Spatiotemporal functional modeling of postseismic deformations after the 2011 Tohoku-Oki earthquake

Postseismic deformations continue to occur for a long period after major earthquakes. Temporal changes in postseismic deformations can be approximated using simple functions. Since the 2011 Tohoku-Oki earthquake, operating global navigation satellite system stations have been continuously accumulating a remarkable amount of relevant data. To verify the functional model, we performed statistical data processing on postseismic deformations due to this earthquake and obtained their spatiotemporal distribution. Moreover, we approximated the postseismic deformations over a relatively wide area with a standard deviation of residuals of 1 cm for approximately 10 years using a combined functional model of two logarithmic and one exponential functions; however, the residuals from the functional model exhibited a marked deviation since 2015. Although the pattern of postseismic deformations remained unaltered after the earthquake, a change in the linear deformation occurred from 2015 to date. We reduced the overall standard deviation of the residuals of > 200 stations distributed over >1000 km to < 0.4 cm in the horizontal component by enhancing the functional model to incorporate this linear deformation. Notably, time constants of the functions were similarly applicable for all stations and components. Furthermore, the spatial distribution of the coefficients of each time constant were nonrandom, and the distribution was spatially smooth, with minute changes in the short wavelengths in space. Thus, it is possible to obtain a gridded model in terms of a spatial function. The spatial distributions of short- and long-period components of the functional model and afterslip and viscoelastic relaxation calculated using the physical model were similar to each other, respectively. Each time function revealed a connotation regarding the physical processes, which provided an understanding of the physical phenomena involved in seismogenesis. The functional model can be used to practical applications, such as discerning small variations and modeling for precise positioning.

Automated summary

Postseismic deformations continue for a long period after major earthquakes and can be approximated using simple functions. Statistical data processing on postseismic deformations due to the 2011 Tohoku-Oki earthquake revealed their spatiotemporal distribution. A combined functional model of three functions was used to approximate the postseismic deformations over a wide area for approximately 10 years, but the residuals from the model deviated significantly since 2015.