Recursive travel-time inversion: A tool for real-time seismic tomography

A new recursive inverse scheme is applied to a currently popular problem named seismic travel-time tomography, in order to enhance the efficiency and reliability in obtaining a new velocity model if a small number of new data are added to a large data set in the past. In comparison with conventional inverse schemes in seismic tomography, either least-squares or iterative types, this scheme does not require large amounts of matrix-type computations but utilizes the amount of modification in model parameters responsible for each new data set. We also introduce the computation of a collocation travel time (i.e., from a given station to every grid point) for the reference velocity model inverted by the data for all the past events, using a ray tracing scheme called the Huygens' method (Saito, 2001), suitable to computations prior to a new event. Combining the above information already stored with the recursive inverse scheme, we can obtain a new or updated velocity model immediately after a new event takes place, because a temporal interval between two events is usually very long in a given local area. Since the model is revised at each recursive step, we perform ray tracings with the updated reference model to get more accurate ray paths and travel times than the conventional inversion schemes that use all the ray tracings for the same reference model. We first showed the validity and stability of the proposed method with synthetic data. We then applied the new approach to the P-wave travel-time data recorded in the Hidaka, south-central Hokkaido, Japan, region, and compared our result with other previous results. Our result shares the overall feature with the previous ones. In addition, a new low-velocity zone is detected in the east of the Hidaka mountains at the depth of 10 km, corresponding to the collision zone of two arcs, due to the use of the updated reference velocity model at each recursive step. We also confirmed that the order of data does not affect the final result, so that the present approach is shown as an appropriate tool for so-called real-time seismic tomography: a updated velocity model is immediately obtained at each time that a new event takes place, in order to monitor temporal variations of model parameters such as velocity structure on the real-time basis.