Bayesian inversion, DSI, and kriging: an improved algorithm
Jonathan A. Kane, William Rodi, Tamás Németh, Kenneth P. Bube, Don Medwedeff, Oleg Mikhailov · 2004
Our goal in this work is to show that the geostatistical interpolation technique of simple kriging and the DSI interpolation method of the gOcad project can be formulated as a special cases of Bayesian inversion. In this way kriging can be extended to include arbitrary non-local data sets related to the parameter being estimated. We further present an efficient computational algorithm that, in some cases, produces and estimated field an order of magnitude faster than standard kriging methods, while requiring much less RAM than the DSI method. As a sample problem we simultaneously invert two data sets related to a 3-D slowness field to obtain an estimate of the slowness at all locations. The data sets we use are sonic logs and traveltime vs. depth picks from checkshots. If only slowness logs were used, it would be a kriging application. The traveltime data are non-local measurements of the slowness. The computational benefits of our algorithm apply to the estimates of slowness itself, but not to calculating the error variances. We present two possible methods, one exact, the other approximate, that circumvent this problem.