The variable projection method for waveform inversion with an unknown source function

References

1. AravkinA.Y., vanLeeuwen T., CalandraH., and HerrmannF.J., 2012. Source estimation for frequency‐domain FWI with robust penalties, 74th EAGE Conference and Exhibition, Expanded Abstracts.
2. ChapmanC.H. and OrcuttJ.A.1985. Least‐squares fitting of marine seismic refraction data. Geophysical Journal – Royal Astronomical Society 82, 339–374.
   [Google Scholar]
3. CraseE., PicaA., NobleM., McDonaldJ. and TarantolaA.1990. Robust elastic nonlinear waveform inversion: Application to real data. Geophysics 55, 527.
   [Google Scholar]
4. Delprat‐JannaudF. and LaillyP.2005. A fundamental limitation for the reconstruction of impedance profiles from seismic data. Geophysics 70(1), R1–R14.
   [Google Scholar]
5. FomelS., BackusM., DeAngeloM., MurrayP. and HardageB.2003. Multicomponent seismic data registration for subsurface characterization in the shallow Gulf of Mexico. Offshore Technology Conference, Expanded Abstracts.
6. GolubG.H. and PereyraV.1973. The differentiation of pseudo inverses and nonlinear least squares problems whose variables separate. SIAM Journal of Numerical Analysis 10, 413–432.
   [Google Scholar]
7. GolubG.H. and PereyraV.2003. Separable nonlinear least‐squares: The variable projection method and its applications. Inverse Problems 19, R1–R26.
   [Google Scholar]
8. KaufmanL.1975. A variable projection method for solving separable nonlinear least squares problems. BIT Numerical Mathematics 15(1), 49–57.
   [Google Scholar]
9. KennettB.L.N., SambridgeM.S. and WilliamsonP.R.1988. Subspace methods for large inverse problems with multiple parameter classes. Geophysical Journal International 94(2), 237–247.
   [Google Scholar]
10. van LeeuwenT. and MulderW.A.2009. A variable projection method for waveform inversion. 71st EAGE Conference and Exhibition, Expanded Abstracts.
11. van LeeuwenT. and MulderW.A.2010. A comparison of seismic velocity inversion methods for layered acoustics. Inverse Problems 26, 015008.
    [Google Scholar]
12. NocedalJ. and WrightS.J.1999. Numerical Optimization . Springer.
    [Google Scholar]
13. PrattR.G.1999. Seismic waveform inversion in the frequency domain, Part I. Geophysics 64, 888–901.
    [Google Scholar]
14. SambridgeM.S., TarantolaA. and KennettB.L.N.1991. An alternative strategy for non‐linear inversion of seismic waveforms. Geophysical Prospecting 39(6), 723–736.
    [Google Scholar]
15. ShippR. and SinghS.2002. Two‐dimensional full wavefield inversion of wide aperture marine seismic streamer data. Geophysical Journal International 151(2), 325–344.
    [Google Scholar]
16. SongZ.M., WilliamsonP.R. and PrattR.G.1995. Frequency‐domain acoustic‐wave modeling and inversion of crosshole data: Part II – Inversion method, synthetic experiments and real‐data results. Geophysics 60, 796–809.
    [Google Scholar]
17. TarantolaA.1986. A strategy for nonlinear elastic inversion of seismic reflection data. Geophysics 51, 1893–1903.
    [Google Scholar]
18. VirieuxJ. and OpertoS.2009. An overview of full‐waveform inversion in exploration geophysics. Geophysics 74, WCC127–WCC152.
    [Google Scholar]
19. WangK., KrebsJ.R., HinkleyD. and BaumsteinA.2009. Simultaneous full‐waveform inversion for source wavelet and earth model. 79th Annual International Meeting, SEG, Expanded Abstracts28, 2537–2541.
    [Google Scholar]
20. YingstD., WangC., ParkJ., BloorR., LeveilleJ. and FarmerP.2011. Application of time domain and single frequency waveform inversion to real data. 73rd EAGE Conference and Exhibition, Expanded Abstracts.
21. ZiolkowskiA., ParkesG., HattonL. and HauglandT.1982. The signature of an air gun array: Computation from near‐field measurements including interactions. Geophysics 47, 1413–1421.
    [Google Scholar]