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On the Effect of Reference Frame Motion on Insar Deformation Estimates

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On the Effect of Reference Frame Motion on Insar Deformation Estimates ON THE EFFECT OF REFERENCE FRAME MOTION ON INSAR DEFORMATION ESTIMATES Hermann Bahr¨ 1, Sami Samiei-Esfahany2, and Ramon F. Hanssen2 1Geodetic Institute, Karlsruhe Institute of Technology, Englerstrasse 7, 76131 Karlsruhe, Germany, [email protected] 2Department of Remote Sensing, Delft University of Technology, Kluyverweg 1, 2629 HS Delft, The Netherlands, [email protected], [email protected] ABSTRACT Observing from a viewpoint on a tectonic plate, the co- ordinate frame of the orbits performs a relative motion in the order of centimetres per year. Neglecting this in In- For processing of interferometric synthetic aperture radar SAR processing is comparable to making an error in the (InSAR) data, precise satellite orbits are required. These interferometric baseline, the size of which is increasing orbits are givenin a referenceframe with respect to which with the temporal baseline. The effect on the interfero- tectonic plates perform a relative motion. Neglecting metric phase is an almost linear trend in range, suggest- this motion can cause temporally increasing baseline er- ing a large scale tilt of the surface. In contrast to tem- rors that induce large scale error ramps into the inter- porally uncorrelated ramps caused by orbital errors, this ferometric phase. The amount of error depends on the kind of trend is correlated in time and cannot be sepa- geographical location and is evaluated globally for the rated from spatio-temporally correlated deformation sig- ENVISAT orbit. Predicted biases of deformation esti- nals. Hence, it can mistakenly be interpreted as an actual mates can reach up to 7 mm/a in some areas. Whereas deformation signal in applications where the signal of in- these biases are not separable from actual deformation terest is a large scale deformationover a long time period, signals by spatio-temporal correlation properties, they are e. g., in monitoring interseismic tectonic motions. well predictable and can easily be accounted for. A most simple correction approach consists in compensating the This contribution investigates the effect of neglecting the plate motion by modifying orbital state vectors, assum- relative tectonic motion on InSAR deformation estimates, ing a homogeneous velocity for the whole plate. This henceforth referred to as the reference frame effect. Af- approach has been tested on Persistent Scatterer Inter- ter a brief review on the ITRF and orbit errors in SAR ferometry (PSI) results over the area of Groningen, the interferometry, the effect will be described in detail and Netherlands. evaluated globally. A simple correction approach will be proposed and applied on ENVISAT PSI results from the Groningen area in the Netherlands. Key words: InSAR; Baseline Error; Reference Frame; ITRF; Plate Tectonics. 2. THE ITRF 1. INTRODUCTION ITRF station positions and velocities are based on obser- vations from space geodetic techniques like Very Long InSAR deformation analysis is based on comparing the Baseline Interferometry (VLBI), Satellite Laser Ranging measured interferometric phase of two images with the (SLR), Global Navigation Satellite Systems (GNSS) and reference phase computed from acquisition geometry. Doppler Orbitography and Radiopositioning Integrated The latter is deduced from precise orbit ephemerides, by Satellite (DORIS). Starting with ITRF88, twelve re- which are commonly expressed in the International Ter- leases have been published to date, continuously improv- restrial Reference Frame (ITRF). This frame is a realisa- ing and refining estimation strategies. The most recent tion of a global coordinate system and defined by a num- ones are ITRF2000 [1], ITRF2005 [2] and ITRF2008 [3]. ber of geodetic stations close to the earth surface. To ac- The oldest observations date from about 1980, and the count for secular tectonic motion, not only positions but number of the respective release approximately specifies also linear velocities are attributed to the ITRF stations. the year of the latest observations included. ITRF2008 comprises positions and velocities of 935 stations, i. e., A common assumption for InSAR processing is that the radio telescopes, SLR lasers, GPS antennas and DORIS reference system of the orbit data does not move with re- beacons. For some stations, multiple solutions have been spect to the earth surface. However, due to plate tecton- estimated for time spans separated by discontinuities like ics, this assumption is not valid at the centimetre level. tectonic events or antenna changes. _____________________________________________________ Proc. ‘Fringe 2011 Workshop’, Frascati, Italy, 23 September 2011 (ESA SP-697, January 2012) (a) Acquisition geometry in the ITRF datum. (b) Acquisition geometry in the reference system of a motionless tec- tonic plate. Figure 1: Geometry of a master acquisition from orbit M at time TM and a slave acquisition from orbit S at time TS. (a) The sensor positions M and S are given in ITRF coordinates, whereas the tectonic plate incorporatingthe acquired region, performs a relative motion#» with respect#» to the ITRF. Assuming a non-deformingplate, this motion can be described by the displacement vector m = (TS − TM ) v of a nearby ITRF station P0. If the motion is neglected for the computation of ∗ ∗ the reference phase, the biased range RS is used in eq. (1), implying a biased perpendicular baseline B⊥. (b) Observing from a viewpoint on the tectonic plate, ITRF coordinates perform a relative motion, which has to be applied to the orbit data to yield an unbiased reference phase. The ITRF is defined by three-dimensional station posi- computed from the simulated ranges RM and RS of mas- tions and velocities (i. e., 6 parameters per station) and ter and slave acquisitions, respectively (see fig. 1) [5]: has thus 14 degrees of freedom (corresponding to seven parameters of a similarity transformation and their rates 4π 4π of change) to define its datum. The three translations φref = − (RM − RS) ≈ − B , (1) and their rates are defined by the centre of mass of the λ λ earth sensed by SLR, and the scale and its rate are fit to the metre convention via SLR and VLBI measurements where λ is the radar wavelength, and B is the compo- [3]. The orientation of the frame is basically arbitrary, nent of the interferometric baseline B in ranging direc- aligning the three orientation parameters and their rates tion. The reference phase is commonly decomposed into recursively to preceding ITRF realisations [1, 2, 3]. For separate contributions of the ellipsoid and the superim- ITRF2000 however, the time evolution of the orientation posed topography. However, this discrimination will not has been explicitly aligned to the geophysical plate kine- apply to the following considerations. matic model NNR-NUVEL-1A [1, 4]. Consequently, this alignment applies recursively to the subsequent releases Errors or residual inaccuracies in orbits may induce an ITRF2005 and ITRF2008. almost linear signal into the interferometric phase (see fig. 2). In this context, only relative errors, i. e., baseline Satellite orbital state vectors are commonly expressed in errors, have a significant impact. Parameterising them by the ITRF datum, because the underlying orbit solutions the temporally variable baseline components B(t) and are generally aligned to the ITRF positions and velocities B⊥(t) (see fig. 1), it has been concluded in [7] that errors ˙ ˙ of a number of ground control points from the tracking in B and B⊥ are negligible. Errors in B induce an network. almost linear error signal in azimuth, whereas errors in B⊥ induce a similar signal in range. From the differential equation: 3. ORBIT ERRORS IN SAR INTERFEROMETRY 4π 4π dδφ = − δB˙ dt − δB dθ , (2) ref λ λ ⊥ In InSAR processing, the reference phase has to be sub- tracted from an interferogram to reveal a potential defor- the relationship between errors δφref in the reference mation signal. It is defined as the theoretical phase mea- phase and baseline errors δB can be inferred, where θ surement that would be obtained in absence of deforma- is the look angle, and ∂B/∂θ = B⊥. Note that t stands tion, atmospheric signals and all kinds of errors. It can be for the acquisition time and actually represents a spatial in the perpendicular baseline due to neglecting the refer- ence#» frame effect can be predicted from the component of v perpendicular to the line of sight: ∗ δB⊥(T ) = B⊥ − B⊥(T ) = v⊥(T − T0) . (4) δB δB δB˙ δB˙ (a) (b) ⊥ (c) (d) ⊥ −π π The component δB in ranging direction can be ignored, since it does not affect the interferometric phase in a sig- Figure 2: Interferometric error signals induced by er- nificant way (see fig. 2). The maximum bias of the refer- rors in particular baseline components, computed for a ence phase in range can be predicted according to eq. (2): full ENVISAT scene of 100 × 100 km [7]. (a) δB = 26 cm. (b) δB⊥ = 26 cm, equivalent to one fringe in ˙ 4π range. (c) δB = 1.7 mm/s, equivalent to one fringe in ∆ δφ (T ) = − v (T − T0) ∆θ , (5) rg ref λ ⊥ azimuth. (d) δB˙ ⊥ = 1.7 mm/s. where ∆θ is the look angle differencebetween near range coordinate, specifying a location along the orbit. In the and far range. For instance, ∆rgδφref = 2π would imply following, a capital T will stand for another timescale, an almost linear error signal of one fringe in range (see fig. 2b). Translating ∆rgδφref into an error in the esti- referencing individual acquisition dates in a long-term ′ context. Derivatives are defined by: x˙ = ∂x/∂t and x′ = mated ground displacement rate D in the line of sight ∂x/∂T . yields: ′ ∆rgδD = −v⊥∆θ . (6) 4. THE REFERENCE FRAME EFFECT Here, the sign has been inverted twice with respect to eq. (5). The first change of sign accounts for the fact 4.1. Description that the reference phase is subtracted from the measured phase, and the second one re-defines a temporally in- Fig. 1 illustrates how the neglect of relative tectonic mo- creasing phase (or range) as negative displacement (sub- tion can bias the computed reference phase.
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