Research reported in this publication was supported by competitive research funding from King Abdullah University of Science and Technology (KAUST). For computer time, this research used the resources of the Supercomputing Laboratory at King Abdullah University of Science & Technology (KAUST) in Thuwal, Saudi Arabia. We would like to thank the reviewer D. Köhn and three anonymous reviewers as well as the editors J. Shragge and S. Operto for their fruitful and constructive comments to improve the paper. We also thank the members of Seismic Wave Analysis Group in KAUST for the helpful discussions. Particularly, we would like to thank N. Masmoudi in KAUST for fruitful comments about the deviation parameters and V. Kazei at KAUST for finding some mathematical errors.