Analysis of Cross Correlations Between Well Logs of Hydrocarbon Reservoirs

Abstract

We carry out a series of cross-correlation analysis of raw well-log data, in order to study the possible connection between natural gamma ray (GR) logs and other types of well logs, such as neutron porosity (NPHI), sonic transient time (denoted usually by DT), and bulk density (RHOB) of oil and gas reservoirs. Three distinct, but complementary, methods are used to analyze the cross correlations, namely, the multifractal detrended cross-correlation analysis (MF-DXA), the so-called Qcc(m) test in conjunction with the statistical test—the χ2(m) distribution—and the cross-wavelet transform (XWT) and wavelet coherency. The Qcc(m) test and MF-DXA are used to identify and quantify the strength of long-range cross correlations between the porosities derived based on the NPHI, DT, and RHOB logs on the one hand, and the GR log that is indicative of the presence of clay minerals in reservoir rocks, on the other hand. The Qcc(m) test describes qualitatively the presence of such cross correlations between the porosity and GR logs. Analysis by the MF-DXA method also indicates that the various porosity logs, the GR log, and the cross correlations between them are multifractal, hence confirming the long-range nature of the correlations. The results are confirmed further by the XWT, and indicate that the porosities estimated based on the NPHI logs are only weakly, if at all, affected by the natural GR radioactivity of reservoir rock and are, therefore, most reliable. The effect of length scale on the correlations and cross correlations was studied in detail. It is shown that such correlations exist at all length scales, and that they are of multifractal type that must be characterized by a spectrum of exponents.