cross-sections

cross-sections Maps and cross-sections are a most fundamental source of geological data, and a large part of an Earth scientist's training entails their preparation and interpretation. Maps and cross-sections are both two-dimensional representations of the spatial distribution of one, or a combination of several, particular data sets, such as rock type and structure. Maps are drawn parallel to the Earth's surface (more properly that of the geoid), whereas cross-sections are generally normal to the surface.

Largely because of the emphasis that oil and gas exploration places on understanding subsurface geological structure, most recent work on cross-sections has concentrated on improving structural cross-sections. They display geological structure within a frame whose horizontal and vertical scales measure distance. Many structural cross-sections, especially those showing the deep structure of a region, will not have equal horizontal and vertical scales. For example, equal vertical and horizontal scales on a 1:100 000 scale cross-section through the crustal thickness of Western Europe, from northern Norway to southern Italy, would make the section 380cm long, but only 35 mm deep. Consequently, vertical exaggeration is often employed to make a cross-section understandable. Remember, however, that vertical exaggeration will artificially increase the inclination of surfaces in the cross-section compared with how they would appear on a true-scale cross-section.

A second type of cross-section in widespread use is the chronostratigraphic cross-section, or Wheeler diagram, which plots distance horizontally against geological time vertically. Thus, instead of showing the geological structure along the chosen line of section, chronostratigraphic sections simply display the presence or absence of stratigraphic units. They are particularly effective where extensive, but subtle, unconformities cause widespread hiatuses, or breaks in the rock record. In the central North Sea, the economic viability of fairly small oilfields depends on chiefly on the geologists' ability to determine accurately from sections the potential volume of the porous reservoir units. Chronostratigraphic sections have been used to correlate palaeontologically dated sandstones, on occasion demonstrating that sandstones thought previously to be isolated are in fact connected together.

Where possible, the line of a structural cross-section should be chosen so that it is roughly at right-angles to the strike of geological structures, such as folds and faults. This has several advantages. It will mean that the cross-section depicts the real, rather than the apparent, inclination of non-horizontal surfaces; it will also mean that plane strain can be assumed. Plane strain expresses the idea that there has been no movement of rock into, or out of, the plane of the cross-section during deformation, and hence, that volume has been preserved.

Drawing a cross-section always entails a certain amount of geological interpretation. The credibility of this interpretation will depend on the degree to which it is independently constrained by additional geological criteria. The cross-section should be based on a high-quality map of the surface geology, preferably supplemented by a series of maps produced at different levels within the sub-surface. Ideally, boreholes drilled along the line of cross-section provide essential information on the depth of key marker horizons whose structure the cross-section depicts.

In the late 1960s, Canadian geologists exploring for oil and gas in the foothills of the Rocky Mountains began testing the geological credibility of their structurally complex cross-sections by unravelling them, or restoring them. They developed the notion of the balanced cross-section in which the credibility of a structural interpretation is improved significantly if the section can be sequentially restored to its undeformed state (Fig. 1). Balanced cross-sections work best in thrust belts of mountain ranges, where the rocks are commonly well exposed, and therefore accessible for detailed field mapping. Further, the layer-cake stratigraphy that characterizes sedimentary successions in many thrust belts, in which beds exhibit consistent thicknesses over large areas, means that the geometry of the units that make up the undeformed template is considerably simpler to deform and restore.

At its simplest, restoration requires only that the beds being restored can be traced to one end of the cross-section, the pin line, where they lie in their original vertical and horizontal position relative to one another. Subsequently, the deformed cross-section is unravelled in the reverse order to that in which the structures formed, starting at the pin line. A restorable, or balanced, cross-section is one in which restoration can be accomplished without needing to introduce, or explain away, deficit and excess areas. In theory, comparison of the length of the restored and deformed cross-sections through a thrust belt enables a direct assessment of the amount of shortening, expressed either as a percentage of the length of the initial restored section, or as the difference in kilometres between the length of the restored and deformed sections. Typical shortening values are 150 km in the Pyrenees, 400 km in the European Alps, and more than 500 km in the Himalayas.

Work in the Appalachians has demonstrated the degree to which the implicit assumption, that shortening is accomplished by displacement on mappable fault planes, can lead to severe underestimates of the amount of shortening. This work records small-scale structures such as cleavage and stylolites, accommodating as much as 25 per cent of the total shortening along a line of cross-section. On the tens to hundreds of kilometres scale of many conventional balanced cross-sections, such structures are usually more or less completely neglected.

The increasing use of computers and digital data storage throughout the geosciences has speeded up the process of producing maps and cross-sections, and has improved considerably the choice of presentation formats. Most exciting, however, is the way in which computers are being used to build three-dimensionally balanced cross-sections, thus obviating the requirement of conventional cross-section construction to demonstrate plane strain. Using algorithms borrowed from fluid dynamics, the latest restoration pro-cedures literally ‘flow’ detached cover successions over three-dimensional, ramp-flat fault systems. These produce balanced cross-sections comprising ramp anticlines and rollover anticlines whose geometry is determined by the curvature of the ramp, the depth to the décollement, and the deformational characteristics of the hanging wall succession undergoing deformation. Isostatic balancing of cross-sections is a fur-ther development that has proved particularly effective in producing reliably constrained cross-sections across extensional basins, such as the North Sea. Here, the deformed section is not only in geometrical equilibrium with its restored equivalent, but the restoration procedure also maintains isostatic equilibrium by taking into account the isostatic consequences of thickening or thinning the lithosphere during deformation.

Jonathan P. Turner