Two techniques for the singular value decomposition (SVD) of large sparse matrices are directly applicable to geophysical inverse problems: subspace iteration and the Lanczos method. Both methods require very little in-core storage and efficiently compute a set of singular values and singular vectors. A comparison of the singular value and vector estimates of these iterative approaches with the results of a conventional in-core SVD algorithm demonstrates their accuracy. Hence, it is possible to conduct an assessment of inversion results for larger sparse inverse problems such as those arising in seismic tomography. As an example, we examine the resolution matrix associated with a crosswell seismic inversion of first arrival times for lateral variations in anisotropy. The application to a set of first arrival times from a crosswell survey at the Grimsel Laboratory emphasizes the utility of including anisotropy in a traveltime inversion. The isotropic component of the estimated velocity structure appears to be well constrained even when anisotropy is included in the inversion. In the case of the Grimsel experiment, we are able to resolve a fracture zone, in agreement with borehole fracture intersections. Elements of the resolution matrix reveal moderate averaging among anisotropy coefficients as well as between anisotropy coefficients and source-receiver static terms. The information on anisotropy, such as the directions of maximum velocity, appears sensitive to lateral variations in velocity and must be interpreted with some caution.