Geomagnetically induced currents (GICs) are quasi-direct current (DC) electric currents that flow in technological conductors during geomagnetic storms. Extreme GICs are hazardous to man-made infrastructure. GICs enter and exit the technological systems, such as the electric power grid, at grounding points, and their magnitudes depend on the currents that flow underground. They are, therefore, a function of the Earth's electrical conductivity, represented at ground level as Earth impedances, as well as the resistance parameters of the power network. Traditional GIC estimation practices are based on Earth impedances obtained from laterally homogeneous or piecewise layered-Earth models. We refer to these methods, collectively, as the 1-D approximation. However, GIC hazard mitigation can be improved with more accurate GIC modeling that takes the spatially heterogeneous Earth's conductivity into account. Here, we propose a modified approximation for GIC estimation that is very similar to the 1-D approximation but is instead derived from empirical 3-D Earth impedances. Our formulation sets up the computation of static, frequency-dependent power line telluric response functions, which, once computed, may be considered part of the power grid system model. These response functions may then be used for historical scenario analysis of GIC hazards and for simplified real-time, albeit approximate, GIC estimation in a power grid. This modest modification to the simpler local field formulation approach avoids real-time integration of geoelectric fields along power lines while taking the realistic 3-D Earth into account in a rigorous manner. Once implemented, the method provides a power grid operator with the benefits of convenience and computational speed for a first look real-time operational GIC hazard assessment. We estimate that the proposed modified 3-D GIC modeling approach produces GIC values that are well within 50% of those obtained with the full-scale power line integration of spatially variable geoelectric fields, for storms comparable in scale to the 2003 Halloween storm, all geological structures, and power lines located in the contiguous United States and other low- to middle-latitude regions.