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Statistical Relations Between Borehole and Surface Data
Reconciliation of measurements made on the surface and in the borehole is often difficult. The most prevalent practice is visual alignment and evaluation of forward synthetics. Recently inverse seismograms have generated more direct involvement and vertical seismic profiles provide more positive information on correlation.
For relations between the forward log synthetic and the well site seismic trace, normalized cross-correlation is the most obvious statistic. Time alignment, polarity, and the coefficient of correlation can often (but not necessarily) be determined. Log editing may be required as well as multiple studies. General scaling curves for seismic data can be derived from the logs in lieu of simple exponentials. Time variant coherency measure quantifies the degree of similarity between the seismic well site trace and the synthetic. The coherency points out problem areas to be corrected or edited to improve the match. Used as a weighting function on both signals, editing can be automated to make wavelet extraction practical. Extracted wavelets provide a good quality control for statistical wavelet processing of seismic data.
Similar procedures may be used between the VSP and log or VSP and seismic data. Time-depth relations are often clarified as the VSP provides a reliable time-depth curve. While poorly sampled relative to the sonic log, it may be used to correct problem zones in the log. The VSP also shows which multiples interfere constructively and which interfere destructively. This can sometimes explain log and seismic discrepancies.
When the forward modeling can be visually and statistically resolved, seismic data become a vehicle for typing the well logs. Statistical measures of lateral change in the seismic response verify changes from borehole conditions. Such measures tend to be of a difficult nature when data quality is variable - just as are visual evaluations. Recognition of lateral changes is an area of potential development.
Controversy exists as to the most appropriate model for the entropy of seismic data. Deconvolution may be based on minimum, maximum, or variable entropy assumptions. If the entropy can be statistically determined, deconvolution can be more effective.
More interchange of information between borehole and surface measurements would seem to be a rewarding endeavor. Indeed, current exploration and exploitation economics demand better use of all available data.
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