Simulation Results Scaling with Grid Size

[Ismael Xique]

Hello! Thanks for the quick response from before. I have run several simulations and it seems to me that the signal returned scales with the grid size. For example, when I run a model with grid resolution of 0.002 (m) and then run the model at 0.005 (m) then the amplitude of the signal after self-response removal grows by a factor of 2.5. The same is true after I run the model with 0.002 and 0.0025 except the scaling factor of the signal is now 1.25. This seems a little strange because the values used in the second example both fall within the range of lambda/10 as recommended, so I believe that this scaling behavior should not be occurring any longer. Any explanation for this behavior would be greatly appreciated. I have attached a set of files I have been working with. The models have a single object in free space with one transmitter and multiple receivers spaced 0.1 (m) apart. The files with selfResp in the title run the model without a target to simulate the self response which is then simply subtracted.  I have also posted an image with the simulation results from the attached files which show that the amplitude scales by a factor of 2 when changing grid resolution from 0.0025 to 0.005 (m). Thank you for your help!

[Craig Warren]

Hi Ismael,

The short answer is that this is expected behaviour. I'll try and explain why...

When you use a #hertzian_dipole source gprMax sets the length of the Hertzian dipole (dl) to the length of the cell in the polarisation direction of the dipole, and you get a dipole moment, i.e. I * dl (current multiplied by Hertzian dipole length). So, by only changing the spatial resolution of your model you are specifying a different source (dipole moment) in each, and hence getting differently scaled results. This behaviour is documented in the User Guide (http://docs.gprmax.com/en/latest/input.html#hertzian-dipole) but it could be made clearer. I'm going to work on this! So to use the same #hertzian_dipole source with models that have different resolutions you must adjust the scaling of the maximum amplitude of the waveform (http://docs.gprmax.com/en/latest/input.html#waveform) you are using, e.g. if you are using a 1mm cubic grid with a scaling of 1, then when you move to a 2mm cubic grid you must set the scaling to 0.5, which means the same dipole moment is being used in both models.

Hope this is clear.

Kind regards,

Craig 

[Ismael Xique]

Hello Craig,

This makes perfect sense. Thank you so much for your help!

-Ismael