A Geostationary Optical Seismometer, Proof of Concept

We discuss the possibility of imaging the propagation of seismic waves from a very large space-based optical telescope. Images of seismic waves propagating at the Earth's surface would be an invaluable source of information for investigating earthquake physics and the effect of the subsurface on earthquake ground motions. This application would require ground displacement measurements at about every 100 m, with centimetric accuracy, and temporal sampling on the order of 1 Hz. A large field of view (>; 105 km2) is required to measure the full extent of a large earthquake in the areas of interest. A geostationary optical telescope with a large aperture appears to be the most promising system. We establish preliminary technical requirements for such a system, which lead us to consider a telescope with an angular field of view of 0.8° and with an aperture greater than 4 m. We discuss and quantify the various sources of noise that would limit such a system: atmospheric turbulence, evolution of ground reflectance and solar incidence angle, and stability of the platform at 1 Hz. We present numerical simulations, which account for these sources of noise. They show that key details of the seismic wave field, hardly detectable using ground-based instruments, would indeed be imaged by such a system. At the upper limit of modern technology, data flow would be about 20-50 Gb·s-1, and data memory would be about 50 Tb.

[1]  J. Ampuero,et al.  Spectral element modeling of spontaneous earthquake rupture on rate and state faults: Effect of velocity‐strengthening friction at shallow depths , 2008 .

[2]  Michel Bouchon,et al.  Observation of Long Supershear Rupture During the Magnitude 8.1 Kunlunshan Earthquake , 2003, Science.

[3]  David L. Fried,et al.  Statistics of a Geometric Representation of Wavefront Distortion: Errata , 1965 .

[4]  K. Feigl,et al.  Radar interferometry and its application to changes in the Earth's surface , 1998 .

[5]  N. Crouzet,et al.  Front- vs. back-illuminated CCD cameras for photometric surveys: a noise budget analysis , 2007, 0809.4255.

[6]  Timothy E. Dawson,et al.  Uniform California Earthquake Rupture Forecast, Version 2 (UCERF 2) , 2009 .

[7]  Rama Chellappa,et al.  Accuracy vs Efficiency Trade-offs in Optical Flow Algorithms , 1996, Comput. Vis. Image Underst..

[8]  L. Andrews Field guide to atmospheric optics , 2004 .

[9]  Thierry Amiot,et al.  The interferometric cartwheel: a multi-purpose formation of passive radar microsatellites , 2002, IEEE International Geoscience and Remote Sensing Symposium.

[10]  Allen J. Bronowicki Vibration Isolator for Large Space Telescopes , 2006 .

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

[12]  R. Kirk,et al.  I. Thermal Evolution of Ganymede and Implications for Surface Features. II. Magnetohydrodynamic Constraints on Deep Zonal Flow in the Giant Planets. III. A Fast Finite-Element Algorithm for Two-Dimensional Photoclinometry , 1987 .

[13]  Jonathan W. Brandt,et al.  Improved Accuracy in Gradient-Based Optical Flow Estimation , 1997, International Journal of Computer Vision.

[14]  W. Marsden I and J , 2012 .

[15]  Thomas S. Pagano,et al.  Prelaunch characteristics of the Moderate Resolution Imaging Spectroradiometer (MODIS) on EOS-AM1 , 1998, IEEE Trans. Geosci. Remote. Sens..

[16]  Xiaoxiong Xiong,et al.  Pre-launch characterization of aqua MODIS scan mirror response versus scan angle for thermal emissive bands , 2007, SPIE Optical Engineering + Applications.

[17]  Richard C. Aster,et al.  Aster , 1906, Botanical Gazette.

[18]  Jonathan C. McDowell,et al.  James Webb Space Telescope , 2004 .

[19]  A. Charo,et al.  Earth science and applications from space: A community assessment and strategy for the future , 2004 .

[20]  J. Churnside,et al.  Wander of an optical beam in the turbulent atmosphere. , 1990, Applied optics.

[21]  Song Yang,et al.  A MODIS Dual Spectral Rain Algorithm , 2007 .

[22]  Sébastien Leprince,et al.  In-Flight CCD Distortion Calibration for Pushbroom Satellites Based on Subpixel Correlation , 2008, IEEE Transactions on Geoscience and Remote Sensing.

[23]  J. Avouac,et al.  Co‐seismic deformation during the Mw7.3 Aqaba Earthquake (1995) from ERS‐SAR interferometry , 2000 .

[24]  Thierry Fusco,et al.  High-resolution imaging through atmospheric turbulence: link between anisoplanatism and intensity fluctuations , 1999, Remote Sensing.

[25]  Carl Tape,et al.  Adjoint Tomography of the Southern California Crust , 2009, Science.

[26]  S. Squyres,et al.  Sources of error in planetary photoclinometry , 1991 .

[27]  David W. Graham,et al.  Prediction and measurement of soil bidirectional reflectance , 1992, IEEE Trans. Geosci. Remote. Sens..

[28]  F. Roddier The effects of atmospheric turbulence on the formation of visible and infrared images , 1979 .

[29]  Davide Bruno,et al.  Geosynchronous synthetic aperture radar: Concept design, properties and possible applications , 2006 .

[30]  Gerhard Meister,et al.  Large-scale bidirectional reflectance model for urban areas , 2001, IEEE Trans. Geosci. Remote. Sens..

[31]  Sebastien Leprince,et al.  Co-registration and correlation of aerial photographs for ground deformation measurements , 2009 .

[32]  P. Bely The Design and Construction of Large Optical Telescopes , 2010 .

[33]  A. McEwen Photometric functions for photoclinometry and other applications , 1991 .

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

[35]  L. C. Andrews,et al.  An Analytical Model for the Refractive Index Power Spectrum and Its Application to Optical Scintillations in the Atmosphere , 1992 .

[36]  J. Tromp,et al.  Seismological Grand Challenges in Understanding Earth’s Dynamic Systems , 2008 .

[37]  R. Wyse,et al.  Deep Astrometric Standards and Galactic Structure , 2005, astro-ph/0509606.

[38]  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.

[39]  J. Avouac,et al.  Deformation due to the 17 August 1999 Izmit, Turkey, earthquake measured from SPOT images , 2002 .

[40]  Rama Chellappa,et al.  Accuracy vs. Efficiency Trade-offs in Optical Flow Algorithms , 1996, ECCV.

[41]  A. Kääb Monitoring high-mountain terrain deformation from repeated air- and spaceborne optical data: examples using digital aerial imagery and ASTER data , 2002 .

[42]  Kenneth Watson Photoclinometry from spacecraft images , 1968 .

[43]  Xavier Briottet,et al.  Direct and inverse radiative transfer solutions for visible and near-infrared hyperspectral imagery , 2005, IEEE Transactions on Geoscience and Remote Sensing.

[44]  C. Bohren,et al.  An introduction to atmospheric radiation , 1981 .

[45]  John C. Geary,et al.  Technology of the LSST focal plane , 2007 .

[46]  Michael Freilich,et al.  Committee on Earth Science and Applications from Space , 2012 .

[47]  John C. Geary,et al.  LSST sensor requirements and characterization of the prototype LSST CCDs , 2009 .

[48]  Sebastien Leprince,et al.  Rupture Process of the 1999 Mw 7.1 Duzce Earthquake from Joint Analysis of SPOT, GPS, InSAR, Strong-Motion, and Teleseismic Data: A Supershear Rupture with Variable Rupture Velocity , 2010 .

[49]  Rémi Michel,et al.  Horizontal coseismic deformation of the 1999 Chi-Chi earthquake measured from SPOT satellite images: Implications for the seismic cycle along the western foothills of central Taiwan , 2003 .

[50]  James R. Irons,et al.  Bidirectional reflectance of selected BOREAS sites from multiangle airborne data , 1997 .

[51]  Jean-Philippe Avouac,et al.  Coseismic surface deformation from air photos: The Kickapoo step over in the 1992 Landers rupture , 2006 .

[52]  R. Noll Zernike polynomials and atmospheric turbulence , 1976 .

[53]  V. N. Dvornychenko,et al.  Bounds on (Deterministic) Correlation Functions with Application to Registration , 1983, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[54]  Didier Massonnet,et al.  Capabilities and limitations of the interferometric cartwheel , 2001, IEEE Trans. Geosci. Remote. Sens..

[55]  Saul Perlmutter,et al.  Back-illuminated, fully-depleted CCD image sensors for use in optical and near-IR astronomy , 2003 .

[56]  S. Holland,et al.  Device Design for a 12.3-Megapixel, Fully Depleted, Back-Illuminated, High-Voltage Compatible Charge-Coupled Device , 2009, IEEE Transactions on Electron Devices.

[57]  T. Lay,et al.  Modern Global Seismology , 1995 .

[58]  Technology of the LSST focal plane , 2007 .

[59]  A. Rosakis,et al.  Supershear and subrayleigh to supershear transition observed in Laboratory Earthquake Experiments , 2005 .

[60]  Olivier D. Faugeras,et al.  Shape From Shading , 2006, Handbook of Mathematical Models in Computer Vision.