Potential field analysis is known to suffer from the problem of "non-uniqueness" in solutions. Gravity data interpretation is a prime example. Anomalous bodies can be detected from the gravity field, but information regarding size, depth, and geometry is not easily discerned. Recently, gravity anomaly studies are augmented by satellite gravity gradient observations, which have the abilities to increase apparent sensitivity of gravity models. This study focuses on the theory of gravity and gravity gradients to implement them for the interpretation of anomalous bodies and reduce uncertainty by linking gravity studies with seismic models. The first part of the study involves developing techniques and testing them with known synthetic examples of a buried horizontal cylinder and a buried solid sphere of anomalous density. The gravity anomalies and gravity gradients are calculated and interpreted, especially in relation to the applicability and influence of edge effects. The second part is to extend this technique to a natural example, the North Atlantic centered by Iceland and the corresponding strong gravity anomaly. A density distribution of the lithosphere and upper mantle is modelled based on the S-wave velocity tomography model SL2013sv (Schaeffer and Lebedev, 2013) and 1D reference density model AK135 (Kennett et al., 1995) using a simple relation between velocity and density (Karato, 1993). Using this density distribution of the mantle, gravity anomalies and their gradients are calculated. The results are compared to observed gravity anomaly models and gravity gradients measured and calculated by the European Space Agency's "Gravity field and steady-state Ocean Circulation Explorer" (GOCE) satellite, respectively. Inferences are made about the lithosphere and upper mantle structure and the benefits of gravity gradients analysis are discussed.