Local interpolation of coseismic displacements measured by InSAR

Abstract Coseismic displacements play a significant role in characterizing earthquake causative faults and understanding earthquake dynamics. They are typically measured from InSAR using pre- and post-earthquake images. The displacement map produced by InSAR may contain missing coseismic values due to the decorrelation of ASAR images. This study focused on interpolating missing values in the coseismic displacement map of the 2003 Bam earthquake using geostatistics with the aim of running a slip distribution model. The gaps were grouped into 23 patches. Variograms of the patches showed that the displacement data were spatially correlated. The variogram prepared for ordinary kriging (OK) indicated the presence of a trend and thus justified the use of universal kriging (UK). Accuracy assessment was performed in 3 ways. First, 11 patches of equal size and with an equal number of missing values generated artificially, were kriged and validated. Second, the four selected patches results were validated after shifting them to new locations without missing values and comparing them with the observed values. Finally, cross validation was performed for both types of patch at the original and shifted locations. UK results were better than OK in terms of kriging variance, mean error (ME) and root mean square error (RMSE). For both OK and UK, only 4 out of 23 patches (1, 5, 11 and 21) showed ME and RMSE values that were substantially larger than for the other patches. The accuracy assessment results were found to be satisfactory with ME and RMSE values close to zero. InSAR data inversion demonstrated the usefulness of interpolation of the missing coseismic values by improving a slip distribution model. It is therefore concluded that kriging serves as an effective tool for interpolating the missing values on a coseismic displacement map.

[1]  Antonio Baldi.  Phase unwrapping by region growing. , 2003, Applied optics.

[2]  M. Pirri,et al.  Coseismic fault rupture detection and slip measurement by ASAR precise correlation using coherence maximization: application to a north-south blind fault in the vicinity of Bam (Iran) , 2006, IEEE Geoscience and Remote Sensing Letters.

[3]  T. Mexia,et al.  Author ' s personal copy , 2009 .

[4]  Noel A Cressie,et al.  Statistics for Spatial Data, Revised Edition. , 1994 .

[5]  David Small,et al.  Using SAR Interferometry and Teleseismic Data to Determine Source Parameters for the 2003 Bam Earthquake , 2005 .

[6]  Jean Taboury,et al.  Measuring near field coseismic displacements from SAR images: Application to the Landers Earthquake , 1999 .

[7]  Noel A Cressie,et al.  Statistics for Spatial Data. , 1992 .

[8]  Christian Bignami,et al.  Finite fault inversion of DInSAR coseismic displacement of the 2009 L'Aquila earthquake (central Italy) , 2009 .

[9]  P. Burrough,et al.  Principles of geographical information systems , 1998 .

[10]  A. Stein,et al.  A comparison of conventional and geostatistical methods to replace clouded pixels in NOAA-AVHRR images , 1998 .

[11]  J. Karl.  Spatial Predictions of Cover Attributes of Rangeland Ecosystems Using Regression Kriging and Remote Sensing , 2010 .

[12]  Peter M. Atkinson,et al.  Geostatistics and remote sensing , 1998 .

[13]  D. Sandwell,et al.  Three-dimensional deformation caused by the Bam, Iran, earthquake and the origin of shallow slip deficit , 2005, Nature.

[14]  Sébastien Leprince,et al.  Automatic and Precise Orthorectification, Coregistration, and Subpixel Correlation of Satellite Images, Application to Ground Deformation Measurements , 2007, IEEE Transactions on Geoscience and Remote Sensing.

[15]  Gianfranco Fornaro,et al.  A two-dimensional region growing least squares phase unwrapping algorithm for interferometric SAR processing , 1999, IEEE Trans. Geosci. Remote. Sens..

[16]  Pablo J. González,et al.  Coseismic Three-Dimensional Displacements Determined Using SAR Data: Theory and an Application Test , 2009 .

[17]  Freek D. van der Meer,et al.  Remote-sensing image analysis and geostatistics , 2012 .

[18]  Francesca Romana Cinti,et al.  InSAR surface displacement field and fault modelling for the 2003 Bam earthquake (southeastern Iran) , 2005 .

[19]  James Jackson,et al.  Surface displacements and source parameters of the 2003 Bam (Iran) earthquake from Envisat advanced synthetic aperture radar imagery , 2005 .

[20]  Hiroyuki Tsutsumi,et al.  Surface Rupture of the 2005 Kashmir, Pakistan, Earthquake and Its Active Tectonic Implications , 2006 .

[21]  Ramon F. Hanssen,et al.  The Interpretation of Bam Fault Kinematics Using Envisat SAR Interferometric Data , 2006 .

[22]  R. Lark.  Optimized spatial sampling of soil for estimation of the variogram by maximum likelihood , 2002 .

[23]  Weidong Li,et al.  Gaps‐fill of SLC‐off Landsat ETM+ satellite image using a geostatistical approach , 2007 .

[24]  Asi Building,et al.  Comparing Ordinary Kriging and Regression Kriging for Soil Properties in Contrasting Landscapes , 2010 .

[25]  M. Kurt,et al.  A Modification to the , 2008 .

[26]  J. Avouac,et al.  Measuring earthquakes from optical satellite images. , 2000, Applied optics.

[27]  Ian Parsons,et al.  Surface deformation due to shear and tensile faults in a half-space , 1986 .

[28]  C. Woodcock,et al.  The use of variograms in remote sensing. I - Scene models and simulated images. II - Real digital images , 1988 .

[29]  T. Wright,et al.  The 2003 Bam (Iran) earthquake: Rupture of a blind strike‐slip fault , 2004 .

[30]  Co-Seismic Surface Displacement Induced by the Bam Earthquake, Iran (26/12/2003, M=6.6): Insights from InSAR, GPS, SPOT5 Analyses and Levelling , 2006 .

[31]  Jack P. C. Kleijnen,et al.  Robustness of Kriging when interpolating in random simulation with heterogeneous variances: Some experiments , 2005, Eur. J. Oper. Res..

[32]  Andrea Antonioli,et al.  Optimal fault resolution in geodetic inversion of coseismic data , 2011 .

[33]  Mike P. Stewart,et al.  A modification to the Goldstein radar interferogram filter , 2003, IEEE Trans. Geosci. Remote. Sens..

[34]  C. Werner,et al.  Radar interferogram filtering for geophysical applications , 1998 .

[35]  R. Reese.  Geostatistics for Environmental Scientists , 2001 .

[36]  Zhiyong Wang,et al.  Monitoring Co-seismic Deformation Fields of Bam Earthquake Using D-InSAR Technique , 2009, 2009 International Conference on Environmental Science and Information Application Technology.

[37]  Jeffrey T. Freymueller,et al.  Coseismic deformation of the 2002 Denali fault earthquake: Contributions from synthetic aperture radar range offsets , 2007 .

[38]  Xinglin Lei,et al.  Mapping active fault associated with the 2003 Mw 6.6 Bam (SE Iran) earthquake with ASTER 3D images , 2004 .

[39]  Mike Rees,et al.  5. Statistics for Spatial Data , 1993 .

[40]  R. Lark,et al.  Geostatistics for Environmental Scientists , 2001 .

[41]  Pierre Briole,et al.  The source motion of 2003 Bam (Iran) earthquake constrained by satellite and ground‐based geodetic data , 2007 .

[42]  Eric J. Fielding,et al.  Displacement field and slip distribution of the 2005 Kashmir earthquake from SAR imagery , 2006 .

[43]  Scott C. Doney,et al.  Evaluation of ocean carbon cycle models with data‐based metrics , 2004 .

[44]  Sebastien Leprince,et al.  The 2005, Mw 7.6 Kashmir earthquake: Sub-pixel correlation of ASTER images and seismic waveforms analysis , 2006 .

[45]  Y. Zhang,et al.  – 20 Statistics-based outlier detection for wireless sensor networks , 2012 .

[46]  K. Sieh,et al.  Detecting co-seismic displacements in glaciated regions: An example from the great November 2002 Denali earthquake using SPOT horizontal offsets , 2008 .

[47]  Mario Costantini,et al.  A novel phase unwrapping method based on network programming , 1998, IEEE Trans. Geosci. Remote. Sens..