In this paper a new approach for joint interpretation of petrophysical measurements acquired by multiple sensors or tools is demonstrated. This approach is based on a mapping function that can be expressed as a linear combination of radial basis functions (RBFs). The theoretical log response equations for the sensors or tools are used to compute a database covering all possible ranges of formation properties, i.e., the solution space. The database is used to construct the mapping function that relates log measurements to formation properties. The solution space can be plotted in 2D or 3D depending on the number of input measurements. The plots provide the petrophysicist with a useful tool to: 1) identify outliers that might denote a model inadequacy, 2) select appropriate equation parameters that might not be obvious from individual logs, and 3) compute a solution consistent with the model equations. The mapping function solutions are computationally fast, unique, and robust. In contrast, traditional multi-tool interpretations based on non-linear minimization techniques often face problems of non-uniqueness and lack of robustness. We demonstrate the new approach using two classic examples. The first is the integration of resistivity and pulsed neutron capture logs to solve simultaneously for water saturations and salinities. This is a non-linear problem that has complex input parameter dependencies. The second example is analysis of thin-beds that have resistivity anisotropy. Even though analytical solutions exist, they are complex and it is difficult to see how, for example, net pay depends on the anisotropy. The choice of these classic examples allows us to show the simplicity of the proposed technique and to benchmark it against the traditional methods.


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