Analysing normal modes of the earth from high-rate GNSS time series

Abstract

Normal modes of the Earth, or Earth’s free oscillations, correspond to a global deformation of the Earth that vibrates at different frequencies, like a bell, after a strong excitation, usually an earthquake of magnitude greater than 6.5. Normal modes of the Earth were first described by Lord Kelvin (Kelvin, 1863) with a computation of the lowest fundamental spheroidal mode 0S2 frequency for a homogeneous Earth model (Lognonné and Clévédé, 2002). With the theory and the deployment of the first long-period sensors in the late 1950s, day-scale Earth’s free oscillation after large earthquakes has been detected by underground instruments such as strainmeters, gravimeters and seismometers (Benioff et al., 1961) (Dziewonski and Gilbert, 1972) (Mendiguren, 1973). In the 1960s, since the U.S. military developed the first satellite navigation system, Transit, the era of Global Navigation Satellite System (GNSS) has arrived. Among all navigation satellite systems, Global Positioning System (GPS), operated by the U.S. Department of Defense (DOD), is currently the world’s most utilized satellite navigation system. With the developments of receiver technology and sampling capability, GPS becomes a powerful tool to study long-period Earth deformations such as plate tectonics and post-glacial rebound, or to monitoring short-period and short-duration motion such as waves generated by earthquakes (Bilich et al., 2008). In recent years, several studies have demonstrated the effective use of GPS in estimating coseismic displacement waveforms induced by an earthquake with accuracies ranging from a few millimeters to a few centimeters. In these studies, two well-known processing strategies, single Precise Point Positioning (PPP) and Different Positioning (DP), have been used to reduce the latency between earthquake occurrence and coseimic displacement waveforms estimation. In this thesis, a new approach named Variometric Approach for Displacements Analysis Standalone Engine (VADASE) is used to detect the normal modes of the Earth. Then the Welch’s PSD estimate is applied to transform the time series into frequency domain. Several simulations have been performed on synthetic time series to investigate the influence of noise level, sampling rate, time series length, window size and overlapping rate of Welch’s method, as well as the influence of stacking. The experiments on real data show the capability of VADASE time series for detecting normal modes of the Earth with the help of the stacking method. Some fundamental modes with small amplitude are not visible because the SNR is not sufficient to lift the signal out of the noise.