Michael B. Heflin

Precise point positioning for the efficient and robust analysis of GPS data from large networks

Networks of dozens to hundreds of permanently operating precision Global Positioning System (GPS) receivers are emerging at spatial scales that range from 100 to 103 km. To keep the computational burden associated with the analysis of such data economically feasible, one approach is to first determine precise GPS satellite positions and clock corrections from a globally distributed network of GPS receivers. Then, data from the local network are analyzed by estimating receiver-specific parameters with receiver-specific data; satellite parameters are held fixed at their values determined in the global solution. This “precise point positioning” allows analysis of data from hundreds to thousands of sites every day with 40-Mflop computers, with results comparable in quality to the simultaneous analysis of all data. The reference frames for the global and network solutions can be free of distortion imposed by erroneous fiducial constraints on any sites.

Plate motion and crustal deformation estimated with geodetic data from the Global Positioning System

We use geodetic data taken over four years with the Global Positioning System (GPS) to estimate (1) motion between six major plates and (2) motion relative to these plates of ten sites in plate boundary zones. The degree of consistency between geodetic velocities and rigid plates requires the (one-dimensional) standard errors in horizontal velocities to be ∼2 mm/yr. Each of the 15 angular velocities describing motion between plate pairs that we estimate with GPS differs insignificantly from the corresponding angular velocity in global plate motion model NUVEL-1A, which averages motion over the past 3 m.y. The motion of the Pacific plate relative to both the Eurasian and North American plates is observed to be faster than predicted by NUVEL-1A, supporting the inference from Very Long Baseline Interferometry (VLBI) that motion of the Pacific plate has sped up over the past few m.y. The Eurasia-North America pole of rotation is estimated to be north of NUVEL-1A, consistent with the independent hypothesis that the pole has recently migrated northward across northeast Asia to near the Lena River delta. Victoria, which lies above the main thrust at the Cascadia subduction zone, moves relative to the interior of the overriding plate at 30% of the velocity of the subducting plate, reinforcing the conclusion that the thrust there is locked beneath the continental shelf and slope.

Seismic cycle and plate margin deformation in Costa Rica: GPS observations from 1994 to 1997

Global Positioning System (GPS) observations in Costa Rica from 1994 to 1997 reveal a complex pattern of motion consistent with the superposition of seismic cycle and secular plate margin deformation. In the south, velocity vectors are consistent with motion of the Panama Block plus postseismic deformation following the 1991 Limon earthquake and interseismic strain due to partial locking of the Middle America Trench (MAT) thrust. In the northwest, sites west of the volcanic arc are moving to the NW as a forearc sliver. Superimposed on this sliver motion are vertical and horizontal interseismic deformations from the adjacent Nicoya segment of the MAT. We apply two different inverse methods to understand the source of the seismic strain in NW Costa Rica. We compare fault-locking models derived using a singular value decomposition inversion with that of a simulated annealing global optimization approach. Both methods yield similar models for partial locking of the thrust interface beneath the Nicoya Peninsula. Our results define an area of nearly fully locked fault beneath the outer coast of the southern portion of the peninsula, with somewhat lower coupling beneath the northern half and with low coupling elsewhere. These initial results show the promise for detailed imaging of the locked portion of a thrust interface responsible for future large subduction zone earthquakes.

Continuous monitoring of surface deformation at Long Valley Caldera, California, with GPS

Continuous Global Positioning System (GPS) measurements at Long Valley Caldera, an active volcanic region in east central California, have been made on the south side of the resurgent dome since early 1993. A site on the north side of the dome was added in late 1994. Special adaptations for autonomous operation in remote regions and enhanced vertical precision were made. The data record ongoing volcanic deformation consistent with uplift and expansion of the surface above a shallow magma chamber. Measurement precisions (1 standard error) for “absolute” position coordinates, i.e., relative to a global reference frame, are 3–4 mm (north), 5–6 mm (east), and 10–12 mm (vertical) using 24 hour solutions. Corresponding velocity uncertainties for a 12 month period are about 2 mm/yr in the horizontal components and 3–4 mm/yr in the vertical component. High precision can also be achieved for relative position coordinates on short (<10 km) baselines using broadcast ephemerides and observing times as short as 3 hours, even when data are processed rapidly on site. Comparison of baseline length changes across the resurgent dome between the two GPS sites and corresponding two-color electronic distance measurements indicates similar extension rates within error (∼2 mm/yr) once we account for a random walk noise component in both systems that may reflect spurious monument motion. Both data sets suggest a pause in deformation for a 3.5 month period in mid-1995, when the extension rate across the dome decreased essentially to zero. Three dimensional positioning data from the two GPS stations suggest a depth (5.8±1.6 km) and location (west side of the resurgent dome) of a major inflation center, in agreement with other geodetic techniques, near the top of a magma chamber inferred from seismic data. GPS systems similar to those installed at Long Valley can provide a practical method for near real-time monitoring and hazard assessment on many active volcanoes.

Site distribution and aliasing effects in the inversion for load coefficients and geocenter motion from GPS data

Precise GPS measurements of elastic relative site displacements due to surface mass loading offer important constraints on global surface mass transport. We investigate effects of site distribution and aliasing by higher-degree (n greater than or equal 2) loading terms on inversion of GPS data for n = 1 load coefficients and geocenter motion. Covariance and simulation analyses are conducted to assess the sensitivity of the inversion to aliasing and mismodeling errors and possible uncertainties in the n = 1 load coefficient determination. We found that the use of center-of-figure approximation in the inverse formulation could cause 10- 15% errors in the inverted load coefficients. n = 1 load estimates may be contaminated significantly by unknown higher-degree terms, depending on the load scenario and the GPS site distribution. The uncertainty in n = 1 zonal load estimate is at the level of 80 - 95% for two load scenarios.

Shortening and thickening of metropolitan Los Angeles measured and inferred by using geodesy

Geodetic observations using the Global Positioning System (GPS) and other techniques record a high rate of north-south shortening in an east-southeast–trending, 5–40-km-wide belt in northern metropolitan Los Angeles, California. Downtown Los Angeles is observed to be converging upon the southern San Gabriel Mountains at 6 mm/yr. Aside from the elastic strain that will be released during earthquakes rupturing the San Andreas and San Jacinto faults, east-west lengthening across northern metropolitan Los Angeles is minor, <2.5 mm/yr. Therefore north-south shortening is accommodated mainly by vertical crustal thickening.

The coseismic geodetic signature of the 1999 Hector Mine earthquake

The M = 7.1 Hector Mine earthquake ruptured the Lavic Lake fault near Twentynine Palms, CA at 09:46 UTC October 16, 1999. Because it occurred near the eastern edge of the Southern California Integrated GPS Network (SCIGN), a network of permanent, continuously recording GPS receivers for measuring the crustal deformation field around Los Angeles, CA, it was possible to determine the deformation associated with the earthquake with unprecedented speed and reliability. Thirty-four stations recorded displacements over the 3-sigma level. The displacements measured with GPS can be modeled by a fault 46.2±2.6 km long, 8.2±1.0 km wide, striking 330°, dipping 84° east, with 301±36 cm right lateral strike-slip, and 145±36 cm of east-up dip-slip, yielding a potency of 1.3 km³ and geodetic moment of 3.8 × 1026 dyne-cm. The trace and dip of the model fault is consistent with the observed ground rupture and seismic focal mechanisms.

Precise determination of Earth's center of mass using measurements from the global positioning system

Global Positioning System (GPS) data from a worldwide geodetic experiment were collected during a 3-week period early in 1991. Geocentric station coordinates were estimated using the GPS data, thus defining a dynamically determined reference frame origin which should coincide with the earth center of mass, or geocenter. The 3-week GPS average geocenter estimates agree to 7-13 cm with geocenter estimates determined from satellite laser ranging, a well-established technique. The RMS of daily GPS geocenter estimates were 4 cm for x and y, and 30 cm for z.

DPOD2008: A DORIS-Oriented Terrestrial Reference Frame for Precise Orbit Determination

While accuracy of tracking station coordinates is of key importance for Precise Orbit Determination (POD) for altimeter satellites, reliability and operationality are also of great concern. In particular, while recent ITRF realizations should be the most accurate at the time of their computation, they cannot be directly used by the POD groups for operational consideration for several reasons such as new stations appearing in the network or new discontinuities affecting station coordinates. For POD purposes, we computed a new DORIS terrestrial frame called DPOD2008 derived from ITRF2008 (as previously done by DPOD2005 with regards to ITRF2005). In a first step, we will present the method used to validate the past ITRF2008 using more recent DORIS data and to derive new station positions and velocities, when needed. In particular, discontinuities in DORIS station positions and/or velocities are discussed. To derive new DORIS station coordinates, we used recent DORIS weekly time series of coordinates, recent GPS relevant time series at co-located sites and also dedicated GPS campaigns performed by IGN when installing new DORIS beacons. DPOD2008 also contains additional metadata that are useful when processing DORIS data, for example, periods during which DORIS data should not be used or at least for which data should be downweighted. In several cases, a physical explanation can be found for such temporary antenna instability. We then demonstrate improvements seen when using different reference frames, such as the original ITRF2008 solution, for precise orbit determination of altimeter satellites TOPEX/Poseidon and Jason-2 over selected periods spanning 1993–2013.

KALREF—A Kalman filter and time series approach to the International Terrestrial Reference Frame realization

The current International Terrestrial Reference Frame is based on a piecewise linear site motion model and realized by reference epoch coordinates and velocities for a global set of stations. Although linear motions due to tectonic plates and glacial isostatic adjustment dominate geodetic signals, at todays millimeter precisions, nonlinear motions due to earthquakes, volcanic activities, ice mass losses, sea level rise, hydrological changes, and other processes become significant. Monitoring these (sometimes rapid) changes desires consistent and precise realization of the terrestrial reference frame (TRF) quasi-instantaneously. Here, we use a Kalman filter and smoother approach to combine time series from four space geodetic techniques to realize an experimental TRF through weekly time series of geocentric coordinates. In addition to secular, periodic, and stochastic components for station coordinates, the Kalman filter state variables also include daily Earth orientation parameters and transformation parameters from input data frames to the combined TRF. Local tie measurements among colocated stations are used at their known or nominal epochs of observation, with comotion constraints applied to almost all colocated stations. The filter/smoother approach unifies different geodetic time series in a single geocentric frame. Fragmented and multitechnique tracking records at colocation sites are bridged together to form longer and coherent motion time series. While the time series approach to TRF reflects the reality of a changing Earth more closely than the linear approximation model, the filter/smoother is computationally powerful and flexible to facilitate incorporation of other data types and more advanced characterization of stochastic behavior of geodetic time series.