Wenbin Shen

Sensitivity of Coulomb stress change to the parameters of the Coulomb failure model: A case study using the 2008 Mw 7.9 Wenchuan earthquake

The Coulomb stress change has been widely employed to interpret mainshock-mainshock and mainshock-aftershock triggering as well as interactions amongst earthquake faults and volcanoes. This quantitative index is computed based on the Coulomb failure criterion and is a function of fault parameters including the source and receiver fault geometries, the friction coefficient on the receiver fault, and Skemptons coefficient of the host rock. Thus, for the robust determination of the Coulomb stress change, the sensitivity of the Coulomb stress change to these model parameters should be thoroughly assessed. However, notwithstanding numerous case studies, almost no systematic investigation of the sensitivity of the Coulomb stress change has been performed. Here we present an error estimator for the Coulomb stress change and then quantitatively investigate the sensitivity of the Coulomb stress change to the fault model parameters for the 2008 Mw 7.9 Wenchuan earthquake. Our results indicate that for this case the Coulomb stress change is the most sensitive to the uncertainty in the dip angle of the receiver fault, while the influences of the uncertainties in the slip model of the source fault, the strike, and rake angles of the receiver fault, and the friction and Skemptons coefficients cannot be neglected. Accordingly, it is crucial to perform a realistic estimate of the uncertainty in the Coulomb stress change. By performing such calculation, future Coulomb stress analyses such as the stress triggering of earthquake sequence and the likelihoods of potential earthquakes could be based on more robust Coulomb stress change maps.

Tightly coupled integration of ionosphere-constrained precise point positioning and inertial navigation systems.

The continuity and reliability of precise GNSS positioning can be seriously limited by severe user observation environments. The Inertial Navigation System (INS) can overcome such drawbacks, but its performance is clearly restricted by INS sensor errors over time. Accordingly, the tightly coupled integration of GPS and INS can overcome the disadvantages of each individual system and together form a new navigation system with a higher accuracy, reliability and availability. Recently, ionosphere-constrained (IC) precise point positioning (PPP) utilizing raw GPS observations was proven able to improve both the convergence and positioning accuracy of the conventional PPP using ionosphere-free combined observations (LC-PPP). In this paper, a new mode of tightly coupled integration, in which the IC-PPP instead of LC-PPP is employed, is implemented to further improve the performance of the coupled system. We present the detailed mathematical model and the related algorithm of the new integration of IC-PPP and INS. To evaluate the performance of the new tightly coupled integration, data of both airborne and vehicle experiments with a geodetic GPS receiver and tactical grade inertial measurement unit are processed and the results are analyzed. The statistics show that the new approach can further improve the positioning accuracy compared with both IC-PPP and the tightly coupled integration of the conventional PPP and INS.

The Quasi-Biennial Vertical Oscillations at Global GPS Stations: Identification by Ensemble Empirical Mode Decomposition

Modeling nonlinear vertical components of a GPS time series is critical to separating sources contributing to mass displacements. Improved vertical precision in GPS positioning at stations for velocity fields is key to resolving the mechanism of certain geophysical phenomena. In this paper, we use ensemble empirical mode decomposition (EEMD) to analyze the daily GPS time series at 89 continuous GPS stations, spanning from 2002 to 2013. EEMD decomposes a GPS time series into different intrinsic mode functions (IMFs), which are used to identify different kinds of signals and secular terms. Our study suggests that the GPS records contain not only the well-known signals (such as semi-annual and annual signals) but also the seldom-noted quasi-biennial oscillations (QBS). The quasi-biennial signals are explained by modeled loadings of atmosphere, non-tidal and hydrology that deform the surface around the GPS stations. In addition, the loadings derived from GRACE gravity changes are also consistent with the quasi-biennial deformations derived from the GPS observations. By removing the modeled components, the weighted root-mean-square (WRMS) variation of the GPS time series is reduced by 7.1% to 42.3%, and especially, after removing the seasonal and QBO signals, the average improvement percentages for seasonal and QBO signals are 25.6% and 7.5%, respectively, suggesting that it is significant to consider the QBS signals in the GPS records to improve the observed vertical deformations.

Monthly GRACE detection of coseismic gravity change associated with 2011 Tohoku-Oki earthquake using northern gradient approach

We demonstrate that the coseismic gravitational changes due to the 2011 Mw = 9.0 Tohoku-Oki earthquake are detectable by GRACE with only 1-month data after the earthquake, which is also supported by a simulation test using the seismic-signal-contained observations synthesized with the signals of a dislocation model prediction. The commonly used destriping to filter correlated errors in GRACE coefficients tends to distort the true coseismic signals in both amplitude and spatial pattern. In order to better retrieve coseismic gravitational signals, we apply a northern gravity gradient approach with the filter of spatial averaging and without destriping. The coseismic northern gravity gradient changes of Tohoku-Oki earthquake are extracted from the monthly data of April 2011, which reveal a positive-negative-positive spatial pattern and agree with the model prediction. The northern gradient approach provides an efficient means to detect coseismic signals and potentially constrain fault slip models with large-scale gravitational changes using limited time span of monthly GRACE solutions.

Comparative study on two methods for calculating the gravitational potential of a prism

The determination of the gravitational potential of a prism plays an important role in physical geodesy and geophysics. However, there are few literatures that provide accurate approaches for determining the gravitational potential of a prism. Discrete element method can be used to determine the gravitational potential of a prism, and can approximate the true gravitational potential values with sufficient accuracy (the smaller each element is, the more accurate the result is). Although Nagy’s approach provided a closed expression, one does not know whether it is valid, due to the fact that this approach has not been confirmed in literatures. In this paper, a study on the comparison of Nagy’s approach with discrete element method is presented. The results show that Nagy’s formulas for determining the gravitational potential of a prism are valid in the domain both inside and outside the prism.

Seasonal Mass Changes and Crustal Vertical Deformations Constrained by GPS and GRACE in Northeastern Tibet.

Surface vertical deformation includes the Earth’s elastic response to mass loading on or near the surface. Continuous Global Positioning System (CGPS) stations record such deformations to estimate seasonal and secular mass changes. We used 41 CGPS stations to construct a time series of coordinate changes, which are decomposed by empirical orthogonal functions (EOFs), in northeastern Tibet. The first common mode shows clear seasonal changes, indicating seasonal surface mass re-distribution around northeastern Tibet. The GPS-derived result is then assessed in terms of the mass changes observed in northeastern Tibet. The GPS-derived common mode vertical change and the stacked Gravity Recovery and Climate Experiment (GRACE) mass change are consistent, suggesting that the seasonal surface mass variation is caused by changes in the hydrological, atmospheric and non-tidal ocean loads. The annual peak-to-peak surface mass changes derived from GPS and GRACE results show seasonal oscillations in mass loads, and the corresponding amplitudes are between 3 and 35 mm/year. There is an apparent gradually increasing gravity between 0.1 and 0.9 μGal/year in northeast Tibet. Crustal vertical deformation is determined after eliminating the surface load effects from GRACE, without considering Glacial Isostatic Adjustment (GIA) contribution. It reveals crustal uplift around northeastern Tibet from the corrected GPS vertical velocity. The unusual uplift of the Longmen Shan fault indicates tectonically sophisticated processes in northeastern Tibet.

Earth’s temporal principal moments of inertia and variable rotation

Based on the gravity field models EGM96 and EIGEN-GL04C, the Earth’s time-dependent principal moments of inertia A, B, C are obtained, and the variable rotation of the Earth is determined. Numerical results show that A, B, and C have increasing tendencies; the tilt of the rotation axis increases 2.1×10−8 mas/yr; the third component of the rotational angular velocity, ω3, has a decrease of 1.0×10−22 rad/s2, which is around 23% of the present observed value. Studies show in detail that both θ and ω3 experience complex fluctuations at various time scales due to the variations of A, B and C.

Atmospheric excitation of polar motion

The polar motion excited by the fluctuation of global atmospheric angular momentum (AAM) is investigated. Based on the global AAM data, numerical results demonstrate that the fluctuation of AAM can excite the seasonal wobbles (e.g., the 18-month wobble) and the Chandler wobble, which agree well with previous studies. In addition, by filtering the dominant low frequency components, some distinct polar wobbles corresponding to some great diurnal and semi-diurnal atmospheric tides are found.

New solution for the Earth’s free wobble and its geophysical implications

In this paper, the theory of the free wobble of the triaxial Earth is developed and new conclusions are drawn: the Euler period should be actually expressed by the first kind of complete elliptic integral; the trace of the free polar motion is elliptic and the orientations of its semi-minor and major axes are approximately parallel to the Earth’s principal axes A and B, respectively. In addition, the present theory shows that there is a mechanism of frequency-amplitude modulation in the Chandler wobble, which might be a candidate for explaining the correlation between the amplitude and period of the Chandler wobble.

Coseismic Gravity and Displacement Signatures Induced by the 2013 Okhotsk Mw8.3 Earthquake.

In this study, Gravity Recovery and Climate Experiment (GRACE) RL05 data from January 2003 to October 2014 were used to extract the coseismic gravity changes induced by the 24 May 2013 Okhotsk Mw8.3 deep-focus earthquake using the difference and least square fitting methods. The gravity changes obtained from GRACE data agreed well with those from dislocation theory in both magnitude and spatial pattern. Positive and negative gravity changes appeared on both sides of the epicenter. The positive signature appeared on the western side, and the peak value was approximately 0.4 microgal (1 microgal = 10−8 m/s2), whereas on the eastern side, the gravity signature was negative, and the peak value was approximately −1.1 microgal. It demonstrates that deep-focus earthquakes Mw ≤ 8.5 are detectable by GRACE observations. Moreover, the coseismic displacements of 20 Global Positioning System (GPS) stations on the Earth’s surface were simulated using an elastic dislocation theory in a spherical earth model, and the results are consistent with the GPS results, especially the near-field results. We also estimated the gravity contributions from the coseismic vertical displacements and density changes, analyzed the proportion of these two gravity change factors (based on an elastic dislocation theory in a spherical earth model) in this deep-focus earthquake. The gravity effect from vertical displacement is four times larger than that caused by density redistribution.