Gravitational Collapse of a Thickened Crust


                              Marianne Casimatis, Laura Matarese, Danielle Sharpe and Katherine Zunica



"All geodynamic processes should be explained by the fundamental principle of the strive for gravitational equilibrium"
 (Ann. Soc. Geol. Belge Bull. 64 (1965) 95-123, as cited in Rey, Vanderhaeghe, Teyssier, 2001)




 


Satellite image of the Tibetan Plateau


Table of Contents


1) Introduction


2) Evolution of the concept of gravitational collapse


3)Tectonic Thickened of the Continental Crust
       a) - subduction zone

       b) - continental collision


4) Forces acting on the thickened crust

       a)  - the concept of isostasy
                    - mechanical vs isostatic equlibrium

       b) - gravitational potential energy

       c) - gravitational force

       d) - lithospheric strength and the Argand ratio


5) Restoring mechanical equlibrium through gravitational collapse

       a) - what is gravitational collapse?

       b) - the regimes and modes of gravitational collapse
                    - divergent vs convergent gravitational collapse
                    - fixed vs free boundary collapse

6) Indications of gravitational collapse in the field


7) Conclusion


8) Reference List..... not finished.....

 


Introduction


The aim of this report is to explain how the thickened crust is deformed by gravity during the process known as gravitational collapse.

The process of gravitational collapsse is important because it helps to explain why we have areas showing surface extension within zones of active convergence, for example, the Himalayas.  Such anomalies in the Earths crust do not conform with modern plate tectonic theory, whereby the earth's lithospheric plates are in motion with respect to one another, and deformation is mostly concentrated along plate boundaries.

An overview of crustal thickening processes during subduction and continental convergence will be presented in section 3.

We will briefly discuss the evolution of the theory of gravitaional collapse in Section 2, before explaining the important concepts and mechanisms involved in this process, such a Gravitational Potential Energy (GPE), Isostasy, Gravitational Force (Fg) and Strength, in section 4.

The two fundamental regimes of gravitational collapse, divergent and convergent collapse, will be examined.  The emphasis of this report will be on divergent gravitational collapse.  The modes of collapse within these categories, these being fixed boundary and free boundary collapse, will also be discussed in section 5.

The last part of this report will focus on the relevance of gravitaional collapse in direct field observations of this mechanical process, using examples from Tibet and the United States.


Evolution of the Concept of Gravitational Collapse


The concept of gravitational collapse began to take shape in the early to mid part of the last century when it was first recognised that large scale gravity-driven flow could be responsible for the horizontal spreading and vertical shortening of an entire thickened crust.

During the 1960's and 1970's, the concept of gravitational collapse took a back seat to the burgeoning theory of plate tectonics.  This was partly due to the early terminology being different from that in use in later years.. Early pioneers in the field, such as Jeffreys, van Bemmelen, Bucher, Ramberg and others, varioulsy described the mechanisms involved in gravitational collapse, but had no formal terminology to emody this new theory.

The 1980's saw a re-emergence of the concept of gravitational collapse wtih the discovery of "surface extension in the same direction as compression driven by active lithospheric plate convergence." (P. Rey et al, 2001)

The role of gravity on tectonic processes was reassessed, and it became accepted that, along with the relative displacement of neighbouring plates, lateral variation in the gravitational potential energy could also cause lithospheric deformation.

This coupling of ideas allowed the tectonic regimes seen in the Western United States and Tibet to be explained.


tibet

A pictoral representation of the Tibetan Plateau. The dark arrows show the direction of movement of the Eurasian and Indian

continental plates.

Tectonic Thickening of the Continental Crust


Crustal thickening initiated by tectonic forces, can arise from continent/continent collision, or from subduction processes.

During continent-continent convergence, both of the crustal plates are too buoyant in relation to the underlying lithosphere for either one of them to sink below the other.  The two masses become compressed, and a high mountain belt will form by folding, thrust faulting, and doubling of the crustal layers as one continent is thrusted on top of the other.  The Himalayan mountain belt and the Tibetan plateau is the largest manifestation of this ongoing process of collision between the Indian and the Eurasian continental plates.




  A pictoral representation of continent-continent collision


During the  convergence of oceanic and continental plates, the less-dense continental plate will override the denser subducting oceanic plate.  The continental margin will be deformed into a folded mountain belt, with volcanic activity contributing to the growth of the mountain belt.



  (a)


(b)
(a) A schematic diagram of a subduction zone, causing an orogenic belt to form on the continent. Thickening of the crust is due to compressive forces and the emplacement of magma. (b) We can see the evolution of a volcanic arc which forms on the continent.

Forces Acting On The Thickened  Crust



There are several main physical factors that are associated with gravitational collapse of a thickened continental lithosphere.  
These are: Isostacy, Gravitational Potential Energy, Gravitational Force, and Strength.


Isostasy

The theory of isostasy states that the mass per unit area of two columns of rock that are above a certain level are equal (*)
This level is called the isostatic compensation level.  In the case of a thickened crust, we place the isostatic compensationl level below the root of the thickened lithosphere.  At this level,  the columns are in isostatic equilibrium.  

Isostatic equilibrium is distinct from mechanical equilibrium.  Mechanical equilibrium is where the sum of the forces exerted within a system are equal to zero.
Isostatic equilibrium does not imply mechanical equilibrium due to the lateral variations of density along the two columns which produce variations in GPE.



The compensation level is shown using the dashed line.
A schematic diagram of isostasy showing an undeformed lithospheric column in B and a thickened crust in column C.
 The compensation level is shown using the dashed line.


Gravitational Potential Energy

GPE is energy that an object has due to its position in a gravitational field.

                                 PE(g) = m. g. y.

                                             Where m = mass of an object
                                                          g = acceleration due to gravity
                                                          y = distance of the object above some reference level
     
This is seen in columns B and C in the diagram above, where there are lateral variations of GPE.  This is given by the lateral variations of density along an equipotential surface that produces gravitational forces within the lithosphere.

The difference of GPE in the two columns will determine if there will be extension or contraction.  The GPE of the column with the higher lithospheric pressure, that is, the vertical stress due to the weight of the overlying rock is equal to the density x gravitational force x depth.

The difference in the GPE of the two columns is the integral, from the top of the column, to the bottom (the compensation level), of the lithospheric pressure of those columns as a function of depth.




This diagram is a pictoral representation of the equation below.
gravitational force =                           minus                                        





If the column with the higher lithospheric pressure has an excess of GPE the gravitational force will drive extension (P. Rey et al 2001, Page 442)


Gravitational Force (Fg)

Gravitational force is where gravity produces motion in a body.*  This force is different to tectonic forces.  Tectonic force produces motion in a body via tectonics, where the driving mechanism is not where an object experiences acceleration under the influence of the Earth's mass, but rather convection of heat and material in the mantle.
The difference in the GPE of the two columns will also be the gravitational force that the two columns apply to each other.


Lithospheric Strength and the Argand Ratio

The gravitational force (Fg), however, must be greater than the resistance forces to produce lateral extension.  These resistive forces include the tectonic force (resistive due to its opposing direction, and therefore sign), and the strength of the surrounding lithosphere.  (P. Rey et al 2001, Page 440)

The strength of the crust plus the mantle, is its amount of natural resistance to pressure.  When the pressure exerted by the gravitational force exceeds the natural resistance and other resistive forces,  lateral spreading will occur. (P. Rey et al 2001, Page 439)

Strength varies due to temperature and depth.  Material becomes weaker as the temperature increases, and the temperature increases with depth. Pressure increases with depth.  
Depth can also be an independent factor for a rheological strength.  

The more stress that is placed upon the material, the closer the total amount of forces come to exceeding the material's strength.

The strength profile of a thickened crust is different to an average crust due to the difference in the amount of crust and mantle.
The ratio of the gravitational force to strength controls the rate of collapse of the thickened crust when the strength of the deforming lithosphere is the sole force which opposes collapse.(P. Rey et al 2001, Page 439).  This ratio is called the Argand ratio where,
                                         

Argand Ratio:


                                               If,                                                         Fg
                                                                                         strength of lithospheric column         >      1      
  

                                                                        the gravitational force will play the active role in deformation.
   



                                                  But if,                                                Fg
                                                                                         strength of lithospheric column         <      1      
                                                                           
                                                  the gravitational force is negligible and has not exceeded the strength of the lithosphere in order to deform it.

                                                                
Top: Shows a balanced GPE with the upper lithosphere in tension and the lower lithosphere in compression.
                                                                                        Bottom: Shows an excess in GPE in the thickened crust.


As we can see, there are a number of factors acting upon our thickened lithosphere,  They are isostasy, GPE, Gravitational Force and Strength.  These are all playing a role in our system.
We can thus say that we have a system that is not in mechanical equilibrium.  

So how does it reach mechanical equilibrium?  We will see in the next section.



Restoring Mechanical Equilibrium Through Gravitational Collapse


The tectonic forces which created the thickened crust have, over time, left the system out of mechanical eqilibrium.

This section of the report discusses a way in which the system regains equilibrium. The system can re-establish equilibrium through gravitational collapse.

What is gravitational collapse?

Gravitational collapse is the mechanism  that reduces the lateral variations in GPE that have developed during the thickening of the crust. (Rey et al, 2001).  Gravitaional collapse is driven by the gravitational force (as described in the previous section). This force acts internally to the system.

Gravitational collapse is not linked to any particular tectonic regime and  its effects are basically confined to the crust.

Gravitational collapse can be divided into two regimes: divergent and convergent. (Nb: For the purposes of this report, we are focussing on divergent collapse).


Divergent Gravitational Collapse

Divergent collapse occurs when there has been previous thickening of the crust. This produces an excess in GPE. Gravitational collapse is facilitated by particles moving away from the area of deformed crust.  

In contrast, convergent collapse occurs when the crust has been previously thinned. The particles move towrd the area of thinning. There is not sufficient evidence to prove the existence of convergent collapse at this time. (Rey et al, 2001).

Evidence for divergent collapse comes from areas such as Tibet and South-west America. These examples will be discussed in the next section of the report.

Why does collapse begin?

Collapse begins due to a change in the balance of forces that support the thickened crust. These forces include; a reduction in tectonic forces and a reduction in the strength of the lithosphere. (Argand ratio discussed previously). ( Rey et al, 2001).

Once collapse is initiated, the movement of mass must be accommodated. the way in which space is provided for is dependent on whether the collapse is 'fixed' or 'free' boundary collapse.

Fixed Boundary Collapse

Fixed boundary collapse results in the horizontal growth of the area of thickened crust. The reduction of lateral variations in GPE is acheived by the transferring of GPE across the deformed area. GPE moves from elevated areas to areas of low GPE. The flow of material moves away from the thickened crust to adjacent areas.

Space for the collapse of the thickened crust is made by a combination of lowering of the moho, uplift of the crust's surface and shortening of the araes adjacent to the orogen (thickened crust).

Fixed boundary collapse is classified into three types depending on the type of deformation involved.


Below: 
Thickened crust prior to gravitational collapse













Diagram to the right: This diagram shows the different ways in which the upper and lower crust deform
in the fixed boundary collapse The structural features which develop will be discussed in the next section of the report.( diagrams from P.Rey lecture notes, geos3003, 2003)













The structaral characteristics of these three types of fixed boudary collapse, with examples, will be discussed in the next section of the report.

Free Boundary Collapse

The free boundary  has to be located  adjacent to the orogen. A 'free boundary' may be an active continental margin. Free boundary collapse may occur when there has been a phase of tectonic divergence acting on the orogen.

The lateral variations in GPE are reduced by dispalcement of the free boundary (induced by the gravitational force). It involves the homogeneous thinning of the orogen. (Rey et al, 2001).

Space for the material is accommodated by the vertical displacement of the moho and the deformed crustal surface.
This diagram shows how the crust deforms during free boundary collapse. You can see how the free boundary is                                                                                                                      displaced and the crust is thinned.




Indications of gravitational collapse in the Field


Up until now we have been talking in terms of theories and experimental results, how then does this translate into the reality? Throughout the world there are a number of geologically significant sites that display physical structures believed to be examples of the processes of gravitational collapse discussed in this paper. The Himalayan Mountains are among the most famous. These mountains run from east China to the straits of Gibraltar and are the result of a thickening lithosphere of Mesozoic of Tertiary origin. With an average elevation of 5000m above sea level and a width of 250km, it contains the highest mountain in the world Everest. 3,000,000km² of this region is the Tibetan Plateau situated at about 5,400m 30°-40°N and 80°-100°E. 


Left: Tibetan ranges, Mt Everest                                                                                                    Right: Basin and Ranges, South west USA

There are further mountain ranges to the north, the Tein Shan and the Altai, which are also part of the same thickening zone. Another area of interest is in Southwest in places called the Basin and Range, the Great Plains, the Coast Ranges and the Traverse ranges. (P.England p.276) lying above 1500m. 

Previously gravitational collapse has been discussed as a result of structural strength, gravitational force, GPE and isostacy. These figures rely on measurements of the density, thickness of lithosphere and depth of Moho. The crust has a constant density of 2800kgm³ and the mantle 400-500kgm³, which translates to a root requirement of 5-7km: 1km of mountain range above sea level. Tibet’s total crustal thickness (root included) should theoretically be about 60-75km. This can be tested seismically by refraction studies to discover the Moho, which comes to 55-70km in Southern Tibet.

Methods of analyzing gravitational collapse:


www.es.usyd.edu.au/geology/people/staff/prey/Teaching/Geol-2001GPHS/index.html

Seismology  is the study of the normal, reflected, refracted and rarefracted primary and secondary waves produced by the mechanical failure of fault zones. Commonly known as earthquakes these seismic disruptions propagate through the earth’s layers in different ways making analysis of the different layers possible and more importantly the depth of the Moho can be deducted. These P and S waves also give information on the kinematics of the fault responsible for the earthquake. Basically P waves or the first motion of the earthquake propagate in such a way that when data from two locations is triangulated the focus of the earthquake can be determined. S waves have shadow zones on the opposite of the earth(between 105 degrees) as they cannot travel through the liquid mantle. P waves can but are refracted at an angle (105-143 degrees are shadow zones). The P waves can also give information on the nature of a fault, as they travel more strongly in one direction of extension or compression depending on their nature. These then can be graphically represented as ‘beach balls’, which correspond with normal, thrust or transform. The white areas are compression and the black extension. 

In the beach ball diagram of Tibet  we can see along the top and bottom boundary thrust faults. Theoretically if only tectonic forces were acting then only trust fault should be in a region of continental convergence as seen here with the collision of the Indian and Eurasian plates. But in the Plateau region we also see normal faults indicating east-west extension.(P.England p.285) These extensional fractures are some of the most characteristic features of gravitational collapse in the field.


Features of gravitational collapse:


In the last section the issue of different types of collapse was raised. Fixed and free boundary collapse are processes which produce individual features that can be used to identify the sub-terrainian movement.(Diagrams displayed in previous section)(P.Rey et al p.444).

Fixed boundary collapse

  1. Upper crustal creates Fans (duplexes of normal faults) and corresponding conjugate

Fans (thrust faults), a thickening of the forelands and little deformation of the ductile basement.

  1. Blind collapse or lower crustal involves the deformation of the basement alone and can be

recognised in a widening of the plateau, thickening of crustal forelands with no associated thrusting. No normal faults or fan features are evident but there is crustal thinning i.e. sedimentation occurs as the area is lower than the surrounding.

  1. The final scenario involves a combination of the other two. There is both deformation of the

brittle crust and the ductile basement giving the faulting patterns of the first and the crustal thinning of the second. This tends to promote partial melting and low pressure, high temperature metamorphic facies as blue shist and glauco-lauconite facies.


Free -boundary collapse

Is the thinning of the entire thickened crust not just sections bounded by faults and inconsistencies. There are normal faults/extensional fractures in the brittle upper crust and ductile flow of the basement. There is usually low angle detachment and dècollement marks the change between these two layers and no flow of material outside of the region.(P.Rey et al p.445) The basin and Range Province in America is believed to be a thickened unit currently under the process of free boundary gravitational collapse. It was formed in the Cainozoic and displays the graben and horst features common in this type of deformation. 

These are linear graben and horst features of the Basin and Range Province in America's Southwest.

From the air it looks like this with the lines showing the areas of subsidence and elevation of the blocks. A cross section of this area would show the classical v shaped fracture zones with strike-slip movement. Over time these feature become more pronounced. This process is deforming the Basin and Range Province at present. This applies as well to Tibet as one of its major features is the Guzuo graben northwest of Mt Everest .


Tibetan plateau showing extensional fractures as normal faults and graben features running north-south and extending east-west.


Other methods of identification:


There are other methods of identification using empirical evidence, logical assumptions and mathematical extrapolations based on the experimental results. Extensional faulting brings deeply buried rocks to the surface (P.England p.297) allowing the analysis of metamorphic peaks and zircon dating of these, history and folding events which give insight into the strengths and depth of the rock at the times of multiple deformation events. This is helpful for the studying the gravitational collapse’s history where a site has already been identified but what about a suspected case? At present the best that can be used is numerical modeling (p.rey p.78), metamorphic core samples and satellite images. Satellite images give some indication of the extent of faulted areas, basins forming and other tectonically anomalous macro features, which are possibly a result of gravitational collapse.



Conclusion


Our aim in this report has been to explain how gravity can deform a thickened crust through gravitational collapse.

There are two distinct processes of gravitational collapse: Divergent and Convergent.  This report has focused on divergent gravitational collapse.

We have seen that, after crustal thickening, there are several physical factors that act in conjunction to deform the crust through gravitational collapse, these being Isostasy, Gravitational Potential Energy, Gravitational Force and Strength.

We have seen that there are two modes of lateral extension of the thickened crust through gravitational collapse, and this depends on the physical boundary conditions.

In fixed-boundary collapse, energy is transferred from regions of high potential energy to regions of low potential energy.  We therefore see lateral growth of the orogen.

In free-boundary collapse, any lateral variations in potential energy are reduced due to the displacement of a free boundary under the action of gravitational forces. (Rey et al. 2001).  We therefore see thinning of the entire orogenic domain.

We have concluded our report with physical examples of divergent gravitational collapse, as seen in Tibet and the south-western United States.



Reference List