First-order and zeroth-order head waves, their sequence, and implications for geoacoustic inversion

The relation between the head wave and an arrival often called a ground wave is analyzed with parabolic equation-based simulations, and an interpretation of such a ground wave as a head wave sequence is presented. For a Pekeris waveguide the envelope of the spectrum of the ground wave arrival corresponds to the spectrum of a single head wave, and spectral peaks correspond to odd multiples of the mode-1 cutoff frequency. This head wave is first order in its ray series classification and its amplitude spectrum goes as ∣S(f)∣∕f, where S(f) is the source amplitude spectrum. Basic variations from a Pekeris waveguide are considered; isospeed layers or a positive sound speed gradient in the seabed can each give rise to arrivals that are zeroth order in ray series classification and higher amplitude. For a sound speed gradient there is either a low-amplitude interference head wave whose properties are akin to a first-order head wave, or a high-amplitude interference head wave or non-interfering refracted wave whose properties are zeroth order and spectra follow ∣S(f)∣. Parametric dependences for distinguishing these arrivals and implications for geoacoustic inversion are discussed.