p177 feasibility of full waveform inversion applied to sub ... - Earthdoc

4candidate for the waveform inversion at 7 Hz (Figure 6). The sediment layer needs strong apriori information on the low and intermediate wavenumbers, whereas the smoothnessrequirements of the velocities within the basalt are less demanding. The top and bottom of thebasalt must be discontinuous and located at the correct depth. Finally, the sub-basalt velocitiesrequire even higher wavenumber information than the sediments.ConclusionWe have identified some of the difficulties of waveforminversion applied to the sub-basalt imaging problem in anoptimistic context where a layer stripping strategy is feasible.We found that the basalt interfaces should remain reasonablydiscontinuous and located at an accurate depth. The inverseproblem is quite linear up to 3 Hz but some more stringentconditions are required in order to start an inversion fromfrequencies of 5 or 7 Hz. In these cases, some strong a prioriinformation is needed in the form of an accuratesediment/basalt interface model, and a very good estimationof the vertical gradient within the sediment and sub-basaltlayers. The basalt layer is less demanding thanks to strongdiving wave information.The vertical gradient within the sediment may be recoveredby stacking velocity analysis or travel time tomography.However, intra basalt reflections are often difficult to identifyFigure 6: True model (grey) and“ideal” starting model (black) foran inversion starting at 7 Hz.and prevent stacking velocity analysis. Nevertheless, strong diving waves at far offsets mightallow the use of travel time tomography to recover the low and intermediate wavenumbercomponents within the basalt layer.The highest degree of difficulty is likely to be encountered when solving for the sub-basaltlayer, even in the case where the velocities are perfectly known down to the base of the basalt.The lack of coherent events in the data coming from the sub-basalt effectively prevents anydetermination of the macro model in this area of the model. Moreover, since only narrowangles illuminate the sub-basalt target, waveform inversion will only be able to provide amigration like image of the sub-basalt sediments.AcknowledgmentWe thank CGG and the Geoscience Research Centre of TotalFinaElf for supporting this work.ReferencesPratt, R. G. and Worthington, M.H., 1990, Inverse theory applied to multi-source cross-holetomography: Part 1: Acoustic-wave equation method. Geophysical Prospecting, 38, 287-310.Pratt, R.G., and Goulty, N.R., 1991. Combining wave equation imaging with traveltimetomography to form high resolution images from crosshole data. Geophysics, 56, 208-224.Pratt, R. G., Song, Z.-M., Williamson, P., Warner, M., 1996, Two-dimensional velocitymodels from wide-angle seismic data by wavefield inversion, Geophys. J. Int., 124, 323-340.Sirgue, L., Pratt, R. G., 2001, An optimal choice of temporal frequencies for imaging:application to waveform inversion, 71 st Annual Meeting of the SEG, San Antonio