On plane-wave reflection from a two-layer marine sediment: A surficial layer with linear sound speed profile overlying an iso-speed basement.

An analysis of plane wave reflection is developed for a two-layer sediment, the top layer consisting of a fine-grained material (mud) with an upward refracting linear sound speed profile. Beneath is a homogeneous basement, and above is homogeneous seawater. A rather curious, exact analytical expression for the reflection coefficient is derived, involving easy to evaluate integrals over finite limits, of the modified Bessel functions of low-integer order. The expression is generally valid for any linear profile with positive gradient in the surficial mud layer and for any sound speed in the basement, either greater than or less than that in the seawater. For "fast" basements, a critical angle always exists that is independent of the sound speed in the mud layer. With a "slow" basement, a quasi-angle of intromission may exist, which depends only weakly on both frequency and the gradient of the profile in the mud, a conclusion that may be relevant to the conditions of the Seabed Characterization Experiment (2017) performed over the New England Mud Patch. With both types of basement, fast and slow, the reflection coefficient, as a function of grazing angle, exhibits fluctuations that are strongly frequency dependent, associated with resonances and anti-resonances in the mud layer.