Multiscale Direct Envelope Inversion: Algorithm and Methodology for Application to the Salt Structure Inversion

For the full-waveform inversion, obtaining a globally optimal solution is difficult when the seismic data do not contain sufficient low-frequency information and the inversion object is a salt structure with a large-scale salt dome. The large salt dome presents difficulty for the inversion of the salt structure; however, it also confers a convenience that can be utilized: A large salt dome makes the events in the seismic record sparse and isolated. We use the envelope to obtain the arrival time of the events in the seismic data and apply multiscale strategies to extract the low-frequency information of the seismic data that relates to the long-wavelength components of the subsurface. In calculating the gradient, the envelope Frechet derivative is used to take advantage of the multiscale envelope for the characteristics of the salt structure. Therefore, the multiscale direct envelope inversion using the window-averaged envelope and the direct envelope Frechet derivative is proposed. To further improve the computational efficiency and inversion quality of the multiscale direct envelope inversion, several auxiliary strategies are proposed: A joint misfit function is designed to make the inversion method more adaptable, and an offset weighting factor is introduced to implement the multioffset inversion method to improve the inversion quality of subsalt. We analyze the antinoise performance of the multiscale direct envelope inversion. The SEG/EAGE salt model is used to test the application effect of the multiscale direct envelope inversion. The antinoise ability and insensitivity to low-frequency data of the method are verified in the numerical experiments.