Numerical Stability and Dispersion Analysis of Finite-Difference Schemes for Wave Equation Time Migration

We exploit finite-difference method schemes to solve the wave equation within the migrated time-domain, offering a robust alternative to traditional depth-domain imaging method. While this formulation approximates the acoustic wave equation used in depth models, specific kinematic terms differ. By applying kinematic ray tracing principles to evaluate propagation, we analyze the stability and dispersion of centered and staggered grid schemes. This evaluation is crucial for validating numerical parameters in simulating seis-mic phenomena, bridging the gap between depth and time migration frameworks. Our results indicate that this wave-type behaves numerically similarly to depth-domain models, except for amplitude differences. More-over, the staggered grid scheme superiorly minimizes numerical dispersion and noise. Consequently, this study demonstrates that wave propagation based on plane wave theory and traveltime analysis is highly viable in the time-migrated domain, laying the groundwork for advanced imaging and inversion techniques using two-way equations.