Application of matrix square root and its inverse to downward wavefield extrapolation

In this paper we propose a method for computation of the square root of the Helmholtz operator and its inverse that arise in downward extrapolation methods based on one-way wave equation. Our approach involves factorization of the discretized Helmholtz operator at each depth by extracting the matrix square root after performing the spectral projector in order to eliminate the evanescent modes. The computation of the square root of the discrete Helmholtz operator and its inverse is done using polynomial recursions and can be combined with low rank matrix approximations to reduce the computational cost for large problems. The resulting square root operator is able to model the propagating modes kinematically correctly at the angles of up to 90 degree. Preliminary results on convergence of iterations are presented in this abstract. Potential applications include seismic modeling, imaging and inversion.