Global seismic tomography and modern parallel computers
Language
English
Obiettivo Specifico
8T. Sismologia in tempo reale
Status
Published
JCR Journal
JCR Journal
Peer review journal
Yes
Volume or Series
4-5/49(2006)
Date Issued
June 5, 2006
Abstract
A fast technological progress is providing seismic tomographers with computers
of rapidly increasing speed and RAM, that are not always properly taken
advantage of. Large computers with both shared-memory and distributedmemory
architectures have made it possible to approach the tomographic
inverse problem more accurately. For example, resolution can be quantified
from the resolution matrix rather than checkerboard tests; the covariance
matrix can be calculated to evaluate the propagation of errors from data to
model parameters; the L-curve method can be applied to determine a range
of acceptable regularization schemes. We show how these exercises can be
implemented efficiently on different hardware architectures.
of rapidly increasing speed and RAM, that are not always properly taken
advantage of. Large computers with both shared-memory and distributedmemory
architectures have made it possible to approach the tomographic
inverse problem more accurately. For example, resolution can be quantified
from the resolution matrix rather than checkerboard tests; the covariance
matrix can be calculated to evaluate the propagation of errors from data to
model parameters; the L-curve method can be applied to determine a range
of acceptable regularization schemes. We show how these exercises can be
implemented efficiently on different hardware architectures.
References
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a new joint model of compressional and shear velocity in the mantle, Geophys.
J. Int., 153, 443–466.
Boschi, L., 2003. Measures of resolution in global body wave tomography,
Geophys. Res. Lett., 30, NO. 19, 1978, doi:10.1029/2003GL018222.
Boschi, L. & Dziewonski, A. M., 1999. “High” and “low” resolution images
of the Earth’s mantle - Implications of different approaches to tomographic
modeling, J. geophys. Res., 104, 25,567–25,594.
Boschi, L., T. W. Becker, G. Soldati, and A. M. Dziewonski, 2006. On
the relevance of Born theory in global seismic tomography, Geophys. Res.
Lett., 33, L06302, doi:10.1029/2005GL025063.
Bunge, H.-P. & Tromp, J., 2003. Supercomputing moves to universities
and makes possible new ways to organize computational research, EOS,
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Dziewonski, A. M., 1984. Mapping the lower mantle: determination of
lateral heterogeneity in P velocity up to degree and order 6, J. geophys.
Res., 89, 5929–5952.
Grand, S. P., 1994. Mantle shear structure beneath the Americas and
surrounding oceans, J. geophys. Res., 99, 11,591–11,621.
Hager, B. H., & R. W. Clayton, 1989. Constraints on the structure of
mantle convection using seismic observation, flow models, and the geoid,
in Mantle Convection-Plate Tectonics and Global Dynamics, edited by W.
R. Peltier, pp. 657–763, Gordon and Breach, Newark, N. J.
Hansen, P. C., 1992. Analysis of discrete ill-posed problems by means of
the L-curve, SIAM review, 34, 561–580.
Inoue, H., Fukao, Y., Tanabe, K. & Y. Ogata, 1990. Whole mantle P wave
travel time tomography, Phys. Earth planet. Inter., 59, 294–328.
L´evˆeque, J. J., L. Rivera, & G. Wittlinger, 1993. On the use of the checkerboard
test to assess the resolution of tomographic inversions, Geophys. J.
Int., 115, 313–318.
Menke, W., 1989. Geophysical Data Analysis: Discrete Inverse Theory,
rev. ed., Academic, San Diego.
Minkoff, S. E., 1996. A computationally feasible approximate resolution
matrix for seismic inverse problems, Geophys. J. Int., 126, 345–359.
Nolet, G., 1985. Solving or resolving inadequate and noisy tomographic
systems, J. Comput. Phys., 61, 463–482.
Nolet, G., R. Montelli, & J. Virieux, 1999. Explicit, approximate expressions
for the resolution and a posteriori covariance of massive tomographic
systems, Geophys. J. Int., 138, 36–44.
Nolet, G., R. Montelli, & J. Virieux, 2001. Reply to comment by Z. S.
Yao, R. G. Roberts and A. Tryggvason on “Explicit, approximate expressions
for the resolution and a posteriori covariance of massive tomographic
systems”, Geophys. J. Int., 145, 315.
Paige, C. C., & M. A. Saunders, 1982. LSQR: an algorithm for sparse linear
equations and sparse least squares, ACM Trans. Math. Soft., 8, 43–71.
Press, W. H., Teukolsky, S. A., Vetterling, W. T. & B. P. Flannery, 1994.
Numerical Recipes in FORTRAN, Cambridge University Press, U. K.
Soldati, G. & L. Boschi, 2004. Whole Earth tomographic models: a resolution
analysis, EOS, Trans. Am. geophys. Un., 85(47), Fall Meet. Suppl.
Su, W.-J., R. L. Woodward & A. M. Dziewonski, 1994. Degree-12 Model
of Shear Velocity Heterogeneity in the Mantle, J. geophys. Res., 99, 4945–
4980.
Tarantola, A., 2005. Inverse Problem Theory and Model Parameter Estimation,
SIAM, Philadelphia.
Trefethen, L. N. & D. Bau III, 1997. Numerical Linear Algebra, Soc. for
Ind. and Appl. Math., Philadelphia, Penn.
van der Hilst, R. D., S. Widiyantoro & E. R. Engdahl, 1997. Evidence for
deep mantle circulation from global tomography, Nature, 386, 578–584.
Vasco, D. W., L. R. Johnson & O. Marques, 2003. Resolution, uncertainty,
and whole-Earth tomography, J. geophys. Res., 108, 2022,
doi:10.1029/2001JB000412.
Wessel, P. & W. H. F. Smith, 1991. Free software helps map and display
data. EOS, Trans. Am. geophys. Un., 72, 445–446.
Woodhouse J. H. & A. M. Dziewonski, 1984. Mapping the upper mantle:
three-dimensional modeling of Earth structure by inversion of seismic
waveforms, J. geophys. Res., 89, 5953–5986.
Yao, Z. S., R. G. Roberts & A. Tryggvason, 1999. Calculating resolution
and covariance matrices for seismic tomography with the LSQR method,
Geophys. J. Int., 138, 886–894.
Yao, Z. S., R. G. Roberts, & A. Tryggvason, 2001. Comment on “Explicit,
approximate expressions for the resolution and a posteriori covariance of
massive tomographic systems” by G. Nolet, R. Montelli and J. Virieux,
Geophys. J. Int., 145, 307–314.
Zhang, J. & G. A. McMehan, 1995. Estimation of resolution and covariance
for large matrix inversions, Geophys. J. Int., 121, 409–426.
a new joint model of compressional and shear velocity in the mantle, Geophys.
J. Int., 153, 443–466.
Boschi, L., 2003. Measures of resolution in global body wave tomography,
Geophys. Res. Lett., 30, NO. 19, 1978, doi:10.1029/2003GL018222.
Boschi, L. & Dziewonski, A. M., 1999. “High” and “low” resolution images
of the Earth’s mantle - Implications of different approaches to tomographic
modeling, J. geophys. Res., 104, 25,567–25,594.
Boschi, L., T. W. Becker, G. Soldati, and A. M. Dziewonski, 2006. On
the relevance of Born theory in global seismic tomography, Geophys. Res.
Lett., 33, L06302, doi:10.1029/2005GL025063.
Bunge, H.-P. & Tromp, J., 2003. Supercomputing moves to universities
and makes possible new ways to organize computational research, EOS,
Trans. Am. geophys. Un., 84, 30–33.
Dziewonski, A. M., 1984. Mapping the lower mantle: determination of
lateral heterogeneity in P velocity up to degree and order 6, J. geophys.
Res., 89, 5929–5952.
Grand, S. P., 1994. Mantle shear structure beneath the Americas and
surrounding oceans, J. geophys. Res., 99, 11,591–11,621.
Hager, B. H., & R. W. Clayton, 1989. Constraints on the structure of
mantle convection using seismic observation, flow models, and the geoid,
in Mantle Convection-Plate Tectonics and Global Dynamics, edited by W.
R. Peltier, pp. 657–763, Gordon and Breach, Newark, N. J.
Hansen, P. C., 1992. Analysis of discrete ill-posed problems by means of
the L-curve, SIAM review, 34, 561–580.
Inoue, H., Fukao, Y., Tanabe, K. & Y. Ogata, 1990. Whole mantle P wave
travel time tomography, Phys. Earth planet. Inter., 59, 294–328.
L´evˆeque, J. J., L. Rivera, & G. Wittlinger, 1993. On the use of the checkerboard
test to assess the resolution of tomographic inversions, Geophys. J.
Int., 115, 313–318.
Menke, W., 1989. Geophysical Data Analysis: Discrete Inverse Theory,
rev. ed., Academic, San Diego.
Minkoff, S. E., 1996. A computationally feasible approximate resolution
matrix for seismic inverse problems, Geophys. J. Int., 126, 345–359.
Nolet, G., 1985. Solving or resolving inadequate and noisy tomographic
systems, J. Comput. Phys., 61, 463–482.
Nolet, G., R. Montelli, & J. Virieux, 1999. Explicit, approximate expressions
for the resolution and a posteriori covariance of massive tomographic
systems, Geophys. J. Int., 138, 36–44.
Nolet, G., R. Montelli, & J. Virieux, 2001. Reply to comment by Z. S.
Yao, R. G. Roberts and A. Tryggvason on “Explicit, approximate expressions
for the resolution and a posteriori covariance of massive tomographic
systems”, Geophys. J. Int., 145, 315.
Paige, C. C., & M. A. Saunders, 1982. LSQR: an algorithm for sparse linear
equations and sparse least squares, ACM Trans. Math. Soft., 8, 43–71.
Press, W. H., Teukolsky, S. A., Vetterling, W. T. & B. P. Flannery, 1994.
Numerical Recipes in FORTRAN, Cambridge University Press, U. K.
Soldati, G. & L. Boschi, 2004. Whole Earth tomographic models: a resolution
analysis, EOS, Trans. Am. geophys. Un., 85(47), Fall Meet. Suppl.
Su, W.-J., R. L. Woodward & A. M. Dziewonski, 1994. Degree-12 Model
of Shear Velocity Heterogeneity in the Mantle, J. geophys. Res., 99, 4945–
4980.
Tarantola, A., 2005. Inverse Problem Theory and Model Parameter Estimation,
SIAM, Philadelphia.
Trefethen, L. N. & D. Bau III, 1997. Numerical Linear Algebra, Soc. for
Ind. and Appl. Math., Philadelphia, Penn.
van der Hilst, R. D., S. Widiyantoro & E. R. Engdahl, 1997. Evidence for
deep mantle circulation from global tomography, Nature, 386, 578–584.
Vasco, D. W., L. R. Johnson & O. Marques, 2003. Resolution, uncertainty,
and whole-Earth tomography, J. geophys. Res., 108, 2022,
doi:10.1029/2001JB000412.
Wessel, P. & W. H. F. Smith, 1991. Free software helps map and display
data. EOS, Trans. Am. geophys. Un., 72, 445–446.
Woodhouse J. H. & A. M. Dziewonski, 1984. Mapping the upper mantle:
three-dimensional modeling of Earth structure by inversion of seismic
waveforms, J. geophys. Res., 89, 5953–5986.
Yao, Z. S., R. G. Roberts & A. Tryggvason, 1999. Calculating resolution
and covariance matrices for seismic tomography with the LSQR method,
Geophys. J. Int., 138, 886–894.
Yao, Z. S., R. G. Roberts, & A. Tryggvason, 2001. Comment on “Explicit,
approximate expressions for the resolution and a posteriori covariance of
massive tomographic systems” by G. Nolet, R. Montelli and J. Virieux,
Geophys. J. Int., 145, 307–314.
Zhang, J. & G. A. McMehan, 1995. Estimation of resolution and covariance
for large matrix inversions, Geophys. J. Int., 121, 409–426.
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