In order to systematically study the relationship between gravity and seafloor topography, we have developed a two-dimensional method for calculating the roughness of geophysical data. Roughness is obtained from the energy level of the data within specified wavebands. It is a representation of the spatial distribution of the frequency content of the studied signal. We assume that geodynamic provinces are areas where the gravity and the topography have a homogeneous frequency content. The comparative study of the roughness of both signals consequently allows us to distinguish areas which are situated in a precise geodynamic state. We have chosen characteristic areas of the Eastern North-Atlantic to show how roughness maps of the free air anomaly and the bathymetry signal can be used to infer geodynamic settings. For most of the areas, we find wide homogeneous provinces for both signals which coincide with the dominant geological features (Azores hot spot and mid-Atlantic ridge). In contrast, along the Iberian margin, differences of the distribution of roughness maxima between gravity and bathymetry signals suggest different compensation mechanisms.