagation in shallow water. In general, these parameters and their profiles are very hard to measure directly, especially the bottom attenuation at low frequencies. A common way to get these parameters is inverting them from the acoustical field data collected by a hydrophone array. Since the true bottom environment is not known, most inversions assume an approximate bottom model, such as a single layer or a half-space. It has been recognized that the “model mismatching” impact is an important issue to be investigated. This work will discuss the distortion of the frequency dependence of the bottom attenuation inverted from the modal attenuation due to the bottom model mismatching. It is found that if an inaccurate layered bottom model is used for the inversion the intrinsic dispersion character of GA parameters will be contaminated under the constraint of the forced data fitting. An analytic expression of the distortion factor ${\mathfrak{D}_{\boldsymbol{m}}}(\boldsymbol{f})$ is obtained using perturbation theory and numerical simulation examples are presented to show how the waveguide dispersion behavior is partially transferred to the intrinsic dispersion of the medium attenuation. A simple way is also suggested to compensate for the distortion factor.