Singular value decomposition-based reconstruction algorithm for seismic traveltime tomography

A reconstruction method is given for seismic transmission traveltime tomography. The method is implemented via the combinations of singular value decomposition, appropriate weighting matrices, and variable regularization parameter. The problem is scaled through the weighting matrices so that the singular spectrum is normalized. Matching the normalized singular values, a regularization parameter varies within the interval [0, 1], and linearly increases with singular value index from a small, initial value rather than a fixed one to eliminate the impacts of smaller singular values´ components. The experimental results show that the proposed method is superior to the ordinary singular value decomposition (SVD) methods such as truncated SVD and Tikhonov (1977) regularization