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

Thu Sep 29 09:28:25 PDT 2016

You’re welcome. I’m afraid we didn’t have sufficient spatial resolution in the geodetic data to warrant a more complex model in Pylith so I just stuck to fitting the analytical solution to the data.

Whilst you have a small pressurised sphere, how big a region do you allow to deform viscoelastically? What is the ratio between that radius and the depth?

James

On 27 Sep 2016, at 16:32, Francisco Delgado <fjd49 at cornell.edu<mailto: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.

Thanks

On Tue, Sep 27, 2016 at 2:24 AM, James Daniel Paul Moore (Dr) <james.moore at ntu.edu.sg<mailto: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<mailto: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<mailto: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

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