It is possible to estimate the elastic properties of underwater sediments using single-channel seismic profiling. The task is greatly simplified if the data are recorded using a geometry that minimizes the horizontal distance between seismic source and hydrophone receiver. This produces signal ray paths that are approximately perpendicular to sediment interfaces and thereby promotes a significant reduction in mathematical complexity. It also promotes well-developed sequences of seismic wavelets that reverberate between interfaces. The amplitudes and phases of individual wavelets in such sequences encode values of propagation parameters such as bulk densities and reflection/absorption coefficients. By analyzing amplitudes and phases, it is possible to remotely estimate sediment properties. Such estimates are often useful for engineering purposes such as dredging and pile driving.