User:YuweiHGeo/sandbox

Analogue Modelling (Geology) -- This is an expansion of original wiki page (some sentences are from the original wiki page)

Pure shear sandbox model of thrust fault formation (This photo and descriptions are from original wiki page)

Analogue Modelling (Geology) is a laboratory experimental method using uncomplicated physical models (such as sandbox) with certain simple scales of time and length to model geological scenarios and simulate geodynamic evolutions.

Because there are numerous limitations for the direct study of Earth —— the timescale of geodynamic processes is exceptionally long, and most of the processes started at the ancient time when there is no human being; the scale of geodynamic processes are enormous, and most of them happen in the internal Earth. Scientists begin making proportional small-scale simulations like those in the natural world to test geological ideas. Analogue models can directly show the whole structural pattern in 3D and cross-section. They are helpful in understanding the internal structures and historical development of Earth deforming regions.

Analogue modelling has been widely used in geodynamic analysis and restoring the development history of different geological phenomena. They could be small-scale —— folding, faulting etc., or large-scale —— tectonic movement, interior Earth structures etc.

History

Analogue modelling has an development history of over 200 years.

The model is showing the simplification of the lateral compression machine for folding simulation that James Hall made. This machine is still presented by the Royal Society of Edinburgh. The materials squeezed in the box are blankets or layers of clay.

It has been used since at least 1812 when James Hall squeezed layers of clay to produce folds similar to those that he had studied at the outcrop. (This sentence is from original wiki page.) Subsequently, the small-scale studies of the fault-propagation fold, thrust fault, and folds etc. in the late 19^th century are all qualitative.

After entering the 20^th century, King Hubbert change the study of analogue modelling to the quantitative method . And the quantitative approach is developed by many scientists later. Due to an expanding variety of geodynamic study, analogue modelling has been used in more and more aspects, especially for the large-scale geological processes. For example, from proto-subduction to subduction (after the concept of plate tectonics was accepted), collision, diapirism, rifting, and so on.

In recent years, the application of analogue modelling is getting wider. Scientists focus on exploring the effects of using different model conditions, to make the analogue modelling more representative.

Components

Scaling

In 1937 King Hubbert described the key principles for scaling analogue models. He defined three types of similarity between models and the natural world: geometric, kinematic and dynamic. (These sentences are from original wiki page.)

Geometric Similarity

To be geometrically similar, lengths in the model and natural example must be proportional and angles must be equal. (This sentence is from original wiki page.) For example, when the length of a natural prototype is $l_{n}^{p}$ (n=1, 2, 3…) and the angle is $\alpha _{n}^{p}$. Correspondingly, the length in the model is $l_{n}^{m}$ and the angle is $\alpha _{n}^{m}$. They need to conform to the following formulas:

${\frac {l_{1}^{m}}{l_{1}^{p}}}={\frac {l_{2}^{m}}{l_{2}^{p}}}={\frac {l_{3}^{m}}{l_{3}^{p}}}={\frac {l_{n}^{m}}{l_{n}^{p}}}$ & $\alpha _{n}^{m}=\alpha _{n}^{p}$

Kinematic Similarity

To be kinematically similar, they must be geometrically similar and the time needed for changes to occur must be proportional. (This sentence is from original wiki page.) For example, when the required time for changing is $t_{n}$:

${\frac {t_{1}^{m}}{t_{1}^{p}}}={\frac {t_{2}^{m}}{t_{2}^{p}}}={\frac {t_{3}^{m}}{t_{3}^{p}}}={\frac {t_{n}^{m}}{t_{n}^{p}}}$

As is known: $v={\frac {l}{t}}$, the velocities ($v$) can be scaled by the following equation:

$v^{p}=v^{m}{\frac {l^{p}t^{m}}{l^{m}t^{p}}}$

Dynamic Similarity

Dynamic similarity additionally requires that the various forces (driving forces and resistive forces ) acting on a point in the model are proportional to those at a corresponding point in nature. (This sentence is from original wiki page.) For example, when the forces ($F_{n}$) acting on the system are $F_{g}$ (gravity), $F_{v}$ (viscous force), and $F_{f}$ (friction):

${\frac {F_{g}^{m}}{F_{g}^{p}}}={\frac {F_{v}^{m}}{F_{v}^{p}}}={\frac {F_{f}^{m}}{F_{f}^{p}}}={\frac {F_{n}^{m}}{F_{n}^{p}}}$

However, since the forces are invisible, it is impassable for scaling the forces and stresses directly. Scaling densities or density contrasts could be used for scaling forces and stresses of analogue modelling. Cauchy momentum equation is usually used for showing the relationship between forces and densities. Stokes’ law is usually used for showing the relationship between forces and density contrasts. By simplifying the equations, the forces and stresses can be scaled by following formulations (while the gravitational acceleration $g^{m}=g^{p}$):

${\frac {F^{m}}{F^{p}}}={\frac {\rho ^{m}(l^{m})^{3}}{\rho ^{p}(l^{p})^{3}}}$(Generating from Cauchy momentum equation )

${\frac {F^{m}}{F^{p}}}={\frac {\Delta \rho ^{m}(l^{m})^{3}}{\Delta \rho ^{p}(l^{p})^{3}}}$(Generating from Stokes’ law )

($\rho$ is density, $\Delta \rho$ is density constant)

However, these two equations can lead to different topography scales.

Experimental Apparatus

Different geodynamic processes are simulated by different experimental apparatus.

Analogue model of caldera formation using flour to represent the upper part of the crust and a balloon to represent the inflating magma chamber (This gif and descriptions are from original wiki page)

For example, lateral compression machines are commonly used in simulating deformations involving lithospheric shortenings, such as folding, thrust faulting, collision, and subduction. Longitudinal compression machines are usually used for fracturing. There is a large variety of devices based on the different sources of forces applied to the material. Some devices have multiple forcing systems because nature is not homogeneous.

Lab Environment

Systems

For the experimental systems, the energy can be supplied externally (to the boundary) and internally (buoyancy forces). If the deformations are only caused by internal forces, it is a closed system. Conversely, if the deformations are caused by external forces or a combination of internal and external forces, it is an open system.

For the open system, the extrusion or stretching forces are imposed externally. However, the buoyancy forces can be generated both externally or internally. The materials and thermal energy can be added to or remove from the system. For the closed system, there is no energy and materials added to the system. Thus, all the deformations are caused by internal buoyancy forces. Only buoyancy-driven deformation can be simulated in a closed system.

Gravity Field

Because the major research object of analogue modelling is Earth, the gravity field that most experiments utilize is ordinarily the Earth’s field of gravity. However, there still a lot of models (such as using of the centrifuge) are supplied in an imitated gravity field. These technologies are usually used in simulating the development of gravity-controlled structures, such as dome formation, diapirism.

The simple analogue modelling of a subduction zone. The materials this model uses are —— for the continental crust (left in layered brown) and oceanic crust (right in layered brown): sand mixture and silicone putty; for the asthenosphere (greenish-blue liquid in the glass tank): glucose syrup. There is a heater in the tank for heating the liquid.

Materials

Analogue modelling uses various materials such as sand, clay, silicone and paraffin wax. (This sentence is from original wiki page.) From qualitative analysis to quantitative analysis of analogue modelling experiments, the varieties of materials changed. Before Hubbert’s scaling theory came out, scientists used natural materials (e.g. clays, soil, and sand) for analogue modelling. However, for the large-scale simulation, analogue modelling should have the geometric, kinematic, and dynamic similarity with nature. If the model has these similarities with nature, the results from the simulation can show the real evaluation (section 2.1). All these different materials represent the natural matters of Earth (such as crust, mantle, and river). The largely rheology-depended deformation and inconstant rheology with the thermal gradient in the nature make the selection of analogue materials difficult. Nevertheless, the rheological characteristic of internal layering was developed by the study of seismology and geochemistry.

To simulate the layers with different properties, different materials are chosen:

Materials for Analogue Modelling

Categories		Examples	Simulation
Granular Materials (various in density, shape, and size)		Quartz Sand, Glass Microbeads, Feldspar Power	Brittle Upper Crust
Low Viscous Materials		Water, Sugar Solution, Honey	Asthenosphere, Sub-lithospheric Mantle
		Corn Syrup, Glucose Syrup	Sinking Slabs
High Linear Viscous Materials		Syrup, Silicone Putty	Ductile Lithoshpere
Visco-elastic Materials		Amorphous Polymers, Biopolymers, Bitumen
Non-linear Viscous Materials	Plastic Materials	Plasticine
	Visco-plastic Materials	Wax, Paraffin
	Visco-elasto-plastic Materials	Gelatin

Advantages

There are many useful properties of analogue modelling:

1. The analogue models can directly show the whole geodynamic processes from start to finish.
2. The geodynamic processes can stop at any time for investigation, and provide the study of 3D structures.
3. The scales of the model can be controlled in a practicable range for the laboratory.
4. The simulation can show different results of geodynamic processes by altering the parameters, and the influence of each parameter is clarified.
5. The results of analogue modelling can be directly used for interpreting the nature if the accuracy of the model is high.
6. Analogue modelling can provide the new thoughts of geological problems.

Disadvantages

Because analogue modelling is the simplification of geodynamic processes, it also has several disadvantages and limitations:

1. The expertise of natural rock properties still needs more research. The more accurate of the input data, more accurate of analogue modelling.
2. There are many more factors in the nature that affect the geodynamic processes (such as isostatic compensation and erosion), and these are most likely heterogeneous systems. Thus they are challenging for simulations (some factors are not even known).
3. The varieties of natural rocks are more than simulated materials; therefore it is difficult to fully restore the real situation.
4. The analogue modelling can not simulate chemical reactions.
5. There are systematic errors to the apparatus, and random errors due to human factors.

Applications

Analogue modelling can be used to simulate different geodynamic processes and geological phenomena, such as small-scale problems —— folding, fracturing, boudinage and shear zone, and large-scale problems —— subduction, collision, diapirism, and mantle convection. The following are some examples of applications of analogue modelling.

The simple analogue modelling of the growth and erosion of an orogenic wedge. This simulation is doing in a glass tank, with layered of different granular materials which represent to the crust. [1]

Compressional Tectonics

The first analogue modelling was built by James Hall for simulating folds. He used a lateral compression machine for the simulation, and this machine still presents in the Royal Society of Edinburgh. The final result got by the model is quite close to the observation from the Berwickshire coast. Although the model he used is simpler than the current ones, the idea is still adopted.

With the application of more complex compression machines, the simulation of compressional tectonics, such as subduction, collision, lithospheric shortening, and formation of fracture, thrust and accretionary wedge, substantially increase in number. If the simulation only focuses on the upper crustal, the model is always built in the glass box (or two lateral glass walls) with a piston and/or wedges to supply forces to layers of granular materials (normally called sandbox). Depends on the different natural problems, erosion (removal of top materials in certain angle), décollement (inset layers with low cohesion, normally glass microbeads), and any other parameters can put into the model; the results can be various.

The simulations of mantle influences are different. Because of the different physical and chemical properties between asthenosphere and lithosphere, viscous materials and heater (for mantle convection) are also used.

The simple analogue modelling of the extension tectonics which showing the formation of normal fault and salt dome (diapirism). This model is built in a glass box. The darker greyish layer is silicone which represents salt, and brownish layers are dry quartz sands which represent the brittle sedimentary rocks. [2]

Extensional Tectonics

The compression machines can also be used in opposite direction for simulating extensional tectonics, such as lithospheric extension, the formation of the rift, normal faulting, boudinage, diapirs. These models can also be built in a glass box which is similar to the above, but instead of thrust force, the tensile force is supplied.

Strike-slip Tectonics

Differ from the vertical crust movement of compression and extension, strike-slip is a horizontal movement (relatively sinistral or dextral). This kind of horizontal movement will create a shear zone and several types of fractures and faults. The model of strike-slip tectonics has two (or more) horizontal basal plates moving in the opposite directions (or only move one of the plates, other are fixed). The visual results are showed from bird's-eye view. Scientists used CT-analysis to collect the cross-section images for the observation of the most influenced area during the simulation.

The simplified analogue modelling setting of shear deformation. This model is built on two separate horizontal plates. The brownish layers are dry sand, wet clay, and viscous materials, such as silicone or polydimethylsiloxane.

Other Applications

Except the basic tectonics’ analogue modelling, there are also some models of volcano systems (formation of the caldera), mantle convection, etc.

See also

• Ÿ Geologic modelling

• Ÿ Numerical modeling (geology)

• Ÿ Earth analog