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Seismic full waveform inversion seeks to make use of the full information based on full wave field modeling to extract quantitative information from seismograms. Its serious nonlinearity and high dependence on initial velocity model often results in unsatisfactory inversion results in paleo-karsts carbonate reservoir characterized by strong heterogeneity. The paper presents an improved strategy of multi-scale inversion to establish velocity field model of waveform tomography. the forward wave equation algorithm was derived in frequency domain, and then the Matrix formalism for the iterative inverse methods is derived by gradient methods to speed up calculation and to avoid convergence to local minimum value. After massive amount of frequencies tests, the appropriate bandwidth are extracted, and the velocity field calculated at low frequency is used as the input of the high frequency. After the iteration, the accurate velocity field is inverted. Finally, frequency domain wave equation full waveform inversion in mathematical and physical models is conducted in order to verify the inverse program. The method of selecting the inverse frequencies is proved to be effective.

Frequency Domain Wave Equation Inversion and Its Application on the Heterogeneous Reservoir Model Data