Ck. Saikia et Dv. Helmberger, APPROXIMATION OF RUPTURE DIRECTIVITY IN REGIONAL PHASES USING UPGOINGAND DOWNGOING WAVE-FIELDS, Bulletin of the Seismological Society of America, 87(4), 1997, pp. 987-998
Recent broadband modeling of regional events suggests that vertical di
rectivity is particularly important at high frequency. Conventionally,
such directivity is obtained by summing a grid of point sources, This
relatively time-consuming procedure can be greatly reduced by introdu
cing directivity time histories appropriate for the various crustal ph
ases in terms of upgoing and downgoing paths that are calculated at on
ly one depth. To achieve this, we formulated frequency-wavenumber solu
tions for a simultaneous computation of surface displacement for three
wave fields, upgoing, downgoing, and the total from a seismic source
buried in a layered medium (Appendix A). The concept of upgoing and do
wngoing wave field is Introduced in the source layer matrix explicitly
before allowing the source coefficients to interact with the propagat
ion of the stress-displacement vector. Using this new algorithm, we ge
nerated a set of upgoing and downgoing wave fields at a fixed depth fo
r different crustal models. We also simulated the effects of rupture p
ropagation using distributed point-source summations and predicted the
same effect by summing the upgoing and downgoing wave fields calculat
ed at a single depth, each convolved with a separate analytical boxcar
function representing the far-field rupture. A library of these new G
reen's functions should prove much. more effective in modeling recorde
d motions than using point-source Green's functions alone.