The effect of a stochastic ocean bottom on underwater acoustic propagation is examined in two previous papers by the authors [J. Acoust. Soc. Amer43, 1395–1403 (1968);44, 1103–1114 (1968)]. In those investigations, the first and second moments of the random acoustic intensity are determined for various source and receiving‐point geometries. In a more recent study by the authors [J. Stat. Phys.2, 279–289 (1970)], the amplitude and decibel amplitude, as well as the intensity, of a random acoustic field are examined. There, each of the three measures of acoustic strength is shown to differ from the others in the analytic properties of its mean value and standard deviation. Therefore, in the present paper, the random‐bottom problem of the two earlier studies is reexamined. In particular, the first and second moments of the total‐field amplitude and decibel amplitude are studied under certain restrictions and are compared with those of the intensity. Furthermore, the first and second moments of the total‐field phase are treated.