Assuming the diffractions are all the same, their autocorrelations are all the same. (Anyway, if not, we are in big trouble, because then we get a smearing together of all their different autocorrelations.) The autocorrelation combines all the diffractions despite their different locations. By combining them, it enhances them. The autocorrelation does the job of merging the energy of all the scatterers.

There is an issue of the cross correlation of one diffractor with another. We'll suppose the cross correlations cancel out because of the random superposition of many shifts and directions. In practice this could fail if there are a small number of very strong ones.

Several people suggested that I should investigate the effect of random scatterers spread throughout the earth instead of having them all at the surface. I agree that is an interesting model to study, but I feared it because we all recognize that reflectors at all different depths will produce different hyperbolas. We dare not autocorrelate such data until we have processed it so that all hyperbolas look the same.

4/27/2000