Higher-order statistics: improved event resolution?

In any area where near-surface earth structure causes one or more small time delays in seismic energy transmission, a seismic trace can be represented as a bandlimited reflectivity signal convolved with a short sequence of scaled copy spikes, each spike representing the delay due to a particular travel path variation. If the pattern (distribution) of spikes or static time shifts can be determined, its effects can be removed from the seismic trace by an explicit deconvolution operation. Accurate estimation of the spike pattern (static distribution function), however, is a key difficulty. The cross-correlation between a multi-shifted seismic trace and a “pilot ” reflectivity trace can be used to estimate the embedded static shift distribution function. For a trace consisting of the simple convolution of a reflectivity series and a short sequence of scaled static delay spikes, with no additive noise, the cross-correlation can perfectly extract the spike sequence. The cross-correlation is bandlimited by the mutual spectra of the input trace and pilot trace, however, and any noise present in the input time series degrades the resolution of the underlying spike sequence, the amount of degradation being inversel