[CIG-SHORT] Problem setting initial conditions

[Oliver Boyd]

I'll be happy to help when you're ready to do so.

On 2/12/14 3:23 PM, "Brad Aagaard" <baagaard at usgs.gov> wrote:

>Oliver,
>
>Sorry, I thought this was implemented. I looked at the code more closely
>and it looks like there are a few pieces missing to output the
>initial_strain and initial_stress fields. I will add it to our
>short-term todo list.
>
>I also think we need to setup a test case for this use case, because we
>have not tested what you are trying to do.
>
>Regards,
>Brad
>
>
>On 02/12/2014 12:21 PM, Oliver Boyd wrote:
>> When I attempt to add initial_strain to the cell_info_field, Pylith
>>tells
>> me for the elastic material that the acceptable values are 'mu' 'lambda'
>> 'density' 'stable_dt_implicit' 'stable_dt_explicit' and for the
>> viscoelastic material, 'mu' 'lambda' 'density' 'stable_dt_implicit'
>> 'stable_dt_explicit' 'maxwell_time'. But with respect to your comments,
>>I
>> can see why I would get zero total_strain in the output of problem 2 if
>> it's only outputting the gradients in the displacements. And I expect
>>then
>> that If I added initial_strain to total_strain from problem 2, it would
>> equal total_strain from problem 1. I guess then that the only thing
>>that's
>> different between the two problems is displacement, which it doesn't
>> appear that I'll be able to fix if I want to change the boundary
>>condition
>> on the fault.
>>
>> Thanks again for your help,
>> Oliver
>>
>> On 2/11/14 3:51 PM, "Brad Aagaard" <baagaard at usgs.gov> wrote:
>>
>>> On 02/11/2014 01:52 PM, Oliver Boyd wrote:
>>>> If I turn off the elastic prestep phase and keep total_time = 0, I
>>>> get no stress or strain written to the hdf5 material files. If I
>>>> increase total_time to 1 yr, I get essentially the same results as
>>>> using the elastic prestep and total_time = 0, which is to say that I
>>>> can match the stress in the material and tractions on the fault, but
>>>> I can't match the strain in the material.
>>>>
>>>> I'm not sure I understand your question regarding output.
>>>>
>>>> If you mean adding initial strain to what I get from running problem
>>>> 2, then yes, the strain resulting from problem 1 is the same as
>>>> adding the initial strain to the output of problem 2. That's because
>>>> in every case I've tried, the strain output from problem 2 is close
>>>> to zero.
>>>
>>> In the output, we are are currently dumping the strains computed from
>>> the gradients in the displacement field. We are not dumping
>>> initial_strain + gradient in the displacement field (what you want to
>>> use in your comparison when you run the full problem without breaking
>>>it
>>> into pieces).
>>>
>>>> If you mean including initial strain in the hdf5 output, I'm not
>>>> sure how to add initial strains to the output. I thought my options
>>>> were cell_data_fields = [total_strain,stress] for elastic materials
>>>> and cell_data_fields = [total_strain,viscous_strain,stress] for
>>>> viscoelastic.
>>>
>>> Note that this is the *info* fields (for parameters, initial
>>>conditions,
>>> etc), not the *data* fields (for solution stuff).
>>>
>>> cell_info_fields = [initial_strain]
>>>
>>> Brad
>>>
>>>>
>>>>
>>>>
>>>> On 2/11/14 2:05 PM, "Brad Aagaard" <baagaard at usgs.gov> wrote:
>>>>
>>>>> Oliver,
>>>>>
>>>>> Did you try turning off the elastic prestep phase?
>>>>>
>>>>> [pylithapp.timedependent] elastic_prestep = False
>>>>>
>>>>> Are the strains the same if you add the initial strain to the
>>>>> output strains? It might be an output issue rather than a setup
>>>>> issue.
>>>>>
>>>>> Brad
>>>>>
>>>>> On 02/11/2014 01:01 PM, Oliver Boyd wrote:
>>>>>> Hi Brad, Yes, that's exactly what I was trying to do, i.e. make
>>>>>> the solution the same at the first time step, but I haven't been
>>>>>> able to match the strains between problem 1 and 2, maybe because
>>>>>> of the elastic prestep phase. I guess I'll have to solve my
>>>>>> problem some other way.
>>>>>>
>>>>>> Thanks again, Brad and Charles, for your help. Oliver
>>>>>>
>>>>>> On 2/10/14 5:05 PM, "Brad Aagaard" <baagaard at usgs.gov> wrote:
>>>>>>
>>>>>>> Oliver,
>>>>>>>
>>>>>>> If you use the same boundary conditions in problems 1 and 2
>>>>>>> and get the same answer in both problems, then your setup with
>>>>>>> initial stress and strain is working properly for problem 2.
>>>>>>> If you want to break up a simulation into pieces so that you
>>>>>>> can solve something different, then your starting point for the
>>>>>>> new simulations should be consistent with where you left off.
>>>>>>> In other words, you can replace the BC and fault conditions,
>>>>>>> etc to change the problem but you need to make sure the
>>>>>>> solution is the same at the first time step.
>>>>>>>
>>>>>>> With a purely elastic material, the stress and strain in the
>>>>>>> domain are irrelevant so you only need to transfer the fault
>>>>>>> tractions (as in examples/2d/subduction/step04). For any bulk
>>>>>>> rheologies with state variables (viscous strain), you may be
>>>>>>> out of luck for right now as we have not implemented a way to
>>>>>>> specify initial state variables for bulk constitutive models.
>>>>>>>
>>>>>>> We recognize that we are getting greater interest in setting
>>>>>>> up these types of complicated simulations, where a user wants
>>>>>>> to take the output of one simulation and use pieces from it as
>>>>>>> input to another simulation. Implementing this right now
>>>>>>> doesn't make sense, because we are about to reorganize a bunch
>>>>>>> of top-level stuff to support multi-physics stuff. As we
>>>>>>> reorganize things it will make sense to set things up so that
>>>>>>> we can swap out the "elastic prestep" phase with an "initial
>>>>>>> condition" phase or a "restart phase" to support this feature.
>>>>>>> The new functionality probably wouldn't be implemented right
>>>>>>> away but we will be able to add it or someone else could add
>>>>>>> it relatively easily.
>>>>>>>
>>>>>>> Regards, Brad
>>>>>>>
>>>>>>>
>>>>>>> On 02/10/2014 08:29 AM, Oliver Boyd wrote:
>>>>>>>> Hi Charles, If I do as you suggest and apply identical
>>>>>>>> boundary conditions in problem 2 as in problem 1 and apply
>>>>>>>> both the initial stresses and strains from problem 1, I get
>>>>>>>> the same output (from visual inspection) from problem 2 as
>>>>>>>> from problem 1. Now I'd like to change the boundary
>>>>>>>> conditions on the fault in problem 2. I want to lock the
>>>>>>>> upper part of the fault and allow the lower to continue to
>>>>>>>> slip in response to the stresses induced by the earthquake
>>>>>>>> in problem 1. At this point, it seems to me that in order to
>>>>>>>> be able to change the boundary conditions on the fault (and
>>>>>>>> perhaps outer boundaries), I'd have to specify both
>>>>>>>> initial_stress and initial displacements within the
>>>>>>>> material? Alternatively, if I have to do this in a single
>>>>>>>> simulation, I could use rate-and-state friction and an
>>>>>>>> earthquake cycle. Ultimately, I might do this, but it could
>>>>>>>> take a complex model a while to run.
>>>>>>>>
>>>>>>>> Oliver
>>>>>>>>
>>>>>>>> On 2/9/14 3:57 PM, "Charles Williams" <willic3 at gmail.com>
>>>>>>>> wrote:
>>>>>>>>
>>>>>>>>> Hi Oliver,
>>>>>>>>>
>>>>>>>>> If you look in the material section of the manual it
>>>>>>>>> explains how initial stresses and strains work.  In a
>>>>>>>>> generic way, the stress is generally computed as:
>>>>>>>>>
>>>>>>>>> stress = material_matrix * (strain - initial_strain) +
>>>>>>>>> initial_stress
>>>>>>>>>
>>>>>>>>> That means that if you have identical boundary conditions
>>>>>>>>> for the two problems, if all of the stress were purely
>>>>>>>>> elastic, your computed stress would just be equal to the
>>>>>>>>> initial stress (the strain would cancel with the initial
>>>>>>>>> strain and not generate any stress).  Since you have some
>>>>>>>>> viscous strain, this won't be quite the case, but I'm
>>>>>>>>> guessing it won't be too far off.  Unfortunately, we don't
>>>>>>>>> yet make use of the other state variables (e.g., viscous
>>>>>>>>> strain), or we could also take that into account.
>>>>>>>>>
>>>>>>>>> Have you tried the following:
>>>>>>>>>
>>>>>>>>> 1.  Apply identical BC for the two problems. 2.  Use both
>>>>>>>>> initial stress and initial strain from problem 1 for
>>>>>>>>> problem 2.
>>>>>>>>>
>>>>>>>>> You should end up with stresses that are pretty much the
>>>>>>>>> same as what you had in problem 1.  The strains will also
>>>>>>>>> look very similar at the beginning, because the computed
>>>>>>>>> strains don't include initial strains. Strains are
>>>>>>>>> computed purely from displacements, and are independent of
>>>>>>>>> the material model.
>>>>>>>>>
>>>>>>>>> Let me know if this helps.  In the meantime, I think I'll
>>>>>>>>> have a look at including all the initial state variables.
>>>>>>>>>
>>>>>>>>> Cheers, Charles
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>> On 10/02/2014, at 11:10 am, Oliver Boyd <olboyd at usgs.gov>
>>>>>>>>> wrote:
>>>>>>>>>
>>>>>>>>>> Hi Charles, Thanks for the suggestion. Yes, the initial
>>>>>>>>>> conditions are different between the two problems. In
>>>>>>>>>> the first, everything is driven by the boundaries. In
>>>>>>>>>> the second, I wanted everything driven internally. The
>>>>>>>>>> initial material stresses and strains in the second
>>>>>>>>>> simulation result from the first simulation. If I keep
>>>>>>>>>> the surficial driving boundary conditions and add
>>>>>>>>>> internal stresses, the resulting material stresses
>>>>>>>>>> double. I tried your suggestion of leaving one of the
>>>>>>>>>> side boundaries free, but it produces very similar
>>>>>>>>>> results.
>>>>>>>>>>
>>>>>>>>>> It also appears that strains are determined by surficial
>>>>>>>>>> boundary conditions while initial stresses are
>>>>>>>>>> determined by db_initial_stresses and db_initial_strains.
>>>>>>>>>> When I specify db_initial_strain, it appears that it's
>>>>>>>>>> converted to stress and then added to db_initial_stress.
>>>>>>>>>> So I'm not sure I'll be able to pass the state from one
>>>>>>>>>> simulation to another.
>>>>>>>>>>
>>>>>>>>>> Do you know where in the code it reads in
>>>>>>>>>> db_initial_strain and where it might convert it to
>>>>>>>>>> stress. Do you think I'd be able to get it to assign
>>>>>>>>>> db_initial_strain to the strain field?
>>>>>>>>>>
>>>>>>>>>> Thanks for your help, Oliver
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> On 2/9/14 1:30 PM, "Charles Williams"
>>>>>>>>>> <willic3 at gmail.com> wrote:
>>>>>>>>>>
>>>>>>>>>>> Sorry for being slow to respond to this, Oliver.  I
>>>>>>>>>>> haven't gone through everything in detail, but one
>>>>>>>>>>> thing I noticed is that your boundary conditions on
>>>>>>>>>>> the external boundaries are different for the two
>>>>>>>>>>> problems, which means that you won't be able to get
>>>>>>>>>>> the same stress/strain state for the two cases.  One
>>>>>>>>>>> possible solution would be to leave one boundary free.
>>>>>>>>>>> I'm not sure if this will work or not, but it's
>>>>>>>>>>> probably worth a shot.
>>>>>>>>>>>
>>>>>>>>>>> Cheers, Charles
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> On 8/02/2014, at 6:50 am, Oliver Boyd
>>>>>>>>>>> <olboyd at usgs.gov> wrote:
>>>>>>>>>>>
>>>>>>>>>>>> Hi Brad, Attached are some figures illustrating what
>>>>>>>>>>>> I mean. In step1Kin, I use Dirichlet boundary
>>>>>>>>>>>> conditions on the domain edges and specified 100 cm
>>>>>>>>>>>> of fault slip on the fault. This generates stresses
>>>>>>>>>>>> and strains in the materials and tractions on the
>>>>>>>>>>>> fault as depicted in the figure step1Kin.png. If I
>>>>>>>>>>>> let this simulation run, the viscoelastic layer will
>>>>>>>>>>>>   relax. But I'd like to change the conditions on the
>>>>>>>>>>>> fault surface. So as a first step, I wanted to
>>>>>>>>>>>> transfer the stresses and strains to step2Kin and
>>>>>>>>>>>> let them relax. In step2Kin, domain boundaries and
>>>>>>>>>>>> fault surface initial displacement is zero. I am
>>>>>>>>>>>> hoping to get step1Kin and step2Kin to show the same
>>>>>>>>>>>> results after 200 years. But they don't. There is the
>>>>>>>>>>>>   expected relaxation in step1Kin, but there is no
>>>>>>>>>>>> relaxation in step2Kin. When I first transferred
>>>>>>>>>>>> just the stress through db_initial_stress and looked
>>>>>>>>>>>> at the stresses, strains, and tractions,
>>>>>>>>>>>> step2Kin_stressini.png, I figured I only needed to
>>>>>>>>>>>> transfer over the strains to make it look like
>>>>>>>>>>>> step1Kin and everything would proceed as expected.
>>>>>>>>>>>> But I haven't figured out how to transfer the
>>>>>>>>>>>> strains properly. When I attempt to transfer both the
>>>>>>>>>>>>   stresses and strains, They appear to be working
>>>>>>>>>>>> against each other.
>>>>>>>>>>>> (step2Kin_stress_strain_ini.png).
>>>>>>>>>>>>
>>>>>>>>>>>> Oliver
>>>>>>>>>>>>
>>>>>>>>>>>> On 2/6/14 4:45 PM, "Brad Aagaard"
>>>>>>>>>>>> <baagaard at usgs.gov> wrote:
>>>>>>>>>>>>
>>>>>>>>>>>>> Oliver,
>>>>>>>>>>>>>
>>>>>>>>>>>>> For the db_initial_strain, you are correct in that
>>>>>>>>>>>>> the values in the spatial database are strain-xx,
>>>>>>>>>>>>> etc.
>>>>>>>>>>>>>
>>>>>>>>>>>>> I don't know what you mean by "seeing the initial
>>>>>>>>>>>>> strain field being set". You can ask for the
>>>>>>>>>>>>> "initial_strain" field to be written as one of the
>>>>>>>>>>>>> cell info fields to check to make sure it is read
>>>>>>>>>>>>> in and matches what you expect the spatial
>>>>>>>>>>>>> database to produce. It does look like we may not
>>>>>>>>>>>>> be including the initial strain in the
>>>>>>>>>>>>> "total_strain" output field. Is this what you mean
>>>>>>>>>>>>> by "not seeing the initial strain field being set"
>>>>>>>>>>>>> or are you seeing the initial strain field not
>>>>>>>>>>>>> affecting the solution in the way you expect?
>>>>>>>>>>>>>
>>>>>>>>>>>>> Brad
>>>>>>>>>>>>>
>>>>>>>>>>>>> On 02/03/2014 09:04 AM, Oliver Boyd wrote:
>>>>>>>>>>>>>> Hi Brad, Thanks for your help. I had initially
>>>>>>>>>>>>>> tried using db_initial_strain as well as several
>>>>>>>>>>>>>> of other things. I did as you suggested below,
>>>>>>>>>>>>>> but do not see the initial strain field being
>>>>>>>>>>>>>> set after running step2Kin. Thanks for reminding
>>>>>>>>>>>>>> me of the use of --component.help. I was trying
>>>>>>>>>>>>>> to figure out what variables I needed to set in
>>>>>>>>>>>>>> db_initial_strain. Based on the manual I thought
>>>>>>>>>>>>>> it was strain-xx Š, but I wasn't sure. I thought
>>>>>>>>>>>>>> I might be able to get to it with
>>>>>>>>>>>>>> help-properties, but I still haven't figured that
>>>>>>>>>>>>>> out. In any case, I'm still doing something
>>>>>>>>>>>>>> wrong.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Thanks again for your help, Oliver
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> On 2/2/14 11:07 AM, "Brad Aagaard"
>>>>>>>>>>>>>> <baagaard at usgs.gov> wrote:
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Oliver,
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> There are separate spatial databases for
>>>>>>>>>>>>>>> initial stress and initial strain.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> [pylithapp.timedependent.materials.upper_crust]
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>> db_initial_stress = spatialdata.spatialdb.SimpleDB
>>>>>>>>>>>>>>> db_initial_stress.label = Initial stress in
>>>>>>>>>>>>>>> upper crust
>>>>>>>>>>>>>>> db_initial_stress.iohandler.filename =
>>>>>>>>>>>>>>> spatialdb/afterslip_stress_uppercrust.spatialdb
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>> db_initial_stress.query_type = nearest
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> # ADD db_initial_strain db_initial_strain =
>>>>>>>>>>>>>>> spatialdata.spatialdb.SimpleDB
>>>>>>>>>>>>>>> db_initial_strain.label = Initial strain in
>>>>>>>>>>>>>>> upper crust
>>>>>>>>>>>>>>> db_initial_strain.iohandler.filename =
>>>>>>>>>>>>>>> spatialdb/afterslip_strain_uppercrust.spatialdb
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>> db_initial_strain.query_type = nearest
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Remember you can use pylith --COMPONENT.help
>>>>>>>>>>>>>>> and --COMPONENT.help-properties and
>>>>>>>>>>>>>>> --COMPONENT.help-components to interrogate
>>>>>>>>>>>>>>> what properties and components are available.
>>>>>>>>>>>>>>> In this case COMPONENT would be
>>>>>>>>>>>>>>> timedependent.materials.upper_crust.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> pylith step1Kin.cfg
>>>>>>>>>>>>>>> --timedependent.materials.upper_crust.help-components
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>> facilities of 'elasticisotropic3d':
>>>>>>>>>>>>>>> db_initial_state=<component name>: Database
>>>>>>>>>>>>>>> for initial state variables. current value:
>>>>>>>>>>>>>>> 'nullcomponent', from {default} configurable
>>>>>>>>>>>>>>> as: nullcomponent, db_initial_state
>>>>>>>>>>>>>>> db_initial_strain=<component name>: Database
>>>>>>>>>>>>>>> for initial strain. current value:
>>>>>>>>>>>>>>> 'nullcomponent', from {default} configurable
>>>>>>>>>>>>>>> as: nullcomponent, db_initial_strain
>>>>>>>>>>>>>>> db_initial_stress=<component name>: Database
>>>>>>>>>>>>>>> for initial stress. current value:
>>>>>>>>>>>>>>> 'nullcomponent', from {default} configurable
>>>>>>>>>>>>>>> as: nullcomponent, db_initial_stress
>>>>>>>>>>>>>>> db_properties=<component name>: Database for
>>>>>>>>>>>>>>> physical property parameters. current value:
>>>>>>>>>>>>>>> 'simpledb', from {default} configurable as:
>>>>>>>>>>>>>>> simpledb, db_properties output=<component
>>>>>>>>>>>>>>> name>: Output manager for elastic material
>>>>>>>>>>>>>>> information. current value:
>>>>>>>>>>>>>>> 'outputmatelastic', from {default} configurable
>>>>>>>>>>>>>>> as: outputmatelastic, output
>>>>>>>>>>>>>>> perf_logger=<component name>: Performance and
>>>>>>>>>>>>>>> memory logging. current value: 'memory_logger',
>>>>>>>>>>>>>>> from {default} configurable as: memory_logger,
>>>>>>>>>>>>>>> perf_logger quadrature=<component name>:
>>>>>>>>>>>>>>> Quadrature object for numerical integration.
>>>>>>>>>>>>>>> current value: 'quadrature', from {default}
>>>>>>>>>>>>>>> configurable as: quadrature
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Brad
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> On 1/31/14 11:26 AM, Oliver Boyd wrote:
>>>>>>>>>>>>>>>> Hello, I'm trying to generate a set of
>>>>>>>>>>>>>>>> initial conditions in one problem and then
>>>>>>>>>>>>>>>> use them in another. The first problem
>>>>>>>>>>>>>>>> calculates the stress changes due to an
>>>>>>>>>>>>>>>> earthquake. Currently, the second problem
>>>>>>>>>>>>>>>> only looks at the viscoelastic response
>>>>>>>>>>>>>>>> (which of course can be done in the first
>>>>>>>>>>>>>>>> problem). Once I get the viscoelastic
>>>>>>>>>>>>>>>> response in the second problem to equal the
>>>>>>>>>>>>>>>> first (if I let the first progress through
>>>>>>>>>>>>>>>> time), I will change the fault interface
>>>>>>>>>>>>>>>> model, but this is not yet implemented.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> I'm able to transfer over the initial stress
>>>>>>>>>>>>>>>> through db_initial_stress but I don't know
>>>>>>>>>>>>>>>> how to transfer the initial strain. I've
>>>>>>>>>>>>>>>> tried putting the initial strain in the
>>>>>>>>>>>>>>>> db_initial_stress.iohandler.filename file
>>>>>>>>>>>>>>>> with the components given by p71 of the
>>>>>>>>>>>>>>>> manual, but they don't appear to have an
>>>>>>>>>>>>>>>> effect when I run the simulation. Attached
>>>>>>>>>>>>>>>> are the files needed for the simulation.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Thanks for your assistance, Oliver
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Flow pylith step1Kin.cfg python
>>>>>>>>>>>>>>>> afterslip_initial_parms.py pylith
>>>>>>>>>>>>>>>> step2Kin.cfg
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> _______________________________________________
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
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>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
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>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
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>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
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>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>> <step2Kin_stress_strain_ini.png><step2Kin_stressini.png><step1Kin.p
>>>>>>>>>>>> ng
>>>>>>>>>>>>> <
>>>>>>>>>>>> st
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> 
>>>>>>>>>>>>ep2Kin.cfg><step1Kin.cfg>______________________________________
>>>>>>>>>>>>__
>>>>>>>>>>>> __
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>
>>> __
>>>>>>>>>>>> __ _ CIG-SHORT mailing list CIG-SHORT at geodynamics.org
>>>>>>>>>>>>
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>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>
>>> Charles A. Williams
>>>>>>>>>>> Scientist GNS Science 1 Fairway Drive, Avalon PO Box
>>>>>>>>>>> 30368 Lower Hutt  5040 New Zealand ph (office):
>>>>>>>>>>> 0064-4570-4566 fax (office): 0064-4570-4600
>>>>>>>>>>> C.Williams at gns.cri.nz
>>>>>>>>>>>
>>>>>>>>>>> _______________________________________________
>>>>>>>>>>> CIG-SHORT mailing list CIG-SHORT at geodynamics.org
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>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>>
>>> _______________________________________________
>>>>>>>>>> CIG-SHORT mailing list CIG-SHORT at geodynamics.org
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>>>>>>>>>
>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>> Charles A. Williams
>>>>>>>>> Scientist GNS Science 1 Fairway Drive, Avalon PO Box 30368
>>>>>>>>>   Lower Hutt  5040 New Zealand ph (office): 0064-4570-4566
>>>>>>>>> fax (office): 0064-4570-4600 C.Williams at gns.cri.nz
>>>>>>>>>
>>>>>>>>> _______________________________________________ CIG-SHORT
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>>>>>>>>
>>>>>>>>
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