Acknowledgments

We would like to thank Shan Qu, Jiang Yuan, Mauricio Sacchi, Jean Virieux and Aaron Stanton for constructive suggestions that improved the manuscript greatly. We are grateful to developers of the Madagascar software package for providing corresponding codes for testing the algorithms and preparing the figures. This work is partially supported by National Basic Research Program of China (Grant NO: 2013 CB228602), National Natural Science Foundation of China (Grant No.41274137), National Science and Technology of Major Projects of China (Grant No. 2011ZX05019-006), National Engineering Laboratory of Offshore Oil Exploration, and the Texas Consortium for Computational Seismology (TCCS).