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

Delay times of compressional body wave phases from both teleseismic and local 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 subducting 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 diffusion equation is used to explain velocity anomalies within the tomographic slab. Temperature differences between the interior of the slab and the ambient mantle are converted to velocity perturbations using the scaling parameter dV p / dT ≈ 4.8 × 10 −4 km s −1 °C −1 for lithosphere material. The optimal values for the parameters in the temperature model are found using a nonlinear optimization that compares the integrated velocity anomalies in the tomographic slab region to integral of high velocities in a synthetic slab derived from a temperature model. The parameters for slab thickness and mantle potential temperature are not uniquely determined; therefore a fixed value for the mantle potential temperature based on laboratory values for the temperature of the spinel‐to‐perovskite transition at 660 km is used. Using 1180°C as the potential temperature, the theoretical temperature model gives an optimal slab thickness of 82 km for a region near 29°S in Tonga. The uncertainty in the thickness is dominated by the uncertainty in the mantle temperature and would be 8 km for an uncertainty of 100° in mantle temperature, but nonsystematic errors are less. In order to enhance the tomographic result the velocity model is biased towards the theoretical slab model. However, a posteriori changes made to the tomogram will most likely violate the fit to the delay time data. To prevent this, the difference between the tomogram and the predicted slab model is projected onto the null‐space of the inversion to remove components which do not satisfy the seismic data. Using only null‐space components to modify the minimum‐norm solution, an enhanced model is obtained which has been biased toward the theoretical solution but has the same data misfit as the minimum‐norm solution. The final image shows a very narrow and continuous 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.