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D. Goldfarb, “A Family of Variable Metric Methods Derived by Variational Means”, Mathematics of Computation., Vol. 24, No. 109, 1970, pp. 23-26.

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• TITLE: Full-waveform Velocity Inversion Based on the Acoustic Wave Equation

  AUTHORS: Wensheng Zhang, Jia Luo

  KEYWORDS: Finite Difference; Acoustic Wave Equation; Full-waveform Inversion; CG Method; BFGS Method; Marmousi Model

  JOURNAL NAME: American Journal of Computational Mathematics, Vol.3 No.3B, October 25, 2013

  ABSTRACT: Full-waveform velocity inversion based on the acoustic wave equation in the time domain is investigated in this paper. The inversion is the iterative minimization of the misfit between observed data and synthetic data obtained by a numerical solution of the wave equation. Two inversion algorithms in combination with the CG method and the BFGS method are described respectively. Numerical computations for two models including the benchmark Marmousi model with complex structure are implemented. The inversion results show that the BFGS-based algorithm behaves better in inversion than the CG-based algorithm does. Moreover, the good inversion result for Marmousi model with the BFGS-based algorithm suggests the quasi-Newton methods can provide an important tool for large-scale velocity inversion. More computations demonstrate the correctness and effectives of our inversion algorithms and code.