Estimating the boundary surface between geologic formations from 3D seismic data using neural networks and geostatistics

The exact locations of horizons that separate geologic sequences are known only at physically sampled locations (e.g., borehole intersections), which, in general, are very sparse. 3D seismic data, on the other hand, provide complete coverage of a volume of interest with the possibility of detecting the boundaries between formations with, for example, contrasted acoustic impedance. Detection of boundaries is hampered, however, by coarse spatial resolution of the seismic data, together with local variability of acoustic impedance within formations. The authors propose a two-part approach to the problem, using neural networks and geostatistics. First, an artificial neural network is used for boundary detection. The training set for the neural net comprises seismic traces that are collocated with the borehole locations. Once the net is trained, it is applied to the entire seismic grid. Second, output from the neural network is processed geostatistically to filter noise and to assess the uncertainty of the boundary locations. A physical counterpart is interpreted for each structure inferred from the spatial semivariogram. Factorial kriging is used for filtering, and uncertainty in the shape of the boundaries is assessed by geostatistical simulation. In this approach, the boundary locations are interpreted as random functions that can be simulated to incorporate their uncertainty in applications. A case study of boundary detection between sandstone and breccia formations in a highly faulted zone is used to illustrate the methodologies.