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Extension of the continental lithosphere

Introduction

The mode of continental lithospheric extension and subsequent basin formation alongcontinental margins and in the interior of continents depends on the rheological stratificationof the lithosphere. For example the strength of the lower crust varies as a function of itscomposition (eg amount of internal radiogenic heat production) and on mantle heat flow. Bychanging the strength ratio of the upper to lower crusts, the distribution of subsidence andfaulting may be predicted. We will use the particle-in-cell finite element code Ellipsis tocreate a two-dimensional model of the layers of the Earth under extension and we will explorewhat impacts various strength changes and initial weaknesses have on lithosphericdeformation, thereby mimicking geological reality.

Background

The lithosphere is the outer shell of the Earth whose boundary is characterised by an abruptdecrease in shear-wave velocities at depths of around 100km. It is comprised of a strongbrittle upper crust, a weaker, more ductile lower crust, and the strong brittle uppermantle lithosphere with the total thickness increasing with age up to 400km in case of oldcontinental lithosphere. The Mohorovicic discontinuity (in short Moho) lies between thecrust and the upper mantle lithosphere and is a seismically defined boundary. The crust canbe either coupled or decoupled from the underlying mantle. If the lower crust deformsentirely in the brittle regime the crust is said to be coupled to the mantle, while if the lowercrust deforms entirely the ductile regime the crust is said to be decoupled from the mantle.Underlying the lithosphere is a weak zone in the upper mantle called the asthenosphere wherethe temperature gradient increases rapidly, and dehydration reactions and changes inmineralogical composition occur. The continental lithosphere is less dense and has a thickercrust than the oceanic lithosphere and is compositionally different.

During extension of the lithosphere, the crust and upper mantle lithosphere are stretched andextended. The way in which they deform is dependent on their rheological properties,pressure, temperature and strain conditions. When the lithospheric is extended hot mantle(asthenosphere) rises to the base of the thinned lithosphere to maintain isostatic equilibrium.The lithosphere cools, contracts, and, while the crust is thinned permanently, the upper mantlelithosphere returns to its original thickness over time. Extension may cease without a newocean basin being formed, creating a failed rift.

Properties to be considered when investigating the dynamics of the layers of the Earth includestress, strain, heat transfer, gravity, fluid mechanics and rock rheology. Many of theseare co-dependent and some simplifications are usually made for computation. Figure 1 showsa representative lithospheric strength profile (yield strength envelope), illustrating thedifferences in strength between continental lithospheric layers as a function of depth.

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Figure 1. Yield strength envelope for the continental lithosphere

StressStress σ is the internal resistance of a material to the distorting effects of an externalforce with units of force per unit area. Strain ε is the dimensionless ratio of change inlength to original length and describes the compressibility of a solid. In a fluid, the rate ofstrain

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˙ ε (velocity gradient) is related to the applied stress σ and the viscosity η (constant for agiven material) by the following

(1)

At laboratory temperatures and pressures, crustal rocks are brittle and behave elastically untilfailing by fracture. An idealised elastic-perfectly plastic rheology is the model used toapproximate the behaviour of ductile materials. Elastic deformation is linear until a yieldstress is reached and maintained whereon the material deforms plastically. Just below theMoho in figure 1 (35km), the straight edge of the yield envelope means the upper mantle(below 35 km) deforms in a brittle fashion. However, this is also strain-rate dependent, and inreality brittle deformation in the upper mantle only occurs when the strain rates are relativelyhigh, ie when the material is deformed relatively rapidly.

When temperatures reach a significant fraction of the melt temperature, atoms anddislocations in the crystal lattice become mobile enough resulting in creep. Dislocations areimperfections in the crystalline lattice structure and creep defines fluid behaviour over longtime scales. Even with a high viscosity, the crust is considered to behave like a fluid thatflows over geological time scales.

Newtonian flow assumes a simple linear relationship between stress and strain, the constantof proportionality being viscosity. As soon as the viscosity is no longer constant, for exampletemperature dependent, the flow is no longer strictly Newtonian. In particular, the viscosity ismodified during yielding, which makes it a function of stress, which breaks the linearrelationship, making it non-Newtonian. This behaviour can be approximated by a so-calledpower-law rheology (see strain weakening), or it can be modelled more realistically by

€

σ =η ˙ ε

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allowing inter-dependence of variables, as is done in Ellipsis. The rheological laws used inEllipsis include very complicated strain and strain-rate dependencies, making the constitutivelaws very non-linear, and effectively non-Newtonian.

One of the most important parameters is the strength ratio of the upper and lower crust, atleast in the absence of pre-existing weaknesses. Extension models are also sensitive tochanges in the ratio of the relative thicknesses of the upper and lower crust. In general,the brittle upper crust is the focus for much of the stress, which is localised in zones withlarge strength ratios. Small strength ratios cause more densely spaced and widely distributedfaulting.

To approximate the brittle behaviour in the strong upper crust overlying the weak ductilelower crust, a yield law, with a maximum shear stress τ yield, describes the stress profile offigure 1:

(2)

where c0 is the cohesion (yield stress at zero pressure), and cp is the pressure dependence ofthe yield stress, p is the pressure and

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˙ ε the strain rate. The relative strength of the upper andlower crust can be calculated by integration of equation (2), which is the area between 0 andthe maximum shear strength in figure 1.

Two different temperature dependent viscosity models can be used in Ellipsis: The complexArrhenius viscosity model and the simpler Frank-Kamenetskii approximation to theArrhenius viscosity. The Arrhenius viscosity (ηarr) is defined as,

nn

nan

arr TREExp

A

−•

×

×

×

=

111

1εη (3)

where A is a scaling factor, n is the stress exponent, Ea is the activation energy, R is theuniversal gas constant (8.314 J/mol.K), T is the temperature (K) and _ is the strain rate.

Here however, we will only use the Frank-Kamenetskii viscosity model, which is expressedas follows:

(4)

where η is the viscosity, T is the temperature (K) and η0 and T1 are constants.

By finding two values for viscosity (ηa and ηb) calculated at two different temperatures (Ta

and Tb) using the Arrhenius viscosity model you can solve the following equations to find theconstants η0 and T1 in the Frank-Kamenetskii viscosity approximation,

aTTaa eT 1

0)( −=ηη (5a)bTT

bb eT 10)( −=ηη (5b)

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τ yield = c0 + cp p( ) f ˙ ε ( )

( ) TTeT 10

−=ηη

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Strain Weakening

When a material is placed under high amounts of strain it can become weaker; this process istermed strain weakening. Strain weakening is implemented in Ellipsis using the power-lawfunction:

( )=εfa

a nε

εε ))(1(1

0−−

0

0

εε

εε

≥

< (4)

where ε is the accumulated plastic strain, ε0 is the saturation strain beyond which no furtherweakening takes place, εn is an exponent which controls the shape of the function and a is amaximum value of strain weakening beyond which no further weakening occurs. Figure 3shows strain weakening behaviour for various exponents (εn).

Fig 2. Strain weakening behaviour showing strength weakening from 100% to 20% after an accumulated strainof 0.5, after which no further weakening occurs. Dashed lines show the effect of the exponential parameter (En)

on the curve (see Equation 4).

Ellipsis Background and Download Information

Ellipsis is a modelling program that simulates large deformations of materials using a finiteelement method where the problem domain is represented using an Eulerian mesh, in whichLagrangian integration points are embedded. Ellipsis has been applied to study a number ofproblems, including two and three-dimensional lithospheric extension, mantle convectionmodelling with a visco-elastic/brittle lithosphere, folding in finely layered visco-elastic rockstructures, and the investigation of continental geotherms, heat flow and the survival ofcratonic lithosphere through geological time.

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Ellipsis is a freely available open source program, which can be downloaded from theGeoFramework site at the California Institute of Technology (www.geoframework.org).

Ellipsis has a long history of development, mainly driven by geodynamic modeller LouisMoresi, including not only Caltech, but also CSIRO and Monash University. Therefore,additional web pages with Ellipsis background information and examples can be found at:

http://www.mcc.monash.edu/twiki/view/Codes/EllipsisCodehttp://www.earthbyte.org/Resources/resources_ellipsis.html

Ellipsis runs on all unix-based computer operating systems (e.g. Linux, Mac OSX, SunSolaris, Windows (using cygwin), etc).

The Ellipsis Input File

The Ellipsis input file is a plain text file which defines all parameters we need to set up for anEllipsis run, ie material geometries, rheologies, boundary conditions, mesh and tracerdefinitions, and output variables. The file contains an enormous number of things that theprogram needs to know, but most of which don't concern us. Lines in the input file that startwith a hash mark (#) represent comments which are ignored by Ellipsis. In the following,those sections in the input file will be highlighted that you may need to alter for your modelruns. The initial sections are:

# GENERAL# ADVECTION-DIFFUSION PARAMETERS# SOLVER RELATED MATTERS# GRID POINTS

We won't have to change anything in these sections, they relate mostly to the resolution andaccuracy of the simulation. The first setup we need to look at is:

# OUTPUT FILES

The file is setup at the moment to give us four visual output files (in ppm file format – agraphics file format like jpg, bmp and gif), ie:

PPM_files=2

The output files will display distribution of temperature, stress and strain. We also need toextract some other data out of these models, as defined in:

# Specifications for graphical output files

We have pre-defined that we are outputting stress profiles at different points along the surface(-more on this later).

Ellipsis Graphical User Interface

In order to make the Ellipsis program easier to use, a graphical user interface (GUI) has beendeveloped here at the University of Sydney. Simulations using Ellipsis must be set up bycreating a text file, called an Ellipsis input file. These files contains a long list of parameters,

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in the format parameter name=parameter value. These parameter settings control all aspectsof the simulations, ranging from the types and locations of different materials in thesimulation, the rheological properties of those materials, parameters controlling how muchinformation Ellipsis should provide about the simulation as it executes as well as the typesand specifications of graphical output files. The parameter values can be numeric, or they canconsist of a text string. In addition, some parameters require lists of numbers or strings to bespecified.

Often groups of these parameters work together, so that it is necessary to ensure that they areconsistent with one another. For example, several parameters are used to define the materialspresent at the start of the simulation, and this is done by specifying regions of various shapes.For rectangular regions we have to define the locations of the top left and bottom right of eachregion, and which material the region consists of. Because we will normally have more thanone such region in a particular simulation, we must enter lists of coordinates, so that we haveone entry for each region. It is difficult to determine the layout of the regions from such lists,and when editing them, the user has to be careful to edit the correct number in each list. Thisbecomes increasingly complex as more regions, and more different region shapes are used.Clearly it would be preferable if such lists could be replaced with a GUI that would plot theregions graphically and allow new regions to be drawn using a mouse. Ellipsis GUIincorporates such a system, not only for material regions, but also for boundary conditionsand tracer regions, as well as providing support for rectangular, triangular and circularregions. The figure below illustrates the main window of the Ellipsis GUI showing thegeometrical editing capability of the GUI.

Figure 3. The visual editor pane of the GUI, showing four rectangular regions. The colour or grey-level in whicheach material appears in the GUI can be specified. Here material 0 (Air) is assigned a light blue colour, material1 (Upper crust) appears in gold, material 2 (Lower crust) appears in orange and material 3 (Mantle) appears in

red. On the left, the rectangle controls are showing, but these can be switched to show circle or triangle controls

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instead. On the right are the controls for defining and choosing materials, together with a list of all the materialregions. There are also controls, which allow individual material regions to be selected and then edited, or

deleted.

To run the Ellipsis GUI, copy the following directory (using cp -r) into your home directoryfrom /geo/services/teaching/geos3003/Prac_extension/ellipsisgui. After you have copied it,the GUI can be run using the command java –jar ellipsisgui.jar &. This will load the GUI andyou will see a window similar to that displayed in figure 3 above. To load an input file simplygo to File -> Load and select the input template you wish to edit.

To add a shape to the model, select the type of geometry you wish to add from the drop downmenu in the upper left of the visualisation window (rectangle, circle or triangle) and then clickand drag the mouse to add the shape. The shape that you add with be made from the currentlyselected material which appears in the drop down menu to the right of the visualisationwindow (Figure 3). To create a shape using a different material, simply select the materialyou wish to use from the drop down menu to the right before creating the shape.

In the Visual Editor window (Figure 3) you will see a window in the bottom right calledMaterial Regions. This windows shows all shapes currently defined in the model. You canmanually edit the boundaries of these shapes by clicking on them and altering theircoordinates. You may also delete shapes by clicking on them in the Material Regions windowand pressing delete.

Model Resolution

Resolution of models in Ellipsis is handled using a multigrid. This technique converges on asolution using a coarsely meshed model, and this solution is used as input for a more finelygridded mesh, which may contain even finer meshes, and that mesh may also contain severalmore nested meshes itself. This is a very computationally efficient method for solving highresolution problems. In Ellipsis input files, different levels relate to the resolution of the finiteelement mesh we are using to solve problem (Fig. 4).

Fig. 4. The meaning of levels in Ellipsis. In this example mgunitx=5 and mgunitz=3. Top: Level 0, 15elements, middle: level 1, 60 elements, bottom: level 2, 240 elements.

Our finite element grid also contains tracers, which can move around within the mesh. Theycarry information about the material properties. The more tracers we use, the higher theresolution of the material properties we can follow through the model run.

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Fig. 5. Tracer_density defined on the finest level. In this example tracer_density=4, meaning thereare four tracers/element both in the x and z direction. So in this case we have 260 elements * 16

tracers/element = 4160 tracers.

There is no hard and fast rule for how many mesh levels and tracers you should use in a givenmodel run. The finer the mesh and the larger the number of tracers, the longer the model runwill take. As consequence, a model run may take any time between just a few minutes toseveral days (of course the geological time period covered by the run, i.e. run-length, also hasan impact on the cpu-time consumed).

The number of particles of the materials (also known as tracers), which are tracked by thesimulation can be controlled by the user. Typically the number of tracers used will be fixedthroughout the simulation area, but if necessary the number of tracers in each part of thesimulation can be varied. The maintenance of a pretty high resolution is important for yoursimulations, which is why they may take a while. But, if for some reason they are taking anextremely long time, you can set mgunitx and mgunitz to less than 8 (e.g., 5) to make thingsrun more quickly. Reducing ‘levels’ from 3 to 2 will greatly speed it up, but is probably toogreat a sacrifice to the resolution. If the simulations are running fairly quickly, feel free to runthem for more increments (via the ‘maxstep’ parameter in the input file).

Boundary Conditions

Another factor that we have to build into the model is boundary conditions. A boundarycondition is the property of a field, either a temperate, pressure or velocity that is kept fixedthroughout the simulation, rather than being allowed to vary dynamically. These boundaryconditions can be at fixed locations, or moving, and the shape of the area to which theboundary condition applies can vary. Commonly they are set at the edges of the simulationarea, to reflect the properties of the neighbouring spaces. We should note that stress andvelocity boundary conditions cannot both occur on the same face of the simulationvolume, if both are also in the same direction, as these are not independent factors.However, it is possible to place orthogonal velocity and stress boundary conditions on thesame face of the simulation. By default, all velocities in a direction normal to a given face arezero, in order to avoid a mesh that expands.

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Exercise: Extension Modelling with Ellipsis

Your taskIn this exercise you will:

1) Evaluate the effect of changing the coupling between the lower crust and the mantleon the style of extension and basin formation during extension, based on Ellipsismodel run outputs I provide you with.

2) Run your own Ellipsis models (we aim for at least 4-6 runs) by focusing on two modelaspects of your choice as listed below:

a. Model with random noiseb. Model with many weak seed(s)

i. try changing the depth of the weak seed(s)ii. try changing the strain weakening parameters

c. Model with weak fault(s)i. try changing the angle of the fault(s)ii. try adding multiple faults

d. Coupled model with laterally varying crustal thicknesse. Test various models with different strain rates (extension velocities)

At the same time you may vary the coupling of the crust and mantle as desired. It isrecommended that you initially only alter one set of parameters, but in your lastcouple of model runs you should combine variations of parameters, eg have a coupleof preexisting faults and a thick lithospheric root somewhere in the model, or embedmaterial weaknesses in your model (other than faults), maybe representing a large saltdome or a hot/weak intrusion in the upper crust together with changing the speed ofextension. Our intention is to find out how the style of deformation and basinformation changes as a function of all these parameters (when do we get wide ornarrow, shallow or deep basins, when do we get magmatic or amagmatic, hot or coldbasins, etc etc).

3) Lastly I have provided you with a number of papers in pdf format in/geo/services/teaching/mars3006/Prac_extension/papers.

Depending on which combinations of parameters you choose you will find variouspapers where similar questions are discussed. Discuss your results based on thepapers of your choice (2-3) and make sure to include all references you have used intoa ref list in the end of your document. Convert all your movies into gif animations(see instructions below). Refer to your gif animations in your report but leave them asseparate files.

The following example (from Artyushkov et al., Tectonophysics 320, 271-310, 2000)illustrates the development of the Ural Mountains collision zone in the Paleozoic. The figureshows in cross-section how many different kinds of weak and strong crustal elements werejuxtaposed during plate collision. A real world question is: what happens when such aheterogenous crustal area is extended again some time later? What kind of basin(s) would weexpect to form?

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Running EllipsisCopy all the files from the course directory into your home directory into your homedirectory. The executable Ellipsis 2d version will be used in this practical exercise, and isinstalled on the School of Geosciences Linux system. It is executed simply by typing in acommand shell:

nohup nice -10 ellipsis2d inputfile &

Where inputfile corresponds to the name of a text input file. Try it with the extension.inputfile you just copied. The “nohup” command means “no hangup”. This means if youaccidentally close the command shell in which you have started this run, or even if you logout, Ellipsis will keep on running. This is important, as runs may take several hours. The“nice” command assigns an appropriate priority to your run, such that the computer does notget totally bogged down from your Ellipsis run.

When you run a program using the “nohup” command, all output that would normally bewritten to the screen will be written to a file called “nohup.out” in your working directory. Inorder to inspect the Ellipsis screen output as it is running, type:

tail –f nohup.out

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This will reproduce the screen output that Ellipsis would normally produce.

NOTE: Please only use the computer that has been assigned to you for running models.

A lot of weird stuff will scroll down the screen, but this is just normal diagnostics. Open upanother terminal and cd into the directory you left Ellipsis running in. You will eventuallynotice some files being created, and they look similar to the ones you looked at in theprevious section. There are the ppm image files, also our stress profiles (out_ext.***.profiles),and node_data (don't worry about these...). To do one simulation, it usually takes around 3hrsdepending on the machine, and its work load. Each of the following sections contains 3simulations to do (~9hrs total, but you just let the machine work overnight etc, ie start a newrun just before you leave the prac on any given day). You will only have to cover 2 sections,but these simulations will take a while (so make sure your input parameters are correct!!).You can edit the inputfile with any text editor such as abiword or gedit. I recommend a simpleeditor such as gedit. Make the changes, save your file (in a new directory!!! The output fileswill overwrite other things of the same name). Then run Ellipsis from that directory, have acoffee, and then check out your results. There are a number of questions for each section.You are required to run your models in its own directory on your scratch space, as theoutput takes up a lot of room. The scratch space is located in /geo/services/scratch

The following sections include a lot on the initial conditions for the model, and its boundaryconditions. The defaults are sensible to start with. For the initial extension simulation setupwe use a three-layer 2-dimensional model, including an upper crust, lower crust, and mantle(including the mantle lithosphere and asthenosphere). These material rectangles are defined inthe Ellipsis input template under the section:

# Material distributions

The extension.input file already contains a number of pre-exsiting weakness types andstructures defined in the template. You can use this file for a template for your own ellipsismodels. The extension.input contains a single weak seed placed in the upper mantle bydefault, defined as the 5th rectangle in the Material_rect=5 section. The template alsocontains a fault and random diffuse weaknesses defined under the headings Fault Triangleand Strain Triangles in the input file, however, these are commented out. If you wouldlike to use the weakness types defined in the model simply uncomment the relevant lines.These weaknesses have been included in the extension.input template really as a guide forhow to implement weaknesses of this type in Ellipsis.

1. Strength of the lower crust

Scroll down till you find the Material labelled:

#: Lower crust

The Lower Crust is Material 2. Find the viscosity parameters (Material_2_viscN0 andMaterial_2_viscT1). The viscosity is a measure of strength for rocks that flow ductilely.

## coupledMaterial_2_viscN0=8.985e5 ## N0 in viscosity modelsMaterial_2_viscT1=14.4 ## T1 in viscosity models

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## decoupled##Material_2_viscN0=3.696e+06 ## N0 in viscosity models##Material_2_viscT1=26 ## T1 in viscosity models

Note: these viscosities are non-dimensional, ie they have been scaled, along with everythingelse, to input into the simulation (see appendix for how to scale real world variables such aslength in km and time in millions of years, or extension speed in km/million years.)

You can alter the coupling of the crust to the mantle by changing the viscosity parameters ofthe lower crust. You can do this using the GUI or by altering the input file with a text editor.Altering the viscosity of the lower crust so that the lower crust deforms entirely the brittleregime couples the crust to the mantle, while altering the viscosity of the lower crust so thatthe lower crust deforms entirely the ductile regime decoupled the crust from the mantle,creating a decoupled system. To model a coupled system uncomment the “coupled” viscosityparameters, while to model a decoupled system uncomment the “decoupled” viscosityparameters.

Results from a simulation where the crust was coupled to the mantle and a weak seed wasplaced in the upper mantle can be found here:

http://www.geosci.usyd.edu.au/users/scott/Ellipsis/Publication_Data/Huisman-Models/Coupled/Single-Seed-ppm0.htm

The Ellipsis simulation templates are set up to produce two sets of image files, ending inppm0 and ppm1. As mentioned above, these files correspond to

ppm0 = temperature and strain localization (shaded in blue)ppm1 = temperature only

The "ppm1" output equivalent to the model link above can be found at:

http://www.geosci.usyd.edu.au/users/scott/Ellipsis/Publication_Data/Huisman-Models/Coupled/Single-Seed-ppm1.htm

and the equivalent movies can be viewed here:

http://www.geosci.usyd.edu.au/users/scott/Ellipsis/Publication_Data/Huisman-Models/Coupled/movies/coupled/level5/single/coupled-hf-single-seed-huisman.00095-ppm0-8.7Ma-level5.gif

To look at ppm0 and ppm1 images that you produce with your model runs, type:

display filename.ppm0 &

where you need to replace filename with the actual name of your file

To see an animation of a series of figures, type:

animate out*ppm0 &

(or ppm1 depending on what you want to look at).

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How does the spacing of faults vary with different strength lower crust (ie.coupled/decoupled)? From your output images, where is the extension actually occurring(hint: look at the blue regions in ppm0)? How does the lower crustal viscosity affect thedistribution of faulting?

We also want to look at what the stress profiles look like using MATLAB. Copy the filesprofile.m and hdrload.m to the directory with your Ellipsis output. Start MATLAB by typing:

matlab &

Run the profile plotting script by typing profile into the MATLAB command prompt.

2. Distribution of faults

The examples so far have had one pre-existing weakness in the system, to act as a nucleus fordeformation. How does the distribution of faulting control the dynamics of extension? Doesthe extension occur along the original faults for the entire length of the simulation? Or do thefaults just act as seed points? Does the system readjust itself if the faults cannot accommodatethe extension?

Try adding faults (using the triangle geometry) with different dips to the model. Theextension.input file already contains one fault inclined at 45˚ in the center of the model whichis commented out. This fault is defined in:

Material_trgl=1 Material_trgl_vert=3 Material_trgl_property=4

Material_trgl_x1=1.3833 Material_trgl_z1=0.3000 Material_trgl_x2=1.6167

Material_trgl_z2=0.0667Material_trgl_x3=1.6167Material_trgl_z3=0.0867

Here the triangle is defined by 3 vertices, which each have an x and z position. The weaknessof the fault is defined by the rheological properties of Material 4. To add more faults, use theGUI to include more triangular weaknesses or alter the input file by hand.NOTE: When using the GUI to add materials make sure that the new materials are alignedwith the boundaries of existing ones (eg. Do not extend a fault above the surface of the uppercrust into the air!).

3. Distributed Material weakness

Uniformly distributed random weaknesses can be included in the model in two ways. Theycan be included simply by uncommenting the appropriate lines in the input file, highlighted inred below.

## Strain Triangles - Uncomment the below lines to include random weakseeds uniformly distributed through the crust

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##Strain_trgl=40##Strain_trgl_value=1,1,1,…##Strain_trgl_x1=0.99,1.98,0.63,…##Strain_trgl_z1=0.18,0.20,0.10,…##Strain_trgl_x2=1.02,2.01,0.66,…##Strain_trgl_z2=0.21,0.23,0.13,…##Strain_trgl_x3=0.96,1.96,0.60,…##Strain_trgl_z3=0.21,0.23,0.13,…##Strain_trgl_mag=0.50,0.50,0.50,…

You can also include random weakness in your model by using the GUI to include manyrandom shapes of Material 4 in your model (Note: since the GUI does not yet allow you todefine regions of pre-strained material).

In model runs with random weakness seedpoints, is strain localised at all weak seedpoints, ornot? If not, how is strain distributed?

4. Intrusions/ Seeds

To include an intrusion in your model use the GUI to place a rectangular block at variousdepths within the lithosphere. Using Material 4 in the GUI, simply select the rectangle shapeoption and draw a small rectangle.

What happens as you change the depth of the seed in your model? How does the distributionof faults change with an intrusion in the mantle? Does it affect the stress field? Where is strainoccuring now?

5. Thick lithospheric roots

We want to simulate the effect of a thick lower crust in one region. We do this by altering thestrength of the continental crust or by altering the temperature of regions of the model. Youcan test to see what effects altering material and thermal properties have on the strengthenvelope of your lithosphere by playing with the Matlab script ellispis_prac_scale.m. Afterdeciding which material properties you which to edit you can create a new material and add itto your model using the GUI or by editing the text input file.

What is the effect of this thickening the crust? Now try a thinner crust in one area by adding asmall rectangle of mantle material (Material 4) at the base of the lower crust in your model.

How is having a thinner crust different from having a thicker? Is the resulting crust strongeror weaker? How does this affect deformation?

6. Extension rates

The extension rate of the simulation is currently 4.5 x 10-10 m/s, which is equivalent to anextension rate of 14cm/year (this is defined in the Ellipsis input template by the BCmoveX1vvariable). Try changing the velocity in the model. Using the GUI go to the BoundaryConditions option in the Visual Editor window and click the Boundary Settings button, whereyou will be able to alter the extension velocity of the right face of the model.

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How does the style of deformation vary? Are the stresses greater or less? Is thestrain/deformation more or less localised? Does any layer preferentially deform more?

Gif AnimationsTo make a gif animation of a set of ppm output files (you will have 2 sets of ppm files foreach model run, ending with ppm0 and ppm1:

ppm2gif.mk 0

Will run a script to take all files in your working directory ending with ppm0 and turn theminto a gif animation, whereas

ppm2gif.mk 1

will do the same for all files ending with ppm1 etc.

Recommended Reading for Extension ModellingDyksterhuis, S., Rey, P., Müller, R.D., and Moresi, L. in press, Initial Weakness Controls on Rift

Architecture: Implications for the Iberian-Newfoundland Margin, in: MARGINS Theoretical andExperimental Earth Science, eds: Karner, G., Manatschal, G. and Pinheiro, L., ColumbiaUniversity Press.

Harry amd Grandell, in press, A Dynamic Model of Rifting Between Galicia Bank and Flemish CapDuring Opening of the North Atlantic Ocean, in: MARGINS Theoretical and ExperimentalEarth Science, eds: Karner, G., Manatschal, G. and Pinheiro, L., Columbia University Press.

Gartrell, A.P., 2000, Rheological controls of extensional styles and the structural evolution of theCarnarvon Basin, Northwest Shelf, Australia, Australian Journal of Earth Sciences, 47, 231-244.

Lavier and Manatschal, 2006, A mechanism to thin the continental lithosphere at magma-poormargins, Nature, 440, 324-328.

Manatschal, 2004, New models for evolution of magma-poor rifted margins based on a review of dataand concepts from West Iberia and the Alps, International Journal of Earth Sciences, 93, 432-466.

Michon, L. and Merle, O., 2003, Mode of lithospheric extension: conceptual models from analoguemodelling, Tectonics, 22 (4).

Wijns et al., 2005, Mode of crustal extension determined by rheological layering, Earth and PlanetaryScience Letters, 236, 120-134.

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Appendix – Non-Dimensional ScalingThe Ellipsis model input parameters are scaled from real world values into dimensionless values in order tominimise computation time and increase the accuracy of the solution. We use the non-dimensional scalingapproach given by:

SN= E Equation (1)

where E is a dimensionless Ellipsis variable, N is the dimensional real world parameter and S is a dimensionalscaling factor.

Scaling from real model length dimensions of 450km wide by 150km deep is done using a length scaling factor(SL) of 1.5 x 105 m resulting in non-dimensional model geometry of 3 units wide by 1 unit deep.

Using a Thermal diffusivity scaling factor (Sκ) of 1 x 10-6 a time scaling factor (St) can be found using:

κSSS Lt2= Equation (2)

With a viscosity scaling factor (Sη) of 1 x 1021 Pa and a gravity scaling factor (Sg) of 1 m/s2, a density scalingfactor (Sρ) can be found:

ηρ S

SSSS tLg ××

= Equation (3)

Using a velocity scale (Su) defined by:

tLu SSS = Equation (4)

a non-dimensional velocity of 67.5 is calculated to achieve a real world strain rate of 1e-15s-1 over the length ofthe model.

Temperature is scaled between non-dimensional values of 0.17 and 1 corresponding to temperatures of 273Kand 1603K respectively using a temperature scale (ST) of 1603K.

For more in-depth information concerning scaling please consult the M A T L A B scaling script

ellispis_prac_scale.m.