[CIG-SEISMO] Reciprocity with SEM3D_Cartesian

[Niu, Jieming]

Hi! All,

I recently ran some simple tests with SEM3D_Cartesian to check the implementation of the reciprocity theorem. As described in the manual, the step source time function is used by the moment tensor simulation, and a pseudo Dirac function with duration of five time steps is used by the single force simulation when “USE_RICKER_FUNCTION” is set false. 

When I compared the numerical spatial derivative of the single force solutions with the MT solution, the shapes of different waveforms are ok, but the time shift between the numerical solution and the direct MT solution is about seven time steps rather than five time steps.  Is there any other information I missed in the simulation?

Also, it seems hard for me to get the same amplitudes of the waveforms.  I assume that if I want to get the same waveform from the numerical derivation, I need to integrate the single force solution first because the source time functions of two different solutions are different.  However, this integration depends on the shape of the pseudo Dirac function and its duration. Is the shape of the pseudo Dirac function a box or a triangle?  

Does anyone have any suggestion? Thanks a million.

Regards,
Jieming