When full waveform inversion (FWI) is performed in the Laplace-Fourier domain, Laplace-Fourier-domain wave modeling, using finite-difference or finite-element methods, is performed to compute the gradient direction. In this case, a complex impedance matrix is composed and factored by direct matrix solvers. Alternatively, iterative matrix solvers may be used. However, solving 3D problems with such methods requires excessive computer memory or computing time, which causes problems in the application of the Laplace-Fourier-domain FWI. To avoid computational overburden in 3D problems, we propose a time-Laplace-Fourier hybrid FWI, in which forward and backward modeling are performed in the time domain and other procedures are conducted in the Laplace-Fourier domain. Our hybrid FWI is applied to two groups of frequencies. Inversions for the first and second groups of frequencies correspond to the Laplace-domain FWI and the Laplace-Fourier-domain FWI, respectively. The graphic processing unit is used to speed up the hybrid inversion algorithm. To verify the feasibility of this technique, the 3D hybrid FWI is applied to the data recorded along the A1 line of the synthetic SEG/EAGE 3D salt model and 3D wide-azimuth real exploration data. Numerical examples show that the hybrid FWI yields reasonable subsurface velocity structures that contribute to the enhancement of reverse-time migration images.

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