In this paper, I have tested several approaches to the bandwidth equalization and phase matching steps of the cross-equalization process. Working in the frequency domain gives a large degree of control over the spectra and phase of the equalized data; however there is a danger of over-parameterizing the problem. Working in the time domain, provides a simple way of reducing the number of degrees of freedom. The best results were obtained by performing the bandwidth equalization in the frequency domain and phase matching in the time domain. An `optimal' cross-equalization method was tested following this procedure, which successfully increased the bandwidth of the difference section.
Working with synthetic data, it is hard to simulate the problems faced while cross-equalizing field data. Specifically, there will be problems in the assumption of stationarity that will need to be addressed, and the noise will never be nicely Gaussian. In these cases it may be possible to work under the assumption that the statistics although not stationary, are at least spatially slowly varying.