Fast-changing dip formation resistivity estimation methods and systems, including a formation resistivity estimation method that includes estimating an initial horizontal resistivity based upon acquired formation logging data and determining an initial value set of one or more value sets. The method further includes determining each additional value set of the one or more value sets using a 1-dimensional inversion initialized with a previously determined value set of the one or more value sets, and displaying a final value set of the one or more value sets. Each of the 1-dimensional inversions is performed using a cross-bedded formation model, and each of the one or more value sets includes one or more parameters selected from the group consisting of a horizontal resistivity, a vertical resistivity, a formation dip angle, a formation azimuth angle, a tool inclination angle, a tool azimuth angle and a depth.