One-Way Wave-Equation Migration Based on Jacobi–Anger Expansion in Arbitrarily Lateral Varying Media

Seismic depth migration by downward continuation using conventional one-way wave-equation operators has three main shortcomings: handling evanescent waves, imaging large angles, and stability of the one-way propagator. Conventional one-way wave-equation propagators have been extensively constructed using approximation theories, such as Taylor series (TS) and other expansions. Although in these, a new operator is calculated at each lateral point of the grid, difficulties persist due to the assumption that the medium is locally homogeneous. Consequently, these propagators exhibit significant weaknesses in imaging complex media. To alleviate these drawbacks, we propose a stable and affordable approach to the one-way wave-equation depth migration algorithm. First, we use a spectral projector (SP) to suppress evanescent modes in an arbitrarily laterally varying velocity model. Next, we apply a coupled Schulz iteration scheme to the Helmholtz operator to obtain the square-root operator. Finally, to address the issue of accurately constructing the extrapolation operator while ensuring stability, we introduce a novel algorithm to approximate the exponential matrix operator using the Jacobi-Anger (JA) expansion. This approximation enables the one-way wave-equation propagator to be constructed solely through matrix multiplication, a feature that facilitates efficient implementation and execution. Through an impulse response test, we demonstrate that our proposed migration algorithm is more accurate than the one using TS expansion and is effective for large angles in media with pronounced lateral velocity variations. We also use models with complex subsurface structures and field data to demonstrate that our approach performs better at imaging intricate and fine-scale features compared to traditional one-way migration methods.