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Construction of Shear Wave Models by Applying Multi-Objective Optimization to Multiple Geophysical Data Sets

  • Lennox ThompsonEmail author
  • Aaron A. Velasco
  • Vladik Kreinovich
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 121)

Abstract

For this work, our main purpose is to obtain a better understanding of the Earth’s tectonic processes in the Texas region, which requires us to analyze the Earth structure. We expand on a constrained optimization approach for a joint inversion least-squares (LSQ) algorithm to characterize a Earth’s structure of Texas with the use of multiple geophysical data sets. We employed a joint inversion scheme using multiple geophysical data sets for the sole purpose of obtaining a three-dimensional velocity structure of Texas in order to identify an ancient rift system within Texas. In particular, we use data from the USArray, which is part of the EarthScope experiment, a 15-year program to place a dense network of permanent and portable seismographs across the continental USA. Utilizing the USArray data has provided us with the ability to image the crust and upper mantle structure of Texas. We prove through numerical and experimental testing that our multiobjective optimization problem (MOP) scheme performs inversion in a more robust, and flexible matter than traditional inversion approaches.

Keywords

Teleseismic Receiver functions Seismographs Body waves Multi-objective optimization Primal-dual interior point method 

Notes

Acknowledgment

We would like to take the time to thank the computational science, mathematical science, and computer science departments from University of Texas at El Paso (UTEP). We would also like to thank Ezer Patlan, Dr. Anibal Sosa, Dr. Rodrigo Romero, Dr. Monica Maceira, and Azucena Zamora for all of their contributions to this work. This work was sponsored by the NSF CREST under Grant Cybershare HRD-0734825.

References

  1. 1.
    Astiz, L., Earle, P., Shearer, P.: Global stacking of broadband seismograms. Seis. Res. Lett. 67, 8–18 (1996)Google Scholar
  2. 2.
    Bashir, L., Gao, S.S., Liu, K.H., Mickus, K.: Crustal structure and evolution beneath the Colorado Plateau and the southern Basin and Range Province: results from receiver function and gravity studies. Geochem. Geophys. Geosyst. 12, Q06008 (2011). doi:10.1029/2011GC003563Google Scholar
  3. 3.
    Bailey, I.W., Miller, M.S., Liu, K., Levander, A.. Vs and density structure beneath the Colorado Plateau constrained by gravity anomalies and joint inversions of receiver function and phase velocity data. J. Geophys. Res. 117, B02313 (2012). doi:10.1029/2011JB0085Google Scholar
  4. 4.
    Bodin, T., Sambridge, M., Tkalcic, H., Arroucau, P., Gallagher, K., Rawlinson, N.: Transdimensional inversion of receiver functions and surface wave dispersion. J. Geophys. Res. 117 (2012). doi:10.1029/2011JB008560Google Scholar
  5. 5.
    Cho, K.H., Herrmann, R.B., Ammon, C.J., Lee, K.: Imaging the upper crust of the Korean Peninsula by surface-wave tomography. Bull. Seismol. Soc. Am. 97, 198–207 (2007)Google Scholar
  6. 6.
    Colombo, D., De Stefano, M.: Geophysical modeling via simultaneous joint inversion of seismic, gravity, and electromagnetic data: Application to prestack depth imaging. Leading Edge 26, 326–331 (2007)CrossRefGoogle Scholar
  7. 7.
    Dzierma, Y., Rabbel, W., Thorwart, M.M., Flueh, E.R., Mora, M.M., Alvarado, G.E.: The steeply subducting edge of the Cocos Ridge: evidence from receiver functions beneath the northern Talamanca Range, south-central Costa Rica. Geochem. Geophys. Geosyst. 12 (2011). doi:10.1029/2010GC003477Google Scholar
  8. 8.
    Gurrola, H., Baker, E.G., Minster, B.J.. Simultaneous time-domain deconvolution with application to the computation of receiver functions. Geophys. J. Int. 120, 537–543 (1995)CrossRefGoogle Scholar
  9. 9.
    Haber, E., Oldenburg, D.: Joint inversion: A structural approach. Inverse Probl. 13, 63–77 (1997)CrossRefzbMATHGoogle Scholar
  10. 10.
    Hansen, P.C.: Discrete inverse problems: Insight and algorithms, 225 pp. Soc. Ind. Appl. Math. Philadelphia, Pa. (2010)Google Scholar
  11. 11.
    Hansen, S.M., Dueker, K.G., Stachnik, J.C., Aster, R.C., Karlstrom, K.E.: A rootless rockies - Support and lithospheric structure of the Colorado Rocky Mountains inferred from CREST and TA seismic data. Geochem. Geophys. Geosyst. 14, 2670–2695 (2013). doi:10.1002/ggge.20143CrossRefGoogle Scholar
  12. 12.
    Hackney, R.I., Featherstone, W.E.: Geodetic versus geophysical perspectives of the gravity anomaly. Geophys. J. Int. 154(1), 35–43 (2003)CrossRefGoogle Scholar
  13. 13.
    Heiskanen, W.A., Moritz, H.: Physical geodesy. W. H. Freeman and Company, San Francisco (1967)Google Scholar
  14. 14.
    Julia, J., Ammon, C.J., Hermann, R., Correig, M.: Joint inversion of receiver function and surface wave dispersion observations. Geophys. J. Int. 142, 99–112 (2000)CrossRefGoogle Scholar
  15. 15.
    Kozlovskaya, E.: An algorithm of geophysical data inversion based on non-probabilistic presentation of a-prior information and definition of pareto-optimality. Inverse Probl. 16, 839–861 (2000)CrossRefzbMATHMathSciNetGoogle Scholar
  16. 16.
    Langston, C.A.: Evidence for the subducting lithosphere under southern Vancouver Island and western Oregon from teleseismic P wave conversions. J. Geophys. Res. 86, 3857–3866 (1981)CrossRefGoogle Scholar
  17. 17.
    Laske, G., Masters, G., Reif, C.: Crust 2.0. the current limits of resolution for surface wave tomography in North America. EOS Trans. AGU 81 F897 (2000). http://igpppublic.ucsd.edu/gabi/ftp/crust2/ CrossRefGoogle Scholar
  18. 18.
    Lees, J.M., Vandecar, J.C.: Seismic tomography constrained by bouguer gravity anomalies: Applications in western Washington. PAGEOPH. 135, 31–52 (1991)CrossRefGoogle Scholar
  19. 19.
    Lin, F.C., Schmandt, B., Tsai, V.C.: Joint inversion of Rayleigh wave phase velocity and ellipticity using USArray: Constraining velocity and density structure in the upper crust. Geophys. Res. Lett. 39, L12303 (2012). doi:10.1029/2012GL052196CrossRefGoogle Scholar
  20. 20.
    Lodge, A., Helffrich, G.: Grid search inversion of teleseismic receiver functions. Geophys. J. Int. 178, 513–523 (2009)CrossRefGoogle Scholar
  21. 21.
    Maceira, M., Ammon, C.J.: Joint inversion of surface wave velocity and gravity observations and its application to central Asian basins s-velocity structure. J. Geophys. Res. 114, B02314 (2009). doi:10.1029/2007JB0005157.CrossRefGoogle Scholar
  22. 22.
    Moorkamp, M., Jones, A.G., Fishwick, S.: Joint inversion of receiver functions, surface wave dispersion, and magnetotelluric data. J. Geophys. Res. 115, B04318 (2010). doi:10.1029/2009JB0006369CrossRefGoogle Scholar
  23. 23.
    Moorkamp, M., Heincke, B., Jegen, M., Roberts, A.W., Hobbs, R.W.: A framework for 3–D joint inversion of MT, gravity and seismic refraction data. Geophys. J. Int. 184, 477–493 (2011)CrossRefGoogle Scholar
  24. 24.
    Nocedal, J., Wright, S.: Numerical optimization. 2nd edn. Springer, New York (2006)Google Scholar
  25. 25.
    Obrebski, M., Kiselev, S., Vinnik, L., Montagner, J.P.: Anisotropic stratification beneath Africa from joint inversion of SKS and P receiver functions. J. Geophys. Res. 115, B09313 (2010). doi:10.1029/2009JB006923Google Scholar
  26. 26.
    Owens, T.J., Crotwell, H.P., Groves, C., Oliver-Paul, P.: SOD: Standing order for data. Seismol. Res. Lett. 75, 515–520 (2004)Google Scholar
  27. 27.
    Sambridge, M.: Geophysical inversion with a neighborhood algorithm I: Searching a parameter space. Geophys. J. Int. 138, 479–494 (1999)CrossRefGoogle Scholar
  28. 28.
    Sambridge, M.: Geophysical inversion with a neighborhood algorithm II: Appraising the ensemble. Geophys. J. Int. 138, 727–746 (1999)CrossRefGoogle Scholar
  29. 29.
    Shearer, P.M.: Introduction to Seismology, 2nd edn. Cambridge University Press, Cambridge (2009)CrossRefGoogle Scholar
  30. 30.
    Shen, W., Ritzwoller, M.H., Schulte-Pelkum, V.: A 3-D model of the crust and uppermost mantle beneath the Central and Western US by joint inversion of receiver functions and surface wave dispersion. J. Geophys. Res. Solid Earth 118 (2013). doi:10.1029/2012JB009602Google Scholar
  31. 31.
    Sosa, A., Velasco, A.A., Velasquez, L., Argaez, M., Romero, R.: Constrained Optimization framework for joint inversion of geophysical data sets. Geophys. J. Int. 195, 197–211 (2013)Google Scholar
  32. 32.
    Stein, S., Wysession, M.: An introduction to seismology, earthquakes, and earth structure. Blackwell, Maiden (2003)Google Scholar
  33. 33.
    Tikhonov, A.N., Arsenin, V.Y.: Solutions if Ill-posed Problems. Winston and Sons, Washington (1977)Google Scholar
  34. 34.
    Vogel, C.R.: Computational methods for inverse problems. SIAM FR23, Philadelphia, (2002)Google Scholar
  35. 35.
    Vozoff, K., Jupp, D.L.B.: Joint inversion of geophysical data. Geophys. J. R. Astr. Soc. 42, 977–991 (1975)CrossRefGoogle Scholar
  36. 36.
    Wilson, D.: Imagining crust and upper mantle seismic structure in the southwestern United States using teleseismic receiver functions. Leading Edge 22, 232–237 (2003)CrossRefGoogle Scholar
  37. 37.
    Wilson, D., Aster, R.: Seismic imaging of the crust and upper mantle using Regularized joint receiver functions, frequency-wave number filtering, and Multimode Kirchhoff migration. J. Geophys. Res. B05305 (2005). doi:10.1029/2004JB003430Google Scholar
  38. 38.
    Wilson, D., Aster, R., Ni, J., Grand, S., West, M., Gao, W., Baldridge, W.S., Semken, S.: Imaging the structure of the crust and upper mantle beneath the Great Plains, Rio Grande Rift, and Colorado Plateau using receiver functions. J. Geophys. Res. 110, B05306 (2005). doi:10.1029/2004JB003492Google Scholar
  39. 39.
    Zhu, L., Kanamori, H.: Moho depth variation in southern California from teleseismic receiver functions. J. Geophys. Res. 105, 2969–2980 (2000)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Lennox Thompson
    • 1
    Email author
  • Aaron A. Velasco
    • 1
  • Vladik Kreinovich
    • 1
  1. 1.Department of Geological SciencesUniversity of Texas at El Paso (UTEP)El PasoUSA

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