Spectral Estimation Techniques for time series with Long Gaps: Applications to Paleomagnetism and Geomagnetic Depth Sounding

Many Earth systems cannot be studied directly. One cannot measure the velocities of convecting fluid in the Earth’s core but can measure the magnetic field generated by these motions on the surface. Examining how the magnetic field changes over long periods of time, using power spectral density estimation provides insight into the dynamics driving the system. The changes in the magnetic field can also be used to study Earth properties - variations in magnetic fields outside of Earth like the ring-current induce currents to flow in the Earth, generating magnetic fields. Estimating the transfer function between the external changes and the induced response characterizes the electromagnetic response of the Earth. From this response inferences can be made about the electrical conductivity of the Earth.However, these types of time series, and many others have long breaks in the record with no samples available and limit the analysis. Standard methods require interpolation or section averaging, with associated problems of introducing bias or reducing the frequency resolution.Extending the methods of Fodor and Stark (2000)- who adapt a set of orthogonal multi-tapers to compensate for breaks in sampling- an algorithm and software package for applying these techniques is developed. Methods of empirically estimating the average transfer function of a set of tapers and confidence intervals are also tested. These methods are extended for cross-spectral, coherence and transfer function estimation in the presence of noise.With these methods, new analysis of a highly interrupted ocean sediment corefrom the Oligocene (Hartl et al., 1993) reveals a quasi-periodic signal in the calibrated paleointensity time series at 2.5 cpMy. The power in the magnetic field during this period appears to be dominated by reversal rate processes with less overall power than the early Oligocene. Previous analysis of the early Oligocene by Constable et al. (1998) detected a signal near 8 cpMy. These results suggest that a strong magnetic field inhibits reversals and has more variability in shorter term field changes. Using over 9 years of data from the CHAMP low-Earth orbiting magnetic satellite and the techniques developed here, more robust estimates of the electromagnetic response of the Earth can be made. The tapers adapted for gaps provide flexibility to study the effects of local time, storm conditions on Earth’s 1-D electromagnetic response as well as providing robust estimates of the C-response at longer periods than previous satellite studies