MEAN AND VARIANCE OF THE ULTRASONIC SIGNAL FROM A SCATTERER BENEATH AROUGH-SURFACE - THEORY

A simple model is presented that predicts the ultrasonic signal from a weakly scattering inclusion beneath a randomly rough water-solid inte rface that is insonified by a normally oriented phase-sensitive transd ucer. The rough surface is modeled by a spatially uniform, normally di stributed random process with a Gaussian autocorrelation function. The effects of roughness are introduced via the phase-screen approximatio n. Analytic series solutions are derived and presented for the mean, m ean square, and mean absolute square of the pulse-echo signal. Rough s urface effects are shown to depend on the depth of the scatterer benea th the surface. The depth dependence of the rough-surface effects is s hown to arise from the statistical dependence of the phase shifts that arise due to the entry and exit of the ultrasound through the rough s urface. The roughness-induced loss of the average signal is found to b e greatest for scatterers immediately below the surface. The average r oughness-induced signal loss is least for scatterers that are farthest from the surface for unfocused transducers or at the focal point for focused transducers and can be modeled by a simple frequency-dependent transmission coefficient in these cases. The variance in the signal i ncreases with the frequency and is relatively large for scatterers imm ediately below the surface. The variance is smallest at the focal poin t, and in the far field for unfocused transducers. The variance is gre atest for the scatterers with the smallest lateral extent and least fo r scatterers with the largest lateral extent. Finally, it is found tha t the power backscattered from a small near-surface scatterer is actua lly increased on the average by the rough surface. (C) 1995 Acoustical Society of America.