We find that higher-order ambient seismic field correlations, specifically C3 (correlation of the coda of correlations) of long-duration data sets from Southern California are symmetric despite the fact that the background wavefield is strongly directional.  We demonstrate that this symmetry arises primarily from the structure of the C3 time series analysis, rather than the diffuse character of the coda. For that reason, the resulting ambient-field Green’s function symmetry may not be diagnostic of correlation quality. We propose an alternative pre-stack processing scheme that constructs C3 correlations from each C1 coda time window, but stacks the results only at the final step of processing. Our pre-stack C3 method essentially avoids the cross-correlation between coda windows from different realizations, which leads to faster convergence and therefore shows potential to extract arrivals at higher frequencies than standard processing.