Inversion of seismic data and quantification of reservoir properties, such as porosity, lithology, or fluid saturation, are commonly executed in two consecutive steps: a geophysical inversion to estimate the elastic parameters and a petrophysical inversion to estimate the reservoir properties. We combine within an integrated formulation the geophysical and petrophysical components of the problem to estimate the elastic and reservoir properties jointly. We solve the inverse problem following a Monte Carlo sampling approach, which allows us to quantify the uncertainties of the reservoir estimates accounting for the combination of geophysical data uncertainties, the deviations of the elastic properties from the calibrated petrophysical transform, and the nonlinearity of the geophysical and petrophysical relations. We implement this method for the inference of the total porosity and the acoustic impedance in a reservoir area, combining petrophysical and seismic information. In our formulation, the porosity and impedance are related with a statistical model based on the Wyllie transform calibrated to well-log data. We simulate the seismic data using a convolutional model and evaluate the geophysical likelihood of the joint porosity-impedance models. Applying the Monte Carlo sampling method, we generate a large number of realizations that jointly explain the seismic observations and honor the petrophysical information. This approach allows the calculation of marginal probabilities of the model parameters, including medium porosity, impedance, and seismic source wavelet. We show a synthetic validation of the technique and apply the method to data from an eastern Venezuelan hydrocarbon reservoir, satisfactorily predicting the medium stratification and adequate correlation between the seismic inversion and well-log estimates for total porosity and acoustic impedance.

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