We develop a grid-search-based inversion method to discriminate between changes of pore pressure and water saturation. In this approach, we build a forward model by combining different rock-physics models and we predict grids of time-lapse attributes within a range of pressure and saturation. The time-lapse measurements from the data are matched with these predicted attributes to find the solution. We suggest using the independent time shifts and time-lapse attenuation to stabilize the inversion result. A synthetic example illustrates the advantages of the inversion workflow. The method helps to visualize how pressure and saturation change the elastic properties. This advantage is also useful in quality control and uncertainty analysis. We apply our method to a real underground blowout example in the North Sea area where gas has leaked into two sand layers at different conditions. We find that gas migrated according to the sand structure with the dipping layer leading to faster migration rates. The inversion results indicate that careful data preparation is crucial, not only to obtain stable inversion performance, but also to capture valuable information when interpreting the blowout development.