[CIG-SHORT] Problem setting initial conditions
Charles Williams
willic3 at gmail.com
Wed Feb 12 12:47:08 PST 2014
Hmm. I guess we don’t include initial strain or initial stress as info fields. I’m not sure if we should include them or not.
Cheers,
Charles
On 13/02/2014, at 9:21 am, Oliver Boyd <olboyd at usgs.gov> 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
>>>>>>>> mailing list CIG-SHORT at geodynamics.org
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>>>>>>>
>>>>>>>
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>>>>>>>
>>>>>>
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>>>>>
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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
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C.Williams at gns.cri.nz
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