G51A-0594 INVITED
Comparison of noise characteristics of GPS position time-series between the San Francisco Bay area and Southern California networks
The continuous GPS networks located in both the San Francisco (SF) Bay region and Southern California have been installed to measure the deformation from long-wavelength, tectonic processes. The long time- series of position changes from the sites that make up these networks allow us to estimate the spectrum of background noise. Once the background noise has been characterized, it can be used as a benchmark to monitor changes in positions and to detect whether future position changes are consistent with the known, background-noise processes. Williams et al [2004] and Langbein [2008] have previously studied the noise characteristics of the Southern California Integrated GPS Network (SCIGN). In this paper, we use the methods of Langbein [2008] to characterize the noise from the Bay Area Regional Deformation (BARD) GPS network for comparison with results from SCIGN. In particular, we examine only the sites for which there exist more than 3.8 years of observations. Compared with more than 200 sites for SCIGN that existed at the time of Langbein's [2008] study, the BARD network, localized to the SF Bay area, has only 25 sites available for analysis. In addition, where the SCIGN network consists predominately of deeply braced monuments, the BARD network has a mix of monument types, including cement piers pinned to underlying rock, casing of borehole strainmeters, and rock pins. Only recently, with the installation of the Plate Boundary Observatory (PBO), have deeply braced monuments been installed in the SF Bay area. Preliminary examination of both the long-term and short-time noise suggests that there are no major differences in noise characteristics between sites in the SF Bay area and those of SCIGN. Furthermore, there are no large, systematic differences in noise between the differing monument types used in the SF Bay area; finer resolution of any differences is limited due to the lack of time-series with long records of observations.
G51A-0595
Mitigation of tropospheric effects on site velocities of the Bay Area Regional Deformation network
The BARD network is a permanent GPS network comprising 40 GPS sites, installed since 1994 in northern California (Romanowicz et al., 1994). Originally started as a collaborative effort of different Bay Area institutions, since the establishment of the Plate Boundary Observatory, it is now focused on real-time data acquisition from stations operated by UC Berkeley, with plans for expansion in collaboration with USGS/Menlo Park. The BARD network streams data to the Berkeley Seismological Laboratory in real-time (sampling rates of 1s and 15s, depending on the site). All sites transmit data using Frame Relay technology which improves reliability in case of earthquake occurrence. Data are archived at the Northern California Earthquake Data Center (NCEDC, http://www.ncedc.org) and are freely available (Neuhauser et al., 2001). The BARD network is currently able to provide high precision (error < 1mm/yr) velocities over most of northern California. In the vicinity of San Francisco Bay, however, heterogeneous tropospheric effects can scatter site coordinates significantly (amplitudes ~ 5 mm) during a single day of measurements. Such effects can be seen when comparing sites from either side of the Bay, or between the Bay and the Great Valley, further inland. With seven sites located less than 15 km from the Hayward fault, the BARD network is well suited for constraining the slip amplitude (currently ~ 5 mm/yr of creep) along the fault's length; however in order to detect small changes in creep rate, such as slip transients, such tropospheric effects need to be mitigated. We will show recent developments, completed over the past year, designed to improve the estimation of troposphere delay over the BARD network by incorporating additional constraints from ground- and air- based meteorological measurements into our processing.
G51A-0596
An attempt to detect preseismic displacement field of the 2008 Iwate-Miyagi Nairiku Earthquake using InSAR small baseline time-series analysis
The Iwate-Miyagi Nairiku Earthquake (Mj 7.2) occurred at 8:43, JST on June 14 2008, in the northeastern Honshu, Japan. This earthquake caused significant amount of ground displacements with more than 2m of uplift and 1.5m of horizontal displacement at the Kurikoma2 GPS station of GEONET network operated by the Geographical Survey Institute (GSI).In a few years prior to the earthquake, the Kurikoma2 station displaced about 1cm and 2cm to the southeast and upward directions, respectively, according to GSI's analysis. We perform an InSAR small baseline (SB) time-series analysis in order to investigate this slow non-steady movement in detail. We applied an InSAR SB time-series analysis based on Schmidt and Bürgmann (2003; JGR, vol. 108). This method can mitigate atmospheric and orbital artifacts, which constitute dominant sources of error, by assuming a temporal smoothness of displacements. We used seven SAR data acquired by PALSAR onboard the ALOS satellite. We selected three interferograms and stacked them after converting to velocity. For the small baseline processing, we selected and processed 17 small-baseline pairs with definition of small baseline to be less than 2000 m for the perpendicular baseline and 1000 days for the temporal baseline. The interferograms were unwrapped and solved for the temporal evolution of displacements with the time steps defined by the SAR acquisition dates. Preliminary results indicate that atmospheric and orbital effects are still higher than the expected amplitude of preseismic displacements. Though the noise may further be mitigated by careful tuning of analysis parameters, our preliminary results suggest that we probably need more realistic atmospheric correction using independent data such as GPS and meteorological data. Acknowledgment PALSAR data are shared by PIXEL (PALSAR Interferometry Consortium to Study our Evolving Land surface), and provided from JAXA under a contract with ERI, Univ. of Tokyo. The ownership of PALSAR data belongs to METI (Ministry of Economy, Trade and Industry) and JAXA.
G51A-0597
Observation Level Versus a Posteriori Atmosphere Loading Corrections in VLBI Analysis
Since station height and troposphere zenith delay parameters are correlated in VLBI solutions, neglecting atmosphere loading corrections at the observation level could affect station heights and zenith delays. With simulations at single stations and with global VLBI network solutions using all world-wide observed VLBI data since 1984 we investigate, whether it is appropriate to apply daily averages of atmosphere loading corrections a posteriori, i.e. to the estimated station heights, or whether it is necessary to rigorously correct the individual observations before the least-squares adjustment. Whereas station heights in 'single station simulations' are clearly recovered by the use of a posteriori atmosphere loading corrections, the effect in VLBI network solutions is more complicated. Due to the small number of stations and the necessary datum constraints of a VLBI free network adjustment, the omission of atmosphere loading corrections at one station can significantly affect the coordinates of other stations of the network. In this case the station heights cannot be recovered by a posteriori corrections at individual stations. Furthermore, the neglected atmosphere loading effect is partially absorbed by the troposphere zenith delay parameters. Thus, we recommend the use of atmosphere loading corrections at the observation level in VLBI analysis.
G51A-0598
Space and time variability of height and gravity in Northeastern Italy
Hydrological mass variations play a major role in the long and seasonal height and gravity variability. On decadal time scale, environment-related variations of GPS height and gravity have not yet been clearly identified mainly because of the temporal extent of most of the available records. We have studied GPS height, gravity and hydrological time series in northeastern Italy with the aim to identify significant common patterns in the space and time domains by using a Principal Component analysis. Both over long and short time scales, GPS height series show signals induced by different phenomena, for example, those related to mass transport in the Earth system. However, it is not easy to unravel the contribution of the different components in the observed behavior. At GPS sites, the information provided by superconducting gravimeter observations and/or absolute gravity measurements offers a unique means to detect and understand mass contributions.
G51A-0599
Multi-temporal InSAR analysis of landslides in Lyngen region, Norway
Recently developed time-series InSAR techniques estimate the temporal characteristics of surface deformation, by combining information obtained from processing of multiple SAR images acquired over time. These techniques also enable us to measure deformation signals in locations where conventional InSAR failed and reduce the error associated with such measurements. Persistent scatterer (PS) methods and short baseline (SBAS) methods are the most popular of these techniques. Each has been optimized assuming a specific scattering mechanism. PS methods work by identifying the ground resolution elements that are dominated by a single scatterer. A persistent scatterer exhibits reduced baseline and temporal decorrelation due to its stable, point-like scattering mechanism. Interferograms formed with a single master scene are analyzed at single look resolution in order to maximize the signal-to-noise ratio (SNR) of the resolution elements containing a single dominant scatterer. In contrast, small baseline methods assume a distributed scattering mechanism and use complex multi-looking of the interferograms in order to improve the SNR. In order to reduce spatial decorrelation, all possible interferograms with a perpendicular baseline below a certain threshold are used in the analysis. In natural terrain, both types of scattering elements can be observed. By using aspects of PS and SBAS approaches, we are able to extend the spatial coverage of each, and thereby increase InSAR applicability in different terrain types. We apply this new approach to study landslides in the Lyngen region, in Northern Norway. Only 3 acquisitions per year, in the summer season, are viable for InSAR processing in this region. The region is also characterized by steep terrain and fjords, which contribute to the observed interferometric decorrelation. A novel algorithm that attempts to correct for the topographically correlated atmospheric phase screen was also implemented during the pre-processing. The hybrid method not only identified the known land slides in the region, it also identified a denser network of reliable scatterers compared to the PS and the SBAS methods.
G51A-0600
An Improved Network Strain Filter for Detecting Transient Deformation Signals
We have developed a tool to detect transient signals such as aseismic fault slip and magmatic intrusion automatically from large-scale (principally GPS) geodetic arrays, referred to as a Network Strain Filter (NSF). The NSF is capable of detecting transient signals in large data sets which may be difficult to identify by visual inspection of individual time series. The underlying principle is to exploit the spatially coherent nature of tectonic signals. The NSF models GPS displacement time series as a sum of contributions from tectonic transients, steady motion due to secular deformation, site-specific local benchmark motion, reference frame errors, and white noise. Transient deformation is represented by a spatial wavelet basis with time varying coefficients estimated using Kalman filtering techniques. A "hyperparameter" is also estimated to constrain the amount of temporal smoothness of the tectonic deformation. As station distribution is irregular and wavelets have local support (non-zero only over a localized domain), the design matrix is generally ill-conditioned. We investigate two strategies for regularizing the problem. The first is explicit spatial smoothing of the transient deformation. The second is to simply exclude wavelet bases that don't span some minimum number of stations. In this case, the smallest wavelet scale is determined such that the residual variance is consistent with the a priori errors of the data. Similarly the degree of spatial smoothing is determined by a priori knowledge of the data errors. To test the performance of the NSF, we carried out numerical tests using the southern California Integrated GPS Network (SCIGN) station distribution with synthetic transients of variable signal to noise ratio. We tested a six-year-long time series with a slow slip event with a duration of three years. Due to the long duration of the transient event, the contributions from secular motion and benchmark wobble make it difficult to identify the transient signal when the signal amplitude is small. We demonstrate that the NSF can identify the transient signal when the amplitude of noise is comparable to that of signal. We also show that for a low signal to noise case where the signal is difficult to identify by eye, the NSF is capable of recovering the transient deformation field. Application of the method to real GPS data from a Japanese GPS network also shows that the NSF can automatically detect transient motions when aseismic events occurred.
G51A-0601
Probability models of the x, y pole coordinates data
The aim of this study is to find the most appropriate probabilistic model for the x, y pole coordinates time series. We have analyzed the IERS eopc04_05 data set covering the period 1962 - 2008. We have also considered the residual x, y pole coordinate time series, which is computed as the difference between the original data and the corresponding least-squares model of the Chandler circle and annual ellipse. Using the measures of skewness and kurtosis of the empirical distribution of the data, we find that the x, y pole coordinates and the corresponding residuals time series cannot be modeled by a normal (Gaussian) distribution. A normal distribution has zero skewness and a kurtosis value of 3. We have fitted several non- Gaussian distributions to the datasets. They include the Generalized Extreme Value distribution, 4-parameter Beta distribution, Johnson SB and SU distributions, Generalized Pareto distribution and Wakeby distribution. Suitability of these distributions as probabilistic models for the x, y pole coordinates and the corresponding residuals time series are discussed.
G51A-0602
InSAR Analysis of the 2006 Slow Slip Event in the Guerrero-Oaxaca Zone using NARR
Aseismic slip, called Slow Slip Event (SSE), have been observed in the last decade by GPS in subduction zones. The SSE occurring in the Guerrero-Oaxaca Mexican subduction zone are among the largest recorded SSE in the world. They are monitored by 14 permanent GPS stations located in along a N-S transects between Mexico city and Acapulco and another E-W transect along the coast. This network allowed to detect recurrent transient motions, observed about each four years since 1998. This result bring new constrains about subduction dynamic and the seismic gap segment observed on the subduction zones. Nonetheless, improving the coverage of geodetic measurement in this area is essential to better determine the spatial distribution of the slip and, then, the released energy during these events. SAR interferometry (InSAR) has the potential to increase spatial density of geodetic measurements. However detecting SSE by InSAR remains a challenge because the related ground deformations are distributed over long distance (hundreds of km) with small gradient and, in the Guerrero zone, crossing zones of low phase coherence. Here, we present a new approach to improve INSAR measurement of such events with application on an SSE that occurred between April 2006 and December 2006, because it is the best documented event by GPS in the area and because ESA archive radar images covers this event. We investigate ENVISAT images along four descending tracks and two ascending tracks crossing the Guerrero zone. We first process interferograms along the descending track 255 (about 500 km × 100 km) covering the permanent GPS network. We compute 32 interferograms based on 12 Envisat images acquired between November 2004 and March 2007. Starting from the topography-corrected interferograms, the first step aims to correct them from atmospheric perturbations, which are the main limiting factor. Among these perturbations, one can distinguish the tropostatic delay, due to troposphere stratification, usually considered as constant at the frame scale (100 km × 100 km) and delays induced by the turbulent phenomena in atmosphere. Our approach focuses on the correction for tropostatic delay that induced a correlation between phase and elevation. For that purpose, we use NARR (North American Regional Reanalysis), a meteorological model of re-analysis of atmospheric data. This model allows us to calculate the tropostatic delay on a grid with nodes separation of 32km. This correction is an important issue, not only to decrease the atmospheric phase screen, but also to reduce the phase variance and then to help to unwrap the phase. We show that NARR provides a good estimation of the tropostatic delay whose variations are of the same order of magnitude that the amplitude of the delay (10-3 rad/m) between Mexico and the coast. To complete the analysis, a correction of the interferograms for interseismic signal occurring before April 2006 and after December 2006 is needed. Finally, a stacking of the corrected interferogram is performed in order to reduce turbulent atmospheric perturbation.
G51A-0603
SAR Offset-Tracking Analysis on ALOS/PALSAR Data for Obtaining the Three- Dimensional Ground Displacements Caused by the 2008 Mw 7.0 Iwate-Miyagi Earthquake, Northeast Japan
Spaceborne interferometric synthetic aperture radar (InSAR) is a powerful technique to map displacements caused by earthquakes. The areas closest to the slipped fault are, however, often displaced too much to be detected by InSAR, leaving decorrelated phase. It was the case for the Iwate-Miyagi earthquake (Mw 7.0) that occurred in the northeastern Japan in June 2008, whose coseismic ground displacements within effectively a few kilometers from the surface extension of the fault could not be measured by InSAR even from several different orbits. Precise measurement of displacements in such gaps is important for constraining the earthquake fault models and hence for understanding the earthquake physics. A useful technique to measure the displacements in the decorrelated areas is SAR offset tracking. I systematically performed offset tracking on ALOS/PALSAR data acquired from six different paths, in order to measure the displacements caused by the Iwate-Miyagi earthquake as precise as possible. For the range offset measurements, it was found that neglecting the offsets due to topography would bias the results by typically a fraction of pixel, equivalent to one to two meters, on mountains having elevation of 1500 to 2000 meters. Azimuth offset measurements from ascending data contained correlated noise with quasi-regular fluctuation, whose amplitude roughly lay within ± 1 meter. This noise did not appear in the azimuth offset measurements from descending data. The cause of the noise may be ionospheric properties, but is not identified at the moment of writing. More than three directions of offset measurements were combined to compute the complete (three- dimensional) displacement field due to the Iwate-Miyagi earthquake. Measurement uncertainty level was estimated to be comparable to or less than 50 cm, from amplitude fluctuations in areas far from the epicentral region. The obtained displacement field is consistent with GPS measurements within the estimated uncertainty level. The offset tracking results in the areas closest to the fault provided good constraints on the fault model estimation (Fukahata et al., this meeting).
G51A-0604
Filtering techniques to enhance signal extraction from geodetic time series
Filtering and time series processing are widely used in astronomy and geophysics. The main goal of filtration
is to extract useful substance/energy/information. From the mathematical point of view extracting of useful
information from the signal can be performed only if we are able to find a basis (functional, vectorial, etc.),
where it is separable from other components and noise. Fourier, wavelet and natural basis of principal
components are often used for this purpose. Fourier basis is especially important, so as the complex
exponents are the proper functions of linear stationary differential/integral operators, which are used for
dynamic systems description.
Correlation analysis is another very important step, needed for linear filtration, which allows projecting the
signal onto the selected basis and finding out its features. If we need to separate useful components, we
need to transform all the signal into the characteristic space, where our component has specific differences
(e.g., frequency band), and build a procedure of separation, or to build a filter.
More difficult aim is to separate useful components from the signal, which has been non-uniformly distorted
by a dynamic system. In this case a system model should be build and an inverse problem could be
formulated. Additional filtration is needed to regularize the solution and prevent the inadmissible
strengthening of noises. We suggest corrective smoothing as such a procedure.
Hence, we find it is important to develop the methods of generalized transfer function modeling and proper
functions search for the cases of different, may be nonlinear systems. It is possible to
do this, if we can find a set of signals, which involves all the interior of the system, making it to response by all
its "essence".
The Earth is a complex dynamic system, whose responses to various processes encompasses a wide variety
of spatial and temporal scales. We demonstrate some of the main ideas of filtration on the examples of Earth
rotation and other geodetic signals, which can be regarded as the integrated response of the Earth to these
processes. They include mass redistribution and interactions among the earth's core, mantle, and crust;
ocean, hydrosphere, cryosphere, atmosphere, and external celestial excitation bodies.
G51A-0605
Validation of continuous horizontal background oscillations of the Earth with the Kamioka laser strainmeters
Recently the existence of the continuous toroidal modes of the Earth free oscillation was found from horizontal seismometers at several quiet stations [Kurrle and Widmer-Schnidrig, 2008]. The sources of Earth background oscillation have not sufficiently been understood although there has been considerable research on the continuous spheroidal oscillation. At present the signal-to-noise ratio for toroidal events is not so much high as for spheroidal ones because the horizontal component of crustal movement has much higher noise level than the vertical component. More investigation of continuous toroidal mode leads to further insights into the Earth background phenomenon. We examined to search the continuous toroidal modes with the Kamioka laser strainmeters although few time period are available to analysis since there are a lot of earthquake events in recent years. Kamioka station in the deep tunnel underground about 1,000m is very low noise environment. The Kamioka 100m laser strainmeters have high sensitivity in the horizontal-component of crustal strain by high level stability of laser frequency. The noise level at quiet time is 5-6× 10-11 strain/rHz at 3-4mHz and about below 3× 10-11 strain/rHz at over 4.5mHz. One type in our strainmeters is an equal arm interferometer detecting difference of strains in the NS and EW directions. This strainmeter is highly sensitive to shear strain, that is toroidal modes, and is less effect for atmospheric pressure. It is possible to detect the continuous horizontal modes since the power spectrum density is estimated about 5 × 10-11 strain/rHz. For pre-analysis with FFT using the period of first half year in 2007, we found the spectrum peaks at the frequencies coincident with fundamental spheroidal and toroidal modes. Some observed spectral lines laid on the frequencies of toroidal modes, 0T29 and 0T33 and so on in the frequency bands where spheroidal and toroidal modes are clearly separated. As another extraction method we also discuss the availability of the phase sensitive detector method applying lock-in detection.
G51A-0606
Extracting the local hydrological contribution to the gravity signal in Strasbourg (France)
Environmental forcings may influence gravity measurements on a broad band of frequencies, ranging from long-term and annual variations to short-period disturbances of a few hours, possibly hiding internal processes of geodynamic interest. Hydrology, in particular, is pointed out to have a 100 nm.s-2 contribution. We investigate the contribution of local hydrology to the superconducting gravimeter installed in the Strasbourg observatory. A deterministic approach will be presented, where both amount and distribution of water masses in the vicinity of the gravimeter have to be determined before calculating newtonian attraction. To this purpose, two multi-depth frequency-domain reflectometer (FDR) probes have been installed. They have been monitoring the variation of the water content of the entire soil thickness since August 2005. A precise local DEM has been established using dGPS. The geometry and heterogeneity of the soil layer have been evaluated thanks to geophysical and geomecanical prospections. This information allows to set up the CLSM (Catchment-based Land Surface Model) in order to evaluate evapotranspiration and lateral water redistribution. This finally allows to calculate water mass variations for a 7-year time period. Results show that daily up to seasonal variations are in good agreement with gravity data. For long term variations, deep water storage and other processes have to be modelled to explain recorded gravity variations.
G51A-0607
The common signal of the geocenter motion in the DORIS and SLR time series
Surface mass redistribution within the Earth system, especially in the atmosphere, oceans, continents and ice sheets, causes the position of the Earth's center of mass (geocentre) to vary in a reference frame attached to the solid Earth. Space techniques as the Doppler Orbitography and Radiopositioning Integrated on Satellite (DORIS) and the Satellite Laser Ranging (SLR) can measure the geocenter motion. DORIS has historically not produced reliable solutions for geocenter, particularly in the Z direction, however we experiment with improvements in radiation pressure modelling described by Gobinddass, M-L et al. (J. Geodesy, submitted) using the GEODYN Orbit Determination and Geodetic Parameter Estimation Software where we explicitly solve for the geocenter signals. In this study, we analyze geocenter motion signals derived from the DORIS and the SLR space geodetic techniques, and comparing with external models. The goal is to underline the common signal found in each of these GSFC solutions and to point out the expected difference of the noise. For this concern, we use statistical tools as the principal component analysis and the multi-variate spectral singular analysis.
G51A-0608
Possible Detection of Ocean Loading Deformation Associated With the 9 November 2007 North Sea Storm Surge Using GPS: Preliminary Results
Storm surges on the north-west European shelf are reasonably common ocean events that affect many coastal areas and pose a serious flood hazard in the UK, the Netherlands and Germany. The 9 November 2007 event was the worst storm surge experienced in almost two decades with nearly catastrophic scale. Crustal deformations of the Earth caused by ocean tide loading can be observed through a number of geodetic techniques and require adequate models to remove their effects within daily or sub-daily position estimates. On the other hand, the deformation associated with such loading processes helps inform the understanding of the Earth interior and can, therefore, be of great interest. The detection and/or separation of the mm to cm-level deformation caused by a storm surge using GPS measurements is not routine. Firstly, due to the short period of the event (which usually lasts less than 24 hours), accurate determination of the sub-daily deformation signal is required and, secondly, the rapidly changing atmospheric pressures associated with intense low pressure systems occurring during surge events, pose some difficulty when estimating tropospheric delays of the GPS observations. In this presentation, continuous GPS measurements from central and north-west Europe are used to determine the sub-daily deformation along the North Sea coast. The Precise Point Positioning (PPP) technique with a recent ambiguity resolution strategy is used to process several days of data continuously and produce two-hourly position estimates. The preliminary GPS results compare well with initial model predictions of the loading deformation and indicate that the vertical component experiences the most significant variation at the several cm-level. In addition, the horizontal components suggest mm-level deformation pointing towards the centre of the storm surge.
G51A-0609
Multiscale Estimation of GPS Velocity Fields
We present a spherical-wavelet-based multiscale representation for three-component velocities on the earth's surface, as a tool to facilitate analysis of geodetic observations in dense GPS networks. We design an efficient inverse problem to determine a set of wavelet coefficients that describe the irregularly distributed observations. Once the velocity field is estimated, we readily compute spatial derivative quantities, such as the strain rate and dilatation rate. In comparison to previous GPS studies, novel aspects of our approach include: (1) an explicit and consistent decomposition of the velocity field into multiple scales at all locations; (2) a minimum scale at which we estimate the velocity field at a particular location that is controlled by local station coverage; (3) inclusion of the vertical velocity observations if they are available; and (4) use of spherical wavelets in representing the velocity field. The multiscale approach has the additional advantage of allowing one to compare estimated quantities in different locations, but at the same scale. We test the method for several synthetic examples, as well as for the NASA REASoN cGPS velocity field for southern California. Thus far we have only concentrated on the spatial representation of a time-dependent displacement field, showing that the multiscale representation is well-suited to identifying and characterizing geophysical signals. Our approach is a step toward monitoring of GPS time series, in hopes of identifying and characterizing transient deformation. By focusing on quantities inferred from multiple sites (e.g., strain rate), our approach does not rely on individual stations, and instead focuses on locally correlated behavior.
G51A-0610
Impact of a mapping function on spurious vertical deformations due to mismodeling of tropospheric delay over Japan
We quantitatively estimate the spurious annual vertical deformations due to the mismodeling of tropospheric delays over Japan through a numerical simulation, and discuss how a mapping function used in the GPS analysis affects characteristics of the resultant spurious vertical deformations in terms of the amplitudes/phases of annual variations or the noise spectrum. For this purpose, we simulate the GPS data for present-day satellite distributions using realistic cumulative tropospheric delays that are calculated using ray tracing and numerical weather models. To obtain the spurious deformations, the simulated GPS data are analyzed by using the GIPSY software in the PPP mode with several different mapping functions. First, we used the NMF in the GPS analysis. As a result, it is found that the amplitudes of the annual vertical deformations increase toward the north, reaching up to 3 mm at around 45° N while the phase lags are uniform throughout Japan and vary by around 220°, indicating spurious subsidence in the middle of February. Next, we used the GMF in the GPS analysis. As a result, it is found that the maximum amplitude of the annual vertical deformations is reduced to 1.5 mm at around 35° N while the phase lags are similar to those obtained by using the NMF. Thus it is found that the spurious signals are mitigated by using mapping functions that are constructed by using direct ray tracing and numerical weather models in the GPS analysis such as the GMF. We will further test other mapping functions such as VMF1 as well. Then we will discuss how a mapping function affects the interpretation of annual vertical deformations over Japan. We will also discuss an impact of a mapping function on the noise characteristics of the spurious vertical deformations in terms of the RMS or a slope of the spectrum.
G51A-0611
A Modified Approach to Estimate the Paleogravity
After a series of modification on my previous approach, I have reached a feasible way to estimate the paleogravity. Same as in previous work, we drill out a vertical lava core cylinder from a typical ancient igneous rock mass, we cut out three pieces of un-decayed sample sectors, from higher position to lower position. By measuring their density D1, D2 and D3 and elastic deformation modulus E1, E2 and E3, respectively, we can find out the paleogravity by following equations: g= Qg /Q, where Q= A21 B32 - A32 B21, Qg = E21 B32 - E32 B21, and where A21= D21 (H2 - H1), A32= D32 (H3 - H2), E21= E2 - E1, E32= E3 - E2, B21=E2/ D2 - E1/ D1, B32=E3/ D3 - E2/ D2. Where Di is the density of sector i, Dij is the average density from sector i to sector j, H is the sector depth from the top of cylinder. Considering the difference between the deformation module Elab measured in lab and the real deformation module during the whole cooling process, we must understand all the deformation modules in above equations as equivalent deformation modules Eeqv , Eeqv = cElab, the equivalent coefficient c could be determined by same type of igneous rock with young age. To calculate the gravity during the solar eclipse, we may take a little modification on Newton's gravitational law, similar to Maxwell's equations, gravitational force is retarded, and it is related to the velocity vector of the gravitational source relative to the observation point, the difference from Newton's law is about the ratio of source velocity vector to light speed.