Some thoughts on the use of InSAR data to constrain models of surface deformation: Noise structure and data downsampling

Repeat-pass Interferometric Synthetic Aperture Radar (InSAR) provides spatially dense maps of surface deformation with potentially tens of millions of data points. Here we estimate the actual covariance structure of noise in InSAR data. We compare the results for several independent interferograms with a large ensemble of GPS observations of tropospheric delay and discuss how the common approaches used during processing of InSAR data affects the inferred covariance structure. Motivated by computational concerns associated with numerical modeling of deformation sources, we then combine the data-covariance information with the inherent resolution of an assumed source model to develop an efficient algorithm for spatially variable data resampling (or averaging). We illustrate these technical developments with two earthquake scenarios at different ends of the earthquake magnitude spectrum. For the larger events, our goal is to invert for the coseismic fault slip distribution. For smaller events, we infer the hypocenter location and moment. We compare the results of inversions using several different resampling algorithms, and we assess the importance of using the full noise covariance matrix

Spatiospectral concentration on a sphere

We pose and solve the analogue of Slepian's time-frequency concentration problem on the surface of the unit sphere to determine an orthogonal family of strictly bandlimited functions that are optimally concentrated within a closed region of the sphere, or, alternatively, of strictly spacelimited functions that are optimally concentrated within the spherical harmonic domain. Such a basis of simultaneously spatially and spectrally concentrated functions should be a useful data analysis and representation tool in a variety of geophysical and planetary applications, as well as in medical imaging, computer science, cosmology and numerical analysis. The spherical Slepian functions can be found either by solving an algebraic eigenvalue problem in the spectral domain or by solving a Fredholm integral equation in the spatial domain. The associated eigenvalues are a measure of the spatiospectral concentration. When the concentration region is an axisymmetric polar cap the spatiospectral projection operator commutes with a Sturm-Liouville operator; this enables the eigenfunctions to be computed extremely accurately and efficiently, even when their area-bandwidth product, or Shannon number, is large. In the asymptotic limit of a small concentration region and a large spherical harmonic bandwidth the spherical concentration problem approaches its planar equivalent, which exhibits self-similarity when the Shannon number is kept invariant.Comment: 48 pages, 17 figures. Submitted to SIAM Review, August 24th, 200

Flexural analysis of uplifted rift flanks on Venus

Knowledge of the thermal structure of a planet is vital to a thorough understanding of its general scheme of tectonics. Since no direct measurements of heat flow or thermal gradient are available for Venus, most estimates have been derived from theoretical considerations or by analog with the Earth. The flexural response of the lithosphere to applied loads is sensitive to regional thermal structure. Under the assumption that the yield strength as a function of depth can be specified, the temperature gradient can be inferred from the effective elastic plate thickness. Previous estimates of the effective elastic plate thickness of Venus range from 11-18 km for the foredeep north of Uorsar Rupes to 30-60 km for the annular troughs around several coronae. Thermal gradients inferred for these regions are 14-23 K km(exp -1) and 4-9 K km(exp -1) respectively. In this study, we apply the same techniques to investigate the uplifted flanks of an extensional rift. Hypotheses for the origin of uplifted rift flanks on Earth include lateral transport of heat from the center of the rift, vertical transport of heat by small-scale convection, differential thinning of the lithosphere, dynamical uplift, and isostatic response to mechanical uploading of the lithosphere. The 1st hypothesis is considered the dominant contributor to terrestrial rift flanks lacking evidence for volcanic activity, particularly for rift structures that are no longer active. In this study, we model the uplifted flanks of a venusian rift as the flexural response to a vertical end load

Geoid, topography, and convection-driven crustal deformation on Venus

High-resolution Magellan images and altimetry of Venus reveal a wide range of styles and scales of surface deformation that cannot readily be explained within the classical terrestrial plate tectonic paradigm. The high correlation of long-wavelength topography and gravity and the large apparent depths of compensation suggest that Venus lacks an upper-mantle low-viscosity zone. A key difference between Earth and Venus may be the degree of coupling between the convecting mantle and the overlying lithosphere. Mantle flow should then have recognizable signatures in the relationships between surface topography, crustal deformation, and the observed gravity field

Evidence for on-going inflation of the Socorro Magma Body, New Mexico, from interferometric synthetic aperture radar imaging

Interferometric synthetic aperture radar (InSAR) imaging of the central Rio Grande rift (New Mexico, USA) during 1992–1999 reveals a crustal uplift of several centimeters that spatially coincides with the seismologically determined outline of the Socorro magma body, one of the largest currently active magma intrusions in the Earth's continental crust. Modeling of interferograms shows that the observed deformation may be due to elastic opening of a sill-like intrusion at a rate of a few millimeters per year. Despite an apparent constancy of the geodetically determined uplift rate, thermodynamic arguments suggest that it is unlikely that the Socorro magma body has formed via steady state elastic inflation

Locations of selected small earthquakes in the Zagros mountains

Author Posting. © American Geophysical Union, 2005. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Geochemistry Geophysics Geosystems 6 (2005): Q03001, doi:10.1029/2004GC000849.The Zagros mountains of southern Iran are marked by a zone of high seismicity and accommodate a significant portion of the convergence between Arabia and Eurasia. Due to the lack of dense local seismic or geodetic networks, the inferred kinematics of the collision in Iran is mainly based on catalogs of teleseismically determined earthquake locations. We surveyed all M w > 4.5 earthquakes in the Harvard Centroid Moment Tensor (HCMT) and International Seismological Centre (ISC) catalogs that occurred in the Zagros mountains during the period 1992–2002 and that were spanned by Interferometric Synthetic Aperture Radar (InSAR) images from the ERS 1 and 2 satellites. We invert the observed deformation for the best fitting point source, single fault plane, and distributed fault slip for four earthquakes and one unexplained deformation event. We find that we can precisely locate earthquakes that are too small to be well-located by either the HCMT or ISC catalogs, allowing us to tie specific earthquakes to active geologic structures.ERS 1 and 2 data were acquired through an ESA category-1 proposal. R. Lohman is partially supported by a NASA New Investigator Program grant award to M. Simons

Some thoughts on the use of InSAR data to constrain models of surface deformation : noise structure and data downsampling

Author Posting. © American Geophysical Union, 2005. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Geochemistry Geophysics Geosystems 6 (2005): Q01007, doi:10.1029/2004GC000841.Repeat-pass Interferometric Synthetic Aperture Radar (InSAR) provides spatially dense maps of surface deformation with potentially tens of millions of data points. Here we estimate the actual covariance structure of noise in InSAR data. We compare the results for several independent interferograms with a large ensemble of GPS observations of tropospheric delay and discuss how the common approaches used during processing of InSAR data affects the inferred covariance structure. Motivated by computational concerns associated with numerical modeling of deformation sources, we then combine the data-covariance information with the inherent resolution of an assumed source model to develop an efficient algorithm for spatially variable data resampling (or averaging). We illustrate these technical developments with two earthquake scenarios at different ends of the earthquake magnitude spectrum. For the larger events, our goal is to invert for the coseismic fault slip distribution. For smaller events, we infer the hypocenter location and moment. We compare the results of inversions using several different resampling algorithms, and we assess the importance of using the full noise covariance matrix.R. Lohman is partially supported by a NASA New Investigator Program grant award to M. Simons