Impact of seismic resolution on geostatistical techniques

Seismic measurements are often incorporated in geostatistical techniques for estimation and simulation of petrophysical properties such as porosity. The good correlation between seismic and rock properties provides a basis for these techniques. Seismic data have a wide spatial coverage not available in log or core data. However, each seismic measurement has a characteristic response function determined by the source-receiver geometry and signal bandwidth. The image response of the seismic measurement gives a filtered version of the true velocity image. Therefore the seismic image we obtain cannot reflect exactly the true seismic velocity at all scales of spatial heterogeneities present in the earth. The seismic response function can be conveniently approximated in the spatial spectral domain using a Born approximation. Our goal is to study how the seismic image response affects the estimation of variograms and spatial scales, and its impact on geostatistical results. Limitations of view angles and signal bandwidth not only smoothes the seismic image, increasing the variogram range, but can also introduce anisotropic spatial structures in the image. We can add value to the seismic data by better characterizing an quantifying these attributes. As an exercise we present example of seismically assisted cosimulation of porosity between wells.