RECEIVER FUNCTION INVERSION USING GENERALIZED PATTERN SEARCH TECHNIQUE

We present a global optimization problem of inverting receiver functions based on Hκ stacking to determine crustal parameters and associated weights using a generalized pattern search (GPS) technique. Previous studies have utilized different approaches for solving the Hκ stacking of receiver functions to determine crustal thickness (H) and Vp-to-Vs ratio (κ) parameters. The optimization in the current study takes into account the previous studies for the employment of the Hκ stacking algorithm and the weights corresponding to different phases.

The GPS technique is among the very few provably convergent and derivative-free methods applicable to linearly constrained optimization (minimization) problems. In order to apply GPS technique, first the maximization problem of Hκ stacking must be converted to a minimization problem. For such a minimization problem, GPS searches for the optimal solution by determining the point that provides the minimum objective function value among a sequence of points in a chosen matrix pattern. Almost, the outputs and results from GPS implementation can be repeated unlike other heuristic search approaches. Not only the outputs, but the number of iterations as well as the number of objective function evaluations remain the same as long as initial values, the lower and upper bounds, as well as the processing machine stay the same. It is also observed that optimal values will have almost identical values irrespective of the initial values, as long as the initial values are within a plausible range.

We tested the implementation of the GPS algorithm using seismic data from more than twenty five seismic stations within Ethiopia and surrounding the East Africa Rift System. The results include: crustal thicknesses ranging from about 25 to 35 km in the Main Ethiopian Rift (MER) and from about 35 to 45 km in the Western and Eastern Ethiopia Plateaus. Also, crustal Vp-to-Vs ratios range from about 1.77 to 2.00 for the MER and from about 1.65 to 1.84 for the Ethiopian Plateaus. These results are consistent with previously published works. The values of the weights for the phases in the receiver functions are also found to be consistent. However, the GPS technique has the advantage of almost exhaustively searching for all five parameters in the parameter search space, and also its results are highly repeatable.