We describe the development and assessment of a new terrestrial reference frame (TRF) based on combining GPS, SLR and VLBI at the observation level over the period 2010–2022. Included in the solution, in addition to station coordinates and precise orbit solutions for all participating satellites, are Earth orientation parameters (EOP) and low-degree zonal coefficients (J2 and J3) of the geopotential. The overall solution concept grew from earlier efforts to realize a TRF using GPS data alone, capitalizing on GPS receivers on the ground and in low-Earth orbit (LEO). Here we add observations from both the SLR and VLBI techniques, which provide the foundation for traditional realizations of the TRF.In linking the GPS and SLR techniques, our approach dispenses with traditional ground survey ties, relying exclusively on space ties from the GRACE and Jason LEO missions. In addition to SLR from these satellites, we include observations from the dedicated LAGEOS satellites, which prove particularly important for recovering low-degree gravity. A major evolution of our approach is the addition of VLBI at the observation level. Lacking a robust tie in Earth orbit for VLBI observations, we apply as constraints the published ground survey ties to nearby GPS stations, enforcing inclusion of the corresponding tracking data in the solutions. The VLBI effort is in the exploratory phase, and further tuning of the strategy is needed to better exploit collocations with both GPS and SLR. About 40% of the participating solution arcs (spanning 2010–2022) now include VLBI and support accurate recovery of UT1 as part of the EOP solution.Though the resulting TRF solution is based on only 12.6 years of data, it is competitive with ITRF2020 in terms of fundamental frame parameters (origin and scale) and their temporal evolution, both linear and seasonal. The relative rates of origin (3D) and scale (at Earth's surface) are 0.2 mm yr-1 and 0.1 mm yr-1 respectively. Absolute scale (at epoch 2015.0) and 3D origin both differ by 2 mm. One advantage of our technique is that precise orbit solutions for both GRACE and Jason missions, defined in the realized TRF, are byproducts of the overall solution. We use the Jason orbit solutions to characterize the impact of contemporary TRF errors on sea level variations (both global and regional) and discuss the implications of these results.

We distinguish between geocenter location and geocenter motion for their different purposes: precise orbit determination (POD) and earth surface mass variation monitoring. We present a method to measure the geocenter location through GPS tracked low earth orbiters (LEO) POD. We propose two methods to apply these geocenter location estimates to earth surface mass variation study. 19 years of daily geocenter locations in IGS14 reference frame are estimated from the POD of GPS tracked LEOs. These estimates are applied to 296 globally distributed GPS ground stations measured in the same reference frame for surface mass variation inversion. The results show that such determined geocenter location reaches sub-millimeter precision in each component judged by RMS of the overlapping differences. The geocenter motion change measured using the 80-station GPS orbit and clock product shows similar annual variation to the degree-1 term of the surface mass variation spherical harmonics determined from the 296-station inversion.

Long-term monitoring of global mass transport within the Earth system improves our ability to mitigate natural hazards and better understand their relations to climate change. Satellite gravity is widely used to monitor surface mass variations for its unprecedented spatial and temporal coverage. However, the gravity data contain signals from visco-elastic deformation in response to past ice sheet melting, preventing us from extracting signals of present-day surface mass trend (PDMT) directly. Here we present a global inversion scheme that separates PDMT and visco-elastic glacial isostatic adjustment (GIA) signatures by combining satellite gravimetry with satellite altimetry and ground observations. Our inversion provides global dual data coverage that enables a robust separation of PDMT and GIA spherical harmonic coefficients. It has the advantage of providing estimates of Earth's long wavelength deformation signatures and their uncertainties. Our GIA result, along with its uncertainty estimates, can be used in future GRACE processing to better assess the impact of GIA on surface mass change. Our GIA estimates include a rapid GIA uplift in the Southeast Alaska and the Amundsen Sea Embayment, due to the visco-elastic response to recent glacial unloading. We estimate the average surface mass change rate from 2002-2010 to be -203 +/- 3 GT center dot a(-1) in Greenland, -126 +/- 18 GT center dot a(-1) in Antarctica and, -62 +/- 5 GT center dot a(-1) in Alaska. The GIA low degree spherical harmonic coefficients are sensitive to rheological properties in Earth's deep interior. Our low-degree GIA estimates include geocenter motion and J2 which provide unique constraints to understand Earth's lower mantle and ice history.

The JTRF2014 realization of terrestrial reference frame has adopted a weekly time series representation that can track dominant non-linear station motions including periodic and random variations. The realization is based on the Kalman filter and smoother algorithms whose time sequential nature would also be suitable for continuous updating of an existing frame as soon as new geodetic data become available.As a part of preparation for the next reference frame realization, we have been examining alternative filter and smoother algorithms based on the square-root information filter (SRIF), known generally for improved numerical accuracy of the covariance matrix represented by a square-root matrix.The new algorithms offer a number of other advantages over the conventional filter/smoother algorithms used in JTRF2014. Namely, the new approach allows us to (1) avoid using some fictitious covariance matrix to initialize the filter, (2) avoid the random-walk constraints for the Helmert parameter sequences, and (3) handle cross-temporal EOP data such as the week-long segments reported by the SLR and DORIS networks. We have also been enhancing the stochastic models of the station position motion to be used by the filter and smoother, including models for non-tidal deformation.

Spatiotemporal coverage gaps and the nature of distant signature sources in Global Navigation Satellite System (GNSS) and The Gravity Recovery and Climate Experiment (GRACE) data require global inversions of data combinations for cross validation and complete and continuous monitoring of surface water mass variations. For spectral completeness, accurate data‐based degree‐1 surface mass variation coefficient or equivalent geocenter motion estimates are also desired but very difficult to obtain. To improve the reliability of such estimates, we carry out a new effort to combine different space geodetic technique data in a Kalman filter and time series approach to Terrestrial Reference Frame realization using an advanced formulation. With origin at the center of mass of the Earth system, the new parameterization now includes site displacements in the state vector explicitly for realistic assessment of their covariance matrices. More robust geocenter motion results are achieved when the displacement information is combined further with GRACE gravity data in a unified inversion. Previously, various systematic effects in GNSS data resulted in rather large discrepancies in global surface mass change estimates when compared with those from GRACE gravity data. Here, we show that significantly improved GNSS data after reprocessing and the refined Estimating the Circulation and Climate of the Ocean (ECCO) bottom pressure model reveal a global surface mass variation pattern that has been largely reconciled with that from GRACE data.

The ITRF2014 candidate solutions DTRF2014 and JTRF2014 provide time-dependent station coordinates accounting for irregular station motions. DTRF2014 by DGFI-TUM expands the secular coordinate model via non-tidal loading corrections caused by changes in the atmosphere and continental water storage. JTRF2014 by JPL follows a time series approach to TRF determination based on Kalman filtering, providing weekly updates to station coordinates. The process noise model of the Kalman filter is derived from non-tidal loading deformations. Global features in station displacements have been studied in the past by determining coefficients of spherical harmonics. So far, studies have mostly focused on individual coordinate components at a time. Typically, the vertical coordinate component is of most interest, since it most often contains the largest signals. In this work, we apply the concept of vector spherical harmonics (VSH) to study temporal variations in station displacements of DTRF2014 and JTRF2014. The advantage of VSH compared to scalar spherical harmonics is that all three coordinate components can be considered at the same time. We estimate VSH coefficients up to degree-2, which includes dipole and quadrupole deformations. Degree-1 deformations represent translations and rotations of the frame, while degree-2 terms contain, inter alia, information on the oblateness of the Earth. We use VSH to analyze station displacements of DTRF2014 and JTRF2014 individually and to conduct comparisons between the two frames. Furthermore, since the temporal variations in both DTRF2014 and JTRF2014 are linked to non-tidal loading deformations, our analysis of temporal variations in VSH coefficients allows for geophysical interpretation.

We review the main concepts underlying the determination of terrestrial reference frames (TRFs) through a recursive algorithm based on Kalman Filtering and Rauch-Tung-Striebel (RTS) smoothing which is currently adopted at Jet Propulsion Laboratory (JPL) to compute sub-secular frame products (JTRFs). We contextualize the TRF determination in the state-space framework and we emphasize connections between frame state, its observability through space-geodetic frame inputs and the similarity transformation which is central to frame definition. We elaborate on the notion of sub-secular frame, enabled by our approach, in constrast to standard TRF products which, secular by construction, are designed to represent the long-term mean physical properties of the frame. Comparisons of JTRF solutions to standard products such as the International Terrestrial Reference Frame (ITRF) suggest high-level consistency in a long-term sense with time derivatives of the Helmert transformation parameters connecting the two TRFs below 0.18 mm/yr. We discuss advantages and limitations of JPL approach to TRF determination and outline lines of inquiries that are currently being researched as part of JTRF development plan.

We review the main steps that led to the construction of JTRF2014, the frame solution the Jet Propulsion Laboratory (JPL) submitted for the realization of ITRF2014. In the first part of this technical note, we recall the main concepts underlying the determination of terrestrial reference frames through Kalman Filtering and Rauch-Tung-Striebel smoothing, currently adopted at JPL to compute sub-secular frame products, and we discuss the main results associated with JTRF2014. In the second part, we adopt a comparative approach and, elaborating on metrics associated with Earth Orientation and Helmert transformation parameters, we analyze JTRF2014 in relation to ITRF2014, the official combined frame computed at the Laboratoire de Recherche en Géodésie of the Institut National de l’Information Géographique et Forestière (IGN) and DTRF2014, produced at the Deutsches Geodätisches Forschungsinstitut of the Technische Universität München. Introduction We present and discuss JTRF2014, the Terrestrial Reference Frame (TRF) the Jet Propulsion Laboratory constructed by combining spacegeodetic inputs from Very Long Baseline Interferometry (VLBI), Satellite Laser Ranging (SLR), Global Navigation Satellite Systems (GNSS) and Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS) submitted for the realization of ITRF2014. Determined through a Kalman filter and RTS smoother assimilating position observations, Earth Orientation Parameters (EOPs), and local ties, JTRF2014 is a sub-secular, 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. JTRF2014 is rotationally aligned to ITRF2008 through the implementation of a No-Net-Rotation (NNR) condition applied at each step of the filter. The kinematic evolution of the station positions is described by superimposing a secular motion, annual, and semi-annual 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. This technical note is conceptually articulated in two parts: The first recalls the main concepts underlying the JPL approach to TRF combination and illustrates the main products associated with JTRF2014;

A Kalman filter and time series approach to the International Terrestrial Reference Frame (ITRF) realization (KALREF) has been developed and used in JPL. KALREF combines weekly or daily SLR, VLBI, GNSS and DORIS data and realizes a terrestrial reference frame in the form of time-variable geocentric station coordinate time series. The origin is defined at nearly instantaneous Center-of-Mass of the Earth system (CM) sensed by weekly SLR data and the scale is implicitly defined by the weighted averages of those of weekly SLR and daily VLBI data. The standard KALREF formulation describes the state vector in terms of time variable station coordinates and other constant parameters. Such a formulation is fine for station positions and their uncertainties or covariance matrices at individual epochs. However, coordinate errors are strongly correlated over time given KALREF’s unique nature of combining different technique data with various frame strengths through local tie measurements and co-motion constraints and its use of random walk processes. For long time series and large space geodetic networks in the ITRF, KALREF cannot keep track of such correlations over time. If they are ignored when forming geocentric displacements for geophysical inverse or network shift geocenter motion studies, the covariance matrices of coordinate differences cannot adequately represent those of displacements. Consequently, significant non-uniqueness and inaccuracies would occur in the results of studies using such matrices. To overcome this difficulty, an advanced KALREF formulation is implemented that features explicit displacement parameters in the state vector that would allow the Kalman filter and smoother to compute and return covariance matrices of displacements. The use of displacement covariance matrices reduces the impact of time correlated errors and completely solves the non-uniqueness problem. However, errors in the displacements are still correlated in time. Further calibrations are needed to accurately assess covariance matrices of derivative quantities such as averages, velocities and accelerations during various time periods. We will present KALREF results of the new formulation and their use along with newly reprocessed RL06 GRACE gravity data in a new unified inversion for geocenter motion.

GRACE and GRACE Follow-On (FO) Level 2 data provide quasi-monthly, band-limited estimates of Stokes (geopotential, spherical harmonic) coefficients mostly reflecting surface mass variability due to non-tidal atmosphere, ocean, and continental hydrology. Although space gravimetry does not directly provide CM-related degree-1 Stokes coefficients, GRACE data have been successfully used over the years to complement time series of station positions from global space-geodetic (SG) network when inverting for Center-of-Mass to Center-of-Network (CM-CN) displacements (Wu et al, 2006). Surficial mass variability observed through GRACE/GRACE-FO can be conveniently converted into load-induced (ENU) deformations at SG observing sites by adopting a spectral (i.e. load Love-number based) formalism and assuming Earth’s response is fully elastic and isotropic. GRACE-derived elastic displacements at observing sites would represent, if accurate, band-limited (degree 2 to 96, or higher if Mascon solutions are adopted) load-induced deformations that can be removed from SG-derived station displacements in order to more accurately recover degree-1 surface deformation signature (and therefore geocenter motion). In this study, we adopt GRACE JPL Mascon RL06 data in conjunction with Preliminary Reference Earth Model-derived load Love numbers to infer elastic displacement at SG sites and remove them from SLR inherently geocentric time series of station positions. In so doing, the residual SLR station displacements, consistently expressed in a geocentric frame, would in principle reflect a degree-1 deformation signature that can be recovered via either surface deformation (Chanard et al, 2018) or translational approach. We will compare the SLR/GRACE (CM-CN) determined in this study to standard estimates of geocenter motion such as ILRS’s and JTRF2014’s estimated via translational approach and spectrally inverted solutions (CM-CF). References Chanard K et al, (2018). JGR-Sol Ea doi:10.1002/2017JB015245 Wu X et al, (2006). JGR-Sol Ea doi:10.1029/2005JB004100.

The Global Geodetic Observing System requirement for the long-term stability of the International Terrestrial Reference Frame is 0.1 mm/year, motivated by rigorous sea level studies. Furthermore, high-quality station velocities are of great importance for the prediction of future station coordinates, which are fundamental for several geodetic applications. In this study, we investigate the performance of predictions from very long baseline interferometry (VLBI) terrestrial reference frames (TRFs) based on Kalman filtering. The predictions are computed by extrapolating the deterministic part of the coordinate model. As observational data, we used over 4000 VLBI sessions between 1980 and the middle of 2016. In order to study the predictions, we computed VLBI TRF solutions only from the data until the end of 2013. The period of 2014 until 2016.5 was used to validate the predictions of the TRF solutions against the measured VLBI station coordinates. To assess the quality, we computed average WRMS values from the coordinate differences as well as from estimated Helmert transformation parameters, in particular, the scale. We found that the results significantly depend on the level of process noise used in the filter. While larger values of process noise allow the TRF station coordinates to more closely follow the input data (decrease in WRMS of about 45%), the TRF predictions exhibit larger deviations from the VLBI station coordinates after 2014 (WRMS increase of about 15%). On the other hand, lower levels of process noise improve the predictions, making them more similar to those of solutions without process noise. Furthermore, our investigations show that additionally estimating annual signals in the coordinates does not significantly impact the results. Finally, we computed TRF solutions mimicking a potential real-time TRF and found significant improvements over the other investigated solutions, all of which rely on extrapolating the coordinate model for their predictions, with WRMS reductions of almost 50%.

In recent years, Kalman filtering has emerged as a suitable technique to determine terrestrial reference frames (TRFs), a prime example being JTRF2014. The time series approach allows variations of station coordinates that are neither reduced by observational corrections nor considered in the functional model to be taken into account. These variations are primarily due to non-tidal geophysical loading effects that are not reduced according to the current IERS Conventions (2010). It is standard practice that the process noise models applied in Kalman filter TRF solutions are derived from time series of loading displacements and account for station dependent differences. So far, it has been assumed that the parameters of these process noise models are constant over time. However, due to the presence of seasonal and irregular variations, this assumption does not truly reflect reality. In this study, we derive a station coordinate process noise model allowing for such temporal variations. This process noise model and one that is a parameterized version of the former are applied in the computation of TRF solutions based on very long baseline interferometry data. In comparison with a solution based on a constant process noise model, we find that the station coordinates are affected at the millimeter level. (C) 2018 COSPAR. Published by Elsevier Ltd. All rights reserved.

Geocentre motion between the centre-of-mass of the Earth system and the centre-of-figure of the solid Earth surface is a critical signature of degree-1 components of global surface mass transport process that includes sea level rise, ice mass imbalance and continental-scale hydrological change. To complement GRACE data for complete-spectrum mass transport monitoring, geocentre motion needs to be measured accurately. However, current methods of geodetic translational approach and global inversions of various combinations of geodetic deformation, simulated ocean bottom pressure and GRACE data contain substantial biases and systematic errors. Here, we demonstrate a new and more reliable unified approach to geocentre motion determination using a recently formed satellite laser ranging based geocentric displacement time-series of an expanded geodetic network of all four space geodetic techniques and GRACE gravity data. The unified approach exploits both translational and deformational signatures of the displacement data, while the addition of GRACE's near global coverage significantly reduces biases found in the translational approach and spectral aliasing errors in the inversion.

We 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).

激电测深方法是一种典型的地球物理勘探方法.它被广泛应用于金属矿勘探及地下水勘探中.对称四极测深方法是野外激电测深的主要方法之一.理论上,激发极化方法很少受到地形的影响,主要是因为激发极化方法的基础是地下极化体受到激发电流的激发而产生的极化效应,从而产生二次极化电流,极化率与激发电流的大小没有直接的相关性.但在实际的应用中,由于地形条件的变化,可能导致测深装置的装置系数发生变化,人为的因素可能导致测深的拟断面图发生畸变,影响测深结果的解译.作者通过理论模型的推导方法,形象直观的演示了单斜地形条件下,对称四极激电测深拟断面图发生变形的过程.并通过新疆某地钨矿实例,说明了单斜地形条件下,对实测对称四极激电测深拟断面图进行修正的重要性.

地面高精度磁法剖面测量是矿产勘查工作中常用的一种地球物理勘查方法,它可以通过在地表覆盖层上的测量,大致了解地下磁性体的地下产状及赋存状态,也可以了解磁性体的大致规模及顶部埋深.由于受地形地貌等客观自然条件的限制,许多地方在进行地面高精度磁法剖面测量时,有许多剖面上的测点无法进行正常测量.作者根据磁性体异常的等值线特性,利用一种等值投影的方法,间接获取剖面上测点的磁异常值.从而巧妙的解决了地面高精度磁法剖面测量中,测线上点位缺失的问题.