Skip to main content
SpringerLink
Log in

Misfit Functionals and Adjoint Sources

  • Chapter
  • First Online:
Full Seismic Waveform Modelling and Inversion

  • 3446 Accesses

Abstract

The early developments of full waveform inversion for 2D acoustic problems (e.g. Tarantola, 1984; Gauthier et al., 1986) were almost immediately followed by the recognition that the choice of a suitable misfit functional is crucial for a successful application to real data. In one of the first large-scale full waveform inversions, Crase et al. (1990) proposed a series of robust misfit measures that are comparatively insensitive to seismic noise. Their study was extended by Brossier et al. (2010). The L 2 distance between observed and synthetic seismograms is efficient for the detection of sharp material contrasts, but the recovery of long-wavelength Earth structure requires misfit functionals that explicitly extract phase information. In their pioneering work, Luo & Schuster (1991) therefore proposed to measure the cross-correlation time shift between observed and synthetic waveforms (Sect. 11.3). This idea was extended by van Leeuwen & Mulder (2010).

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Aki, K., Richards, P. G.: Quantitative Seismology, 2nd edn. University Science Books, Herndon, VA (2002)

    Google Scholar 

  • Bamberger, A., Chavent, G., Hemons, Ch., Lailly, P.: Inversion of normal incidence seismograms. Geophysics 47(5), 757–770 (1982)

    Article  Google Scholar 

  • Brossier, R., Operto, S., Virieux, J.: Which data residual norm for robust elastic frequency-domain full waveform inversion? Geophysics 75, R37–R46 (2010)

    Article  Google Scholar 

  • Cara, M.: Filtering of dispersed wave trains. Geophys. J. R. astron. Soc. 33, 65–80 (1973)

    Google Scholar 

  • Chen, P., Zhao, L., Jordan, T. H.: Full 3D tomography for the crustal structure of the Los Angeles region. Bull. Seism. Soc. Am. 97(4), 1094–1120 (2007)

    Article  Google Scholar 

  • Crase, E., Pica, A., Noble, M., McDonald, J., Tarantola, A.: Robust elastic nonlinear waveform inversion – Application to real data. Geophysics 55(5), 527–538 (1990)

    Article  Google Scholar 

  • Dahlen, F. A., Hung, S.-H., Nolet, G.: Fréchet kernels for finite-frequency traveltimes – I. Theory. Geophys. J. Int. 141, 157–174 (2000)

    Article  Google Scholar 

  • Dziewonski, A. M., Mills, J, Bloch, S.: Residual dispersion measurement – a new method of surface wave analysis. Bull. Seism. Soc. Am. 62, 129–139 (1972)

    Google Scholar 

  • Fichtner, A., Kennett, B. L. N., Igel, H., Bunge, H.-P.: Theoretical background for continental- and global-scale full-waveform inversion in the time-frequency domain. Geophys. J. Int. 175, 665–685 (2008)

    Article  Google Scholar 

  • Fichtner, A., Kennett, B. L. N., Igel, H., Bunge, H.-P.: Full seismic waveform tomography for upper-mantle structure in the Australasian region using adjoint methods. Geophys. J. Int. 179, 1703–1725 (2009)

    Article  Google Scholar 

  • Fichtner, A., Kennett, B. L. N., Igel, H., Bunge, H.-P.: Full waveform tomography for radially anisotropic structure: new insights into present and past states of the Australasian upper mantle. Earth Planet. Sci. Lett. 290, 270–280 (2010)

    Article  Google Scholar 

  • Gauthier, O., Virieux, J., Tarantola, A.: Two-dimensional nonlinear inversion of seismic waveforms: numerical results. Geophysics 51(7), 1387–1403 (1986)

    Article  Google Scholar 

  • Gee, L. S., Jordan, T. H.: Generalized seismological data functionals. Geophys. J. Int. 111, 363–390 (1992)

    Article  Google Scholar 

  • Igel, H., Djikpéssé, H., Tarantola, A.: Waveform inversion of marine reflection seismograms for P impedance and Poisson’s ratio. Geophys. J. Int. 124(2), 363–371 (1996)

    Article  Google Scholar 

  • Korenaga, J., Holbrook, W., Singh, S., Minshull, T.: Natural gas hydrates on the Southeast U.S. margin: constraints from full waveform and travel time inversions of wide-angle seismic data. J. Geophys. Res. 102, 15345–15365 (1997)

    Article  Google Scholar 

  • Kristekova, M., Kristek, J., Moczo, P., Day, S. M.: Misfit criteria for quantitative comparison of seismograms. Bull. Seism. Soc. Am. 96, 1836–1850 (2006)

    Article  Google Scholar 

  • Kristekova, M., Kristek, J., Moczo, P.: Time-frequency misfit and goodness-of-fit criteria for quantitative comparison of time signals. Geophys. J. Int. 178, 813–825 (2009)

    Article  Google Scholar 

  • Lerner-Lam, A. L., Jordan, T. H.: Earth structure from fundamental and higher-mode waveform analysis. Geophys. J. R. Astron. Soc. 75, 759–797 (1983)

    Google Scholar 

  • Liu, Q., Tromp, J.: Finite-frequency sensitivity kernels for global seismic wave propagation based upon adjoint methods. Geophys. J. Int. 174, 265–286 (2008)

    Article  Google Scholar 

  • Luo, Y., Schuster, G. T.: Wave-equation traveltime inversion. Geophysics 56, 645–653 (1991)

    Article  Google Scholar 

  • Nyman, D. C., Landisman, M.: The display-equalized filter for frequency-time analysis. Bull. Seism. Soc. Am. 67, 393–404 (1977)

    Google Scholar 

  • Sieminski, A., Liu, Q., Trampert, J., Tromp, J.: Finite-frequency sensitivity of surface waves to anisotropy based upon adjoint methods. Geophys. J. Int. 168(3), 1153–1174 (2007a)

    Article  Google Scholar 

  • Sigloch, K., Nolet, G.: Measuring finite-frequency body-wave amplitudes and traveltimes. Geophys. J. Int. 167, 271–287 (2006)

    Article  Google Scholar 

  • Sigloch, K., McQuarrie, N., Nolet, G.: Two-stage subduction history under North America inferred from multiple-frequency tomography. Nat. Geosci. 1, 458–462 (2008)

    Article  Google Scholar 

  • Strang, G., Nguyen, T.: Wavelets and Filter Banks. Wellesley-Cambridge Press, Cambridge (1996)

    Google Scholar 

  • Tape, C., Liu, Q. Y., Maggi, A., Tromp, J.: Seismic tomography of the southern California crust based upon spectral-element and adjoint methods. Geophys. J. Int. 180, 433–462 (2010)

    Article  Google Scholar 

  • Tarantola, A.: Inversion of seismic reflection data in the acoustic approximation. Geophysics 49, 1259–1266 (1984)

    Article  Google Scholar 

  • Thomson, D. J.: Spectrum estimation and harmonic analysis. Proc. IEEE 70, 1055–1096 (1982)

    Article  Google Scholar 

  • Tibuleac, I. M., Nolet, G., Michaelson, C., Koulakov, I.: P wave amplitudes in a 3-D Earth. Geophys. J. Int. 155, 1–10 (2003)

    Article  Google Scholar 

  • Tromp, J., Tape, C., Lui, Q.: Seismic tomography, adjoint methods, time reversal and banana-doughnut kernels. Geophys. J. Int. 160, 195–216 (2005)

    Article  Google Scholar 

  • van Leeuwen, T., Mulder, W. A.: A correlation-based misfit criterion for wave-equation traveltime tomography. Geophys. J. Int. 182, 1383–1394 (2010)

    Article  Google Scholar 

  • Zhou, C., Cai, W., Luo, Y., Schuster, G., Hassanzadeh, S.: Acoustic wave-equation traveltime and waveform inversion of crosshole seismic data. Geophysics 60, 765–773 (1995)

    Article  Google Scholar 

  • Sieminski, A., Liu, Q., Trampert, J., Tromp, J.: Finite-frequency sensitivity of body waves to anisotropy based upon adjoint methods. Geophys. J. Int. 171(1), 368–389 (2007b)

    Article  Google Scholar 

  • Bleibinhaus, F., Hole, J. A., Ryberg, T., Fuis, G. S.: Structure of the California Coast Ranges and San Andreas Fault at SAFOD from seismic waveform inversion and reflection imaging. J. Geophys. Res. 112, doi:10.1029/2006JB004611 (2007)

    Google Scholar 

  • Bozdağ, E., Trampert, J.: Misfit functions for full waveform inversion based on instantaneous phase and envelope measurements. Geophys. J. Int., in press (2010)

    Google Scholar 

  • Dessa, J. X., Operto, S., Kodaira, S., Nakanishi, A., Pascal, G., Virieux, J., Kaneda, Y.: Multiscale seismic imaging of the eastern Nankai trough by full waveform inversion. Geophys. Res. Lett. 31, doi:10.1029/2004GL020453 (2004)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Earth Sciences, Utrecht University, Budapestlaan 4, 3584, CE, Utrecht, The Netherlands

    Andreas Fichtner

Authors
  1. Andreas Fichtner
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Andreas Fichtner .

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Fichtner, A. (2011). Misfit Functionals and Adjoint Sources. In: Full Seismic Waveform Modelling and Inversion. Advances in Geophysical and Environmental Mechanics and Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15807-0_11

Download citation

Publish with us

Policies and ethics

Search

Navigation