Research article Special Issues

A Multi-Objective Optimization Framework for Joint Inversion

  • Received: 01 December 2015 Accepted: 18 March 2016 Published: 23 March 2016
  • Different geophysical data sets such as receiver functions, surface wave dispersion measurements, and first arrival travel times, provide complementary information about the Earth structure. To utilize all this information, it is desirable to perform a joint inversion, i.e., to use all these datasets when determining the Earth structure. In the ideal case, when we know the variance of each measurement, we can use the usual Least Squares approach to solve the joint inversion problem. In practice, we only have an approximate knowledge of these variances. As a result, if a geophysical feature appears in a solution corresponding to these approximate values of variances, there is no guarantee that this feature will still be visible if we use the actual (somewhat different) variances. To make the joint inversion process more robust, it is therefore desirable to repeatedly solve the joint inversion problem with different possible combinations of variances. From the mathematical viewpoint, such solutions form a Pareto front of the corresponding multi-objective optimization problem.

    Citation: Thompson Lennox, Velasco Aaron A., Kreinovich Vladik. A Multi-Objective Optimization Framework for Joint Inversion[J]. AIMS Geosciences, 2016, 2(1): 63-87. doi: 10.3934/geosci.2016.1.63

    Related Papers:

  • Different geophysical data sets such as receiver functions, surface wave dispersion measurements, and first arrival travel times, provide complementary information about the Earth structure. To utilize all this information, it is desirable to perform a joint inversion, i.e., to use all these datasets when determining the Earth structure. In the ideal case, when we know the variance of each measurement, we can use the usual Least Squares approach to solve the joint inversion problem. In practice, we only have an approximate knowledge of these variances. As a result, if a geophysical feature appears in a solution corresponding to these approximate values of variances, there is no guarantee that this feature will still be visible if we use the actual (somewhat different) variances. To make the joint inversion process more robust, it is therefore desirable to repeatedly solve the joint inversion problem with different possible combinations of variances. From the mathematical viewpoint, such solutions form a Pareto front of the corresponding multi-objective optimization problem.


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    [1] Bashir, L ., S.S. Gao, K.H. Liu, and K. Mickus. (2011) 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.
    [2] Bailey, I. W., M.S. Miller, K. Liu, and A. Levander. (2012) 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. doi: 10.1029/2011JB0085.
    [3] C ho, K. H., R. B. Herrmann, C. J. Ammon, and K. Lee. (2007) Imaging the upper crust of the Korean Peninsula by surface-wave tomography. Bulletin of the Seismological Society of America ,97: 198-207.
    [4] Colombo, D ., and M. De Stefano. (2007) Geophysical modeling via simultaneous joint inversion of seismic, gravity, and electromagnetic data: Application to prestack depth imaging. The Leading Edge ,26: 326-331.
    [5] Dzierma, Y ., W. Rabbel, M.M. Thorwart, E.R. Flueh, M.M. Mora, and G.E. Alvarado. (2011) 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. doi: 10.1029/2010GC003477
    [6] Gurrola, H ., E. G. Baker, and B.J. Minster. (1995) Simultaneous time-domain deconvolution with application to the computation of receiver functions. Geophys. J. Int. ,120: 537-543.
    [7] J in, G ., and J. B. Gaherty. (2014) Surface Wave Measurement Based on Cross-correlation. Geophys. J. Int, submitted .
    [8] Haber, E ., and D. Oldenburg. (1997) Joint inversion: a structural approach. Inverse Problems ,13: 63-77.
    [9] Hansen, P. C. (2010) Discrete Inverse Problems: Insight and Algorithms, 225pp., Soc. for Ind. and Appl. Math., Philadelphia, Pa .
    [10] Hansen, S. M., K.G. Dueker, J.C. Stachnik, R.C. Aster, and K.E. Karlstrom. (2013) 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. doi: 10.1002/ggge.20143
    [11] Julia, J ., C. J. Ammon, R. Hermann, and M. Correig. (2000) Joint inversion of receiver function and surface wave dispersion observations. Geophys. J. Int. ,142: 99-112.
    [12] Kozlovskaya, E . (2000) An algorithm of geophysical data inversion based on non-probabilistic presentation of a-prior information and definition of pareto-optimality. Inverse Problems ,16: 839-861.
    [13] Langston, C. A. (1981) Evidence for the subducting lithosphere under southern Vancouver Island and western Oregon from teleseismic P wave conversions. J. Geophys. Res. ,86: 3857-3866.
    [14] Laske, G ., G. Masters and C. Reif. (2000) Crust 2.0. The Current Limits of Resolution for Surface Wave Tomography in North America. EOS Trans AGU ,81: F897http://igpppublic.ucsd.edu/gabi/ftp/crust2/.
    [15] Le es, J.M. and J. C. Vandecar. (1991) Seismic tomography constrained by bouguer gravity anomalies: Applications in western Washington. PAGEOPH ,135: 31-52.
    [16] Ligorria, J. P., and C. J. Ammon. (1999) Iterative deconvolution and receiver-function estimation, Bull. Seismol. Soc. Am. ,89: 1395-1400.
    [17] Maceira, M ., and C.J. Ammon. (2009) Joint inversion of surface wave velocity and gravity observations and its application to central Asian basins s-velocity structure. J. Geophys Res. ,114: B02314. doi: 10.1029/2007JB0005157
    [18] Nocedal, J. and S.J. Wright (2006). Numerical Optimization. 2nd edn. Springer, New York, NY
    [19] Obrebski, M ., S. Kiselev, L. Vinnik, and J. P. Montagner. (2010) Anisotropic stratification beneath Africa from joint inversion of SKS and P receiver functions. J. Geophys. Res. ,115: B09313. doi: 10.1029/2009JB006923
    [20] Owens, T. J., H. P. Crotwell, C. Groves, and P. Oliver-Paul. (2004) SOD: Standing Order for Data. Seismol. Res. Lett. ,75: 515-520.
    [21] Sambridge, M . (1999) Geophysical inversion with a neighborhood algorithm I: searching a parameter space. Geophys. J. Int. ,138: 479-494.
    [22] Shearer, P. M. (2009) Introduction to Seismology, Second Edition, Cambridge University Press. Cambridge .
    [23] Shen W., M. H. Ritzwoller, and V. Schulte-Pelkum. (2013) 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. doi: 10.1029/2012JB009602
    [24] So sa, A ., A.A. Velasco, L. Velasquez, M. Argaez, and R. Romero. (2013) Constrained Optimization framework for joint inversion of geophysical data sets. Geophys. J. Int. ,195: 197-211.
    [25] Stein, S ., and M. Wysession. (2003) An Introduction to Seismology Earthquakes and Earth Structure. Blackwell, Maiden, Mass .
    [26] Thompson, L ., A. A. Velasco, V. Kreinovich, R. Romero, and A. Sosa. (2016) 3-D Shear Wave Based Models of the Texas Region Using 1-D Constrained Multi-Objective Optimization. Journal of Geophysical Research, (submitted for publication) .
    [27] Tikhonov, A. N., and V.Y. Arsenin. (1977) Solution of Ill-Posed Problems. VH Winston & Sons. Washington, D.C. .
    [28] Vogel, C. R. (2002) Computational Methods for Inverse Problems. SIAM FR23, Philadelphia .
    [29] Vozoff, K. and D. L. B. Jupp. (1975) Joint inversion of geophysical data. Geophys. J. Roy Astr. Soc. ,42: 977-991.
    [30] Wilson, D . (2003) Imagining crust and upper mantle seismic structure in the southwestern United States using teleseismic receiver functions. Leading Edge ,22: 232-237.
    [31] Wilson, D ., and R. Aster. (2005) 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. doi: 10.1029/2004JB003430
    [32] Wilson, D ., R. Aster, J. Ni, S. Grand, M. West, W. Gao, W.S. Baldridge, and S. Semken. (2005) 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. doi: 10.1029/2004JB003492
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