A back projection method of reconstruction is adapted to invert seismic travel time data for velocity structure. Adaptations are made so that the inhomogeneous and anisotropic ray sets and the three-dimensional geometries commonly dealt with in seismic experiments can be handled with greater success. Jacobi iteration, deconvolution, and ray weighting work well in augmenting the basic back projection method to produce a well-focused image. These methods succeed by amounts that depend on the quality of the ray coverage. Also, the ability to reconstruct an accurate image when the data include moderate amounts of noise is shown to be good. Comparison of inversions produced with back projection tomography and with damped least squares indicate that the two methods are comparable in their ability to reconstruct an image of the actual structure. The back projection approach, however, is much more computer efficient. In practice, this allows for the construction of more detailed inversions. ¿ American Geophysical Union 1988