Synthesis of Realistic Petrophysical Logs Using Truncated Fractal Levy Flights

We use truncated fractal Levy motion (fLm) to generate synthetic well logs, in order to reproduce more closely well statistics than with the commonly used Gaussian distribution. Four parameters are required to define the truncated fLm: alpha, which determines the shape of the fLm, C which is an equivalent of the standard deviation, H which corresponds to the strength of the spatial correlation, andlambda which is a cut-off value for the Levy distribution. We present a method to estimate these parameters from real well logs and an algorithm to generate realistic synthetic logs with the truncated fLm. An application to real data is shown.