Combined logarithmic and exponential function model for fitting postseismic GNSS time series after 2011 Tohoku-Oki earthquake

Mikio Tobita

doi:10.1186/s40623-016-0422-4

Abstract

The time series of a postseismic deformation is commonly fitted by a logarithmic or exponential decay function. However, the high-quality postseismic Global Navigation Satellite System (GNSS) time series of the 2011 Mw 9 Tohoku-Oki earthquake indicates that a single decay function cannot be used to represent the postseismic behaviour. We therefore combined the logarithmic (log) and exponential (exp) decay functions and developed methods for obtaining global solutions using nonlinear least squares calculations for such complex functions. Our models significantly improved the fitting performance of the postseismic time series and the prediction performance of the evolution of postseismic deformation. The solutions obtained by the proposed models and methods enabled distinction between the contributions of the log and exp functions, and explanation of characteristic phenomena such as the subsidence that occurs immediately after an earthquake is reversed to an uplift. The analysis of the solutions may suggest that there has been a continuous increase in the contribution of viscoelastic relaxation to postseismic deformation in eastern Japan, whereas the contribution of afterslip has rapidly decreased. The short-term prediction performance and the universal applicability of the proposed models to the Tohoku-Oki earthquake have contributed to the detection of a slow-slip event in the Tokai region. Rather than the existence of a unique single relaxation time for each surface site, our results suggest a unique single relaxation time for each postseismic deformation mechanism at a given subsurface location. Although the predictions were highly dependent on the assigned steady velocities and the long-term relaxation time constants, they indicate that the coseismic subsidence of the Yamoto station in Miyagi prefecture will recover around the year 2020. The estimated relaxation time constants of the present models appeared to be uniform throughout eastern Japan.

Highlights

Since the 2011 off the Pacific coast of Tohoku Earthquake (Tohoku-Oki earthquake), crustal deformation has continued to occur in eastern Japan (Ozawa et al 2012; Geospatial Information Authority of Japan (GSI) 2015a)
The Yamoto, Choshi, Miyako, and Minase stations [(a)–(d) in Fig. 1] were used for the main modelling for we investigated the use of a natural logarithmic function, natural exponential function, double natural exponential functions with short and long relaxation time constants, and double natural logarithmic functions with short and long relaxation time constants as the fitting model functions for the Global Navigation Satellite System (GNSS) time series data, this paper mainly discusses the use of the following three model functions, which were found to be better than the above four: D(t) = aln(1 + t/b) + c − dexp(−t/e) + Vt, (1)
We proposed combined logarithmic and exponential function models for fitting high-signal-to-noise ratio (S/N) GNSS postseismic deformation data of the 2011 Tohoku-Oki earthquake

Summary

Introduction

Since the 2011 off the Pacific coast of Tohoku Earthquake (Tohoku-Oki earthquake), crustal deformation has continued to occur in eastern Japan (Ozawa et al 2012; GSI 2015a). The primary mechanisms of the postseismic deformations are commonly recognized as afterslip and viscoelastic relaxations. The relative contributions of the afterslip and viscoelastic relaxations remain unclear (Sun and Wang 2015). Attempts have been made to use function fitting regression analysis to investigate postseismic deformation (Takahashi et al 2004; Hashimoto et al 2006; Nishimura 2014). The time series of a postseismic deformation is commonly fitted by a logarithmic or exponential decay function. The postseismic time series of the 2011 Tohoku-Oki earthquake observed by the GNSS Earth Observation Network System (GEONET) indicates that a single decay function cannot be used to represent the postseismic behaviour (GSI 2014; Tobita and Akashi 2015; Fig. 2)

Objectives

Methods

Results

Discussion

Conclusion