We have measured the penetration resistance force of a plate moving vertically througha granular medium. We first examine an object approaching the solid bottom boundary of a granular sample (analogous to approaching a flat rock or the top of a treasure chest buried at a beach). We find that the proximity of a solid surface can decrease the penetration force and that the depth dependence of the force indicates the characteristic roughness of the surface. Surprisingly, near the bottom boundary we find that the penetration resistance has an exponential dependence on the distance from the bottom. This dependence demonstrates that, despite the long range nature of force propagation in granular media, there is an intrinsic length scale to jamming due to a locally applied stress. We have also performed the converse penetration measurement in which we measure the force needed for an object to penetrate upwards from the bottom of a granular bed.