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

[Petersson, Anders]

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
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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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