Petrophysical seismic inversion conditioned to well-log data: Methods and application to a gas reservoir Miguel Bosch 1 , Carla Carvajal 2 , Juan Rodrigues 1 , Astrid Torres 2 , Milagrosa Aldana 3 , and Jesús Sierra 4 ABSTRACT Hydrocarbon reservoirs are characterized by seismic, well- log, and petrophysical information, which is dissimilar in spatial distribution, scale, and relationship to reservoir properties. We combine this diverse information in a unified inverse-problem formulation using a multiproperty, multiscale model, linking properties statistically by petrophysical relationships and condi- tioning them to well-log data. Two approaches help us: 1 Mark- ov-chain Monte Carlo sampling, which generates many reservoir realizations for estimating medium properties and posterior mar- ginal probabilities, and 2 optimization with a least-squares iter- ative technique to obtain the most probable model configuration. Our petrophysical model, applied to near-vertical-anglestacked seismic data and well-log data from a gas reservoir, includes a de- terministic component, based on a combination of Wyllie and Wood relationships calibrated with the well-log data, and a ran- dom component, based on the statistical characterization of the deviations of well-log data from the petrophysical transform. At the petrophysical level, the effects of porosity and saturation on acoustic impedance are coupled; conditioning the inversion to well-log data helps resolve this ambiguity. The combination of well logs, petrophysics, and seismic inversion builds on the cor- responding strengths of each type of information, jointly improv- ing 1 cross resolution of reservoir properties, 2 vertical reso- lution of property fields, 3 compliance to the smooth trend of property fields, and 4 agreement with well-log data at well positions. INTRODUCTION The 3D characterization of hydrocarbon reservoirs requires inte- grating information across medium properties at different spatial scales and distributions: 1 high-resolution well-log information at irregularly distributed well paths, 2 uniformly sampled informa- tion from 3D seismic data with low vertical resolution, 3 petro- physical information relating reservoir properties and scales, and 4 geostatistical information relating property fields in space. Common procedures rely on stepwise processing of the different types of data and information seismic, well log, petrophysical, and geostatisti- cal and their combination in various work flows. The goal of our work is to describe a method to integrate this information into a uni- fied inversion scheme, accounting for nonlinear relations across me- dium properties and data as well as the combination of uncertainties related to the various information components. The combination of well-log data and seismic information for es- timating reservoir and elastic medium properties has motivated the development of different techniques. In Doyen 1988, well-log po- rosities are extrapolated by correlation with the acoustic impedance estimated from seismic data, using the well-known cokriging tech- nique. An additional step in integrating seismic data within geo- statistical methods is described by Haas and Dubrule 1994, who propose a method to generate acoustic impedance realizations con- ditioned to the well-log data and seismic stacked data simulated by 1D convolution of the model reflectivity. Also, Torres-Verdin et al. 1999 focus on the problem of generating realizations of acoustic impedance and discrete facies types jointly honoring stacked seis- Manuscript received by the Editor 5 March 2008; revised manuscript received 17 September 2008; published online 4 February 2009. 1 Universidad Central of Venezuela, Geophysical Simulation and Inversion Laboratory, Engineering Faculty, Caracas, Venezuela. E-mail: miguel.bosch @ucv.ve. 2 Universidad Central of Venezuela, Geophysical Simulation and Inversion Laboratory, and Universidad Simón Bolivar, Department of Earth Sciences, Cara- cas, Venezuela. 3 Universidad Simón Bolivar, Department of Earth Sciences, Caracas, Venezuela. E-mail: maldana@usb.ve. 4 IGS Services and Consulting, Caracas, Venezuela. E-mail: jesus.sierra@igs-sc.com. © 2009 Society of Exploration Geophysicists. All rights reserved. GEOPHYSICS, VOL. 74, NO. 2 MARCH-APRIL 2009; P. O1–O15, 11 FIGS. 10.1190/1.3043796 O1 Downloaded 13 Apr 2009 to 200.44.243.220. Redistribution subject to SEG license or copyright; see Terms of Use at http://segdl.org/