[CIG-SEISMO] source discretization in SW4 (Avinash Nayak)

[Avinash Nayak]

Dear Anders,
Many thanks for your helpful explanation and the references. I really
appreciate it.
Thanks.
Sincerely yours,
Avinash

On Fri, Oct 30, 2015 at 1:54 PM, Petersson, Anders <petersson1 at llnl.gov> wrote:
> Dear Avinash,
> The source discretization in SW4 is based on enforcing moment conditions
> that mimic the properties of a Dirac distribution, or its derivative. We
> use the approach developed by Walden for Helmholtz equation. He wrote a
> rather mathy paper where it is derived: J. Walden, Numer. Meth. Part.
> Diff. Eq. v. 15, pp. 503-520 (1999).
>
> To get 4th order accuracy we impose 5 smoothness conditions for moment
> tensor sources and 4 conditions for point forces. To make the source
> weights continuous in the source location, one additional condition is
> added. This is used to improve convergence for source optimization. In the
> end, the source stencil becomes 6 points wide in each direction, resulting
> in a 6x6x6 grid point cube surrounding the source location. The formulas
> are skewed near a free surface, allowing the source to be located on the
> boundary.
>
> The source discretization is done completely independent of the material
> model, so sources can be located anywhere in the computational domain, but
> avoid putting them in the super-grid damping layers.
>
> In terms of our papers, the information about source discretization is
> somewhat scattered. Here are a few suggestions:
>
> [PS-14] N.A. Petersson, and B. Sjogreen, "Super-grid Modeling of the
> Elastic Wave Equation in Semibounded Domains", Communications in
> Computational Physics, 16, pp. 913-955 (2014).
>
>
>
>                                           [SP-14] B. Sjogreen, and N.A. Petersson, "Source Estimation by Full
> Wave Form Inversion", Journal of Scientific Computing, 59(1), pp. 247-276,
> DOI: 10.1007/s10915-013-9760-6, (2014).
>
>
> [PS-10] N.A. Petersson and B. Sjogreen, "Stable grid refinement and
> singular source discretiztion for seismic wave simulations" Communications
> in Computational Physics, v. 8, no. 5, pp. 1074-1110 (2010).
>
> [NPSK-07] S. Nilsson, N.A. Petersson, B. Sjogreen, H.-O. Kreiss, "Stable
> difference approximations for the elastic wave equation in second order
> formulation" SIAM J. Numer. Anal. v. 45, pp 1902-1936, (2007).
>
>
>
> Anders
>
> On 10/30/15, 12:00 PM, "CIG-SEISMO on behalf of
> cig-seismo-request at geodynamics.org" <cig-seismo-bounces at geodynamics.org on
> behalf of cig-seismo-request at geodynamics.org> wrote:
>
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>>   1. source discretization in SW4 (Avinash Nayak)
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>>----------------------------------------------------------------------
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>>Message: 1
>>Date: Fri, 30 Oct 2015 02:25:09 -0700
>>From: Avinash Nayak <avinash07guddu at gmail.com>
>>To: cig-seismo at geodynamics.org
>>Subject: [CIG-SEISMO] source discretization in SW4
>>Message-ID:
>>       <CA+ebHSe1Ge7aWsGyomardisepFfUa4qnB=spH5DH_-T_YeEToA at mail.gmail.com>
>>Content-Type: text/plain; charset=UTF-8
>>
>>Hello,
>>I am a beginner in SW4 and I am hoping for some help about source
>>discretization.
>>
>>In SW4, is it required to put the source inside a volume of homogenous
>>elastic properties as in some other finite difference codes ?
>>
>>How many grid points wide is the stencil for discretizing a point
>>source ? Given that source discretization in SW4 is mentioned to be
>>4th (p) order accurate (Chapter 4, Installation manual 1.1), following
>>requirement Q >= p-1+s (in paper Petersson and Sjogreen [2009] Stable
>>grid refinement ..,LLNL-JRNL-419382) , is the stencil 4/5 points wide
>>for single force (s=0) /moment sources (s=1) (assuming equality sign)
>>along a particular dimension ?
>>
>>How close can we put a source to a sharp velocity contrast ? What is
>>the discretization procedure for a source on the boundary (i.e.
>>vertical force on free surface in Lamb's problem).
>>Is there a reference where I can read about these things ?
>>I will really appreciate your help.
>>
>>Thanks.
>>Regards,
>>Avinash
>>
>>
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-- 

Avinash Nayak,
PhD Candidate,
Berkeley Seismological Laboratory,
Department of Earth and Planetary Science,
University of California, Berkeley