Multiscale InSAR Time Series (MInTS) analysis of surface deformation

[1] We present a new approach to extracting spatially and temporally continuous ground deformation fields from interferometric synthetic aperture radar (InSAR) data. We focus on unwrapped interferograms from a single viewing geometry, estimating ground deformation along the line-of-sight. Our approach is based on a wavelet decomposition in space and a general parametrization in time. We refer to this approach as MInTS (Multiscale InSAR Time Series). The wavelet decomposition efficiently deals with commonly seen spatial covariances in repeat-pass InSAR measurements, since the coefficients of the wavelets are essentially spatially uncorrelated. Our time-dependent parametrization is capable of capturing both recognized and unrecognized processes, and is not arbitrarily tied to the times of the SAR acquisitions. We estimate deformation in the wavelet-domain, using a cross-validated, regularized least squares inversion. We include a model-resolution-based regularization, in order to more heavily damp the model during periods of sparse SAR acquisitions, compared to during times of dense acquisitions. To illustrate the application of MInTS, we consider a catalog of 92 ERS and Envisat interferograms, spanning 16 years, in the Long Valley caldera, CA, region. MInTS analysis captures the ground deformation with high spatial density over the Long Valley region.

[1]  H. Whitney.  Non-Separable and Planar Graphs. , 1931, Proceedings of the National Academy of Sciences of the United States of America.

[2]  G. Fornaro,et al.  Modeling surface deformation observed with synthetic aperture radar interferometry at Campi Flegrei caldera , 2001 .

[3]  J. C. Savage,et al.  Postseismic relaxation and transient creep , 2005 .

[4]  Gianfranco Fornaro,et al.  A new algorithm for surface deformation monitoring based on small baseline differential SAR interferograms , 2002, IEEE Trans. Geosci. Remote. Sens..

[5]  Paolo Berardino,et al.  Uplift and magma intrusion at Long Valley caldera from InSAR and gravity measurements , 2009 .

[6]  Paul A. Rosen,et al.  Transient strain accumulation and fault interaction in the eastern California shear zone , 2001 .

[7]  R. Dennis Cook,et al.  Cross-Validation of Regression Models , 1984 .

[8]  B. Hager,et al.  The effects of rheological layering on post-seismic deformation , 2006 .

[9]  Michele Manunta,et al.  A small-baseline approach for investigating deformations on full-resolution differential SAR interferograms , 2004, IEEE Transactions on Geoscience and Remote Sensing.

[10]  R. Hanssen.  Radar Interferometry: Data Interpretation and Error Analysis , 2001 .

[11]  Paul Lundgren,et al.  Southern San Andreas-San Jacinto fault system slip rates estimated from earthquake cycle models constrained by GPS and interferometric synthetic aperture radar observations , 2009 .

[12]  James L. Davis,et al.  Geodesy by radio interferometry: The application of Kalman Filtering to the analysis of very long baseline interferometry data , 1990 .

[13]  W. V. McCarthy,et al.  Discriminant Analysis with Singular Covariance Matrices: Methods and Applications to Spectroscopic Data , 1995 .

[14]  D. Schmidt.  Time-dependent land uplift and subsidence in the Santa Clara Valley , 2003 .

[15]  Per Christian Hansen,et al.  REGULARIZATION TOOLS: A Matlab package for analysis and solution of discrete ill-posed problems , 1994, Numerical Algorithms.

[16]  Ingrid Daubechies,et al.  Ten Lectures on Wavelets , 1992 .

[17]  M. Stone.  Cross‐Validatory Choice and Assessment of Statistical Predictions , 1976 .

[18]  Thomas R. Walter,et al.  Estimating the Effect of Satellite Orbital Error Using Wavelet-Based Robust Regression Applied to InSAR Deformation Data , 2011, IEEE Transactions on Geoscience and Remote Sensing.

[19]  Deformation near the Casa Diablo geothermal well field and related processes Long Valley caldera, Eastern California, 1993–2000 , 2003 .

[20]  Fabio Rocca,et al.  SAR monitoring of progressive and seasonal ground deformation using the permanent scatterers technique , 2003, IEEE Trans. Geosci. Remote. Sens..

[21]  P. Rosen,et al.  Interferometric Synthetic Aperture Radar Geodesy , 2007 .

[22]  S. Mallat.  A wavelet tour of signal processing , 1998 .

[23]  Christophe Delacourt,et al.  Tropospheric corrections of SAR interferograms with strong topography. Application to Etna , 1998 .

[24]  Stéphane Mallat,et al.  A Wavelet Tour of Signal Processing - The Sparse Way, 3rd Edition , 2008 .

[25]  J. Langbein.  Deformation of the Long Valley Caldera, California: inferences from measurements from 1988 to 2001 , 2003 .

[26]  R. Bennett.  Instantaneous deformation from continuous GPS: Contributions from quasi-periodic loads , 2008 .

[27]  David T. Sandwell,et al.  Fault creep along the southern San Andreas from interferometric synthetic aperture radar, permanent scatterers, and stacking , 2003 .

[28]  L. Rivera,et al.  Coseismic Deformation from the 1999 Mw 7.1 Hector Mine, California, Earthquake as Inferred from InSAR and GPS Observations , 2002 .

[29]  Falk Amelung,et al.  Postseismic Mantle Relaxation in the Central Nevada Seismic Belt , 2005, Science.

[30]  C. W. Chen,et al.  Two-dimensional phase unwrapping with use of statistical models for cost functions in nonlinear optimization. , 2001, Journal of the Optical Society of America. A, Optics, image science, and vision.

[31]  John B. Rundle,et al.  Shallow and peripheral volcanic sources of inflation revealed by modeling two‐color geodimeter and leveling data from Long Valley Caldera, California, 1988–1992 , 1995 .

[32]  Richard M. Goldstein,et al.  Atmospheric limitations to repeat‐track radar interferometry , 1995 .

[33]  Paolo Berardino,et al.  Surface deformation of Long Valley caldera and Mono Basin, California, investigated with the SBAS-InSAR approach , 2007 .

[34]  M. Doin,et al.  Ground motion measurement in the Lake Mead area, Nevada, by differential synthetic aperture radar interferometry time series analysis: Probing the lithosphere rheological structure , 2007 .

[35]  James Foster,et al.  Mitigating atmospheric noise for InSAR using a high resolution weather model , 2005 .

[36]  George E. Hilley,et al.  Resolving vertical tectonics in the San Francisco Bay Area from permanent scatterer InSAR and GPS analysis , 2006 .

[37]  Rowena B. Lohman,et al.  Some thoughts on the use of InSAR data to constrain models of surface deformation: Noise structure and data downsampling , 2005 .

[38]  H. Zebker,et al.  A new method for measuring deformation on volcanoes and other natural terrains using InSAR persistent scatterers , 2004 .

[39]  Y. Bock,et al.  Anatomy of apparent seasonal variations from GPS‐derived site position time series , 2001 .

[40]  M. Simons,et al.  A multiscale approach to estimating topographically correlated propagation delays in radar interferograms , 2010 .

[41]  Per Christian Hansen,et al.  Regularization Tools version 4.0 for Matlab 7.3 , 2007, Numerical Algorithms.

[42]  C. Werner,et al.  Satellite radar interferometry: Two-dimensional phase unwrapping , 1988 .

[43]  D. Hill,et al.  An episode of reinflation of the Long Valley Caldera, eastern California: 1989–1991 , 1993 .

[44]  Keith L. McLaughlin,et al.  Seismic Location Bias and Uncertainty in the Presence of Correlated and Non-Gaussian Travel-Time Errors , 2009 .

[45]  Robert W. King,et al.  Estimating regional deformation from a combination of space and terrestrial geodetic data , 1998 .

[46]  Frank H. Webb,et al.  Neutral atmospheric delay in interferometric synthetic aperture radar applications: Statistical description and mitigation , 2003 .

[47]  Clifford H. Thurber,et al.  Parameter estimation and inverse problems , 2005 .

[48]  Steffen Knospe,et al.  Covariance Estimation for dInSAR Surface Deformation Measurements in the Presence of Anisotropic Atmospheric Noise , 2010, IEEE Transactions on Geoscience and Remote Sensing.

[49]  Per Christian Hansen,et al.  A Matlab Package for Analysis and Solution of Discrete Ill-Posed Problems , 2008 .

[50]  Fabio Rocca,et al.  Permanent scatterers in SAR interferometry , 2001, IEEE Trans. Geosci. Remote. Sens..

[51]  Andrew Hooper,et al.  A multi‐temporal InSAR method incorporating both persistent scatterer and small baseline approaches , 2008 .

[52]  A. Newman,et al.  Constraints on continued episodic inflation at Long Valley Caldera, based on seismic and geodetic observations , 2009 .

[53]  Seymour Geisser,et al.  The Predictive Sample Reuse Method with Applications , 1975 .

[54]  K. Feigl,et al.  The displacement field of the Landers earthquake mapped by radar interferometry , 1993, Nature.

[55]  G. Peltzer,et al.  Fluid-controlled faulting process in the Asal Rift, Djibouti, from 8 yr of radar interferometry observations , 2007 .

[56]  Gene H. Golub,et al.  An analysis of the total least squares problem , 1980, Milestones in Matrix Computation.

[57]  M. Simons,et al.  An aseismic slip pulse in northern Chile and along‐strike variations in seismogenic behavior , 2006 .

[58]  J. C. Savage,et al.  Near‐field postseismic deformation associated with the 1992 Landers and 1999 Hector Mine, California, earthquakes , 2003 .

[59]  F. Amelung,et al.  Post-Seismic Mantle Relaxation in the Central Nevada Seismic Belt Detected by InSAR: Implication for Basin and Range Dynamics , 2006 .

[60]  Fabio Rocca,et al.  Nonlinear subsidence rate estimation using permanent scatterers in differential SAR interferometry , 2000, IEEE Trans. Geosci. Remote. Sens..

[61]  C. Ji,et al.  Distribution of slip from 11 Mw > 6 earthquakes in the northern Chile subduction zone , 2006 .

[62]  David L. Donoho,et al.  WaveLab and Reproducible Research , 1995 .

[63]  J. Avouac,et al.  Tropospheric phase delay in interferometric synthetic aperture radar estimated from meteorological model and multispectral imagery , 2007 .