# Tectonic modeling

Series Exploring for Oil and Gas Traps Treatise in Petroleum Geology Predicting the occurrence of oil and gas traps Exploring for structural traps R.A. Nelson, T.L. Patton, S. Serra Web page AAPG Store

## Information provided

Models are representations of natural structures. They are used when direct analysis of various aspects of natural structures is either difficult or impossible.

There are two types of models:

• Physical (including rock mechanics models, photoelastic models, and geometry models)
• Mathematical (including mechanics models and geometry models)

## Physical models

Physical models are constructed from rocks or a variety of materials including clay, sand, and putty.

• Rock mechanics models are designed and run to gain information on the strength and deformation mechanisms of rocks when subjected to various loads and displacements under controlled conditions of pressure, temperature, strain rate, and pore fluid pressure and chemistry. The starting configuration of these models is usually a right circular cylinder composed of the rock(s) being studied.
• Photoelastic models provide information on stress magnitude and orientation. They are made of transparent materials such as clear plastics or gelatins. When deformed and examined in polarized light, these materials exhibit color fringes and alternating light and dark bands. From these, we can determine the stress intensity and the orientation of the principal stresses at any point in the model.
• Geometric models reproduce the shape of naturally occurring structures. The starting configuration is usually a layered rectangular block or some variation thereof. Displacements are imposed at the boundaries of the block to create the desired deformation. The hope is that if we can create a good geometric analog of a natural structure under conditions we specify and control, then we will gain a better understanding of the conditions that influence the development of the natural structure. This highlights an important role of these models: they generate hypotheses or ideas regarding the development and final shape of natural structures—ideas that may not occur to us even after careful study of structures in the field.

## Mathematical models

Mathematical models consist of equations that describe the interrelationship of parameters thought to be important in the development of natural structures.

• Mechanics models use various analytic and numerical techniques (finite element, distinct element, finite difference) to simulate deformation. Input parameters are undeformed shape, mechanical properties of the model materials, displacements, and displacement rate. The models yield information on deformed shape, displacement trajectories, and the orientation and magnitude of stress and strain in the model at various stages of displacement.
• Geometry models examine the development of structures, mainly in 2-D, by applying various simplified kinematic or displacement rules. These models do not provide direct information on the structural effects of environmental parameters during deformation (e.g., rock strength, overburden pressure, temperature, strain rate).

## How to use it

Models offer insight into how natural structures may have developed. For structures where geometry is poorly constrained by outcrop, seismic, or well data, models may suggest reasonable options for completing the structural interpretation.

Quantitative data derived from a model can be confidently applied to natural structures only if the model has been accurately and completely scaled with respect to the natural counterpart. In practice, this degree of scaling may be achieved in numerical models and mechanical physical models. It is often difficult to achieve in geometrical physical models. Nevertheless, partially scaled and even nonscaled models can still help generate ideas on structure development.

“No absolute or final decision can be made about the admissibility of a given modeling technique; the decision must always depend on the interest of the experimenter, the accuracy and urgency of the required prediction, and the availability of other techniques. Often the modeling technique which most flagrantly flouts the similarity [scaling] rules is the most useful one in practice”.[1]

## Modeling concepts

• Paterson, M. S., 1987, Problems in the extrapolation of laboratory rheological data: Tectonophysics, v. 133, p. 33–43, DOI: 10.1016/0040-1951(87)90278-2.
• Patton, T. L., Serra, S., Humphreys, R. J., Nelson, R. A., 1995, Building conceptual structural models from multiple modeling sources: an example from thrust-ramp studies: Petroleum Geoscience, v. 1, p. 153–162, DOI: 10.1144/petgeo.1.2.153.
• Gretener, P. E., 1981, Reflections on the value of laboratory tests on rocks, in Carter, N. L., Friedman, M., Logan, J. M., Stearns, D. W., eds., Mechanical Behavior of Crustal Rocks: American Geophysical Union Monograph 24, p. 323–326.
• Hubbert, M. K., 1937, Theory of scale models as applied to the study of geologic structures: Geological Society of America Bulletin, vol. 48, p. 1459–1520.
• Spalding, D., B., 1962, The art of partial modeling: 9th Symposium on Combustion, p. 833–843.
• Stearns, D. W., Couples, G. D., Jamison, W. R., Morse, J. D., 1981, Understanding faulting in the shallow crust: contributions of selected experimental and theoretical studies, in Carter, N. L., Friedman, M., Logan, J. M., Stearns, D. W., eds., Mechanical Behavior of Crustal Rocks: American Geophysical Union Monograph 24, p. 215–229.

## Physical models

### Rock mechanics models

• Scott, T., E., Nielsen, K., C., 1991, The effects of porosity on the brittle-ductile transition in sandstones: Journal of Geophysical Research, v. 96, p. 405–414, DOI: 10.1029/90JB02069.
• Dunn, D., E., LaFountain, L., J., Jackson, R., E., 1973, Porosity dependence and mechanism of brittle fracture in sandstones: Journal of Geophysical Research, vol. 78, p. 2403–2417, DOI: 10.1029/JB078i014p02403.
• Handin, J., Hager, R., V., Jr., Friedman, M., Feather, J., N., 1963, Experimental deformation of sedimentary rocks under confining pressure: pore pressure tests: AAPG Bulletin, vol. 47, p. 717–755.
• Logan, J., M., Lin, P., 1991, The interaction of two closely spaced cracks: a rock model study: Journal of Geophysical Research, vol. 96, p. 21667–21675, DOI: 10.1029/91JB02273.
• Donath, F., A., 1970, Some information squeezed out of rock: American Scientist: vol. 58, p. 53–72.
• Renner, J., Rummel, F., 1996, The effect of experimental and microstructural parameters on the transition from brittle failure to cataclastic flow of carbonate: Tectonophysics, vol. 258, p. 151–169, DOI: 10.1016/0040-1951(95)00192-1.

### Photoelastic models

• Gallagher, J., J., Friedman, M., Handin, J., Sowers, G., M., 1974, Experimental studies relating to microfractures in sandstone: Tectonophysics, vol. 21, p. 203–247, DOI: 10.1016/0040-1951(74)90053-5.
• Bombolakis, E., G., 1968, Photoelestic study of initial stages of brittle fracture in compression: Tectonophysics, v. 6, p. 461–473, DOI: 10.1016/0040-1951(68)90072-3.
• Bell, R., T., Currie, J., B., 1964, Photoelastic experiments related to structural geology: Proceedings of the Geological Association of Canada, vol. 15, p. 33–51.

### Geometry models

• Dixon, J., M., Liu, S., 1992, Centrifuge modeling of the propagation of thrust faults, in McClay, K., R., ed., Thrust Tectonics: London, Chapman and Hall, p. 53–69.
• Ge, H., Jackson, M., P., A., Vendeville, B., C., 1997, Kinematics and dynamics of salt tectonics driven by progradation: AAPG Bulletin, v. 81, p. 398–423.
• Dooley, T., McClay, K., 1997, Analog modeling of pull-apart basins: AAPG Bulletin, v. 81, p. 1804–1826.
• Vendeville, B., C., Jackson, M., P., A., 1992, The rise of diapirs during thin-skinned extension: Marine and Petroleum Geology, v. 9, p. 331–353, DOI: 10.1016/0264-8172(92)90047-I.
• Letouzey, J., Colletta, B., Vially, R., Chermette, J., C., 1995, Evolution of salt-related structures in compressional settings, in Jackson, M., P., A., Roberts, D., G., Snelson, S., eds., Salt tectonics: a global perspective: AAPG Memoir 65, p. 41–60.
• Weinberg, D., M., 1979, Experimental folding of rocks under confining pressure, part VII: partially scaled models of drape folds: Tectonophysics, vol. 54, p. 1–24, DOI: 10.1016/0040-1951(79)90109-4.
• Withjack, M., O., Islam, Q., T., LaPointe, P., R., 1995, Normal faults and their hangingwall deformation: an experimental study: AAPG Bulletin, v. 79, p. 1–18.
• McClay, K., 1996, Recent advances in analogue modelling: uses in section interpretation and validation, in Buchanan, P., G., Nieuwland, D., A., eds., Modern Developments in Structural interpretation, Validation and Modelling: Geological Society of London Special Publication no. 99, p. 201–255.
• Guglielmo, G. Jr., Jackson, M., P., A., Vendeville, B., C., 1997, Three-dimensional visualization of salt walls and associated fault systems: AAPG Bulletin, v. 81, p. 46–61.
• Naylor, M., A., Laroque, J., M., Gauthier, B., D., M., 1996, Understanding extensional tectonics: insights from sandbox models, in Roure, F., Ellouz, N., Shein, V., S., Skvortsov, I., eds., Geodynamic Evolution of Sedimentary Basins: Editions Technip, p. 69–83.
• Morse, J., 1977, Deformation in ramp regions of overthrust faults: experiments with small-scale rock models: Wyoming Geological Association 29th Annual Field Conference Guidebook, p. 457–470.
• Storti, F., Salvini, F., McClay, K., 1997, Fault-related folding in sandbox analogue models of thrust wedges: Journal of Structural Geology, v. 19, p. 583–602, DOI: 10.1016/S0191-8141(97)83029-5.

## Mathematical models

### Mechanics models

• Couples, G., D., Stearns, D., W., 1978, Analytical solutions applied to structures of the Rocky Mountain foreland on local and regional scales, in Matthews, V., III, ed., Laramide Folding Associated with Basement Block Faulting in the Western United States: Geological Society of America Memoir 151, p. 313–335.
• Crans, W., Mandl, G., 1980, On the theory of growth faulting; part II (a): genesis of the “unit”: Journal of Petroleum Geology, vol. 3, p. 209–236, DOI: 10.1111/jpg.1980.3.issue-2.
• Strayer, L., M., Hudleston, P., J., 1997, Numerical modeling of fold initiation at thrust ramps: Journal of Structural Geology, vol. 19, p. 551–566, DOI: 10.1016/S0191-8141(96)00109-5.
• Shimamoto, T., Hara, I., 1976, Geometry and strain distribution of single-layer folds: Tectonophysics, vol. 30, p. 1–34, DOI: 10.1016/0040-1951(76)90135-9.
• Patton, T., L., Fletcher, R., C., 1995, Mathematical block-motion model for deformation of a layer above a buried fault of arbitrary dip and sense of slip: Journal of Structural Geology, vol. 17, p. 1455–1472, DOI: 10.1016/0191-8141(95)00034-B.
• Johnson, A., 1977, Styles of Folding: Amsterdam, Elsevier, 406 p.
• Jamison, W., R., 1996, Mechanical models of triangle zone evolution: Bulletin of Canadian Petroleum Geology, vol. 44, p. 180–194.
• Gangi, A., F., Min, K., D., Logan, J., M., 1977, Experimental folding of rocks under confining pressure; part IV: theoretical analysis of faulted drape folds: Tectonophysics, vol. 42, p. 227–260, DOI: 10.1016/0040-1951(77)90169-X.