Abstract
Difference methods have been routinely used to compute velocity and acceleration from precise positioning with global navigation satellite systems (GNSS). A low sampling rate (say a rate not greater than 1 Hz, for example) has been always implicitly assumed for applicability of the methods, because random measurement errors are significantly amplified, either proportional to the sampling rate in the case of velocity or square-proportional to the sampling rate in the case of acceleration. Direct consequences of a low sampling rate are the distortion of the computed velocity and acceleration waveforms and the failure to obtain almost instantaneous values of velocity and acceleration. We reformulate the reconstruction of velocity and acceleration from very high-rate (50 Hz) precise GNSS as an inverse ill-posed problem and propose the criterion of minimum mean squared errors (MSE) to regularize solutions of velocity and acceleration. We successfully apply the MSE-based regularized method to reconstruct the very high-rate velocity and acceleration waveforms, the peak ground velocity (PGV) and the peak ground acceleration (PGA) from 50 Hz precise point positioning (PPP) position waveforms for the 2013 Lushan Mw6.6 earthquake. The reconstructed results of velocity and acceleration are shown to be in good agreement with the motion patterns in the PPP position waveforms and correctly recover the earthquake signal. The reconstructed GNSS-based PGA values are a few hundred times smaller than those from the strong motion seismometers.
Highlights
Seismic ground motion is fundamental for determination of earth structure and inversion of rupture processes of earthquakes (Aki and Richards 1980; Lay and Wallace 1995) and for both design and construction of seismic resistantDisaster Prevention Research Institute, Kyoto University, Uji, Kyoto 611-0011, JapanSichuan Earthquake Administration, Chengdu, People’s Republic of ChinaCollege of Marine Geosciences, Ocean University of China, Qingdao, People’s Republic of Chinaglobal navigation satellite systems (GNSS) Research Center, Wuhan University, Wuhan 430071, People’s Republic of ChinaSchool of Geomatics, Xi’an University of Science and Technology, Xi’an 710054, People’s Republic of China man-made structures in earthquake engineering and seismic hazard analysis
Earthquake engineering and seismic hazard analysis have to be practically simplified by focusing on a few important parameters such as magnitudes of earthquakes, seismic intensity, peak ground acceleration (PGA), peak ground velocity (PGV) and natural frequencies of structures
We may note that attitude information does not affect the peak ground acceleration under the assumption of correct scaling factors, but the horizontal and vertical components of PGA and PGV can become unreliable without attitude information, as is exactly the case of strong motion seismometers
Summary
Seismic ground motion is fundamental for determination of earth structure and inversion of rupture processes of earthquakes (Aki and Richards 1980; Lay and Wallace 1995) and for both design and construction of seismic resistant. GNSS precise positioning has been well applied to compute velocities and accelerations with a low sampling rate for many years (see, e.g., Kleusberg et al 1990; Jekeli and Garcia 1997; Bruton and Schwarz 2002; Serrano et al 2004; Gatti 2018); recent experiments in sports have demonstrated that GNSS accelerations can be in error that can be as large as a few g (see, e.g., Waldron et al 2011; Buchheit et al 2014). In this paper, we will reformulate the determination of velocity and acceleration from GNSS precise positioning as a standard inverse ill-posed problem and apply regularization to reconstruct PGA and PGV from GNSS measurements for earthquake engineering and seismic hazard analysis applications. The Fredholm’s integral equation (6) of the first kind has been systematically investigated by Schneider (1968, 1984) and becomes popular for gravitational recovery from short-arc orbital measurements of satellite tracking (see, e.g., Schneider 1968, 1984; Ilk et al 2005)
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