Frequency-domain waveform inversion based on the angle-domain filtered gradient

Correlating the source and receiver wavefields, which are travelling in a similar direction, isolates the long wavelength features of the gradient. This selective correlation is effectively achieved using the angledomain imaging condition. We propose a frequency-domain waveform inversion algorithm based on the angle-domain filtered gradient. Since a large reflection angle in the imaging condition implies that the source and receiver wavefiels are travelling in a similar direction, the filtered gradient based on the large cut-off angle has a long wavelength component. As the cut-off angle is decreased, the proposed inversion method moves from the tomographic type inversion to the classic waveform inversion. Numerical examples show that the waveform inversion based on the angle-domain filtered gradient generates a long wavelength structure without low frequency information.