When dealing with reservoir characterization using seismic, whatever the algorithm used for inverting the seismic data into reservoir properties, one has to deal with the fact that the reservoir properties varies in space in a way that is controlled by the structural features of the reservoir. There are basically two ways to deal with this kind of non stationarity of the reservoir properties:

1. steer the inversion algorithm with a number of moving parameters taking the structural features into account at a local scale
2. work on the coordinate system to handle the structural non stationarity The paper shows that only the structural anamorphosis of the coordinate system opens the way to a correct implementation of local stationary models In other words working with moving steering of algorithms will create artifacts as soon as the ranges of reservoir property variations become larger than structural ranges.

An example taken from actual seismic attribute processing illustrates the case.