Balancing Cross Sections by Computer
Balancing is an essential process in constructing cross sections through folded and faulted terranes. A balanced cross section is not necessarily correct, but an unbalanced one is wrong.
Cross-sectional area and bed length of each stratigraphic unit, as well as fault offsets, are adjusted in balancing, so that the deformed structure can be restored back to an assumed undisturbed condition without gain or loss of material (cross-sectional area). Offsets of boundaries across a given fault should be consistent in all units. Balancing does not mean that shortening must be the same at all levels or in all deformed stratigraphic units; indeed one of the conclusions of this paper is that equality and synchroneity of shortening are extremely unlikely.
Computer balancing of cross sections does nothing that cannot be done manually using pencil and paper. However, most hand-balanced cross sections are geometric transforms in which a deformed stage is balanced with respect to an originally undeformed stage. This can be done even though it may be geometrically impossible to reach the deformed state from the undeformed one along the fault paths specified. In contrast, forward modeling by computer simulates progressive movement along fault planes, so that each balanced cross section includes within it an infinite number of balanced cross sections of intermediate stages.
All balancing involves approximations. This follows from the fundamental geometric fact that it is not possible to transform a plane figure with a given area and perimeter into another figure with the same area and perimeter without passing through intermediate stages in which one or both parameters must change.
Figures & Tables
Quantitative Geometry of Thrust and Fold Belt Structures
Exploration for petroleum requires much data, and the principles with which to interpret them. Because well and seismic data are extremely expensive in fold and thrust belts, application of simply geometric principles can multiply the effectiveness of geological and geophysical interpretations. Geometry of layerd rocks, expressed by maps, cross sections, and seismic profiles, is the basis for interpreting the geological structure. This publication contains 7 chapters covering thrust faults, generation of folds, and thrust and fold time and sequence from the geometric perspective.