Numerical modeling of elastic waves propagation in isotropic vertically inhomogeneous media

Sitamai W. Ajiduah, Gary F. Margrave and P. F. Daley

ABSTRACT

A method for calculation of complete theoretical seismograms for coupled P-Sv wave propagation in a vertically inhomogeneous media has been studied. Called the AMM method (for Alekseev-Mikhailenko), it is based on a combination of partial separation of variables via a finite Hankel transform over lateral coordinates and finite-differencing in time and depth. Results of theoretical seismograms for an isotropic vertically inhomogeneous model are presented in this paper and the effects of incidence angle and free-surface on component amplitudes are also investigated. Amplitudes from the AMM computations are compared with computations from the exact Zoeppritz equations for angles up to 60 degrees. All the computed amplitudes from AMM methods matched Zoeppritz amplitude at near vertical incidence up to 10 degrees (0.5km source-receiver offset). The P-P AMM and the P-P Zoeppritz amplitudes have the same trend for all pre-critical and post-critical angles; at the critical angle, Zoeppritz predicts an abrupt rise in amplitude while the AMM amplitudes show a gradual rise with a maximum beyond critical angle. The P-S amplitudes predicted from Zoeppritz matched with P-S AMM amplitudes only at near offset.

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