During the past eight years, north-central Oklahoma has experienced a significant increase in seismicity. Although the disposal of large volumes of wastewater into the Arbuckle Group-basement system has been statistically correlated to this increased seismicity, our understanding of the actual mechanisms involved is somewhat superficial. To address this shortcoming, I served as the geophysicist in an integrated study to characterize and model the Arbuckle-basement system to increase our understanding of the subsurface dynamics during the wastewater-disposal process. I constructed a 3D geological model that integrates 3D seismic data, well logs, core measurements and injection data. Poststack-data conditioning and seismic attributes provided images of faults and the rugose top of the basement, while a modified-Hall analysis provided insights into the injection behavior of the wells. Using a Pareto-based history-matching technique, I calibrated the 3D models using injection rate and pressure data. The history-matching process showed the dominant parameters to be formation-water properties, permeability, porosity, and horizontal anisotropy of the Arbuckle Group. Based on the pressure buildup responses from the calibrated models, I identified sealing and conductive characteristics of the key faults. My analysis shows the average porosity and permeability of Arbuckle Group to be approximately 7% and 10 mD, respectively over the study area. The simulation models also showed pockets of non-uniform and large pressure buildups in these formations indicating that faults play an important role in fluid movement within the Arbuckle Group-basement system. To further improve our understanding of the basement in Oklahoma, its plumbing system and tectono-thermal history, I depth-migrate a 3D pre-stack seismic volume in north central Oklahoma where recent studies have highlighted the presence of basement igneous sills (BIS), expressed as intra-basement seismic reflectors (IBR), possibly associated with the Mid-Continent Rift. The depth-migrated data allows me to better delineate the geophysical characteristics of the BIS, and I integrate it with outcrop observations and well log data to constrain our geological interpretations. Further, I create geologically-realistic 2D seismic forward models of the sills to assess if their synthetic seismic attribute response can be utilized for improving current interpretation workflows for igneous intrusions in other regions. I find that (1) depth-migration of the seismic volume provides better imaging of the geometry of the BIS, (2) 2D forward models show that distinct geometries for fault-controlled basement sill steps can be distinguished in seismic reflection data and (3) salient geometric features of the BIS observed in outcrops are consistent to those in the depth-migrated seismic data. To better delineate such basement intrusions, I evaluate current limits and assumptions of seismic resolution. Beginning in 1973 with Widess’ analysis of reflector wedge models, the conventionally understood limit of vertical seismic resolution has been λ/4 for noise contaminated data. However, this model and resolution limits do not represent the full range of models that might be present in nature. In this dissertation, I examine three algorithms designed to increase the limit or at least quantify vertical seismic resolution: spectral balancing, bandwidth extension and the Hölder exponent. I find that spectral balancing provides a useful, but limited improvement of seismic resolution. I find that although bandwidth extension attempts to resolve beds below tuning frequencies by extending the magnitude spectrum, the corresponding phase spectrum interference patterns are not properly unraveled. Events that were previously resolved appear sharper, while those that were not are now corrupted. The goal of the Hölder exponent is to use the shape of the magnitude spectrum to characterize the underlying reflectivity as being blocky, spikey, or smooth. My work shows that the resolution of thin beds below tuning remains an important problem in the geophysics community that is often poorly understood and for which permanent solutions are still to be found.