1 Atmospheric Density Admittance Function for Gravity Reduction Mahmoud Abd El-Gelil 1 , Spiros Pagiatakis 1 , and Ahmed El-Rabbany 2 1 Department of Earth & Space Science & Engineering York University, Toronto, Canada, mahmoud@yorku.ca and spiros@yorku.ca 2 Department of Civil Engineering, Ryerson University, Toronto, Canada, rabbany@ryerson.ca 1. Introduction Recent rapid improvements in technology has created extremely precise measuring systems that are affected by the smallest effects that were once much too small to be detected. The superconducting gravimeter is no exception; it is a sensitive device, which can detect minute changes in surface gravity at the nanogal level. Gravity variations are caused by many physical phenomena e.g. lunar and solar tides, Earth rotation, atmospheric and ocean loading, and others (e.g., Crossley and Xu, 1998; Goodkind, 1999; Hinderer and Crossley, 2000). It is, with no doubt, a challenge to identify and/or separate minute signal(s) of interest in a specific band of interest. Atmospheric mass change is one of the most significant environmental phenomena that affects Earth surface gravity. There are two approaches that are usually followed to model the atmospheric pressure effect on gravity signals: physical and empirical. The latter is also called “the admittance function” or “the transfer function” method and represents the response of gravity to atmospheric pressure variation. In this paper we take a new approach that allows us to model the response of gravity to air density variations rather than to the air pressure as it has traditionally been done. The atmospheric correction to gravity is achieved by using air density time series that are synthetically produced from temperature, pressure and humidity time series recorded simultaneously with gravity at Canada’s fundamental gravity station, in Cantley PQ. A constant admittance is not adequate to describe the air pressure or density effect, which is admittedly frequency dependent. This frequency-dependent admittance that was first introduced by Warburton and Goodkind, (1977) and later by Crossley et al., (1995), Neumeyer, (1995) and others, shows that it increases smoothly and monotonically from 0.2 µgal/mbar at low frequencies (<0.3 cpd) to about 0.35 µgal/mbar at high frequencies (>1 cpd). However, Sun et al., (2002) found that the admittance is 0.378 µgal/mbar at low frequencies and decreases to 0.147 µgal/mbar at high frequencies. In this paper, we adopt an alternative approach for the determination of the admittance that is based on the least-squares (LS) product spectrum of the air density and gravity time series. The air density is synthetically produced from pressure, temperature and humidity records using the equation of state of the atmosphere. The air density admittance is then estimated from common spectral peaks identified in the gravity and air density series, using the product spectrum and rigorous statistical analysis tools. The common spectral peaks in both gravity and air density series are suppressed to estimate their amplitudes and phases and subsequently the yearly admittance amplitude and phase in the band 700h to 2h. Finally, the weighted LS regression is used to estimate the admittance as a function of frequency. 2. Atmospheric Density The atmospheric density can be calculated using the equation of state of the atmosphere, which after some lengthy derivation gives the total air density as a function air pressure P, temperature T: