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Data Analysis in Thermomechanical Analogue Modelling


The outcome of the experiments lead to various implications. Even the first experiments using colophony demonstrated the ability of the apparatus to maintain a temperature gradient and to deform a layer of rheologically layered material. The reverse thrust scenario being compressed with a strain rate of 10-14s-1
(scaled to nature) showed isotherms being advected by the moving material. In this case, the conductive thermal equilibration is slower than the advection. The deformation of isotherms has been performed and documented, and also in slower experiments it could be shown that the thermal equilibration did not keep up with the ongoing deformation.

The experiment using sand as brittle upper crust implies the necessity for correct scaling of density. A heavy orogen building up causes an instability, sinking down to the model base. In a natural scenario, the density inversion would lead to subsidence of the dense material, down into the mantle. However, such a scenario is extremely unrealistic. Nevertheless, the rise of diapirs could be modelled using this combination of materials.

During the relaxation phase of the experiments, the stresses in the upper mantle changed from a horizontally compressive to an extensional regime. This is in accordance with the predictions by Dewey (1988) or England & Thompson (1984), who, however, suggested time scales of up to 120Ma for the extension and erosion of the orogenes. The relaxation phase also suggests that the paraffin waxes used as analogue materials do not show completely Newtonian behaviour. This is in accordance with measurements
of Mancktelow (1988).

Although the analogue experiments presented were done primarily to demonstrate the possibility of scaled thermomechanical modelling, they still can be compared to real geological scenarios. The models shown scale to around 150km in length and incorporate the crust and the lithospheric mantle (50km thickness). The pre-defined weak zones affect the lower crust, but quickly penetrate the upper crust. The mantle showed ductile deformation only. The shear zone of the lower crust did deform the Moho, but the mantle did not develop shear zones.

A scenario containing a large thrust can be found in the urals, at the boundary between Europe and Asia. The collision of the Eastern European and the Kazachian plate started around 310Ma ago in the Middle Carboniferous (Zonenshain et al., 1994). During the collision, the shortening along the Main Uralian Front (MUF) was between 12.5km and 16.7km (Perez-Estaun et al., 1997), and convergence rates between 1 cm/a and 3 cm/a can be assumed (Zonenshain et al., 1994). The interpretation of the "Urals Seismic Experiment and Integrated Studies" (URSEIS) profile given by Steer et al. (1998) shows various structures, the MUF and the Moho being the most prominent ones (Figure 11). According to Steer et al. (1998), the Moho is a structural detachment, as is the case in the analogue experiments. The dip of the MUF corresponds well to the dip of the thrust in the analogue experiments presented, the scaling of length being correct within 30%. Since the Uralian Orogenesis ended about 210Ma ago (Echtler & Hetzel, 1997) and shows no significant remobilisation (Seward et al., 1997), the Urals had more time to equilibrate than the corresponding relaxation time of the models. Therefore, the topography of the Uralian Moho is less intensive than in the analogue model adjacent to the MUF.

Figure 11. URSEIS Interpretation and correlation with analogue models. (a) Interpretation of "Urals Seismic Experiment and Integrated Studies", reproduced after Steer et al. (1998): The Main Uralian Fault (MUF) is the dominant feature, besides the Moho. Interpretation of the Alexandrovka Reflection Sequence (ARS) is still unclear. (b) Enlargement of inset in (a), according to the scaling of the experiments presented. East and West are reversed for coincidence with the analogue experiments. (c) Enlargement of the dashed inset in (a), corresponding to a length scaling about 30% smaller than in the experiments. (d) - (f) sketches of the experiments T1 - T3. The angle of the thrust corresponds well to the angle of the MUF. The thickness of the crust appears to be scaled correctly within 30 %. Topography of the real Moho is less than in the experiments, probably due to the longer equilibration. (Click for enlargement)

The Alexandrovka Reflection Sequence (ARS) in the URSEIS profile at a depth of 80-100 km coincides with the base of the experiments. It can be interpreted as a continuation of the MUF, as a rheological boundary due to material or phase changes, or as a local fault zone within the mantle (Steer et al., 1998). The analogue experiments presented do not show evidence for penetration of the thrust zone into the mantle. If the ARS is a continuation of the MUF, it has not been formed synorogenically. Either the Alexandrovka Reflection Sequence is an older structure just as the MUF, or one of the alternative interpretations has to be used.

Sediments being subducted between colliding continents are probably softer than the continental plates (England & Holland, 1979). Due to buoyant forces, these sediments can be assumed to be extruded upwards during the collision (Mancktelow, 1995). This concept has been applied to the Higher Himalayan Crystalline (HHC) between the Main Central Thrust (MCT) and the Southern Tibetan Detachment (STD) (Grujic et al., 1996). The Himalayas are a comparatively young orogen: the MCT was active until 6-2 Ma ago (McDougall et al., 1993; Metcalfe, 1993). Therefore, the time scales for the collapse have not passed yet.

Figure 12. INDEPTH Interpretation and correlation with analogue models. (a) Interpretation of the "International Deep Profiling of Tibet and the Himalaya" seismic profile, reproduced after Nelson et al. (1996): The Main Frontal Thrust (MFT) and the Main Central Thrust (MCT) are reverse faults, the Southern Tibet Detachment (STD) is a normal thrust. In between MCT and STD, a wedge of material is thought to be extruded (Grujic et al., 1996). (b) Enlargement of the left part of (a), scaled to fit the analogue experiments presented. North and South are reversed for coincidence with the analogue experiments. (c) - (e) sketches of the experiments W1 - W3. The geometry of the wedge as well as the topography of the Moho (lower boundary of the mafic lower crust) coincide well. Nevertheless, the model represents a scenario 2.7 times smaller than the features of the Tibetan Himalayas. (Click for enlargement)

Although the length scales of the Higher Himalaya are larger than the lengths modelled by the analogue experiments presented, the geometry of the models is similar to that of the Himalayas according to the interpretation of the "International Deep Profiling of Tibet and the Himalaya" (INDEPTH) seismic profile (Figure 12). The convergence rate between the Indian and the Asian plates has been estimated by Henry et al. (1997) from various sources to be in the range 1.5-2.0 cm/a, which is in the range modelled by the analogue models presented. Since in the wedge experiments the deformation data obtained from the photos did not represent the deformation in the whole model, the data should be interpreted with care. Nevertheless, the wedge of weak material has been extruded between the two colliding blocks (Figure 13).

Figure 13. Photos of extruded wedges. The photos show details of the experiments containing a weak wedge. All experiments show extrusion of the wedge visible after removal of the Jet-Plast. For the wedge, the deformation seen at the model side is not representative for the whole experiment. (Click for enlargement)

Newer numerical models of Beaumont et al. (2001) and analysis of topographical data by Clark & Royden (2000) show evidence for a channel of weak material instead of a wedge. To verify this concept by using analogue models, a way has to be found to model larger lengths either by choosing different materials, or by modifying the parameters of the apparatus.

The main points from the data analysis presented in the previous chapter apply to both types of orogenes. The steepness of the natural roots suggests convergence rates rather on the higher side of the ranges quoted above: 3 cm/a for the Urals, 2 cm/a for the Himalayas.

Dextral shear has been observed in the experiments at both ends of the thrust or the weak zone. The tip of the footwall block is not accessible in nature, but in the area of the upper crust where the thrust cuts the surface indicators for dextral simple shear should occur.

The analysis of the bulk stress data as well as the distribution of differential stresses predict remanent stresses in the orogenes, at least for some Ma after the deformation. In the Urals, these remanent stresses might have decayed by now, but in the Himalayas,
remanent stresses are suggested by the analogue models.

The method of thermomechanical analogue modelling has proven the ability to produce, analyse and present data for continental collision on lithospheric scales. It has been shown that the set-up used is able to reproduce and visualize the deformation of isotherms. The machine is ready to use and the experimental techniques as well as the procedures for data analysis were tested and proved to give reproducable results.


From the work with the apparatus for thermomechanical analogue modelling and from the first experiments, several suggestions arise for future machines and applications.

One important point is to learn more about the materials involved. For the analogue materials, measurement of the stress exponent n is necessary, as well more accurate estimates of the other flow properties. On the other hand, the data for natural rocks also lacks certain points. The data quoted in the literature is gained mostly from samples of some cubic centimetres, while it is applied to layers some ten kilometres thick and at strain rates some orders of magnitude less than those used to obtain the data.

Maybe in future experiments it might also be possible to introduce the important surface process erosion and sedimentation, without disturbance of the thermal equilibrium. The use of microwaves could be a way to include local heat production into the model.

Presently (December 2001), the apparatus is used for a Masters Thesis (Diplomarbeit of Philip Schiwek) to examine the onset of subduction at the (still) passive continental margin of Galicia. For these experiments, the scaling of density is extremely important, and the use of thin layers of lead powder embedded into the wax layers seems to be promising.

The machine presented is able to produce extensional regimes as well as compressive scenarios. The rise of diapirs or rifting processes can be modelled, maybe using sand as a brittle overburden. Additionally, the collisional experiments could be continued, examining the extensional phase of the collapse

In future thermomechanical experiments, the bottom temperature sensor should be fixed to the model base directly. All obstacles in the experimental domain must be avoided. The small floating PT100 temperature probes are permissible. Other sensors could be inserted into the models, such as piezoelectric stress sensors. Thus, the stress analysis presented in this work could be verified. Anyway, a second strain gauge for the second piston is necessary. Due to different material fluxes behind the pistons, the bulk stresses imposed to the plates are not equal. By also measuring the material level on the rear side of the pistons, the pure loading component could be identified.

A less steep temperature gradient in the model should be able to provide larger viscosity contrasts at the model Moho. Nevertheless, it is necessary to have the base of the model molten to decrease friction at the bottom of the model and to allow material flux behind the pistons for isostatic equilibration.

An important factor in the experiments is the analysis of the data obtained. As errors induced by the process of digitization of the marker positions can influence the results, an automated procedure for the strain analysis would largely improve both the quality and the quantity of data. It would also be easier to take into account more marker particles at more time steps.

For further experiments modelling the Higher Himalayas, the scaling of the experiments must be recalculated. Using a different set of gears, the motor could provide higher deformation rates, resulting in a smaller scaling factor for length, so that larger natural scenarios could be modelled. However, the experimental techniques for these models must also be refined to reduce boundary effects within the weak wedge or the newly suggested channel.

Probably one of the most important applications for thermomechanical analogue modelling lies in its interplay with numerical models. Although simulating large internal deformations in combination with discrete detachment zones still seems to pose numerical problems, the increasing power of computers keeps up with the refinement of data analysis in analogue experiments. The disadvantage of laboratory models to be limited to physical material properties does not exist in numerical models. On the other hand, analogue models include the physics implicitly, whereas numerical models can only simulate the processes they are programmed to simulate. Therefore, analogue models could be used to calibrate numerical models, which can then extend the results to nature. Only if a numerical model is able to reproduce a simple analogue model close enough, the computer code is justified to model geological scenarios.

Analogue modelling needs to be advanced further and further to provide an additional instrument for the Geologist. In this work, a major step forward has been done.


I want to express my gratitude towards Djordje Grujic, David Tanner and Jan Behrmann, who contibuted to this paper with many discussions. Beate Söhngen did the invaluable work of digitizing the data. Grant BE1041 by the Deutsche Forschungsgemeinschaft financed large parts of the project.


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