User:YuweiHGeo/sandbox

 Analogue Modelling (Geology) -- This is an expansion of original wiki page (some sentences are from the 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. 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 fold s etc. in the late 19th century are all qualitative.

After entering the 20th 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:

$$v^p=v^m\frac{l^pt^m}{l^mt^p}$$

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.

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.

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.

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:

= 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.

Compressional Tectonics
The first analogue modelling was built by James Hall for simulating fold s. 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.

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.

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 =


 *  Geologic modelling


 *  Numerical modeling (geology)


 *  Earth analog