GPR gpr12061 Dispatch: July 22, 2013 CE: N/A Journal MSP No. No. of pages: 15 PE: George 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 UNCORRECTED PROOF Geophysical Prospecting doi: 10.1111/1365-2478.12061 Full-waveform inversion for macro velocity model reconstruction in look-ahead offset VSP: numerical SVD-based analysis Ilya Silvestrov 1 , Dmitry Neklyudov 1 , Clement Kostov 2 and Vladimir Tcheverda 1 ∗ 1 Institute of Petroleum Geology and Geophysics SB RAS, Novosibirsk, Russia, and 2 Schlumberger Moscow Research, Moscow, Russia Received December 2012, revision accepted June 2013 ABSTRACT Full-waveform inversion is currently considered as a potential tool for improving depth-velocity models for areas with complex geology. It is well-known that success of the inversion is very sensitive to the available low-frequency content of the data. In the paper we investigate this issue considering a look-ahead offset VSP survey and applying singular value decomposition (SVD) analysis of a linearized forward map as the main tool. We demonstrate with this technique the difference between the sequential full-waveform inversion strategy and the original time-domain approach proposed in the early 1980s. We emphasize the role of the lowest frequency in the data, which is necessary for reliable velocity model inversion in particular cases. Finally we show the existence of a trade-off between the lowest frequency and a regularization parameter of the inversion procedure. The presented approach may be adapted to answer general questions regarding the quality of data and acquisition system parameters required for feasible full-waveform inversion. Key words: Seismics, Full-waveform inversion, Velocity analysis, Numerical study. Q1 INTRODUCTION Constructing a smooth velocity model (propagator, macro velocity) in the depth domain, which is responsible for cor- rect wave propagation traveltimes, is a key element of up- to-date seismic data processing in areas with complex local geology. Theoretically it could be obtained, along with the subsurface structure, by the full-waveform inversion (FWI) technique matching observed and synthetic seismograms. The least-squares norm is usually used for such matching, though other criteria are also considered. To minimize the misfit func- tion and to find the elastic parameters of the subsurface, it- erative gradient-based algorithms are usually applied. Such an approach to solving a seismic inverse problem, which was originally proposed by Lailly (1983) and Tarantola (1984), has been developed and studied in a great number of publica- tions (see Virieux and Operto 2009 and references therein). ∗ E-mail: cheverdava@ipgg.nsc.ru However, the straightforward application of FWI recon- structs reliably only the reflectivity component of the sub- surface but fails to provide a smooth velocity model. Failure of the full- waveform inversion to recover the smooth ve- locity component was shown by numerical experiments in the earliest works of Mora (1988), Alekseev and Dobrinski (1976) and Gauthier, Virieux and Tarantola (1986). How- ever, the reason is not the insensitiveness of the least-squares criterion to smooth variations of the solution. As Jannane et al. (1989) showed, such information resides in the least- squares misfit function and may be thus extracted in princi- ple. The shape of this function, however, differs significantly with respect to various velocity components. The function is nearly quadratic with respect to high-oscillating perturba- tions, which are mostly responsible for reflections. Perturba- tions of the long-scaled velocity component, responsible for wave propagation traveltimes, lead to a very complicated and non-linear behaviour of the misfit function (see e.g., Sirgue 2003). This is heuristically related with the so-called ‘cycle- skip’ problem: phase shifts greater than a half-period between C  2013 European Association of Geoscientists & Engineers 1