Fast and accurate earthquake location within complex medium using a hybrid global-local inversion approach

A novel hybrid approach for earthquake location is proposed which uses a combined coarse global search and fine local inversion with a minimum search routine, plus an examination of the root mean squares （RMS） error distribution. The method exploits the advantages of network ray tracing and robust formulation of the Frrchet derivatives to simultaneously update all possible initial source parameters around most local minima （including the global minimum） in the solution space, and finally to determine the likely global solution. Several synthetic examples involving a 3-D complex velocity model and a challenging source-receiver layout are used to demonstrate the capability of the newly-developed method. This new global-local hybrid solution technique not only incorporates the significant benefits of our recently published hypocenter determination procedure for multiple earthquake parameters, but also offers the attractive features of global optimal searching in the RMS travel time error distribution. Unlike the traditional global search method, for example, the Monte Carlo approach, where millions of tests have to be done to fmd the final global solution, the new method only conducts a matrix inversion type local search but does it multiple times simultaneously throughout the model volume to seek a global solution. The search is aided by inspection of the RMS error distribution. Benchmark tests against two popular approaches, the direct grid search method and the oct-tree important sampling method, indicate that the hybrid global-local inversion yields comparable location accuracy and is not sensitive to modest level of noise data, but more importantly it offers two-order of magnitude speed-up in computational effort. Such an improvement, combined with high accuracy, make it a promising hypocenter determination scheme in earthquake early warning, tsunami early warning, rapid hazard assessment and emergency response after strong earthquake occurrence.

Complex eigenvalues and group velocities of normal modes in shallow water with a lossy bottom

For the stratified shallow water with a lossy bottom, the distribution and asymptotic behavior of mode eigenvalues in the complex plane are discussed on the basis of the Pekeris cut. The analysis shows that even in the shallow water with a low-speed lossy bottom there may be the proper modes which satisfy the radiation condition at infinite depth. It is also shown that when the ratio between the densities of the seawater and seabottom is close to one, there exist only a finite number of improper modes . An iterative method for evaluating the complex eigenvalues and group velocities of normal modes is presented and some numerical results are given.