The methods in use for surface wave tomography based on the Backus-Gilbert approach are reviewed, the focus being on deriving lateral variations in phase or group velocities as inferred from average velocities along paths that traverse an area of study. The technique is described for a flat and a spherical Earth. Similar to the Backus-Gilbert method, where the resolution is to be evaluated by the length of the averaging interval, the present (two-dimensional) case has the resolution evaluated by the linear size of the averaging area. The simplest averaging area is a circle, the radius then being adopted as the estimated resolution. When the paths tend to lie along some preferred direction, the area is fitted with an ellipse. A method is given for estimating the lengths and orientations of the axes of the ellipse. We describe a technique for determining lateral variations of surface wave phase velocity from azimuthal anomaly data. Two sample cases are discussed to illustrate the techniques, the Black Sea basin