It has already been established that by cross-correlating ambient noise time series received on the upward and downward steered beams of a drifting vertical array one can obtain a subbottom layer profile. Strictly, the time differential of the cross correlation is the impulse response of the seabed. Here it is shown theoretically and by simulation that completely uncorrelated surface noise results in a layer profile with predictable amplitudes proportional to those of an equivalent echo sounder at the same depth as the array. The phenomenon is simulated by representing the sound sources as multiple random time sequences emitted from random locations in a horizontal plane above a vertical array and then accounting for the travel times of the direct and bottom reflected paths. A well-defined correlation spike is seen at the depth corresponding to the bottom reflection despite the fact that the sound sources contain no structure whatsoever. The effects of using simultaneously steered upward and downward conical beams with a tilted or faceted seabed and multiple layers are also investigated by simulation. Experimental profiles are obtained using two different vertical arrays in smooth and rough bottom sites in the Mediterranean. Correlation peak amplitudes follow the theory and simulations closely.