The classic integration of seismically-derived attributes into geocellular models by collocated cokriging is revisited, leading to improved geocellular modeling results above the seismic bandwidth in between wells. This paper shows a practical approach to the challenge of downscaling and integration of the seismic acoustic-impedance (seismic AI) attribute by calibrating it to the heterogeneity defined by the log-derived acoustic impedance (log AI). The approach is a reduction of the downscaling method by full cokriging to a simpler stepwise sequential-kriging to estimate the required parameters for stochastic simulation. The proposed approach is to create a downscaled-model AI by combining the low-frequency seismic attribute with a predicted high-frequency component before it is integrated into the porosity model using log well data. The current tools of preference, collocated cokriging and/or collocated co-simulation, assume proportionality between the variogram structures for both the synthetic log AI and the seismic AI. The problem with this assumption is that the modeled attribute may closely resemble the original low resolution data. If the correlation between attributes is significant, then the resulting "downscaled" realizations by collocated methods look diffuse, so they are unsatisfactory for use in high resolution geocellular models. The downscaling approach is redefined in this study by performing analytical computations and verifications with real reservoir data. A proper second-order downscaling approach for seismic AI must be based on full cokriging and non-collocated co-simulation using the logs and seismic. A complete integration should also reproduce the higher-order geological heterogeneity, which is contained in the high-resolution well logs but not normally shown in the seismic attributes. The numerical complications of cokriging and the lack of robust tools in most existing software have motivated the development of practical collocated solutions that can be implemented with less effort. The contribution of this study is that it provides an alternative non-collocated workflow for better representation of the vertical heterogeneity in geocellular models by downscaling seismic prior to integration.

You can access this article if you purchase or spend a download.