In the correct processing and interpretation of time sections gathered over complicated heterogeneous structures, acoustic assumptions no longer suffice and elastic effects need to be taken into consideration. This study presents numerical modeling results obtained with the Fourier method. Two classes of important geophysical problems were considered. The first class of problem was wave propagation in structures with both vertical and horizontal heterogeneities. Results of the calculations showed strong generation of converted phases and head waves. Generation of these phases is strongly dependent upon the velocity contrasts in the medium. The second class of problem was wave propagation in structures which contain both fluids and solids. The time sections recorded in the fluid regions again showed strong converted phases which could easily be misinterpreted as genuine acoustic reflections. The numerical results for the fluid-solid model proved to be in agreement with physical model results.The presence of many phases on the time sections and snapshots requires that the elastic modeling method give accurate amplitudes and distinguish between P-waves and S-waves since otherwise their interpretation can become prohibitively complicated. In this respect, the Fourier method appears suitable because of its high accuracy and its ability to distinguish between P- and S-waves through respectively applying the numerical divergence and curl.