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We study the influence of vertical fault block motion on the hydrodynamics of continental rift systems in this paper using finite element analysis. Numerical solutions to governing groundwater flow and heat transport equations within independently moving fault blocks are obtained using triangular elements. Hybrid, four-node “slip elements” developed for this study are employed along fault surfaces; standard three-node elements are used everywhere else. The model is used in a sensitivity study to assess the effects of permeability variations, subsidence/erosion rates, and water table configuration on basin hydrodynamics. Idealized simulations of rifting over a 1.5 m.y. period were constructed using two (horst and graben) fault blocks that are vertically offset by 4.5 km during the simulation period. Numerical results indicate that significant interaction between different fluid flow–impelling mechanisms (compaction-, topography-, and density-driven flow) occurs over a permeability range of 10−16.5 to 10−14.5 m2. Many of the flow fields, especially those in high-permeability (10−14.5 m2) horst and graben blocks, produce areas of high and low heat flow relative to conductive conditions. Models which incorporate alternating layers of permeable and less permeable layers indicate that the truncation/reconnection of aquifers can induce transient thermal and hydrologie behavior. The sensitivity results suggest a plausible mechanism for transient fluid flow on geologic timescales (105 to 107 years) within faulted basins and may help to explain the occurrence of some banded ore deposits or multiple episodes of sediment diagenesis preserved within the sedimentary rock record.