Estimation of modal wavenumbers is important for inference of geoacoustic properties and matched field processing in shallow water waveguides. However, it is challenging in a range-dependent environment, because modal content varies locally in response to changes in the environment. Moreover, the scales of the spatial variations in the waveguide may be on the same order as the range aperture required for resolvability of the individual modes. To this end, high-resolution (HR) wavenumber estimation methods have been widely used. In this paper, the matrix pencil and MUSIC algorithms are generalized to geometry involving a synthetic horizontal aperture (SHA) formed by a towed acoustic source and a fixed full-spanning vertical line array (VLA). The performance of the proposed methods is evaluated by simulated data in a noisy shallow water environment. Numerical results show that, when compared with the previous methods, the proposed methods significantly outperform the previous methods in terms of aperture requirement.