APPROXIMATION OF RUPTURE DIRECTIVITY IN REGIONAL PHASES USING UPGOINGAND DOWNGOING WAVE-FIELDS

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.