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Joint inversion of rock properties from sonic, resistivity and density well‐log measurements

Well‐log data are processed in order to derive subsurface physical parameters, namely rock porosity, fluid saturations and permeability. This step involves the selection and inversion of experimental constitutive equations, which are the link between the rock parameters and geophysical measurements. In this paper we investigate the rock parameter observability and the reliability of well‐log data processing. We present a visual analysis of the constitutive equations and of the inverse problem conditioning, when using independently, or jointly, log data from different domains. The existence of a common set of rock properties (cross‐properties) that influence different measurements, makes it possible to reduce the ambiguities of the interpretation. We select a test case in a reservoir scenario and we explore how to determine rock porosity and fluid saturation from sonic, conductivity and density logs. We propose a Bayesian joint inversion procedure, which is able to control the conditioning problems, to efficiently take into account input data and model uncertainty and to provide a confidence interval for the solution. The inversion procedure is validated on a real well‐log data set.