Spatial analysis of oil reservoirs using detrended fluctuation analysis of geophysical data
We employ the detrended fluctuation analysis (DFA) technique to investigate spatial properties of an oil reservoir. This reservoir is situated at Bacia de Namorados, RJ, Brazil. The data correspond to well logs of the following geophysical quantities: sonic, gamma ray, density, porosity and electrical resistivity, measured in 56 wells. We tested the hypothesis of constructing spatial models using data from fluctuation analysis over well logs. To verify this hypothesis, we compare the matrix of distances of well logs with the differences in DFA exponents of geophysical quantities using a spatial correlation function and the Mantel test. Our data analysis suggests that the sonic profile is a good candidate for representing spatial structures. Then, we apply the clustering analysis technique to the sonic profile to identify these spatial patterns. In addition, we use the Mantel test to search for correlations between DFA exponents of geophysical quantities.