SUMMARY
Using a numerical integral method, we deduced a set of formulae for the co-seismic internal deformation in a spherically symmetric earth model, simultaneously taking self-gravitation, compressibility and realistically stratified structure of the Earth into account. Using these formulae, we can calculate the internal deformation at an arbitrary depth caused by an arbitrary seismic source. To demonstrate the correctness of our formulae, we compared our numerical solutions of radial functions with analytical solutions reported by Dong & Sun based on a homogeneous earth model; we found that two sets of results agree well with each other. Our co-seismic internal Green's functions in the near field agree well with the results calculated by the formulae of Okada, which also verifies our Green's functions. Finally, we calculated the Coulomb stress changes on the Japanese Islands and Northeast China induced by the Tohoku-Oki Mw 9.0 earthquake using the methods described above. We found that the effect of layered structure plays a leading role on the near field, while curvature occupies a dominant position on the deep region of the far field. Through a comparison of the Coulomb stress changes at a depth of 10 km on a layered earth model calculated by our method along with the corresponding results of Okada, we found that the discrepancy between them in near field was ∼31.5 per cent, and that of far field was >100 per cent of the signals.
Closed-Form Expressions of Multilayered Planar Green's Functions That Account for the Continuous Spectrum in the Far Field
