FAST ITERATIVE SOLUTION OF SPARSELY SAMPLED SEISMIC INVERSE PROBLEMS

One of the problems in linearized seismic inverse scattering, which ha s received little attention so far, is the existence of large gaps in the acquisition geometry due to the use of a limited number of sources and receivers. Frequently used Born inversion methods do not take thi s kind of sampling effect into account. Therefore, especially for thre e-dimensional problems, the results may suffer from serious artefacts. These problems are partially overcome by using iterative methods, bas ed on the minimization of an error norm. For two-dimensional test prob lems, we have found that iterative methods give significantly more acc urate results for sparsely sampled data. For large-scale seismic inver se problems, the rate of convergence of any iterative method is extrem ely important. We have found that fast convergence rates can be achiev ed with the aid of methods that are preconditioned with the Born inver se scattering operator. In particular, the rate of convergence of the preconditioned successive overrelaxation method and the preconditioned Krylov subspace method have been found to be much faster than the wid ely used conjugate gradient method. With these new methods, we have ob tained acceptable results for problems containing as many as 90 000 un knowns, after only four iterations.