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

[Francisco Delgado]

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.

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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