This study was undertaken to complete the dislocation theory presented by Sun et al. for a spherical earth model with special treatment of coseismic deformations for a surface rupture. The previous theory is valid only for inner sources, but the coseismic deformations for a surface rupture source remain unsolved. Therefore, this study deals with the special case of coseismic deformations for a surface rupture dislocation. For this purpose, we ﬁrst derive the relation between the dislocation Love numbers and the conventional Love numbers, that is, the tidal, press, and shear Love numbers, based on the Okubo reciprocity theorem. Then we derive the corresponding Green’s functions for coseismic displacement, potential/geoid, gravity and strain changes using Okubo asymptotic solutions. Finally, we present numerical results of those Green’s functions for four independent seismic sources. Then we discuss the computation of coseismic deformations at the singular point—epicentre. As a case study, the computations of the coseismic deformations caused by the 2011 Tohoku-Oki earthquake (Mw 9.0) with considering the new Green’s functions as a constrain validates the theoretical model established in this study.
Citation: Wenke Sun and Jie Dong, Relation of dislocation Love numbers and conventional Love numbers and corresponding Green’s functions for a surface rupture in a spherical earth model , Geophysical Journal International, (2013) 193, 717–733