On planetary surfaces, meteorite impacts create craters with a morphology which will evolve with time, influenced either by external (atmospheric) or by internal (tectonics, metamorphism) processes. On Earth, numerous erosional processes from climate (water, wind, ice) will slowly erase this topographic anomaly, while tectonics and/or other internal processes will also alter the geomorphologic signature. However, the geophysical signature of impact structure is usually well-preserved. This work aims at modeling the erosive evolution of simple and complex crater topography, and of the associated geophysical signature, to understand its evolution over time.