Two-dimensional detrended fluctuation (2D-DFA) analysis has been carried out to correlate the Hurst index surface with corresponding irregularities of the cooper surface, because of the localised corrosion attacks after exposure in substitute ocean water for a period of three months. The 2D-DFA was applied on SEM images, in order to calculate the Hurst index surface and analyse the fractal properties of the copper surface. The Hurst index was linked with the fractal dimension . The results showed the existence of two surface range scales -sizes, where the fluctuation function for copper corroded surface exhibits power law behaviour, which is compatible with fractal properties. The calculated values of Hurst index surface are compatible with persistent processes of corrosion attacks. The results suggest that the surface morphology of the formed layer changes because of the metal grain transition from more ordered arrangement to a highly random (disordered) grain array.