We use finite-difference modeling to illustrate direct-P and direct-SV radiation produced by land-based, vertical-displacement sources such as vertical vibrators and vertical impacts, sources that reflection seismologists have used for decades to image subsurface targets. We are particularly interested in understanding the nature of SV radiation that these sources create. Such insight will be important for those in the seismic interpretation community who are interested in S-wave reflection seismology. One distinction between our work and that of earlier investigators is that we go beyond traditional assumptions that a propagation medium has a flat surface and is isotropic and homogeneous throughout the model space. Instead, we use models composed of small finite-difference cells that allow earth anomalies with dimensions of only a few feet to be near a source station. These small irregularities are expressed as variations in propagation velocities in a small population of model cells, or as slight changes in surface elevation. These small, realistic, near-source irregularities cause robust direct-SV illumination to travel in near-vertical takeoff angles from a surface-based source station and to often travel in true-vertical takeoff angles. We also depart from the conventional practice of calculating direct-P and direct-SV radiation produced by only a single vertical vibrator. Instead, we model direct-P and direct-SV illumination produced by arrays of 2, 3, and 4 inline vertical vibrators. We find that vibrator arrays create SV-mode beam forming that causes a rich amount of direct-SV radiation to occur inside the critical takeoff-angle cone below a source station that extends from to from vertical. We consider our source-radiation models to be more realistic representations of conditions encountered in actual seismic field practice than previous models that use oversimplified earth conditions. Our purpose is to provide interpreters information that will let them decide if common, surface-based, land sources such as vertical vibrators can be used to illuminate geologic targets with direct-P and direct-SV illuminating wavefields rather than limiting the use of these sources to P-wave imaging only, as has been standard practice for several decades. Our results indicate that vertical vibrators and vertical impacts produce illuminating wavefields that are appropriate for imaging deep geologic targets. Our models apply to the total family of surface-based, vertical-displacement sources, which includes vertical vibrators and accelerated weight drops.