Methods and related systems are described relating to an inversion approach for interpreting the geophysical electromagnetic data. The inversion can be constrained by using a multiphase fluid flow simulator (incorporating pressure data if available) which simulates the fluid flow process and calculates the spatial distribution of the water saturation and the salt concentration, which are in turn transformed into the formation conductivity using a resistivity-saturation formula. In this way, the inverted invasion profile is consistent with the fluid flow physics and moreover accounts for gravity segregation effects. Jointly with the pressure data, the inversion estimates a parametric one-dimensional distribution of permeability and porosity. The fluid flow volume is directly inverted from the fluid-flow-constrained inversion of the electromagnetic data. The approach is not limited by the traditional interpretation of the formation test, which is based on a single-phase model without taking into account invasion or assuming that the fluid, for example mud-filtrate, has been cleaned up from the formation testing zone. The joint inversion of the electromagnetic and pressure data provides for a more reliable interpretation of formation permeability. One advantage of the approaches described herein, is its possible generalization to three-dimensional geometries, for example dipping beds and highly deviated wells.