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CANADIAN JOURNAL of EXPLORATION GEOPHYSlCS | June 2013

In full waveform inversion, the objective function plays a key role in successfully obtaining high quality velocity images. In this paper, an objective function composed of a non-smooth data fidelity term and a non-smooth regularization term is presented. The non-smooth data fidelity term is essentially a Student’s t formulation, derived by maximizing a likelihood function. The nonsmooth regularization term is a potential function chosen among L1 norm (convex but non-differentiable at zero), hyperbolic secant function (convex and differentiable), or GM function (differentiable but non-convex), and derived by maximizing a priori information from the Markov Random Fields. The quasi-Newton L-BFGS algorithm is incorporated into a frequency-domain multiscale scheme to solve the new objective function, so as to obtain a global minimum solution. The method is insensitive to large error and has a good ability of preserving sharp edges. Two examples are used to illustrate the performance of the method. The results show that the FWI method proposed in this paper can capture blocky structures and/or small-scale structures in the presence of null traces, bad traces or linear coherent noise.