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Results
SUMMARY The extension of the velocity-model domain to subsurface offsets solves the local-minima problem of data-fitting waveform inversion. By regularizing the extended-model data-fitting inversion with the addition of an image-focusing term to the objective function, we achieve robust global convergence of the waveform inversion problem. The method shares with full waveform inversion the advantage of simultaneously solving for all the wavelengths of the model, but it also has the global convergence characteristics of wave-equation migration velocity analysis. The numerical implementation of the proposed inversion method requires the solution of an extended wave-equation where velocity is a convolutional, instead of scalar, operator. The resulting method is therefore computationally intensive, and more computationally efficient approximations would be beneficial. Numerical tests performed on synthetic data modeled assuming a modified Marmousi model demonstrate the global convergence as well the high-resolution potential of the method.
- Geophysics > Seismic Surveying > Seismic Processing (1.00)
- Geophysics > Seismic Surveying > Seismic Modeling > Velocity Modeling > Seismic Inversion (1.00)
SUMMARY Tomographic Full waveform inversion (TFWI) provides a framework to invert the seismic data that is immune to cycle-skipping problems. This is achieved by extending the wave equation and adding an offset axis to the velocity model. However, this extension makes the propagation considerably more expensive because each multiplication by velocity becomes a convolution. We provide an alternative formulation which computes the backscattering and the forward scattering components of the gradient separately. To maintain high resolution results of TFWI, the two components of the gradient are first mixed and then separated based on a Fourier domain scale separation. This formulation is based on the born approximation where the medium parameters are broken into a long wavelength and short wavelength components. This approximation has an underlying assumption that the data contain primaries only without multiples. After deriving the equations, we test the theory with synthetic examples. The results of the Marmousi model show that convergence is possible even with large errors in the initial model that would have prevented convergence to conventional FWI.