Figure 12 indicates that the hydraulic head data fall into two groups: the Wolfcampian, Virgilian, and Missourian profiles form one group with higher head values and higher gradients, and the Mississippian and Cambrian-Ordovician-Silurian profiles form a second group with lower head values and lower gradients.
The cross-section cuts through, from top to bottom, the Cenozoic strata [Tertiary Laramide Basin Fill], the Mesozoic strata [Cretaceous Pierre and Niobrara Shales and Dakota Sandstone; Jurassic sediments], and the Paleozoic strata [Permian (Upper Permian, Lower Permian: Wolfcampian), Pennsylvanian (Virgilian, Missourian, Desmoinesian, Basal Pennsylvanian), Mississippian, Silurian, Ordovician, and Cambrian formations].
The data (Figure 12) show that these lowermost units must be considerably more permeable (shallow hydraulic gradient) than the Virgilian-Missourian and Wolfcampian units (steeper hydraulic gradient) and, based on the separation of the hydraulic head values, must be hydraulically isolated.
To replicate these transitions in the Virgilian-Missourian and Wolfcampian, low-permeability segments referred to as chokes are inserted in the model.
The broad horseshoe shape of the Dakota outcrop is difficult to model with a two-dimensional grid, and potentiometric maps indicate that the Dakota is not hydraulically connected to the Wolfcampian because of the presence of the low-permeability Upper Permian-Jurassic unit .
By altering the flux until the head gradient matched the data (Darcy's equation (2) shows that there is a direct relationship between flux and hydraulic gradient), it was found that 0.0003 [m.sup.3] [d.sup.-1] of water (109,500 [m.sup.3] per 1 m.y.) enters each of the Wolfcampian (cross-sectional area 15,239 [m.sup.2]) and Desmoinesian (cross-sectional area 18,287 [m.sup.2]) and 0.0007 [m.sup.3] [d.sup.-1] (255,500 [m.sup.3] per 1 m.y.) of water enters the Virgilian-Missourian (cross-sectional area 33,526 [m.sup.2]).
However, for the 3.5, 3, 2, and 0 Ma models, the eastern BC values were calculated by interpolation between the 4.5 Ma model hydraulic head values and present-day hydraulic head values obtained from potentiometric surface maps of the Wolfcampian and Mississippian (Figures 9 and 11; ); see [h.sub.E] = [h.sub.i] arrows in Figure 13.