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Bayesian Kriging optimizes the velocity law parameters so that residual depth mismatches at the well locations are minimized and tied to the well depth markers.
The inputs are:
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Step 1: Time interpretations and well depth markers.
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Step 2: Velocity law and range of acceptable velocity law parameter values, also considered as "a priori" Bayesian constraints.
The outputs are:
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Step 3: A best estimated depth “trend” map minimizing the depth residuals (not tied to the wells), resulting from “a posteriori” velocity laws parameters which have been best estimated within the range of “a priori” bayesian constraints on velocity law parameters.
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Step 4: A best estimated depth map tied to the wells, which combines kriged depth trend and tying residuals at the well locations.
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Step 5: A depth uncertainty map computed as a combination of kriging variances of the depth trend and residuals.
References:
Omre, H. 1987, Bayesian kriging merging observations and qualified guesses in kriging. Math. Geol, 19 (1), 25-39
Abrahamsen, P. 1993, Bayesian Kriging for Seismic Depth conversion of Multi-layer Reservoir, in A. Soares (ed.) « Geostatistics Troia ‘92 ». Pp. 385-398
