Vertical deformation model on postseismic phase using exponential and logarithmic function based on InSAR

The Palu MW7.4 earthquake occurred on September 28, 2018, with the epicenter at 119.86°, 0.72°. The severe shaking caused severe damage in Central Sulawesi, especially in Palu. We conducted a postseismic deformation study to determine the deformation pattern and reduce future earthquakes’ impact.Interferometric Synthetic Aperture Radar(In SAR) data were processed using Li CSBAS to get the time series. The time series data were fitted to exponential and logarithmic functions to determine the mechanism of postseismic deformation. The exponential model identified the influence of the viscoelastic mechanism, and the logarithm identified the afterslip mechanism. The Palu earthquake was fitted to logarithmic and exponential, but the logarithmic was more significant than an exponential function.Afterslip mechanism predominates, and viscoelastic mechanisms play a minor role in this postseismic deformation.

Transient postseismic slip and aftershock triggering:A case study of the 2008 M_W7.9 Wenchuan Earthquake,China

In this study,we investigate how a stress variation generated by a fault that experiences transient postseismic slip(TPS)affects the rate of aftershocks.First,we show that the postseismic slip from Rubin-Ampuero model is a TPS that can occur on the main fault with a velocity-weakening frictional motion,that the resultant slip function is similar to the generalized Jeffreys-Lomnitz creep law,and that the TPS can be explained by a continuous creep process undergoing reloading.Second,we obtain an approximate solution based on the Helmstetter-Shaw seismicity model relating the rate of aftershocks to such TPS.For the Wenchuan sequence,we perform a numerical fitting of the cumulative number of aftershocks using the Modified Omori Law(MOL),the Dieterich model,and the specific TPS model.The fitting curves indicate that the data can be better explained by the TPS model with a B/A ratio of approximately 1.12,where A and B are the parameters in the rate-and state-dependent friction law respectively.Moreover,the p and c that appear in the MOL can be interpreted by the B/A and the critical slip distance,respectively.Because the B/A ratio in the current model is always larger than 1,the model could become a possible candidate to explain aftershock rate commonly decay as a power law with a p-value larger than 1.Finally,the influence of the background seismicity rate r on parameters is studied;the results show that except for the apparent aftershock duration,other parameters are insensitive to r.

Coseismic and postseismic slip ruptures for 2015Mw 6.4 Pishan earthquake constrained by static GPS solutions

On 3 July 2015, a Mw 6.4 earthquake occurred on a blind fault struck Pishan, Xinjiang,China. By combining Crustal Movement Observation Network of China（CMONOC） and other Static Global Positioning System（GPS） sites surrounding Pishan region, it provides a rare chance for us to constrain the slip rupture for such a moderate event. The maximum displacement is up to 12 cm, 2 cm for coseismic and postseismic deformation, respectively,and both the deformation patterns show a same direction moving northeastward. With rectangular dislocation model, a magnitude of Mw6.48, Mw6.3 is calculated based on coseismic, postseismic deformation respectively. Our result indicates the western Kunlun range is still moving toward Tarim Basin followed by an obvious postseismic slip associated with this earthquake. To determine a more reasonable model for postseismic deformation, a longer GPS dataset will be needed.

Influences of the heterogeneity of viscoelastic medium on postseismic deformation of the 2008 M_(W) 7.9 Wenchuan earthquake

The study of postseismic deformation is important for constraining the viscoelastic properties of the Earth and inverting the post-earthquake process.The levelling survey revealed that the area near Bei-chuan elevated 5.3 cm about two years after the M_(W) 7.9 Wenchuan earthquake(05/12/2008),during which the area underwent significant downward movement.The GPS horizontal displacements showed a non-monotonic variation after the Wenchuan earthquake.In this study,a 3-D viscoelastic finite element model is employed to simulate the coseismic and postseismic deformation of the Wenchuan earthquake.The numerical simulations show that the lateral heterogeneity across the Longmenshan fault plays an important role in the postseismic displacements.The results reveal that the coseismic defor-mation is not sensitive to the horizontal heterogeneity,but the postseismic deformation is sensitive to it.The postseismic deformation of the horizontally heterogeneous model is generally consistent with the observations of all geodetic surveys,such as GPS,InSAR and levelling,but not for the horizontally homogenous model.We also find that the non-monotonous variation of the postseismic deformation of the Wenchuan earthquake could be explained by a viscoelastic relaxation model with lateral heterogeneous medium across the Longmenshan fault.

Effective relaxation time and viscosity of the earth inferred from the postseismic vertical deformations of the 1990 MS=7.0 Gonghe earthquake

The postseismic vertical deformation rates of the 1990 Gonghe M S=7.0 earthquake appears to have decreased exponentially. Based on Okada′s coseismic surface displacement solution caused by a uniform fault slip in an elastic homogeneous half space, we derived its postseismic surface displacement by using a single layer standard linear solid model, and further derived a simplified formula for determining the effective relaxation time and viscosity of the earth, which is independent of the dislocation parameters of the causative fault. From the postseismic vertical deformation of the 1990 Gonghe earthquake, we inferred that the effective relaxation time defined by τ = η/μ is 2.6 years, and the effective viscosity η is about 10 18 Pa·s.

Rapid afterslip and short-term viscoelastic relaxation following the 2008 M_W7.9 Wenchuan earthquake

Significant postseismic deformation of the 2008 M W 7.9 Wenchuan earthquake has been observed from GPS data of the first 14 days after the earthquake. The possible mechanisms for the rapid postseismic deformation are assumed to be afterslip on the earthquake rupture plane and viscoelastic relaxation of coseismiclly stress change in the lower crust or upper mantle. We firstly use the constrained least squares method to find an afterslip model which can fit the GPS data best. The afterslip model can explain near-field data very well but shows considerable discrepancies in fitting far-field data. To estimate the effect due to the viscoelastic relaxation in the lower crust, we then ignore the contribution from the afterslip and attempt to invert the viscosity structure beneath the Longmenshan fault where the Wenchuan earthquake occurred from the postseismic deformation data. For this purpose, we use a viscoelastic model with a 2D geometry based on the geological and seismological observations and the coseismic slip distribution derived from the coseismic GPS and InSAR data. By means of a grid search we find that the optimum viscosity is 9×10 18 Pa·s for the middle-lower crust in the Chengdu Basin, 4×10 17 Pa·s for the middle-lower crust in the Chuanxi Plateau and 7×10 17 Pa·s for the low velocity zone in the Chuanxi plateau. The viscoelastic model explains the postseismic deformation observed in the far-field satisfactorily, but it is considerably worse than the afterslip model in fitting the near-fault data. It suggests therefore a hybrid model including both afterslip and relaxation effects. Since the viscoelastic model produces mainly the far-field surface deformation and has fewer degree of freedoms （three viscosity parameters） than the afterslip model with a huge number of source parameters, we fix the viscositiy structure as obtained before but redetermine the afterslip distribution using the residual data from the viscoelastic modeling. The redetermined afterslip distribution becomes physically more reasonable; it is more localized and exhibits a pattern spatially complementary with the coseismic rupture distribution. We conclude that the aseismic fault slip is responsible for the near-fault postseismic deformation, whereas the viscoelastic stress relaxation might be the major cause for the far-field postseismic deformation.

Crustal deformation on the Chinese mainland during 1998—2004 based on GPS data

This study focuses on resolving moderate amounts of crustal motion at the continental scale based on a large volume of global positioning system（GPS） data during 1998e2014. A state-of-the-art GPS processing strategy was used to resolve position time series and velocities from carrier beat phases for all available data. Position time series were closely analyzed to estimate linear constant, coseismic displacements, postseismic motions, and other parameters. We present coseismic offsets inferred from the GPS data for the 2010 Yushu and 2014 Yutian earthquakes, and also illustrate transient postseismic motions following the 2001 Kokoxili, 2008 Wenchuan, and 2011 Tohoku-Oki earthquakes. Since not all GPS position time series dominated by postseismic motions can be modeled and corrected reasonably, we present contemporary horizontal velocities from 2009 to 2014 for campaign stations and from 1998 to 2014 for continuous stations, irrespective of postseismic deformations. Our study concludes that we need to accumulate observations over a greater duration and apply accurate postseismic modeling to correct for transient displacement in order to resolve reasonable interseismic velocity.

Viscoelastic relaxation of the upper mantle and afterslip following the 2014 M_(W)8.1 Iquique earthquake

An improved understanding of postseismic crustal deformation following large subduction earthquakes may help to better understand the rheological properties of upper mantle and the slip behavior of subduction interface.Here we construct a three-dimensional viscoelastic finite element model to study the postseismic deformation of the 2014 M_(W)8.1 Iquique,Chile earthquake.Elastic units in the model include the subducting slab,continental and oceanic lithospheres.Rheological units include the mantle wedge,the oceanic asthenosphere and upper mantle.We use a 2 km thick weak shear zone attached to the subduction fault to simulate the time-dependent stress-driven afterslip.The viscoelastic relaxation in the rheological units is represented by the Burgers rheology.We carry out grid-searches on the shear zone viscosity,thickness and viscosity of the asthenosphere,and they are determined to be 10^(17)Pa s,110 km and 2×10^(18)Pa s,respectively.The stress-driven afterlsip within the first two years is up to~47 cm and becomes negligible after two years(no more than 5 cm/yr).Our results suggest that a thin,low-viscosity oceanic asthenosphere together with a weak shear zone attached to the fault are required to better reproduce the observed postseismic deformation.

Seismologic applications of GRACE time-variable gravity measurements

The Gravity Recovery and Climate Experiment（GRACE） has been measuring temporal and spatial variations of mass redistribution within the Earth system since2002. As large earthquakes cause significant mass changes on and under the Earth＇s surface,GRACE provides a new means from space to observe mass redistribution due to earthquake deformations. GRACE serves as a good complement to other earthquake measurements because of its extensive spatial coverage and being free from terrestrial restriction. During its over 10 years mission,GRACE has successfully detected seismic gravitational changes of several giant earthquakes,which include the 2004 Sumatra–Andaman earthquake,2010 Maule（Chile） earthquake,and 2011 Tohoku-Oki（Japan） earthquake. In this review,we describe by examples how to process GRACE timevariable gravity data to retrieve seismic signals,and summarize the results of recent studies that apply GRACE observations to detect co- and post-seismic signals and constrain fault slip models and viscous lithospheric structures. We also discuss major problems and give an outlook in this field of GRACE application.

Study of main body element of crustal strain and its relationship with moderate-strong earthquakes

In this paper, progress in strain study of blocks and faults by GPS data are discussed, and the concept that active structures between blocks are the main body of crustal strain is clarified. By energy transfer principle of elastic mechanics, the relation between strain around faults and tectonic force on fault surfaces is set up and main body element model of crustal strain is constructed. Finally, the relation between mechanical evolution of model and seismogenic process of Kunlun earthquake （Ms=8.1） is discussed by continuous GPS data of datum stations. The result suggests that the relatively relaxed change under background of strong compressing and shearing may help to trigger moderate-strong earthquakes.

Dynamic mechanisms of the post-seismic deformation following large events:Case study of the 1999 Chi-Chi earthquake in Taiwan of China

The mechanism of postseismic deformation related to strong earthquakes is important in geodynamics, and presumably afterslip or viscoelastic relaxation is responsible for the postsesimic deformation. The 1999 Chi-Chi, Taiwan of China, earthquake occurred in the region where GPS observation station is most densely deployed in the world. The unprecedented GPS data provides a unique opportunity to study the physical processes of postseismic deformation. Here we assume that the interactions of viscoelastic relaxation, afterslip, fault zone collapse, poroelastic rebound, flow of underground fluids, and all these combined contribute to the surface displacements following the main shock. In order to know the essence of the postseismic deformation after the strong event, fault zone collapse, poroelastic rebound, flow of underground fluids, and so on, are represented equivalently by the variations of the focal medium properties. Therefore, the viscoelastic relaxation, afterslip, and the variations of the equivalent focal medium properties are inverted by applying the GPS temporal series measurement data with viscoelastic finite element method. Both the afterslip rate distribution along the fault and the afterslip evolution with time are obtained by means of inversion. Also, the preliminary result suggests that viscosities of the lower crust and the upper mantle in Taiwan region is 2.7×1018 and 4.2×1020 Pa·s, respectively. Moreover, the inversion results indicate that the afterslip contributing to postseismic deformation of 44.6% in 450 days after the Chi-Chi earthquake, with 34.7% caused by the viscous relaxation and 20.7% by other factors such as fault zone collapse, poroelastic rebound, and the flow of liquids.