Head waves and ground waves are strongly linked with properties of the seabed, and thus provide a useful measure for geoacoustic inversion. For a Pekeris waveguide, the ground wave can be interpreted as sequence of first-order (or classical) head waves, called a head-wave sequence [Choi and Dahl, J. Acoust. Soc. Am. 116, 2529 (2004)]. (The term first-order originates from a ray series classification.) The presence of a sound-speed gradient in the sediment gives rise to very different effects. Here, the first-order head wave is replaced by either a lower-amplitude interference head wave whose properties are akin to a first-order head wave, or a higher-amplitude interference head wave or related diving wave whose properties are zeroth-order. There is also a shift in the dominant frequency of the first-arriving head wave in the transition regime between these arrivals. In this talk, nomenclature for head waves based on the ray series classification is suggested, parametric dependencies for distinguishing these arrivals are discussed, the criterion to estimate the frequency shift is presented, and some implications for geoacoustic parameter estimation are discussed. Synthetic data and results are obtained using the RAM parabolic equation algorithm. [Research supported by ONR Ocean Acoustics.]