Multi-fractal Random Walk and Its Application in Petro-physical Quantities
This chapter analyzes some properties of the porosity of rocks based on gamma radiation, sound transmission, and neutron porosity. It suggests that shale layers in the reservoir create negative correlations between the large fluctuations of the Gamma radiation series and the neutron porosity, and positive correlations between the Gamma radiation and the sound transmitting time. The chapter explains three applied indicators (i.e., measured natural gamma, neutron porosity logs and sonic logging) before showing how the multi fractal random walk approach works in this context. It focuses on the probability distribution and assumes that the cascading process starts from a large scale, which eventually tends to small scales. In order to model non-Gaussian petro-physical data, the multi-fractal random walk (MRW) method may be implemented, which takes into account the correlation between local variances in the time series. The resulting curves are referred to as well-logging of the petro-physical quantities in terms of the American Petroleum Institute (API).