comparison of analytical model with gprMax result

[Rohit Karnena]

Dear sir

              I have been working on development of an analytical model for bistatic GPR scenario. Currently I am reproducing few analytical models that available in literature (standard models like Kruk's model, Busch's model etc.). On comparing result of analytical model (MATLAB simulation) and result of same scenario in gprMax, the results are matching in received time. Eq. (11) in attached paper. But the results produce a huge difference in amplitude. Amplitude of gprMax result is very low. I hope gprMax tool can validate any analytical model. I couldn't find where it is wrong. 

If possible try to help.

Thank you

Regards

Rohit

[Antonis Giannopoulos]

Hi Rohit,

Great effort and not an easy undertaking! 

In making a comparison with an analytical solution you must make sure the all the conditions imposed for the validity of the approximations used to obtain the analytical solution are met. For example equations (6) and (7) need to be fulfilled in both models. (6) is relatively easily to be done but (7) must also hold and an equivalent numerical model needs to be constructed. In other words, if the separation of Tx and Rx is not fulfilling (7) for all frequencies in the model then the solution is not applicable. Finally in (3) a discussion about the source wavelet needs clarification. W needs to be connected to the current on a Hertzian dipole in the model and the notion of an effective wavelet is very good for the work presented there but needs to be carefully made equivalent to the original description of a source current density that gprMax will use for a theoretical source. Few points of advise:

1. Don't start with finite dipoles but with infinitesimal sources for which the models are easier to compare. A finite dipole model theoretically has more assumptions in it and is not as easy to validate and should be another step. 

2. The excitation of a theoretical hertzian dipole in gprMax and one having a physical model of the structure are different. The theoretical source assumes a known current pulse of the dipole. A proper model that includes the structure of the antenna uses a voltage pulse at the feeding point. 

3. Unless the excitations are equivalent there is no easy way to make sense of the amplitudes. The number themselves to not mean a lot as they depend on input parameters that are not often realistic. For convenience we use '1' as amplitude for the current pulse in a hertzian dipole. This is not really as realistic in practice but also a Hertzian dipole does not exist in practice as it is a very inefficient antenna! It is a great convenience though!

I would recommend to normalise your results to their respective maximums. If they fit on time of arrival (as they most likely do) and then on shape and relative amplitude variation between them then you are at a good place as the difference is on an arbitrary constant that is not important. If the rate of attenuation and shape of the wavelets are not matching then there is something else that needs to be checked and mostly will be about the equivalence of the input conditions assuming that your implementation of Jans's and Evert's work is correct. Obviously, gprMax has regions of validity as any numerical model. These needs to be respected as well but I am sure you know this given the work you are trying to do.

Good luck and will be interested to see the results of this comparisons!

Best wishes

Antonis