Comparison of mapping schemes for reservoir characterization

Often one is interested in the relationships between various types of geological data, such as depth, formation thickness, position, permeability, porosity, etc. However, geological data are difficult to analyze due to their spatial complexity, and because obvious analytical maps of one type of data onto another seldom exist. Typically, multivariate regression techniques are used to correlate geological data. This approach requires often stringent assumptions about the functional form of the data. Here, we compare a method that does not require such assumptions: Alternating Conditional Expectation (ACE), with two other approaches that do: Geostatistics and MATLAB. The ACE method, developed by Breiman and Friedman (1985), is an iterative optimal transformation that maximizes the correlation between the transformed dependent variable and the sum of the transformed independent variables. Even with multiple independent variables, the specific functional dependence of each variable can be found. A thorough geostatistical analysis of the full data set is treated as the ground truth, against which the two other methods are compared. The field example from the South Belridge diatomite, Kern County, CA, involves correlating the true vertical depths of diatomic layer boundaries with their x (EW) and y (NS) coordinates. The geological data from approximately 70 wells in an area about 1000 feet by 1000 feet have been used. We compare how well the three methods can smooth and interpolate the data to produce layer mappings. In the end, the most laborious of the three methods, geostatistics with Surfer as a plotting tool, wins hands down. The other two methods are far more limited.