On characterizing heterogeneities from velocity logs using Hölderian regularity analysis: A case study from Algerian tight Devonian reservoirs

Abstract

This paper aims at studying the singularity behavior of geophysical well logs to understand the geological model by extracting valuable information that cannot be derived using the conventional analysis techniques. Since well logs exhibit unpredictable spatial variations associated to a regularity evolving both in time and space, they are modeled by multifractional Brownian motions (mBm). These stochastic processes are indexed by the local Hölder exponent H which measures the degree of the regularity at every depth.First, synthetic logs have been simulated to assess the performance of the three suggested methods for estimating the local Hölder function H(z): Peltier and Lévy-Véhel (PLV), Bianchi and the detrending moving (DMA) algorithms. The obtained results illustrates that the PLV algorithm is the most efficient regularity estimator.Then, the regularity analysis is implemented on P- and S-wave velocity logs recorded at four Algerian exploration wells crossing two reservoirs, specifically the Devonian and Silurian reservoirs. Our findings showed good correlations between the local regularity functions H(z) and the lithological changes, and each change is marked by jumps of H value. In addition, as can be confirmed by the interpretation of petrophysical logs, the resulting local regularity profiles can indicate the distribution of clays and fluids present in the reservoirs. It is worth noting that the suggested regularity analysis might be of a high interest in investigating facies changes as well as in characterizing geological heterogeneities of subsurface.