Porosity from seismic data: A geostatistical approach

Using a geostatistical technique called cokriging, the areal distribution of porosity is estimated first in a numerically simulated reservoir model, then in an oil‐bearing channel‐sand of Alberta, Canada. The cokriging method consistently integrates 3-D reflection seismic data with well measurements of the porosity and provides error‐qualified, linear mean square estimates of this parameter. In contrast to traditional seismically assisted porosity mapping techniques that treat the data as spatially independent observations, the geostatistical approach uses spatial autocorrelation and crosscorrelation functions to model the lateral variations of the reservoir properties. In the simulated model, the experimental root‐mean square porosity error with cokriging is 50 percent smaller than the error in predictions relying on a least‐squares regression of porosity on seismically derived transit time in the reservoir interval. In the Alberta reservoir, a cross‐validation study at the wells demonstrates that the cokriging procedure is 20 percent more accurate, in a mean square sense, than a standard regression method, which accounts only for local correlations between porosity and seismically derived impedances. In both cases, cokriging capitalizes on areally dense seismic measurements that are indirectly related to porosity. As a result, when compared to estimates obtained by interpolating the well data, this technique considerably improves the spatial description of porosity in areas of sparse well control.