Geophysical characterization of the subsurface is an integral part of the industry's effort to decrease ambiguity during exploration, development, and production. Over several decades, advances in geophysical technology (e.g., 3D seismic, AVO, depth imaging, 4D seismic, wide/full azimuth acquisition, etc.) have allowed geophysicists to routinely produce more accurate “best technical case” images of the subsurface. Given the impressive nature of these advances, our nongeophysical colleagues might be tempted to think that geophysicists have eliminated uncertainty from our subsurface images. Nothing could be further from the truth. Most (if not all) of the time, geophysical characterization of the subsurface involves estimating solutions to ill-posed inverse problems. This ill-posedness stems from a variety of sources, including insufficient measurements and physical phenomena like seismic anisotropy.