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Figure 2. Relation between normal-incidence reflectivity and sand/shale ratio in very thin-bedded sand-shale layers. The back line is obtained using Backus average for thin layers, with blocked average values of sand and shale properties from well log. Curves show the result of computations using Monte Carlo simulation to incorporate the variability of sand and shale velocity, density, and impedance. The blue curve is the mean of the distributions obtained from the simulations, and the red and green dotted curves are the 10 percentile and 90 percentile curves, respectively. We see clearly the pitfalls of ignoring variability.
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