In this paper we propose GREASE, a distributed algorithm to deploy mobile sensors in an unknown environment with obstacles and field asperities that may cause sensing anisotropies and non uniform device capabilities. These aspects are not taken into account by traditional approaches to the problem of mobile sensor self-deployment. GREASE works by realizing a grid-shaped deployment throughout the Area of Interest (AoI) and adaptively refining the grid to find new sensor positions to cover the target area more precisely in the zones where devices experience reduced movement, sensing and communication capabilities. We give bounds on the number of sensors necessary to cover an AoI with obstacles and noisy zones. Simulations show that GREASE provides a fast deployment with precise movements and no oscillations, with moderate energy consumption.