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References

This page is a running, DOI-rich bibliography of every misfit that sweep_loss implements (or plans to). When a loss has multiple "foundational" papers all are listed. Sorted alphabetically by first author.

A. Data-domain Lp norms and robust M-estimators

  • Aravkin, A. Y., van Leeuwen, T. & Herrmann, F. J. (2011). Robust FWI using Student-t distribution. SEG Technical Program Expanded Abstracts, pp. 2669-2673. doi:10.1190/1.3627747
  • Beaton, A. E. & Tukey, J. W. (1974). The fitting of power series, meaning polynomials, illustrated on band-spectroscopic data. Technometrics 16, 147-185. doi:10.1080/00401706.1974.10489171
  • Brossier, R., Operto, S. & Virieux, J. (2010). Which data residual norm for robust elastic frequency-domain full waveform inversion? Geophysics 75 (3), R37-R46. doi:10.1190/1.3379323
  • Bube, K. P. & Langan, R. T. (1997). Hybrid L1/L2 minimisation with applications to tomography. Geophysics 62 (4), 1183-1195. doi:10.1190/1.1444219
  • Bube, K. P. & Nemeth, T. (2007). Fast line searches for the robust solution of linear systems in the hybrid l1/l2 and Huber norms. Geophysics 72 (2), A13-A17. doi:10.1190/1.2431639
  • Charbonnier, P., Blanc-Feraud, L., Aubert, G. & Barlaud, M. (1997). Deterministic edge-preserving regularisation in computed imaging. IEEE Trans. Image Process. 6 (2), 298-311. doi:10.1109/83.551699
  • Crase, E., Pica, A., Noble, M., McDonald, J. & Tarantola, A. (1990). Robust elastic nonlinear waveform inversion: application to real data. Geophysics 55 (5), 527-538. doi:10.1190/1.1442864
  • Geman, S. & McClure, D. E. (1985). Bayesian image analysis: an application to single photon emission tomography. Proc. Stat. Comp. Sect., ASA, 12-18. (no DOI; see permanent record)
  • Guitton, A. & Symes, W. W. (2003). Robust inversion of seismic data using the Huber norm. Geophysics 68 (4), 1310-1319. doi:10.1190/1.1598124
  • Ha, T., Chung, W. & Shin, C. (2009). Waveform inversion using a back-propagation algorithm and a Huber function norm. Geophysics 74 (3), R15-R24. doi:10.1190/1.3112572
  • Huber, P. J. (1964). Robust estimation of a location parameter. Ann. Math. Stat. 35 (1), 73-101. doi:10.1214/aoms/1177703732
  • Lailly, P. (1983). The seismic inverse problem as a sequence of before-stack migrations. In: Conference on Inverse Scattering: Theory and Application, SIAM, Philadelphia, 206-220. (no DOI)
  • Tarantola, A. (1984). Inversion of seismic reflection data in the acoustic approximation. Geophysics 49 (8), 1259-1266. doi:10.1190/1.1441754
  • Virieux, J. & Operto, S. (2009). An overview of full-waveform inversion in exploration geophysics. Geophysics 74 (6), WCC1-WCC26. doi:10.1190/1.3238367

B. Correlation / amplitude-normalised (planned)

  • Choi, Y. & Alkhalifah, T. (2012). Application of multi-source waveform inversion to marine streamer data using the global correlation norm. Geophysical Prospecting 60 (4), 748-758. doi:10.1111/j.1365-2478.2012.01079.x
  • Fomel, S. (2007). Local seismic attributes. Geophysics 72 (3), A29-A33. doi:10.1190/1.2437573
  • Routh, P., Krebs, J., Lazaratos, S., et al. (2011). Encoded simultaneous source full-wavefield inversion for spectrally-shaped marine streamer data. SEG Technical Program Expanded Abstracts, pp. 2433-2438. doi:10.1190/1.3627697
  • van Leeuwen, T. & Mulder, W. A. (2010). A correlation-based misfit criterion for wave-equation traveltime tomography. Geophys. J. Int. 182 (3), 1383-1394. doi:10.1111/j.1365-246X.2010.04681.x

C. Envelope / instantaneous phase (planned)

  • Bozdağ, E., Trampert, J. & Tromp, J. (2011). Misfit functions for full waveform inversion based on instantaneous phase and envelope measurements. Geophys. J. Int. 185 (2), 845-870. doi:10.1111/j.1365-246X.2011.04970.x
  • Fichtner, A., Kennett, B. L. N., Igel, H. & Bunge, H.-P. (2008). Theoretical background for continental- and global-scale full-waveform inversion in the time-frequency domain. Geophys. J. Int. 175 (2), 665-685. doi:10.1111/j.1365-246X.2008.03923.x
  • Wu, R.-S., Luo, J. & Wu, B. (2014). Seismic envelope inversion and modulation signal model. Geophysics 79 (3), WA13-WA24. doi:10.1190/geo2013-0294.1
  • Yuan, Y. O., Simons, F. J. & Tromp, J. (2016). Double-difference adjoint seismic tomography. Geophys. J. Int. 206 (3), 1599-1618. doi:10.1093/gji/ggw233

D. Frequency / Laplace domain (planned)

  • Pratt, R. G., Shin, C. & Hicks, G. J. (1998). Gauss-Newton and full Newton methods in frequency-space seismic waveform inversion. Geophys. J. Int. 133 (2), 341-362. doi:10.1046/j.1365-246X.1998.00498.x
  • Shin, C. & Min, D.-J. (2006). Waveform inversion using a logarithmic wavefield. Geophysics 71 (3), R31-R42. doi:10.1190/1.2194523
  • Shin, C. & Cha, Y. H. (2008). Waveform inversion in the Laplace domain. Geophys. J. Int. 173 (3), 922-931. doi:10.1111/j.1365-246X.2008.03768.x
  • Shin, C. & Cha, Y. H. (2009). Waveform inversion in the Laplace-Fourier domain. Geophys. J. Int. 177 (3), 1067-1079. doi:10.1111/j.1365-246X.2009.04102.x
  • Bednar, J. B., Shin, C. & Pyun, S. (2007). Comparison of waveform inversion, part 2: phase approach. Geophys. Prospect. 55 (4), 465-475. doi:10.1111/j.1365-2478.2007.00618.x

E. Travel-time / picking (planned)

  • Luo, Y. & Schuster, G. T. (1991). Wave-equation traveltime inversion. Geophysics 56 (5), 645-653. doi:10.1190/1.1443081
  • Marquering, H., Dahlen, F. A. & Nolet, G. (1999). Three-dimensional sensitivity kernels for finite-frequency traveltimes: the banana-doughnut paradox. Geophys. J. Int. 137 (3), 805-815. doi:10.1046/j.1365-246x.1999.00837.x
  • Hale, D. (2013). Dynamic warping of seismic images. Geophysics 78 (2), S105-S115. doi:10.1190/geo2012-0327.1
  • Ma, Y. & Hale, D. (2013). Wave-equation reflection traveltime inversion with dynamic warping and full-waveform inversion. Geophysics 78 (6), R223-R233. doi:10.1190/geo2013-0004.1

F. Convolution / matching-filter (planned)

  • Luo, S. & Sava, P. (2011). A deconvolution-based objective function for wave-equation inversion. SEG Technical Program Expanded Abstracts, pp. 2788-2792. doi:10.1190/1.3627773
  • Warner, M. & Guasch, L. (2016). Adaptive waveform inversion: Theory. Geophysics 81 (6), R429-R445. doi:10.1190/geo2015-0387.1
  • Zhu, H. & Fomel, S. (2016). Building good starting models for FWI using adaptive matching filtering misfit. Geophysics 81 (5), U61-U72. doi:10.1190/geo2015-0596.1

G. Normalized integration method (planned)

  • Donno, D., Chauris, H. & Calandra, H. (2013). Estimating the background velocity model with the normalised integration method. 75th EAGE Conference & Exhibition. doi:10.3997/2214-4609.20130411

H. Optimal transport (planned)

  • Cuturi, M. (2013). Sinkhorn distances: lightspeed computation of optimal transport. NeurIPS 26. (arXiv:1306.0895)
  • Engquist, B. & Froese, B. D. (2014). Application of the Wasserstein metric to seismic signals. Comm. Math. Sci. 12 (5), 979-988. doi:10.4310/CMS.2014.v12.n5.a7
  • Engquist, B., Froese, B. D. & Yang, Y. (2016). Optimal transport for seismic full waveform inversion. Comm. Math. Sci. 14 (8), 2309-2330. doi:10.4310/CMS.2016.v14.n8.a9
  • Métivier, L., Brossier, R., Mérigot, Q., Oudet, E. & Virieux, J. (2016). Measuring the misfit between seismograms using an optimal transport distance: application to full waveform inversion. Geophys. J. Int. 205 (1), 345-377. doi:10.1093/gji/ggw014
  • Métivier, L., Allain, A., Brossier, R., Mérigot, Q., Oudet, E. & Virieux, J. (2018). Optimal transport for mitigating cycle skipping in FWI: a graph-space transform approach. Geophysics 83 (5), R515-R540. doi:10.1190/geo2017-0807.1
  • Yang, Y., Engquist, B., Sun, J. & Hamfeldt, B. F. (2018). Application of optimal transport and the quadratic Wasserstein metric to full-waveform inversion. Geophysics 83 (1), R43-R62. doi:10.1190/geo2016-0663.1

I. Extended / wavefield-coupled (listed, NOT implemented)

These objectives couple the misfit with the forward problem itself (extended-image volumes, wavefield reconstruction, …) and therefore do not fit a pure loss(syn, obs) interface. They are listed for completeness:

  • Symes, W. W. & Carazzone, J. J. (1991). Velocity inversion by differential semblance optimisation. Geophysics 56 (5), 654-663. doi:10.1190/1.1443082
  • van Leeuwen, T. & Herrmann, F. J. (2013). Mitigating local minima in full-waveform inversion by expanding the search space. Geophys. J. Int. 195 (1), 661-667. doi:10.1093/gji/ggt258
  • Chauris, H. & Plessix, R.-E. (2012). Investigating the differential waveform inversion. 74th EAGE Conference & Exhibition. doi:10.3997/2214-4609.20149790