Inversion of Vertical Wavefield Variation to Obtain a Velocity Model through Integration

One of the main weaknesses of the Born approximation is its limited accuracy for large size perturbations. Thus, in FWI, our Born approximated gradients tend to capture only the edges of such perturbations if low frequencies are missing. In this new rendition of an FWI algorithm, we update vertical velocity variations by inverting the vertical wavefield variations. The resulting vertical variation of the velocity induces long wavelength updates of the velocity through integration, and thus, low frequencies are not needed. We calculate the vertical wavefield variation by downward continuation using the double-square-root equation. We employ the adjoint-state method to derive the gradient for vertical velocity variation. Examples validate the feasibility of the proposed FWI method for data missing low frequencies.