Stacking with dual bootstrap resampling

A new kind of stacking scheme, based on the hypothesis testing of signal significance and coherence, is proposed. The significance of stacked data is evaluated by running two kinds of bootstrap resampling, one for standard bootstrap and the other for preparing noise stacks by scrambling relative time-shifts between traces. This dual bootstrap procedure allows us to formulate a two-sample problem for signal significance, which is shown to be more reliable than standard bootstrap estimates. The statistics of noise obtained in dual bootstrap resampling is also used when assessing the coherence of data with the empirical distribution function, in which the effect of noise is deconvolved by rescaling. Unlike conventional non-linear stacks such as Nth-root stack and phase-weighted stack, the new stack can recover signals even when the signal-to-noise ratio (S/N) is low, and compared to simple linear stack, the number of traces required for unambiguous signal detection is reduced by up to two orders of magnitude. The new scheme, called dual bootstrap stack, could facilitate a range of geophysical data processing when trying to detect subtle signals by stacking low S/N data.