| Abstract: | Seismic reflection methods are being developed at the University of Manitoba to aid in determining fine crustal structure in the Precambrian of Manitoba and northwestern Ontario. Present-day environmental concern as well as mineshaft conditions necessitate the detonation of several smaller charges repeated, say, I times and followed by ‘vertical’ stacking. To obtain the familiar √I improvement in signal-to-noise (S:N) amplitude ratio applying the straight-sum (SS) method, one assumes, among other things, that both S:N ratio and signal variance are the same on all traces. Dropping these assumptions, as we must for our data, it becomes necessary to apply weighting coefficients to optimize the S:N ratio of the stacked trace. We still assume the signal shapes to be the same for repeated shots, so for the jth trace on the record of the ith shot we model the time series as: tij=ai (sj+nij); where ai is a scaling factor. The proper weights wi are then shown to be proportional to σsi/σ2ni where σ2 is variance, or to γi/ai where γi is S:N power ratio. Applying the weighted-stack (WS) method gives S:N amplitude ratios which are, on average, 55% of the optimal ratios expected from WS theory compared with only 24% for the SS method. The 45% shortfall in WS performance is ascribed mainly to trace-alignment (or time-delay) errors. Varying noise levels on individual traces, slight dissimilarity of signal shape, and correlated noise may also contribute to a lesser extent (in decreasing order of significance). This WS method appears to strike a good practical balance between S:N improvement and processing efficiency. |
