Comment on “An analysis of VLF electric field spectra measured in Titan's atmosphere by the Huygens probe” by J. A. Morente et al.

Abstract

Simões (2011), Comment on "An analysis of VLF electric field spectra measured in Titan's atmosphere by the Huygens probe" by J. A. Morente et al.,

Reply to comment by R. Grard et al. on “An analysis of VLF electric field spectra measured in Titan's atmosphere by the Huygens probe”

“…Appendix A: Reply to Appendix A of Grard et al [2011] A1. Introduction [32] The Huygens probe included an electrical dipole antenna for detecting the natural electric field in Titan's atmosphere.…”

“…[39] Grard et al [2011] assert in section 5 that "[d]ue to the fact that the phases are arbitrarily assumed to be zero, the Figure A1a. inverse DFT analysis necessarily yields an arbitrary signal with a meaningless peak at time zero" and now, in a clear contradiction, they claim "[t]his condition can only be met if one also includes the symmetrical part of the late time response with respect to t = 0, in other words, if one violates the causality principle."…”

“…In section 2 of Grard et al [2011], the different steps of our analysis procedure are described, emphasizing two points which, according to them, invalidate the results given by our methodology. These points are as follows:…”

“…Regarding the different steps constituting the analysis procedure, Grard et al [2011] state: “The first three steps, though debatable, might possibly help emphasizing, in a qualitative way, spectral components so long as they exist… Adding zeroes to the time series at step (iv) does not contribute any information at all; it merely smooth out the spectrum and provide an interpolation that is not justified, from a mathematical point of view, ….” Contrary to this last statement, the fourth step is the one with a more solid mathematical background; specifically, in Shannon's theorems, also known as sampling theorems. The frequency sampling theorem [ Brigham , 1988, p.86] states that a time‐limited function g ( t ), that is g ( t ) = 0 for ∣ t ∣ > t max , is uniquely determined from the equidistant samples of its Fourier transform, G ( f ), whenever the step frequency Δ f fulfills the condition Δ f ≤ (2 t max ) −1 .…”

“…Before being applied to the data sent by the Huygens probe from Titan's atmosphere, our methodology was checked using analytical functions and the data generated by the TLM numerical simulation of Titan's atmosphere. Grard et al [2011] criticize our analysis procedure. In this reply, we deconstruct their arguments one by one, showing that the analysis procedure, repeatedly checked, does not generate artificial resonances and remains valid.…”