Seismogram synthesis for piecewise heterogeneous media

We present a semi-analytical, semi-numerical method to simulate wave propagation in piecewise heterogeneous media that the Earth presents. Wave propagation in such media will highlight the reflections/transmissions at interfaces, while the volume heterogeneities in each geological formation generate scattered waves that are superimposed on the boundary waves to cause fluctuations in amplitude and phase. The numerical method is a straightforward extension to irregular multilayered media of the generalized Lipmann-Schwinger integral equation formulated in terms of volume scattering and boundary scattering. Compared to the finitedifference and finite-element methods for heterogeneous media, the boundary-volume integral equation technique enjoys a distinct characteristic of the explicit use of the boundary conditions of continuities for displacement and traction across subsurface interfaces, which provides sufficient accuracy for simulating the reflection/transmission across irregular interfaces. The resultant global coefficient matrix is sparse and narrow-banded. We discuss several aspects of seismic modeling implementation in order to make the calculations more efficient. The accuracy of the method is tested by comparing with the analytical solutions for a semicircular alluvial valley, which confirms that sampling at three elements per wavelength is sufficient to ensure the accuracy for general applications. To show the applicability of the method, we calculated synthetic seismograms that show significant impact of volume heterogeneities on seismic responses in a layered medium system.