Secular Motion Research Articles

Viscoelastic behavior of the crust around the Longmenshan Thrust Belt inferred from post-seismic deformation of the 2013 Lushan earthquake, China

Seven continuous GPS stations are located on the hanging wall of the Longmenshan Thrust Belt, and post-seismic deformation data of the 2013 Lushan earthquake have been recorded for nearly four years following the earthquake. We transform the data from a global reference frame to the South China Block reference frame, and then, the secular motion and post-seismic deformation of the Wenchuan earthquake are excluded using an exponential fit model. Based on our results, the viscosities of the low velocity zone at a depth of ∼25 km and of the middle and lower crust around the Longmenshan Thrust Belt are obtained as 2.75×1017Pa·s and 2.56×1018Pa·s, respectively. The post-seismic rebound, which was observed near the Lushan epicenter, may represent the occurrence of overslip during the earthquake. The more complex structural style may have produced weaker fault activity along the southern segment of the Longmenshan Thrust Belt than along its middle and northern segments.

Structure of a Protobinary System: An Asymmetric Circumbinary Disk and Spiral Arms

Abstract We investigate the gas structures around young binary stars using three-dimensional numerical simulations. Each model exhibits circumstellar disks, spiral arms, and a circumbinary disk with an inner gap or cavity. The circumbinary disk has an asymmetric pattern rotating at an angular velocity of approximately one-fourth of the binary orbit of the moderate-temperature models. Because of this asymmetry, the circumbinary disk has a density bump and a vortex, both of which continue to exist until the end of our calculation. The density bump and vortex are attributed to enhanced angular momentum, which is promoted by the gravitational torque of the stars. In a hot model (c ≥ 2.0), the asymmetry rotates considerably more slowly than in the moderate-temperature models. The cold models (c ≤ 0.02) exhibit eccentric circumbinary disks, the precession of which is approximated by a secular motion of the ballistic particles. The asymmetry in the circumbinary disk does not depend on the mass ratio, but it becomes less clear as the specific angular momentum of the infalling envelope increases. The relative accretion rate onto the stars is sensitive to the angular momentum of the infalling envelope. For envelopes with constant angular momentum, the secondary tends to have a higher accretion rate than the primary, except in very low angular momentum cases. For envelopes with a constant angular velocity, the primary has a higher accretion rate than the secondary because gas with low specific angular momentum falls along the polar directions.

Motional resonances of three-dimensional dual-species Coulomb crystals

We investigate the motional resonances of dual-species Coulomb crystals comprised of 9Be+ and 24Mg+ ions held in a 4-rod linear Paul trap. Our experimental data and simulations show that the secular motion of such mixed crystals has rich dynamics. Their secular spectra can differ significantly from those of pure ion crystals. We propose a simple model based on mechanical coupling with Coulomb interactions between the two different ion species that explains many features of the secular spectrum. Our findings contribute to a more reliable identification of the ion species in mixed crystals.

Programs of time-optimal control in the problem of rendezvous transfer of spacecraft with low transversal thrust

We study the problem of determining time-optimal control of in-plane rendezvous transfer of spacecraft with low transversal thrust. We use the Pontryagin maximum principle to determine the optimal control program. Motion is considered in the vehicle centric system with linearized equations. We recognize secular and periodic components of relative motion. Motion control is accomplished by the reversal of the thrust acceleration component. We study the general problem controlling the periodic and secular components at the same time (joint optimal control program). Also we study partial problems determining separate control programs for secular and periodic components of planar motion. Solving partial problems made it possible to determine the structure of the joint optimal control program. We found that the adjustment of secular motion components contains no more than two phases of constant acceleration. The adjustment of periodic motion components consists of a sequence of boost and deceleration phases, the number of which in a single pass does not exceed three.

Interseismic Coupling and Slow Slip Events on the Cascadia Megathrust

In this study, we model geodetic strain accumulation along the Cascadia subduction zone between 2007.0 and 2017.632 using position time series from 352 continuous GPS stations. First, we use the secular linear motion to determine interseismic locking along the megathrust. We determine two end member models, assuming that the megathrust is either a priori locked or creeping, which differ essentially along the trench where the inversion is poorly constrained by the data. In either case, significant locking of the megathrust updip of the coastline is needed. The downdip limit of the locked portion lies ∼ 20–80 km updip from the coast assuming a locked a priori, but very close to the coast for a creeping a priori. Second, we use a variational Bayesian Independent Component Analysis (vbICA) decomposition to model geodetic strain time variations, an approach which is effective to separate the geodetic strain signal due to non-tectonic and tectonic sources. The Slow Slip Events (SSEs) kinematics is retrieved by linearly inverting for slip on the megathrust the Independent Components related to these transient phenomena. The procedure allows the detection and modelling of 64 SSEs which spatially and temporally match with the tremors activity. SEEs and tremors occur well inland from the coastline and follow closely the estimated location of the mantle wedge corner. The transition zone, between the locked portion of the megathrust and the zone of tremors, is creeping rather steadily at the long-term slip rate and probably buffers the effect of SSEs on the megathrust seismogenic portion.

What drives 20th century polar motion?

Astrometric and geodetic measurements show that the mean position of Earth's spin axis drifted through the solid crust toward Labrador, Canada at an average speed of 10.5±0.9 cm/yr during the 20th century. Understanding the origins of this secular polar motion (SPM) has significance for modeling the global climate, as it provides a link to ice mass balance and sea-level rise. A perplexing issue, however, is that while glacial isostatic adjustment (GIA) models satisfactorily explain the direction of SPM, the associated prediction of the amplitude is insufficient. Our Bayesian GIA analysis, with constraints from relative sea-level and vertical land motion data, reveals that this process only accounts for 33±18% of the observed SPM amplitude. This shortfall motivates a more broadly scoped reassessment of SPM drivers. To address this, we assemble a complete reconstruction of Earth's surface mass transport derived from recent advancements in modeling the global 20th century cryospheric, hydrologic, oceanic, and seismogenic mass exchange. The summed signals, nonetheless, cannot fully reconcile the observed SPM, even when considering the error statistics of each driver. We investigate an additional excitation source: changes in Earth's inertia tensor caused by mantle convection. Sophisticated models have recently been advanced in tectonic plate reconstructions, in conjunction with geoid and seismic tomographic models. Here we use these models to compute new estimates of SPM. While the convection-driven SPM has considerable uncertainty, the average direction of 283 recent models aligns with the residual SPM (within 2.7∘±14.8∘), significantly reducing the gap between observation and prediction. We assert that one key mechanism for driving 20th century SPM is long-term mass movement due to mantle convection.

Greedy Automatic Signal Decomposition and Its Application to Daily GPS Time Series

AbstractThe recognition of transient motion in terrestrial continuous Global Positioning System (GPS) time series implies the knowledge of certain time functions that we assume to be ever present in the time series. By assuming that the permanent time functions are the long‐term secular velocity of the Earth and the seasonal oscillations, we define the total remaining signal as transient motion. Here we adopt the multitransient as a versatile function for modeling transient motion over a range of time scales. We define the multitransient as the sum of two or more transient decaying functions with different characteristic time scales and identical onset times. We then demonstrate the greedy approach to fitting the time series by using a minimum number of multitransients (sparse functions) in addition to the permanent time functions in a linear regression. The Greedy Automatic Signal Decomposition algorithm decomposes the signal into three parts: (1) background seasonal motion, (2) secular and transient motion, and (3) a residual (noise). We describe the greedy algorithm with synthetic examples before demonstrating its application to time series of daily GPS solutions. The implementation of the multitransient allows for a more realistic plate‐trajectory model, whereby a full range of transient signal time scales, from short‐duration slow slip to longer‐duration processes such as postseismic slab accelerations or postseismic decay, can all be estimated with the same function. Since Greedy Automatic Signal Decomposition algorithm automatically estimates trend, its application to a GPS network allows for the common mode filter to be applied seamlessly.

A semi-analytical model of the Galilean satellites’ dynamics

The Galilean satellites' dynamics has been studied extensively during the last century. In the past it was common to use analytical expansions in order to get simple models to integrate, but with the new generation computers it became prevalent the numerical integration of very sophisticated and almost complete equations of motion. In this article we aim to describe the resonant and secular motion of the Galilean satellites through a Hamiltonian, depending on the slow angles only, obtained with an analytical expansion of the perturbing functions and an averaging operation. In order to have a model as near as possible to the actual dynamics, we added perturbations and we considered terms that in similar studies of the past were neglected, such as the terms involving the inclinations and the Sun's perturbation. Moreover, we added the tidal dissipation into the equations, in order to investigate how well the model captures the evolution of the system.

Quantitative evaluation of space charge effects of laser-cooled three-dimensional ion system on a secular motion period scale**Project supported by the National Key Research and Development Program of China (Grant No. 2017YFA0304401), the National Natural Science Foundation of China (Grant Nos. 11622434, 11474318, 91336211, and 11634013), the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB21030100), Hubei

In this paper, we introduce a method of quantitatively evaluating and controlling the space charge effect of a laser-cooled three-dimensional (3D) ion system in a linear Paul trap. The relationship among cooling efficiency, ion quantity, and trapping strength is analyzed quantitatively, and the dynamic space distribution and temporal evolution of the 3D ion system on a secular motion period time scale in the cooling process are obtained. The ion number influences the eigen-micromotion feature of the ion system. When trapping parameter q is ∼0.3, relatively ideal cooling efficiency and equilibrium temperature can be obtained. The decrease of axial electrostatic potential is helpful in reducing the micromotion heating effect and the degradation in the total energy. Within a single secular motion period under different cooling conditions, ions transform from the cloud state (each ion disperses throughout the envelope of the ion system) to the liquid state (each ion is concentrated at a specific location in the ion system) and then to the crystal state (each ion is subjected to a fixed motion track). These results are conducive to long-term storage and precise control, motion effect suppression, high-efficiency cooling, and increasing the precision of spectroscopy for a 3D ion system.

Analysis of Secular Ground Motions in Istanbul from a Long-Term InSAR Time-Series (1992–2017)

The identification and measurement of ground deformations in urban areas is of great importance for determining the vulnerable parts of the cities that are prone to geohazards, which is a crucial element of both sustainable urban planning and hazard mitigation. Interferometric synthetic aperture radar (InSAR) time series analysis is a very powerful tool for the operational mapping of ground deformation related to urban subsidence and landslide phenomena. With an analysis spanning almost 25 years of satellite radar observations, we compute an InSAR time series of data from multiple satellites (European Remote Sensing satellites ERS-1 and ERS-2, Envisat, Sentinel-1A, and its twin sensor Sentinel-1B) in order to investigate the spatial extent and rate of ground deformation in the megacity of Istanbul. By combining the various multi-track InSAR datasets (291 images in total) and analysing persistent scatterers (PS-InSAR), we present mean velocity maps of ground surface displacement in selected areas of Istanbul. We identify several sites along the terrestrial and coastal regions of Istanbul that underwent vertical ground subsidence at varying rates, from 5 ± 1.2 mm/yr to 15 ± 2.1 mm/yr. The results reveal that the most distinctive subsidence patterns are associated with both anthropogenic factors and relatively weak lithologies along the Haramirede valley in particular, where the observed subsidence is up to 10 ± 2 mm/yr. We show that subsidence has been occurring along the Ayamama river stream at a rate of up to 10 ± 1.8 mm/yr since 1992, and has also been slowing down over time following the restoration of the river and stream system. We also identify subsidence at a rate of 8 ± 1.2 mm/yr along the coastal region of Istanbul, which we associate with land reclamation, as well as a very localised subsidence at a rate of 15 ± 2.3 mm/yr starting in 2016 around one of the highest skyscrapers of Istanbul, which was built in 2010.

Magnetic field amplification by the r-mode instability

We discuss the magnetic field enhancement by unstable r-modes (driven by the gravitational radiation reaction force) in rotating stars. In the absence of a magnetic field, gravitational radiation exponentially increases the r-mode amplitude α, and accelerates differential rotation (secular motion of fluid elements). For a magnetized star, differential rotation enhances the magnetic field energy. Rezzolla et al (2000–2001) argued that if the magnetic energy grows faster than the gravitational radiation reaction force pumps energy into the r-modes, then the r-mode instability is suppressed. Chugunov (2015) demonstrated that without gravitational radiation, differential rotation can be treated as a degree of freedom decoupled from the r-modes and controlled by the back reaction of the magnetic field. In particular, the magnetic field windup does not damp r-modes. Here we discuss the effect of the back reaction of the magnetic field on differential rotation of unstable r-modes, and show that it limits the generated magnetic field and the magnetic energy growth rate preventing suppression of the r-mode instability by magnetic windup at low saturation amplitudes, α ≪ 1, predicted by current models.

Geodetic Imaging of Time-Dependent Three-Component Surface Deformation: Application to Tidal-Timescale Ice Flow of Rutford Ice Stream, West Antarctica

We present a method for inferring time-dependent three-component surface deformation fields given a set of geodetic images of displacements collected from multiple viewing geometries. Displacements are parameterized in time with a dictionary of displacement functions. The algorithm extends an earlier single-component (i.e., single line of sight) framework for time-series analysis to three spatial dimensions using combinations of multitemporal, multigeometry interferometic synthetic aperture radar (InSAR) and/or pixel offset (PO) maps. We demonstrate this method with a set of 101 pairs of azimuth and range PO maps generated for a portion of the Rutford Ice Stream, West Antarctica, derived from data collected by the COSMO-SkyMed satellite constellation. We compare our results with previously published InSAR mean velocity fields and selected GPS time series and show that our resulting three-component surface displacements resolve both secular motion and tidal variability.

JTRF2014, the JPL Kalman filter and smoother realization of the International Terrestrial Reference System

AbstractWe present and discuss JTRF2014, the Terrestrial Reference Frame (TRF) the Jet Propulsion Laboratory constructed by combining space‐geodetic inputs from very long baseline interferometry (VLBI), satellite laser ranging (SLR), Global Navigation Satellite Systems (GNSS), and Doppler orbitography and radiopositioning integrated by satellite submitted for the realization of ITRF2014. Determined through a Kalman filter and Rauch‐Tung‐Striebel smoother assimilating position observations, Earth orientation parameters, and local ties, JTRF2014 is a subsecular, time series‐based TRF whose origin is at the quasi‐instantaneous center of mass (CM) as sensed by SLR and whose scale is determined by the quasi‐instantaneous VLBI and SLR scales. The dynamical evolution of the positions accounts for a secular motion term, annual, and semiannual periodic modes. Site‐dependent variances based on the analysis of loading displacements induced by mass redistributions of terrestrial fluids have been used to control the extent of random walk adopted in the combination. With differences in the amplitude of the annual signal within the range 0.5–0.8 mm, JTRF2014‐derived center of network‐to‐center of mass (CM‐CN) is in remarkable agreement with the geocenter motion obtained via spectral inversion of GNSS, Gravity Recovery and Climate Experiment (GRACE) observations and modeled ocean bottom pressure from Estimating the Circulation and Climate of the Ocean (ECCO). Comparisons of JTRF2014 to ITRF2014 suggest high‐level consistency with time derivatives of the Helmert transformation parameters connecting the two frames below 0.18 mm/yr and weighted root‐mean‐square differences of the polar motion (polar motion rate) in the order of 30 μas (17 μas/d).

Continuous GPS measurements of crustal deformation in Garhwal-Kumaun Himalaya

We report GPS measurements of crustal deformation from five continuous sites in the Garhwal Kumaun Himalaya. The motion at these sites confirms strain accumulation on the Main Himalayan Thrust (MHT) under the Outer and Lesser Himalaya with a slip deficit rate of 18 mm/year over a width of ∼100 km. Apart from secular plate motion, these sites also exhibit seasonal variations. We model these seasonal variations using the global models of atmospheric and hydrological loads. The influence of these loads is maximum in the vertical component which decreases in the north and then in the east component. All the four sites in the Himalayan region and a site at Delhi show consistency between the observed seasonal variations with that predicted by the model. However, the annual variations in the horizontal component of displacement time series at BDRI (Badrinath) GPS site are not consistent with the predictions which could be due to local site conditions.

The Influence of Orbital Resonances on the Water Transport to Objects in the Circumprimary Habitable Zone of Binary Star Systems

Abstract We investigate the role of secular and mean motion resonances on the water transport from a belt of icy asteroids onto planets or embryos orbiting inside the circumprimary habitable zone (HZ) of a binary star system. In addition, the host-star has an accompanying gas giant planet. For a comparison, we perform two case studies where a secular resonance (SR) is located either inside the HZ close to 1.0 au (causing eccentric motion of a planet or embryos therein) or in the asteroid belt, beyond the snow line. In the latter case, a higher flux of icy objects moving toward the HZ is expected. Collisions between asteroids and objects in the HZ are treated analytically. Our purely dynamical study shows that the SR in the HZ boosts the water transport; however, collisions can occur at very high impact speeds. In this paper, we treat for the first time, realistic collisions using a GPU 3D-SPH code to assess the water loss in the projectile. Including the water loss into the dynamical results, we get more realistic values for the water mass fraction of the asteroid during an impact. We highlight that collisions occurring at high velocities greatly reduce the water content of the projectile and thus the amount of water transported to planets or embryos orbiting inside the HZ. Moreover, we discuss other effects that could modify our results, namely the asteroid’s surface rate recession due to ice sublimation and the atmospheric drag contribution on the asteroids’ mass loss.

Secular chaotic dynamics in hierarchical quadruple systems, with applications to hot Jupiters in stellar binaries and triples

Hierarchical quadruple systems arise naturally in stellar binaries and triples that harbour planets. Examples are hot Jupiters (HJs) in stellar triple systems, and planetary companions to HJs in stellar binaries. The secular dynamical evolution of these systems is generally complex, with secular chaotic motion possible in certain parameter regimes. The latter can lead to extremely high eccentricities and, therefore, strong interactions such as efficient tidal evolution. These interactions are believed to play an important role in the formation of HJs through high-eccentricity migration. Nevertheless, a deeper understanding of the secular dynamics of these systems is still lacking. Here, we study in detail the secular dynamics of a special case of hierarchical quadruple systems in either the ‘2+2' or ‘3+1' configurations. We show how the equations of motion can be cast in a form representing a perturbed hierarchical three-body system, in which the outer orbital angular-momentum vector is precessing steadily around a fixed axis. In this case, we show that eccentricity excitation can be significantly enhanced when the precession period is comparable to the Lidov–Kozai oscillation time-scale of the inner orbit. This arises from an induced large mutual inclination between the inner and outer orbits driven by the precession of the outer orbit, even if the initial mutual inclination is small. We present a simplified semi-analytic model that describes the latter phenomenon.

Planetary chaos and the (In)stability of Hungaria asteroids

The Hungaria asteroid group is located interior to the main asteroid belt, with semimajor axes between 1.8 and 2 AU, low eccentricities and inclinations of 16–35 degrees. Recently, it has been proposed that Hungaria asteroids are a secularly declining population that may be related to the Late Heavy Bombardment (LHB) impactors (Cuk, 2012; Bottke et al., 2012). While Cuk (2012) and Bottke et al. (2012) have reproduced a Hungaria-like population that declined exponentially, the real Hungarias were never confirmed to be unstable to the same degree. Here we find that the stability of Hungarias is strongly dependent on the evolution of the eccentricity of Mars, which is chaotic and unpredictable on Gyr timescales. We find that the high Martian eccentricity chiefly affects Hungarias through close approaches with Mars, rather than planetary secular modes. However, current minimum perihelia of Hungarias (over Myr timescales) are not diagnostic of their long-term stability due to a number of secular and mean motion resonances affecting the Hungaria region Milani et al., 2010. We conclude that planetary chaos makes it impossible to determine the effective lifetimes of observed Hungarias. Furthermore, long-term changes of Martian eccentricity could lead to variable Hungaria loss over time. We speculate that some of the most stable Hungarias may have been placed in their present orbit when the eccentricity of Mars was significantly higher than today.

The pseudopotential for quadrupole fields up to q = 0.9080

Pseudopotential models for radio frequency (rf) electric fields are widely used. However, these approximate and sometimes intuitively introduced methods, can sometimes lead to ambiguities and false conclusions. While a classical model works well for quadrupole fields with small q where the Mathieu parameter β≤0.4 there has been some discussion in the literature of the behavior of a pseudopotential, and, in particular, the secular frequency of ions for larger q near the far end of the stability zone (for example, near qmax≈0.908045 for a=0). This paper analyzes carefully the behavior of secular frequencies calculated both numerically and analytically and demonstrates that the classical formula for the secular frequency in the pseudopotential, ω=βΩ/2remains valid up to β=1. This means that both the secular frequency and the pseudopotential function well depth increase monotonically with q inside the stability zone. However, some models state that the well depth, identified as the pseudopotential function calculated at the edge of a quadrupole aperture, should be zero at both the low q and high q boundaries of the stability zone, with a maximum somewhere between. It is shown that the paradox that the acceptance is zero at both ends of the stability zone and hence the pseudopotential well depth and the pseudopotential quadratic coefficient should be zero at both boundaries of the stability zone is resolved by introducing for large q a pseudopotential well depth and a pseudopotential well width as separate pseudopotential objects to characterize the acceptance, while a quadratic pseudopotential function is used to describe the secular motion of ions but not the acceptance for large q.

Secular Orbit Evolution in Systems with a Strong External Perturber—A Simple and Accurate Model

Abstract We present a semi-analytical correction to the seminal solution for the secular motion of a planet’s orbit under gravitational influence of an external perturber derived by Heppenheimer. A comparison between analytical predictions and numerical simulations allows us to determine corrective factors for the secular frequency and forced eccentricity in the coplanar restricted three-body problem. The correction is given in the form of a polynomial function of the system’s parameters that can be applied to first-order forced eccentricity and secular frequency estimates. The resulting secular equations are simple, straight forward to use, and improve the fidelity of Heppenheimers solution well beyond higher-order models. The quality and convergence of the corrected secular equations are tested for a wide range of parameters and limits of its applicability are given.

Sympathetic Ground State Cooling and Time-Dilation Shifts in an Al27+ Optical Clock

We report on Raman sideband cooling of ^{25}Mg^{+} to sympathetically cool the secular modes of motion in a ^{25}Mg^{+}-^{27}Al^{+} two-ion pair to near the three-dimensional (3D) ground state. The evolution of the Fock-state distribution during the cooling process is studied using a rate-equation simulation, and various heating sources that limit the efficiency of 3D sideband cooling in our system are discussed. We characterize the residual energy and heating rates of all of the secular modes of motion and estimate a secular motion time-dilation shift of -(1.9±0.1)×10^{-18} for an ^{27}Al^{+} clock at a typical clock probe duration of 150ms. This is a 50-fold reduction in the secular motion time-dilation shift uncertainty in comparison with previous ^{27}Al^{+} clocks.