Reply to comment by R. C. Moore and M. T. Rietveld on ‘‘Geometric modulation: A more effective method of steerable ELF/VLF wave generation with continuous HF heating of the lower ionosphere’’

[1] We thank Moore and Rietveld [2009] (hereafter referred to as MR09) for their comments to Cohen et al. [2008] (hereafter referred to as CA08). MR09 consider the two following conclusions of CA08 concerning the generation of ELF/VLF (0.3–30 kHz) waves with typical amplitude modulation (AM) and geometric modulation of ionospheric High-Frequency (HF) heating: 1) ‘‘Geometric modulation can enhance ELF/VLF wave generation by up to 11 dB over the conventional AM method’’, and 2) ‘‘Geometric modulation also allows directional launching of the signal into the Earth-ionosphere waveguide, forming an unprecedented steerable large-element ELF/VLF ionospheric phased array’’. [2] MR09 refer to Figure 6 of Barr et al. [1988], which appears to show that 3–5 dB amplitude gains at longdistances can be achieved by tilting an AM HF beam by 15 toward that receiver (and conversely, a 3–5 dB reduction results from an HF beam tilted 15 away from the receiver), i.e., oblique AM HF heating. These observations are a straightforward consequence of phasing of ELF/VLF radiating currents across the heated region as a result of the variable propagation delay of the HF signal to the ionosphere [see Barr et al., 1988, Figure 7]. MR09 therefore claim that 3–5 dB of the 7–11 dB amplitude gain, and 6–10 dB of the 14 dB directionality of geometric modulation reported by CA08, may result from the oblique nature of the HF beam. [3] The experiment of Barr et al. [1988] is actually first reported by Barr et al. [1987], which was cited and described by CA08. The 1987 paper also discusses a related but more advanced experiment in which the HF beam alternates between two regions in the ionosphere, one directed toward a distant ( 500 km) receiver, and one directed away, effectively creating two independent but anti-phase ELF/VLF sources. The distance between these two sources is controlled by the two oblique HF beam angles. The amplitude at the distant receiver is found to be dependent on the distance between the two sources, and varying (due to constructive and destructive interference) by 4–6 dB. These results are much more relevant to the observations of CA08 since they involve controllable phasing of independent ELF/VLF sources yet also intrinsically include the simpler non-controllable phasing resulting from a single oblique AM HF beam. While the discussion of Barr et al. [1988] may often be important for the interpretation of AM HF heating observations, they are significantly less important for interpreting experiments where multiple beam locations are utilized, such as the two-element array experiment presented by Barr et al. [1987]. [4] Oblique AM HF heating as discussed by MR09 does not fall into the category of ‘‘conventional AM method’’ as referred to by CA08. The 7–11 dB amplitude gains and 14 dB directionality was made in comparison to vertical AMheating, as is used in many ELF/VLF generation experiments. Additionally, vertical AMHFheating possesses the same azimuthal symmetry as the circle sweep, whereas the amplitude gains achieved with oblique AM HF heating occur only along one direction, so a comparison to vertical AM HF heating is more appropriate. Nonetheless, we consider here the contribution of oblique AM HF heating (since it has been brought to fore by MR09) and show that the phasing created by oblique AM HF heating can at best account for a small part of the amplitude gains and directionality associated with geometric modulation and reported by CA08. [5] The observations of CA08 relate more closely to the mechanism of an ELF/VLF phased array as presented by Barr et al. [1987]. Geometric modulation intrinsically utilizes HAARP facility’s new capability to steer the HF beam at 100-kHz rates over a 2D area, enabling dozens of beam locations in each ELF/VLF period. Since the relative phases of each element are determined by the controllable order in which the HF beam heats these locations within the ELF/VLF period (whereas the phasing effect of an oblique beam is dictated by geometry), geometric modulation does in fact represent an unprecedented technique for controlled ELF/VLF directionality, one that cannot be reproduced with single-location oblique AM HF heating as discussed by Barr et al. [1988].