Noise alignment in trim statics

Charles P. Ursenbach, John C. Bancroft

It has been shown (e.g., Cox, 1999, Section 7.9.2) that one difficulty of the cross- correlation procedure in trim statics is that it is possible to have spurious reproduction of signal. This phenomenon is quantified and is shown, in the limits of large fold, small correlation window, and large maximum allowable shift, to behave as a simple function of these variables for physically reasonable wavelet lengths. A quantitative expression for the cross-correlation coefficient of purely random traces is obtained which appears to be valid within certain limits. These results are of particular value in that they allow one to predict what choice of cross-correlation parameters are likely to result in spurious alignment of noise.