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Analogue modelling is a laboratory experimental method using uncomplicated physical models (such as a sandbox) with certain simple scales of time and length to model geological scenarios and simulate geodynamic evolutions. There are numerous limitations affecting the direct study of the Earth. Firstly, the timescales of
geodynamic Geodynamics is a subfield of geophysics dealing with dynamics of the Earth. It applies physics, chemistry and mathematics to the understanding of how mantle convection leads to plate tectonics and geologic phenomena such as seafloor spreading, mo ...
processes are exceptionally long (millions of years), and most of the processes started long before human records. Secondly, the length scales of geodynamic processes are enormous (thousands of kilometres), and most of them happen at depth within the Earth. Thus, scientists began making proportional small-scale simulations of features 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 the progressive development of Earth's deforming regions. Analogue modelling has been widely used for geodynamic analysis and to illustrate the development of different geological phenomena. Models can explore small-scale processes, such as
folding Fold, folding or foldable may refer to: Arts, entertainment, and media * ''Fold'' (album), the debut release by Australian rock band Epicure *Fold (poker), in the game of poker, to discard one's hand and forfeit interest in the current pot *Above ...
and
faulting In geology, a fault is a planar fracture or discontinuity in a volume of rock across which there has been significant displacement as a result of rock-mass movements. Large faults within Earth's crust result from the action of plate tectoni ...
, or large-scale processes, such as tectonic movement and interior Earth structures.


History

Analogue modelling has a 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 an outcrop. This idea of modelling led to many other small-scale studies, such as fault-propagation fold,
thrust fault A thrust fault is a break in the Earth's crust, across which older rocks are pushed above younger rocks. Thrust geometry and nomenclature Reverse faults A thrust fault is a type of reverse fault that has a dip of 45 degrees or less. If ...
, and folds in the late 19th century. These studies were all qualitative. King Hubbert came up with the theory of scaling in 1937, meaning that the study of analogue modelling became
quantitative Quantitative may refer to: * Quantitative research, scientific investigation of quantitative properties * Quantitative analysis (disambiguation) * Quantitative verse, a metrical system in poetry * Statistics, also known as quantitative analysis ...
. The
quantitative approach Quantitative research is a research strategy that focuses on quantifying the collection and analysis of data. It is formed from a deductive approach where emphasis is placed on the testing of theory, shaped by empiricist and positivist philosop ...
was further developed by many scientists later. As the field of geodynamic study expanded, analogue modelling increased, especially for large-scale geological processes. Examples include proto-subduction
subduction Subduction is a geological process in which the oceanic lithosphere is recycled into the Earth's mantle at convergent boundaries. Where the oceanic lithosphere of a tectonic plate converges with the less dense lithosphere of a second plate, ...
in plate tectonics,
collision In physics, a collision is any event in which two or more bodies exert forces on each other in a relatively short time. Although the most common use of the word ''collision'' refers to incidents in which two or more objects collide with great fo ...
, diapirism, and
rift In geology, a rift is a linear zone where the lithosphere is being pulled apart and is an example of extensional tectonics. Typical rift features are a central linear downfaulted depression, called a graben, or more commonly a half-graben wi ...
ing.


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.


Geometric similarity

To be geometrically similar, lengths in the model and natural example must be proportional and angles must be equal. When the length of a natural prototype (p) is l_n^p (n=1, 2, 3...) and the angle is \alpha_n^p. Correspondingly, the length in the model (m) is l_n^m and the angle is \alpha_n^m. They need to conform to the following formulas: \frac=\frac=\frac=\frac & \alpha_n^m=\alpha_n^p For example, 1 centimetre in the model represents 1 kilometre in nature.


Kinematic similarity

To be kinematically similar, they must be geometrically similar and the time needed for changes to occur must be proportional. When the required time for changing is t_n: \frac=\frac=\frac=\frac For example, 1 second in the model represents 1 thousand years in the nature. As is known: v=\frac, the velocities (v) can be scaled by the following equation: v^p=v^m\frac


Dynamic similarity

When the models and the natural world are geometrically and kinematically similar, dynamic similarity additionally requires that the various forces acting on a point in the model are proportional to those at a corresponding point in nature. When the forces (F_n) acting on the system are F_g ( gravity), F_v ( viscous force), and F_f ( friction): \frac=\frac=\frac=\frac However, since the forces acting in the nature are unmeasurable, it is impossible to scale the forces and stresses directly. Scientists have been using different formulas to convert forces into the parameters that can be measured.
Cauchy momentum equation The Cauchy momentum equation is a vector partial differential equation put forth by Cauchy that describes the non-relativistic momentum transport in any continuum. Main equation In convective (or Lagrangian) form the Cauchy momentum equation is ...
is usually used for showing the relationship between forces and densities (\rho is density): \frac=\frac(Generating from
Cauchy momentum equation The Cauchy momentum equation is a vector partial differential equation put forth by Cauchy that describes the non-relativistic momentum transport in any continuum. Main equation In convective (or Lagrangian) form the Cauchy momentum equation is ...
) Stokes' law is usually used for showing the relationship between forces and
density contrast Density contrast is a parameter used in galaxy formation to indicate where there are local enhancements in matter density. :\Delta=\frac It is believed that after inflation, although the universe was mostly uniform, some regions were slightly d ...
s (\Delta\rho is density constant): \frac=\frac(Generating from Stokes' law) (While the gravitational acceleration g^m=g^p) Since the
densities Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematicall ...
and
density contrast Density contrast is a parameter used in galaxy formation to indicate where there are local enhancements in matter density. :\Delta=\frac It is believed that after inflation, although the universe was mostly uniform, some regions were slightly d ...
s are proportional to forces and stresses, it is easy to scale
densities Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematicall ...
or
density contrast Density contrast is a parameter used in galaxy formation to indicate where there are local enhancements in matter density. :\Delta=\frac It is believed that after inflation, although the universe was mostly uniform, some regions were slightly d ...
s instead of scaling forces and stresses. 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 shortening, such as
folding Fold, folding or foldable may refer to: Arts, entertainment, and media * ''Fold'' (album), the debut release by Australian rock band Epicure *Fold (poker), in the game of poker, to discard one's hand and forfeit interest in the current pot *Above ...
,
thrust fault A thrust fault is a break in the Earth's crust, across which older rocks are pushed above younger rocks. Thrust geometry and nomenclature Reverse faults A thrust fault is a type of reverse fault that has a dip of 45 degrees or less. If ...
ing, collision, and
subduction Subduction is a geological process in which the oceanic lithosphere is recycled into the Earth's mantle at convergent boundaries. Where the oceanic lithosphere of a tectonic plate converges with the less dense lithosphere of a second plate, ...
. 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 experimental systems, the energy can be supplied externally (at the boundary) and internally (
buoyancy Buoyancy (), or upthrust, is an upward force exerted by a fluid that opposes the weight of a partially or fully immersed object. In a column of fluid, pressure increases with depth as a result of the weight of the overlying fluid. Thus the pr ...
forces). If the deformation is only caused by internal forces, it is a
closed system A closed system is a natural physical system that does not allow transfer of matter in or out of the system, although — in contexts such as physics, chemistry or engineering — the transfer of energy (''e.g.'' as work or heat) is allowed. In ...
. 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, many models are carried out using simulated gravity, for example, by use of a
centrifuge A centrifuge is a device that uses centrifugal force to separate various components of a fluid. This is achieved by spinning the fluid at high speed within a container, thereby separating fluids of different densities (e.g. cream from milk) or l ...
. These technologies are usually used in studying development of gravity-controlled structures, such as dome formation, and diapirism.


Materials

Analogue modelling uses various materials, such as sand,
clay Clay is a type of fine-grained natural soil material containing clay minerals (hydrous aluminium phyllosilicates, e.g. kaolin, Al2 Si2 O5( OH)4). Clays develop plasticity when wet, due to a molecular film of water surrounding the clay parti ...
, silicone and paraffin wax. Different materials came into use for quantitative analysis of analogue modelling experiments, compared to qualitative analysis. Before Hubbert's scaling theory, scientists used natural materials (e.g. clays, soil, and sand) for analogue modelling. For large-scale simulation, analogue modelling should have geometric, kinematic, and dynamic similarity with nature. If the model has these similarities, results from simulation will be more accurate. All these different materials represent the natural features of Earth (such as crust, mantle, and river). Selection of analogue materials is difficult, because of the largely
rheology Rheology (; ) is the study of the flow of matter, primarily in a fluid (liquid or gas) state, but also as "soft solids" or solids under conditions in which they respond with plastic flow rather than deforming elastically in response to an appli ...
-dependent deformation and inconstant
rheology Rheology (; ) is the study of the flow of matter, primarily in a fluid (liquid or gas) state, but also as "soft solids" or solids under conditions in which they respond with plastic flow rather than deforming elastically in response to an appli ...
influenced by the
thermal gradient A temperature gradient is a physical quantity that describes in which direction and at what rate the temperature changes the most rapidly around a particular location. The temperature gradient is a dimensional quantity expressed in units of degree ...
in nature. The rheological characteristic of internal layering was developed by the study of seismology and
geochemistry Geochemistry is the science that uses the tools and principles of chemistry to explain the mechanisms behind major geological systems such as the Earth's crust and its oceans. The realm of geochemistry extends beyond the Earth, encompassing the e ...
. To simulate layers with different properties, different materials are chosen:


Advantages

There are many useful properties of analogue modelling: # Analogue models can directly show whole geodynamic processes from start to finish. # Geodynamic processes can be stopped at any time for investigation, and allow the study of 3D structures. # The scales of the model can be controlled in a practicable range for the laboratory. # The simulation can show different results of geodynamic processes by altering the parameters, and the influence of each parameter is clarified. # The results of analogue modelling can be directly used for interpreting nature if the accuracy of the model is high. # Analogue modelling can provide new ways of thinking about geological problems.


Disadvantages

Because analogue modelling involves the simplification of geodynamic processes, it also has several disadvantages and limitations: # The study of natural rock properties still needs more research. The more accurate the input data, the more accurate the analogue modelling. # There are many more factors in 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). # The variation of natural rocks is greater than in simulated materials; therefore it is difficult to fully model the real situation. # Analogue modelling cannot simulate
chemical reaction A chemical reaction is a process that leads to the chemical transformation of one set of chemical substances to another. Classically, chemical reactions encompass changes that only involve the positions of electrons in the forming and breakin ...
s. # There are systematic errors in 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 Fold, folding or foldable may refer to: Arts, entertainment, and media * ''Fold'' (album), the debut release by Australian rock band Epicure *Fold (poker), in the game of poker, to discard one's hand and forfeit interest in the current pot *Above ...
, fracturing,
boudinage Boudinaged quartz vein in shear foliation, Starlight Pit, Fortnum Gold Mine, Western Australia. Boudinage is a geological term for structures formed by extension, where a rigid tabular body such as hornfels, is stretched and deformed amids ...
and shear zone, and large-scale problems –
subduction Subduction is a geological process in which the oceanic lithosphere is recycled into the Earth's mantle at convergent boundaries. Where the oceanic lithosphere of a tectonic plate converges with the less dense lithosphere of a second plate, ...
, collision, diapirism, and
mantle convection Mantle convection is the very slow creeping motion of Earth's solid silicate mantle as convection currents carrying heat from the interior to the planet's surface. The Earth's surface lithosphere rides atop the asthenosphere and the two form ...
. The following are some examples of applications of analogue modelling.


Compressional tectonics

The first analogue model was built by James Hall for simulating folds. He used a lateral compression machine for the simulation, and this machine is still shown in the Royal Society of Edinburgh. The final result from the model is quite close to observation of the Berwickshire coast. Although the model he used is simpler than current ones, the idea remains in use. The use of more complex compression machines substantially increases the number of simulations of compressional tectonics, including
subduction Subduction is a geological process in which the oceanic lithosphere is recycled into the Earth's mantle at convergent boundaries. Where the oceanic lithosphere of a tectonic plate converges with the less dense lithosphere of a second plate, ...
, collision, lithospheric shortening, fracture formation, thrust and
accretionary wedge An accretionary wedge or accretionary prism forms from sediments accreted onto the non- subducting tectonic plate at a convergent plate boundary. Most of the material in the accretionary wedge consists of marine sediments scraped off from the ...
. 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). Depending on the different natural features, erosion (removal of top materials at a certain angle),
décollement Décollement () is a gliding plane between two rock masses, also known as a basal detachment fault. Décollements are a deformational structure, resulting in independent styles of deformation in the rocks above and below the fault. They are ass ...
(inserted layers with low cohesion, normally glass microbeads), and any other parameters can put into the model, producing various results. Simulations of mantle influences vary. Because of the different physical and chemical properties between the asthenosphere and lithosphere, viscous materials and a heater (for
mantle convection Mantle convection is the very slow creeping motion of Earth's solid silicate mantle as convection currents carrying heat from the interior to the planet's surface. The Earth's surface lithosphere rides atop the asthenosphere and the two form ...
) are also used. ]


Extensional tectonics

Compression machines can also be used in reverse for simulating extensional tectonics, such as lithospheric extension, the formation of
rift In geology, a rift is a linear zone where the lithosphere is being pulled apart and is an example of extensional tectonics. Typical rift features are a central linear downfaulted depression, called a graben, or more commonly a half-graben wi ...
s, normal faulting,
boudinage Boudinaged quartz vein in shear foliation, Starlight Pit, Fortnum Gold Mine, Western Australia. Boudinage is a geological term for structures formed by extension, where a rigid tabular body such as hornfels, is stretched and deformed amids ...
and diapirs. These models can also be built in a glass box which is similar to the above, but instead of thrust force,
tensile force In physics, tension is described as the pulling force transmitted axially by the means of a string, a rope, chain, or similar object, or by each end of a rod, truss member, or similar three-dimensional object; tension might also be described as t ...
is applied.


Strike-slip tectonics

Strike-slip tectonics Strike-slip tectonics or wrench tectonics is the type of tectonics that is dominated by lateral (horizontal) movements within the Earth's crust (and lithosphere). Where a zone of strike-slip tectonics forms the boundary between two tectonic plates, ...
differ from the dominantly vertical crust movements associated with shortening and extension, being dominantly horizontal in character (in relative terms sinistral or dextral). This kind of horizontal movement will create a shear zone and several types of fractures and faults. A typical model used for strike-slip tectonics has two (or more) horizontal basal plates moving in opposite directions (or only move one of the plates, other are fixed). The visual results are shown 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.


See also

*
Geologic modelling Geologic modelling, geological modelling or geomodelling is the applied science of creating computerized representations of portions of the Earth's crust based on geophysical and geological observations made on and below the Earth surface. A ge ...
* Numerical modeling (geology) * Earth analog


References

{{Reflist Structural geology