A Wavelet Toolkit for Visualization and Analysis of Large Data Sets in Earthquake Research

Abstract — Wavelets have a wide range of useful functions that permit them to effectively treat problems such as data compression, scale-localization analysis, feature extraction, visualization, statistics, numerical simulation, and communication. We discuss their features and their use in an integrated manner to handle large-scale problems in earthquake physics and other nonlinear problems in the solid earth geosciences.

[1]  Zachary Adam Garbow,et al.  Remote data analysis, visualization and problem solving environment (PSE) based on wavelets in the geosciences , 2004 .

[2]  Gordon Erlebacher,et al.  Current Trends and Demands in Visualization in the Geosciences , 2001 .

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

[4]  Ami Marowka,et al.  The GRID: Blueprint for a New Computing Infrastructure , 2000, Parallel Distributed Comput. Pract..

[5]  Emmanuel J. Candès,et al.  The curvelet transform for image denoising , 2002, IEEE Trans. Image Process..

[6]  Gordon Erlebacher,et al.  Case study: Visualization and analysis of high Rayleigh number - 3D convection in the Earth's mantle , 2002, IEEE Visualization, 2002. VIS 2002..

[7]  Kim B. Olsen,et al.  Three-Dimensional Simulation of a Magnitude 7.75 Earthquake on the San Andreas Fault , 1995, Science.

[8]  Zachary Adam Garbow,et al.  Interactive Web-Based Map: Applications to Large Data Sets in the Geosciences , 2001 .

[9]  Roger G. Barry,et al.  Glacier monitoring within the Global Climate Observing System* , 2000, Annals of Glaciology.

[10]  Masamu Aniya,et al.  The use of satellite and airborne imagery to inventory outlet glaciers of the Southern Patagonia Icefield, South America , 1996 .

[11]  D. Donoho Unconditional Bases Are Optimal Bases for Data Compression and for Statistical Estimation , 1993 .

[12]  Y. Ben‐Zion Stress, slip, and earthquakes in models of complex single-fault systems incorporating brittle and creep deformations , 1996 .

[13]  Peter Mora,et al.  Visualization of large particle systems , 2002 .

[14]  Geoffrey C. Fox,et al.  Grid services for earthquake science , 2002, Concurr. Comput. Pract. Exp..

[15]  Xiaoming Huo,et al.  Beamlets and Multiscale Image Analysis , 2002 .

[16]  Tim Melbourne,et al.  Periodic Slow Earthquakes from the Cascadia Subduction Zone , 2002, Science.

[17]  Gordon Erlebacher,et al.  Role of Wavelets in the Physical and Statistical Modelling of Complex Geological Processes , 2004 .

[18]  W. Sweldens The Lifting Scheme: A Custom - Design Construction of Biorthogonal Wavelets "Industrial Mathematics , 1996 .

[19]  V. Prasad,et al.  Three-dimensional confocal microscopy of colloids. , 2001, Applied optics.

[20]  D. Yuen,et al.  Properties of near surface marine sediments from wavelet correlation analysis , 2002 .

[21]  Andreas Rieder,et al.  Wavelets: Theory and Applications , 1997 .

[22]  Nigel Wood,et al.  A New Finite-Difference Diffusion Scheme , 1996 .

[23]  O. Vasilyev,et al.  A Fast Adaptive Wavelet Collocation Algorithm for Multidimensional PDEs , 1997 .

[24]  Zachary Adam Garbow,et al.  Web-Based Interrogation of Large-Scale Geophysical Data Sets and Clustering Analysis of Many Earthquake Events From Desktop and Handheld Computers , 2002 .

[25]  Norman H. Sleep,et al.  Hotspots and Mantle Plumes' Some Phenomenology , 1990 .

[26]  D. Yuen,et al.  Plume structures in the hard‐turbulent regime of three‐dimensional infinite Prandtl number convection , 1993 .

[27]  M. V. Dyke,et al.  An Album of Fluid Motion , 1982 .

[28]  M. Simons,et al.  A satellite geodetic survey of large-scale deformation of volcanic centres in the central Andes , 2002, Nature.

[29]  David A. Yuen,et al.  Capabilities of 3‐D wavelet transforms to detect plume‐like structures from seismic tomography , 2000 .

[30]  R. Strelitz New Tools for Visual Analysis of Multivariate Data from Large Scale Climate Simulations , 2002 .

[31]  E. Foufoula‐Georgiou,et al.  Wavelet analysis for geophysical applications , 1997 .

[32]  David A. Yuen,et al.  Geophysical Applications of Multidimensional Filtering with Wavelets , 2002 .

[33]  Michael Unser,et al.  Wavelet Projections for Volume Rendering , 1999, Eurographics.

[34]  A F Laine,et al.  Wavelets in temporal and spatial processing of biomedical images. , 2000, Annual review of biomedical engineering.

[35]  Emmanuel J. Candès,et al.  Curvelets and Curvilinear Integrals , 2001, J. Approx. Theory.

[36]  Ian Foster,et al.  The Grid 2 - Blueprint for a New Computing Infrastructure, Second Edition , 1998, The Grid 2, 2nd Edition.

[37]  T. Chan,et al.  Multiscale and multiresolution methods : theory and applications , 2002 .

[38]  David A. Yuen,et al.  Multi-Resolution Clustering Analysis and Visualization of Around One Million Synthetic Earthquake Events , 2002 .

[39]  Detlev Marpe,et al.  Design of a highly efficient wavelet-based video coding scheme , 2002, IS&T/SPIE Electronic Imaging.

[40]  Gordon Erlebacher,et al.  Web-Based interrogation of large-scale geophysical data sets from handheld devices , 2003 .

[41]  G. Davies,et al.  Ocean bathymetry and mantle convection: 1. Large‐scale flow and hotspots , 1988 .

[42]  Shinji Toda,et al.  Evidence from the ad 2000 Izu islands earthquake swarm that stressing rate governs seismicity , 2002, Nature.