A comparison between the behavior of objective functions for waveform inversion in the frequency and Laplace domains

In the frequency domain, gradient-based local-optimization methods of waveform inversions have been unsuccessful at inverting subsurface parameters without an accurate starting model. Such methods could not correct automatically for poor starting models because multiple local minima madeitdifficulttoapproachthetrueglobalminimum.Inthis study,wecomparedthebehaviorofobjectivefunctionsinthe frequency and Laplace domains. Wavefields in the Laplace domain correspond to the zero-frequency component of a damped wavefield; thus, the Laplace-domain waveform inversion can image smooth velocity models. Objective functions in the Laplace-domain inversion have a smoother surface and fewer local minima than in the frequency-domain inversion.Weappliedthewaveforminversiontoa2Dsliceof the acoustic SEG/EAGE salt model in the Laplace domain and recovered smooth velocity models from inaccurate initial velocity conditions.We also successfully imaged velocities of the salt, SEG overthrust, and Institut Francais du PetroleMarmousimodelswiththefrequency-domaininversion method by using the inverted velocity model of the Laplacedomaininversionastheinitialmodel.

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