# Initial Results from SQUID Sensor: Analysis and Modeling for the ELF/VLF Atmospheric Noise
## 1 Introduction  
Extremely low frequency (ELF, defined here as 300-3000 Hz) and very low frequency (VLF, defined here as 3-30 kHz) radio waves have efficient long-range propagation (attenuation rates typically a few dB/Mm at VLF and much smaller, of the order of a few tenths dB/Mm at ELF) in the so-called earth-ionosphere waveguide [1] and comparatively deep penetration into conducting medium such as Earth and seawater. Consequently, they have wide applications ranging from naval communication [2] and geophysical prospecting [3] to underground communication [4]. In order to radiate electromagnetic waves, the dimensions of antenna need to be of the order of the wavelength of the radiation to have an efficiency of any practical significance. Many naval transmitters use tuning elements to force the the antenna to resonate at the working frequency to compensate the shortage of the antenna size. However, the tuning elements provide reasonable efficiency and sized antenna of the transmitter at the expense of a very small resonate bandwidth of the antenna. Consequently, traditional analysis and modeling for ELF/VLF noise are concentrated on narrow-band characteristics (typical bandwidth is 5% of the center frequency). A detailed description of this work can be found in [5]. Recently, ionosphere heating has provided a new way to generate wideband ELF/VLF communication signals, which can raise the communication rate significantly [6]. Experimental results show that the communication bandwidth at 1.51 kHz reaches as high as 400 Hz [7], which encourageus to study the wideband characteristics of the ELF/VLF noise. Mixed Gaussian distribution and Hall model are adopted to describe the probability density function (pdf) of the wideband ELF and VLF noise, respectively in [7]. However, the analysis is limited in specific data and the fitting performance of the model need more sufficient comparison with other widely used models. Magnetic field sensors are preferred for receiver instead of electric field sensors because they can provide superior noise response at the low end of the frequency range [8]. Nowadays, available magnetic field receivers are fluxgates [9], total field magnetometers [10], induction coils [11], and others [12]. They all have their pros and cons. Fluxgates are not sensitive enough for the application of communication. However, total field magnetometers are not fast enough to provide efficient communication. For the induction coil, two different types of magnetic antennas are constructed, i.e., with or without ferrite core at the center. Although antennas with ferrite core have smaller size, it is a concern that the sensitivity will change with temperature and strong fields can cause nonlinear response [8]. On the other hand, the size of antenna with air core is very large. The gain of traditional magnetic receiver is frequency-varying and the calibration need to inject a series of known-amplitude signals at the input of the preamplifier. Even for the Atmospheric Weather Electromagnetic System for Observation, Modeling, and Education (AWESOME) receiver including an internal calibration circuit which generates a pseudorandom digital sequence 1023 b long, with bit frequency of \(\sim\)256 kHz, the amplitude response of the receiver is only about \(\sim\)250 Hz and up to 200 individual frequency components are processed separately [13]. Furthermore, the sensitivity of the magnetic antenna is limited by the bandwidth of the signal, i.e., it behaves poorer for receiving wideband signals. The 3-dB cutoff frequencies of AWESOME are at about 800 Hz where the line transformer begins to attenuate the signal, and at 47 kHz where the antialiasing-filter cutoff lies. The noise floor of the AWESOME receiver with 200 Hz bandwidth over the VLF range (18\(\sim\)30 kHz) is about 4\(\sim\)5 fT [13]. However, the noise floor of the receiver with the same bandwidth over the ELF/VLF range of interest (1.5\(\sim\)4.5 kHz) will increase significantly.