RESOLVING SEISMIC ANISOTROPY - SPARSE-MATRIX METHODS FOR GEOPHYSICAL INVERSE PROBLEMS

Two techniques for the singular value decomposition (SVD) of large spa rse matrices are directly applicable to geophysical inverse problems: subspace iteration and the Lanczos method. Both methods require very l ittle in-core storage and efficiently compute a set of singular values and singular vectors. A comparison of the singular value and vector e stimates of these iterative approaches with the results of a conventio nal in-core SVD algorithm demonstrates their accuracy. Hence, it is po ssible to conduct an assessment of inversion results for larger sparse inverse problems such as those arising in seismic tomography. As an e xample, we examine the resolution matrix associated with a crosswell s eismic inversion of first arrival times for lateral variations in anis otropy. The application to a set of first arrival times from a crosswe ll survey at the Grimsel Laboratory emphasizes the utility of includin g 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 e xperiment, we are able to resolve a fracture zone, in agreement with b orehole fracture intersections. Elements of the resolution matrix reve al moderate averaging among anisotropy coefficients as well as between anisotropy coefficients and source-receiver static terms. The informa tion on anisotropy, such as the directions of maximum velocity, appear s sensitive to lateral variations in velocity and must be interpreted with some caution.