G53C-01 INVITED
Zeroing in on small-scale features in coseismic inversions: how low can we go?
First order goals in inversions of geodetic data may include determining the location and orientation of the fault plane and the earthquake magnitude, perhaps in near real-time for use in disaster response efforts. Other possible targets include the study of the interaction between seismicity and Coulomb stress changes or earthquake triggering through stress transfer from the lower crust. In all cases, it is essential to know how confident we can be about the conclusions we draw from the data, requiring that we assess not only the contribution from data error, but also from errors in the models we use in inversions. Current methods of inverting geodetic data for coseismic fault slip often rely on simple elastic half space or layered space models to describe the crustal response to dislocations on a given fault plane, and they always (necessarily) rely on fault planes parameterizations that are much simpler than the true rupture geometry. The neglect of the 3D variations in rigidity that exist within the real Earth can bias inversion results, whether the goal is determining the optimal fault plane geometry associated with a particular event or to find the best-fitting co-seismic slip distribution. For many tectonically active areas, such as Southern California, sophisticated models of crustal elastic moduli and fault plane geometries are available. However, inversions using the full 3D elastic structure and/or meshes that include fault interactions and non-planar ruptures are very computationally expensive. Here, we explore the sensitivity of models to these simplifications as part of an effort to determine a priori which assumptions are reasonable for particular families of coseismic inversion problems.
G53C-02 INVITED
Measuring Surface Deformations Induced by Present-Day Ice Melting in Svalbard
The vertical movement of the Earth's surface is the result of a number of internal processes in the solid Earth, tidal forces, and mass redistribution in the atmosphere, oceans, terrestrial hydrosphere, and cryosphere. Close to ice sheets and glaciers, the changes in the ice loads can induce large vertical motions at intra-seasonal to secular time scales. The GPS and VLBI antennas in Ny-AAlesund, Svalbard, which started observations in 1991 and 1994, respectively, observe vertical uplift rates on the order of 7 mm/yr and even higher for some geodetic solutions, which are considerably larger than those predicted by post-glacial rebound models (order 2 mm/yr). Despite the differences in secular uplift determined for the different sites and solutions, the inter- annual signal appears to be rather consistent across the different solutions. The time series exhibit a significant nonlinear behavior, with increased uplift rates starting some time in 2000. A local GPS campaign network, which has been reoccupied annually since 1998, reveals a tilting away from the neighboring ice sheet. The Svalbard ice sheets exhibit large melting during the last century and increased melting since about 2000. We compare the observed vertical motion to the motion predicted by loading models using a detailed ice model with annual time resolution as forcing. The model predictions correlate well with the observations both with respect to the inter-annual variations and the spatial pattern of long-term trends. The regression coefficients for predicted and observed inter-annual variations in height is 1.03±0.36, while the regression coefficient for the predicted and observed spatial pattern turns out to be 1.12±0.38. Estimates of the predicted secular trend in height due to post-glacial rebound and present-day melting are on the order of 5.5 mm/yr and thus smaller than the observed secular trend in height. This difference between predicted and observed secular trends may be due to reference frame effects or model biases.
G53C-03
Determining the Timing of Helheim Glacial Earthquakes from Glacier-Based GPS Time Series
GPS data acquired on Helheim glacier, East Greenland, in the Arctic summer 2007 demonstrate significant temporal variations in glacier flow during glacial earthquakes. There is no coseismic offset in GPS position time series, but there is a significant change in the velocity of the glacier near the time of the earthquake. It would be useful to use the GPS time series to obtain a constraint on the timing of the earthquake that is independent from the seismic data, in order to investigate the mechanism of the glacial earthquake. We have tested several approaches for estimation of the time of the velocity change, including matched filter, curve-fitting, and Kalman estimator. However, providing an accurate (few minutes or better) constraint has been difficult, in part because of the level of systematic noise in the time series (due most likely to the poor multipath environment of the glacier), and also because of semidiurnal signals in the glacier due presumably to the ocean tidal flexure of the glacier. Attempts to separate the tidal signal from the earthquake signal using an EOF analysis have not been successful, because the EOF analysis results in the two signals, of presumably different origin, are described by the same temporal eigenfunction, unexpectedly indicating that these signals have the same spatial variability. We present our analyses, and discuss the particular challenges for GPS in this application.
G53C-04
Position-gram - A Visual Method for Detecting Transient Events in Continuous GPS Time Series
Continuous Global Positioning System (CGPS) time series provide excellent observations for detecting crustal deformation at various length and time-scales. With the increasing precision and length of the time series, new modes of deformation, such as slow slip events and sub-continental scale changes in crustal velocities, can be detected. However, non-tectonic surface movements and measurement noise limit our ability to detect and quantify tectonic-induced transient deformation. Two common methods for reducing noise level in CGPS time series, spatial filtering and periodic seasonal fitting, significantly improve the secular tectonic signal, but fail when transient deformation events are embedded in the time series. We developed a new visually-based method for detecting transient events in CGPS time series. The development was inspired by wavelet analysis presentations that use color to present quantitative information about relationships between time and frequency domains. Here we explore the relationship between time and space domains. The displacement information is color coded according to spline fitting of each time series. This 3-D information (time, space, and displacement in color) allows easy detection of spatio-temporal patterns, which can serve as indicators for transient deformation events. We tested the new method with CGPS time series from three regions with different spatial scales: the Pacific Northwest, Southern California, and the entire continental US. The Pacific Northwest study confirmed that our proposed methodology is capable of detecting transient events and mapping their lateral distribution. The Southern California study detected a new transient event near the intersection of the San Andreas and San Jacinto faults, far from any known creeping fault segments. Finally the continental scale analysis revealed regionally correlated crustal movements in the Basin and Range and California, but uncorrelated with sites in eastern US. Such signal was previously filtered out, but may represent a different mode of sub-continental transient deformation.
G53C-05
Slepian-function analysis of gravity perturbations recorded by the Gravity Recovery And Climate Experiment (GRACE), with applications to the detection of earthquakes from space
Traditionally, the global gravity field
has been represented and analyzed as a spherical harmonic expansion, if not in the space domain. In the
last few years,
localizing bases such as wavelets, radial basis functions and
spherical cap harmonics have entered the fray. One of the most recent
additions is the analysis of spherical data using "Slepian
functions". Slepian functions are are optimally concentrated in the spatial and/or
the spectral domain. They are combinations of spherical
harmonics and as such eminently suitable for the study of
potential fields. Because of their localizing character, Slepian
expansion coefficients excel at capturing spatially limited,
geophysically relevant signals, while minimizing contributions from
degrees outside the spectral band of interest; this improves the
sparsity of the representation of the signal and enhances the
signal-to-noise ratio. This property is especially useful for the time
series of the expansion coefficients of the time-variable terrestrial
gravity anomaly field, such as are available from GRACE.
In previous work, we have shown the applicability of the Slepian basis
to analyze geodetic measurements contaminated by spatial data gaps, as
an inverse problem for the unkown source generating the
noise-contaminated measurements; we have studied the statistics of
using them as data windows to form "multi-taper" spectral estimates
over spatially localized regions; and we have applied a subset of
azimuthally invariant Slepian functions to the recovery of the
coseismic signal due to the 2004 Great Sumatran earthquake.
In this presentation, we present several methodological improvements
that should make the analysis of geodetic data in the Slepian basis a
matter of routine processing. Two of those are generic, in that they
involve the development of a fast Slepian transform on the sphere to
analyze directionally varying signals over a complete set of Euler
angle triplets, and the statistical appraisal of the significance of
the signal detected from the time series. The third is more
specifically tailored to the study of the permanent deformation due to
earthquakes: it involves the projection of the measurements onto a
small set of asymmetric Slepian functions defined on circular domains,
each of which is reminiscent of a multipole in the expansion of the
seismic moment-tensor response, and the comparison of the obtained
results with predictions based on seismic normal-mode summation.
We present results of a systematic survey of all earthquakes above
magnitude 7.5 that occurred worldwide between April 2002 and
present. So far, only the Sumatran earthquake (a magnitude of around
9.2) displays a coherent, significant, and unequivocally detectable
change in gravitational potential, although several other, smaller
earthquakes have components that contain signal above noise level. For
the analysis we compare predictions of the coseismic gravitational
anomaly from the reported seismic moment tensor using normal mode
summation with the estimates made directly from the data. We comment on the detectability of large
earthquakes at the current resolution of the GRACE experiments with an eye
towards future missions.
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G53C-06
Estimating tropospheric phase delay in SAR interferograms using Global Atmospheric Models
The main limiting factor on the accuracy of Interferometric SAR (InSAR) measurements comes from phase propagation delays through the Earth's troposphere. The delay can be divided into a stratified component, which correlates with the topography and often dominates the tropospheric signal in InSAR data, and a turbulent component. The stratified delay can be expressed as a function of atmospheric pressure P, temperature T, and water vapor partial pressure e vertical profiles. We compare the stratified delay computed using results from global atmospheric models with the topography-dependent signal observed in interferograms covering three test areas in different geographic and climatic environments: Lake Mead, Nevada, USA, the Haiyuan fault area, Gansu, China, and Afar, Republic of Djibouti. For each site we compute a multi-year series of interferograms. The phase-elevation ratio is estimated for each interferogram and the series is inverted to form a timeline of delay-elevation ratios characterizing each epoch of data acquisition. InSAR derived ratios are in good agreement with the ratios computed from global atmospheric models. This agreement shows that both estimations of the delay-elevation ratio can be used to perform a first order correction of the InSAR phase. Seasonal variations of the atmosphere significantly affect the phase delay throughout the year, aliasing the results of time series inversions using temporal smoothing or data stacking when the acquisitions are not evenly distributed in time. This is particularly critical when the spatial shape of the signal of interest correlates with topography. In the Lake Mead area, the irregular temporal sampling of our SAR data results in an interannual bias of amplitude ~2~cm on range change estimates. In the Haiyuan Fault area, the coarse and uneven data sampling results in a bias of up to ~0.5~cm/yr on the line of sight velocity across the fault. In the Afar area, the seasonal signal exceeds the deformation signal in the phase time series. In all cases, correcting interferograms from the stratified delay helps removing these biases. Finally we suggest that the phase delay correction can potentially be improved by introducing a non-linear dependance to the elevation, as consistent non-linear relationships are observed in many interferograms as well as in global atmospheric models.
G53C-07
Use of Global Meteorological Model to Correct for Stratified Tropospheric Delays in SAR Data: Application to Active Mexican Stratovolcanoes.
Artefacts induced by temporal changes of water content within the tropospheric layer have long been recognised as the main limitation for the use of InSAR data in order to detect magma movement at depth beneath stratovolcanoes (Delacourt, 1998). Difficulty in discriminating between tropospheric artefacts and deformation induced by magma accumulation or withdrawal at depth is mainly due to the similarity of the expected signal centred on the volcanic edifice. However it is of prime importance to be able to detect magma storage which is the most reliable precursor for volcanic eruptions. We processed time series of InSAR data acquired by ENVISAT from December 2002 to August 2006 at Popocatépetl and Colima Volcano (Mexico) using both the Stanford method for persistent scatterers and a derived small baseline approach (Hooper, 2008). Tropospheric delays are estimated for each interferogram using temperature, pressure and water content profiles from the North American Regional Reanalysis (NARR), a global atmospheric model provided by the National Centers for Environmental Prediction. A strong seasonal effect is observed leading to maximum value for delays of 10 rad/km corresponding to 4 fringes on the volcano slopes. These delays are validated using the correlation between the wrapped phase and the elevation as well as spectrometer data acquired by the Medium Resolution Imaging System (MERIS) onboard on the ENVISAT platform. The tropospheric effect is removed from the wrapped phase which improves the unwrapping process. On Popocatépetl no significant deformations were observed. We could not detect any deep magma storage zone beneath Colima volcano, but its summit area exhibits a constant and almost linear subsidence of more than 1.5 cm/year mainly related to recent volcanic deposits loading. References: Delacourt, P. Briole and J. Achache, Tropospheric corrections of SAR interferograms with strong topography. Application to Etna. Geophys. Res. Lett., 25, 2849- 2852, 1998 Hooper, A., A Multi-Temporal InSAR Method Incorporating Both Persistent Scatterer and Small Baseline Approaches. Geophys. Res. Lett., 35, L 16302, doi:10.1029/2008GL034654, 2008.
G53C-08
Joint Inversion of Time-variable Elevation and Gravity to Reveal Seasonal and Inter- annual Changes of the Volume Density of Martian Snow
The Martian atmosphere seasonally exchanges CO2 with the surface by repeating condensation and sublimation, causing seasonal growth and decay of the polar CO2 snow caps. These processes leave two kinds of geodetic signatures, i.e. seasonal changes of the Martian gravity field and of surface elevation of the snow-covered regions. These were simultaneously observed by Doppler tracking of MGS as time-variable J3 component [Konopliv et al., 2006], and by laser altimetry from the satellite [Smith et al., 2001], respectively. Here we study gradual increase of the volume density of the Martian snow due to compaction, by combining the two data sets 1999-2001 covering three Martian winters. We tried three models, (model 1) constant density throughout the year, (model 2) gradually increasing density with the same peak value, and (model 3) gradually increasing density with different peak values for the three winters, and found that the agreement between the two data sets gets better as we increase the number of parameters. We found that light fresh snow of about 0.1 g/cm3 slowly becomes denser reaching about 1.0 g/cm3 or more immediately before it thaws. From analogy to terrestrial H2O snow, we suggest densification mechanisms such as gravity-driven compaction and/or sintering of CO2 crystals. The densities reached their maxima when solar longitude was 60|85 degrees (northern hemisphere, equivalent to May-Jun. of the Earth) and 240|265 degrees (southern hemisphere, Nov.-Dec.). The maximum snow density varies slightly from year to year, and between hemispheres. In the second southern winter, the density became as high as ~1.6 g/cm3 possibly reflecting enhanced mixing ratio of silicate particles by a large-scale dust storm that occurred around the South Pole early in 2000 (solar longitude 270-285 degrees). We also evaluated sources of systematic errors, such as atmospheric pressure variations (factor A), influence of elastic deformation of the solid Mars by snow loads onto the two observed quantities, gravity (factor B) and elevation (factor C). Among them, factor B might introduce systematic underestimation of snow densities, but inferred load Love numbers of Mars suggest that this error would not exceed ten percent.