We here propose a method for computing synthetic seismograms based on a direct integration in the ω-k domain for a buried explosive point source with receivers on the free surface. The medium is assumed to be transversely isotropic, vertically inhomogeneous and anelastic with any desired continuous or discontinuous velocity function. The eigenvalue problem studying the wave propagation in stratified anelastic media is formulated as a set of first order ordinary differential equations. The coefficient matrix of the systems thus formed depends on the elastic parameters of the media. Without recourse to the assumption that the coefficient matrix is constant, the displacement components on the free surface can be calculated by integrating directly the differential systems involved using a higher order Runge-Kutta method. In case that the medium is homogeneous, the propagator propagates the wavefields across the homogeneous zones in one step, bypassing the expensive Runge-Kutta integration scheme and reduces the computation time significantly.
The proposed method has the virtue of algorithmic simplicity. With minor modification, the solution for a a vertical point force acting on the free surface (Vibroseis) or a VSP configuration can be obtained.
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