Waveguide invariant approximation in variable bathymetry using generalized Taylor expansion

Recently, a fixed eighth-order Taylor series expansion was employed to approximate the waveguide invariant for range estimation in weakly range-dependent environments with variable bathymetry [Byun, Song, and Cho, JASA 149, 1363–1370 (2021)]. In this presentation, we introduce a generalized Taylor expansion approach that enables flexible control over the expansion order. This approach allows us to determine the appropriate order needed for convergence toward the analytical solution and provides insight into how convergence behavior varies with range. Experimental validation shows reduced angular dependency at longer ranges and highlights the practical effectiveness of low-order approximations in environments with a small maximum angle of arrival.