Abstract We present an automatic inversion method for data acquired in a vertical well by the sonic, induction, and density borehole logging tools. The method is designed for oil-bearing or gas-bearing formations drilled with oil-base mud. The inversion accounts for challenging scenarios where the tool sensors are affected by filtrate invasion, gas phase, complex mineralogy and mechanical damage. The output consists of porosity and radial distributions of fluid saturations and pore shape extending several feet from the wellbore. The output is robust, accurate, and consistent with radial investigation depths of all the tools. The formation model assumed in the inversion has homogeneous porosity and radially varying pore shape, oil, gas, and water saturation. Radial changes in fluid saturation and pore shape are caused by filtrate invasion and mechanical damage respectively. The data for different tools are simulated from sonic and electromagnetic forward solvers, linked to the formation model through a saturation-resistivity transform and an effective medium rock physics model. The inversion estimates formation properties such that the simulated data match the measured data. For the first time, sonic data for both dipole flexural wave and monopole compressional-headwave are included. These data are sensitive to porosity and pore shape effects, and the compressional-headwave additionally provides sensitivity to gas saturation in soft formations. The inversion was tested on synthetic data and applied to two field data sets for gas-bearing formations. The results are visualized as 2D images with radial distribution of formation properties at each log depth. The images characterize radial depth of filtrate invasion and mechanical damage, which can guide completion and production decisions. The inversion also provides far-field saturation and porosity. The far-field properties are in overall good agreement with core data and traditional interpretation, with differences from traditional interpretation in key intervals. Quality controls enable checking validity of models assumed in the inversion. The results demonstrate an efficient inversion framework for guiding formation evaluation decisions in challenging scenarios.