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Abstract
Seismic travel-time tomography, like most geophysical inverse problems, is often posed as a set of underdetermined linear equations. While seismic tomography has become a powerful technique to image the interior structure of the Earth, the images obtained do not represent unique solutions. Most often the minimum-norm or minimum-gradient solution is chosen. However, alternative solutions can be generated (which equally satisfy the seismic data) by incorporating nullspace components into the solution. By definition these components in the nullspace will not affect the data misfit. We develop a projection operator, referred to as the "nullspace shuttle", which projects any vector in the model space onto the nullspace.
In order to enhance tomographic images, additional a priori knowledge is added to the minimum-norm solution. The nullspace shuttle is used to project the changes made to the minimum-norm solution onto the nullspace; only those a posteriori changes which are consistent with the seismic data are permitted. Here the nullspace enhancement technique is applied to subduction zones throughout the western Pacific. The minimum-norm tomographic images obtained using a global ISC data set are biased towards a theoretical model for slab temperatures. Assuming to first order that the velocity variations within the slab are caused by cooler slab temperatures, the velocity perturbations in the tomograms should be consistent with a theoretical model for slab temperatures; temperature anomalies are converted to velocity perturbations using dV/dT. The nullspace shuttle is employed to guarantee that the enhanced model still satisfies the seismic travel times.
The minimum-norm velocity models obtained for the Kuril, Japan, Izu and Tonga subduction zones are compared to the enhanced images which have been biased towards the theoretical slab models. The enhanced images show much more continuous, narrow high velocity slab regions with P-wave velocity perturbations on the order of 6-7%. Using a nonlinear optimization, the optimal values for the physical parameters such as slab thickness and potential mantle temperature are determined, such that the theoretical model most closely resembles the tomograms. The values calculated for slab thickness are compared for the different subduction regions.
