[CIG-SHORT] Benchmark Pylith with viscoelastic analytic solution for a pressurized sphere

[Matthew Knepley]

On Tue, Sep 27, 2016 at 10:32 AM, Francisco Delgado <fjd49 at cornell.edu>
wrote:

> HI James, thanks for your feedback. Do you have examples of how to
> implement the viscoelastic model with Pylith. So far increasing the number
> of nodes does not provide a data fit for the analytic solution of a very
> small pressurised sphere.
>

Did you check that the PyLith solution converges with the correct rate (2nd
order) to some solution? even if its not your analytic.

   Matt


> Thanks
>
> On Tue, Sep 27, 2016 at 2:24 AM, James Daniel Paul Moore (Dr) <
> james.moore at ntu.edu.sg> wrote:
>
>> Hi Francisco,
>>
>> converse to Charles’ point about a refined mesh, you might also want to
>> note that the solution presented in Paul’s book is an approximate solution
>> for a half-space. The error term is of order (R_2/d)^3, where R_2 is the
>> total radius of the chamber plus the outer deformable shell. When we
>> applied a very similar model to the magma chamber at Santorini we only
>> found an error of 1% from using an analytical solution (1, sup S4). Your
>> disagreement appears to be about 2.4% and could correspond to R_2/d ~ 0.28,
>> though that seems a little high.
>>
>> all the best,
>>
>> James
>>
>> 1) http://onlinelibrary.wiley.com/doi/10.1002/2014JB011540/full
>> #footer-support-info
>>
>>
>> On 27 Sep 2016, at 06:01, Charles Williams <willic3 at gmail.com> wrote:
>>
>> Hi Francisco,
>>
>> Does the analytical solution include the initial elastic solution, and
>> are you also using this in PyLith (I believe it is the default)?  Another
>> possible issue is to make sure that your definition of viscosity is the
>> same for the analytical and numerical solutions.  There is a factor of two
>> that sometimes appears (look at the viscosity definitions in the PyLith
>> manual and Paul’s book).
>>
>> Cheers,
>> Charles
>>
>> p.s.  Also, what are the dimensions of the cavity compared to the depth?
>> If this ratio is large, you will probably need a very refined mesh to
>> accurately capture the solution.
>>
>>
>> On 27/09/2016, at 9:52 AM, Francisco Delgado <fjd49 at cornell.edu> wrote:
>>
>> Dear Pylith developers,
>>
>> I'm trying to simulate the ground displacement produced by a small
>> pressurised cavity surrounded by a viscoelastic shell (equation 7.105 from
>> Segall's Earthquake and Volcano Deformation book) and Pylith does a good
>> job within a few mm of uncertainty. The difference between the analytic and
>> the numerical solution is at most 0.6 mm for a signal with a maximum
>> amplitude of 2.49 cm, however I've noticed that this last figure increases
>> as time goes forward, very small but in the end negligible variations
>> (evident in the attached plot, the profiles are calculated for the point of
>> maximum uplift).
>>
>> <sphere_visco.png>. Is this a typical issue of numerical viscoelastic
>> models or is it related to the relatively low resolution of the finite
>> element mesh??
>>
>> Thanks
>>
>> --
>> --------------------------------------------------------
>> Francisco Delgado
>> PhD student in Geological Sciences
>> Cornell University
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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
>>
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>
>
>
> --
> --------------------------------------------------------
> Francisco Delgado
> PhD student in Geological Sciences
> Cornell University
>
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