Realistic FDTD GPR Antenna Models Optimized Using a Novel Linear/Nonlinear Full-Waveform Inversion

[Armando Schneider]

Hello,

From my understanding, the FWI algorithm used in the paper uses explicit Jacobian matrix? Does the algorithm need to compute adjoint wavefield and cross-correlate to the source wavefield? 

Cheers,

[Iraklis Giannakis]

Hello,

In contrast to typical FWI problems, in this one we have a limited number of unknowns (around 10) so using adjoint wavefield and cross-correlation is not necessary. The derivatives with respect to permittivity and conductivity for a given pulse are calculated using equations 33-36 .The problem here is that one of the parameters to be estimated is the shape of the pulse. Therefore calculating the Jacobian should take this into account i.e. we need to find the derivative of the shape of the pulse with respect to permittivity and conductivity, and how changing these properties affects the pulse and consequently the error function. This is why calculating the Jacobian becomes so tricky and results to equation 32. 

You can always approximate the derivatives with finite differences since the number of the unknowns are not that large and it will not greatly increase the amount of times you will have to run FDTD. 

Hope that this was helpful.

Best,

Iraklis