Slab temperature and thickness from seismic tomography 1. Method and application to Tonga

Delay times of compressional body wave phases from both teleseismic and loc al events are used to invert for a high-resolution P wave velocity model in the Tonga subduction zone. The images obtained show a high-velocity subduc ting slab with velocity deviations of the order of 3-4%. Assuming to first order that the positive velocity anomalies within the slab are caused by a temperature effect, a theoretical slab temperature model based on the diffu sion equation is used to explain velocity anomalies within the tomographic slab. Temperature differences between the interior of the slab and the ambi ent mantle are converted to velocity perturbations using the scaling parame ter dV(p)/dT approximate to 4.8 x 10(-4) km s(-1) degrees C-1 for lithosphe re material. The optimal values for the parameters in the temperature model are found using a nonlinear optimization that compares the integrated velo city anomalies in the tomographic sl;lb region to integral of high velociti es In a synthetic slab derived from a temperature model. The parameters for slab thickness and mantle potential temperature are not uniquely determine d; therefore a fixed value for the mantle potential temperature based on la boratory values for the temperature of the spinel-to-perovskite transition at 660 km is used. Using 1180 degrees C as the potential temperature, the t heoretical temperature model gives an optimal slab thickness of 82 km for a region near 29 degrees S in Tonga. The uncertainty in the thickness is dom inated by the uncertainty in the mantle temperature and would be 8 km for a n uncertainty of 100 degrees in mantle temperature, but nonsystematic error s are less. In order to enhance the tomographic result the velocity model i s biased towards the theoretical slab model. However, a posteriori changes made to the tomogram will most likely violate the fit to the delay time dat a. To prevent this, the difference between the tomogram and the predicted s lab model is projected onto the null-space of the inversion to remove compo nents which do not satisfy the seismic data. Using only null-space componen ts to modify the minimum-norm solution, an enhanced model is obtained which has been biased toward the theoretical solution but has the same data misf it as the minimum-norm solution. The final image shows a very narrow and co ntinuous slab with maximum velocity anomalies of the order of 6-7%; many of the gaps within the slab, as well as artifacts around the slab which were present in the minimum-norm solution, are absent in the biased image.