Facies Recognition Using Multifractal Hurst Analysis: Applications to Well-Log Data
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Facies Recognition Using Multifractal Hurst Analysis: Applications to Well-Log Data Eliseo Hernandez-Martinez · Teresa Perez-Muñoz · Jorge X. Velasco-Hernandez · Armando Altamira-Areyan · Luis Velasquillo-Martinez
Received: 10 May 2012 / Accepted: 28 January 2013 / Published online: 23 February 2013 © International Association for Mathematical Geosciences 2013
Abstract Well-log (radioactivity, density and resistivity) analysis constitutes a standard approach for inferring lithology from wells. However, due to inherent complexity of the signals (such as highly heterogeneous deep-water sedimentary sequences) lithology recognition is not straightforward. We used a rescaled range analysis, calibrated with cores, to recognize lithological patterns from signal recorded along wireline logs. The detected intervals coincide with zones of visual electro-facies associations proposed by geologist well-log interpreters. In addition, we propose a rescaled range multifractal analysis to identify ranges of well-log signal complexities, which could be related to sedimentary process variations at specific stratigraphic order cycles. Keywords Well-log data · Electro-facies associations · R/S analysis · Multifractal analysis · Deep-water sequences · Cyclostratigraphy 1 Introduction Hydrocarbon reservoir characterization requires geological models based on the integration of geophysical, petrophysical and reservoir engineering information involving geological modeling, the determination of petrophysical properties of the rocks, production data analysis, and other available field information. Among the most common E. Hernandez-Martinez () · T. Perez-Muñoz · J.X. Velasco-Hernandez Programa Estratégico de Matemáticas Aplicadas y Computación, Instituto Mexicano del Petróleo, Eje Central Lázaro Cádenas 152, San Bartolo Atepehuacan, Gustavo A. Madero, Apartado Postal 14-805, 07730, Distrito Federal, Mexico, Mexico e-mail: [email protected] A. Altamira-Areyan · L. Velasquillo-Martinez Programa de Geología y Exploración, Instituto Mexicano del Petróleo, Eje Central Lázaro Cádenas 152, San Bartolo Atepehuacan, Gustavo A. Madero, Apartado Postal 14-805, 07730, Distrito Federal, Mexico, Mexico
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Math Geosci (2013) 45:471–486
sets of information are well-logs, cores, seismic data, pressure tests, and more. In particular, in the identification and correlation of stratigraphic units (i.e., lithological description), the core and seismic interpretations play important roles. Nevertheless, in practice only a small percentage of wells have cores, and seismic data is not recovered in most mature fields, while well-logs are often recovered in most of the wells. The adequate interpretation of well-logs allows for determining the different properties of rocks, such as permeability, density, resistivity, and porosity, among others. Well-log analysis is a useful tool for the lithological description of wells, however, due to the inherent complexity of the signals (e.g., pressure, saturation and types of fluids, size, and form of pores), the identificati
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