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 conditioning them to well-log data. Two approaches help us: (1) Markov-chain Monte Carlo sampling, which generates many reservoir realizations for estimating medium properties and posterior marginal probabilities, and (2) optimization with a least-squares iterative technique to obtain the most probable model configuration. Our petrophysical model, applied to near-vertical-anglestackedseismic data and well-log data from a gas reservoir, includes a deterministic component, based on a combination of Wyllie and Wood relationships calibrated with the well-log data, and a random 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 corresponding strengths of each type of information, jointly improving (1) cross resolution of reservoir properties, (2) vertical resolution of property fields, (3) compliance to the smooth trend of property fields, and (4) agreement with well-log data at well positions.

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