Mechanical modelling in structural geology and tectonics - past, present and future

In structural geology and tectonics, most fundamental advances have come through observation. However, mechanical and kinematical modelling has provided an understanding of physical processes, as well as ideas for further investigation. As in other sciences, the main techniques in tectonics have been three: analytical, physical and numerical. For past and present times, I will compare and contrast these techniques, concentrating on their advantages, disadvantages, and dangers. For the future, I will attempt to predict their development, even though this exercise may be subjective and risky. Analytical modelling has had a long but erratic history, punctuated by occasional breakthroughs. Outstanding examples have been the theories of folding and flexure. The main advantages of the method are mathematical precision and elegance. The main disadvantages are (1) high requirements of mathematical ability, and (2) difficulties in incorporating nonlinear behaviour or complex boundary conditions. Physical modelling had a long history, but a slow start, until Hubbert (1937) formulated the rules for proper scaling. The method has developed very rapidly in the last few decades. Of great importance have been technical breakthroughs, especially (1) the use of weak materials, for which a centrifuge is not necessary, (2) the addition of surface processes, and (3) the development of visualization in 2D and 3D. The main advantages of the method are that (1) the results are real, visual, and instructive, (2) the models have good resolution, (3) sedimentation and erosion are simple to apply, (4) the experimenter has little need of experience in mathematics. The main disadvantages are that (1) the results are not easily reproducible, (2) the work may be time-consuming, even physically demanding, (3) boundary conditions may be difficult to control, (4) the range of suitable model materials is small, and (5) the exercise may appear childish to newcomers. Numerical modelling has the shortest history, but its development has been almost exponential in the last few decades, in pace with computers. The main advantages of the method are (1) reproducibility, (2) speed, (3) ability to incorporate non-linear behaviour, (4) ease of investigation of different parameters, (4) ease of presentation of results, (5) an appearance of sophistication. The main disadvantages are (1) high cost or unavailability of some software, (2) possible programming mistakes, (3) possible numerical errors. Ironically perhaps, the main danger of the method may be its ease of application. There is a current tendency for numerical modelling to substitute for good observations. Although physical modelling may remain useful for testing new ideas, the future probably lies in numerical modelling. I foresee many new developments in the numerical modelling of nonlinear processes, especially those involving feedback between mechanical, thermal and chemical aspects, as well as fluid flow, in two or three dimensions, and on all scales up to that of planet Earth. On the other hand, I would urge prudence in accepting some of the result