Stability and practically stability comparison criteria of impulsive integro-differential systems with fixed moments of impulse effects are established by cone-Lyapunov functions through comparing with impulsive ordinary differential equations.

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Based on arbitrarily wide-angle wave equations, a reverse-time propagation scheme is developed by substituting the partial derivatives of depth and time with central differences. The partial derivative of horizontal direction is replaced with high order difference. The imaging condition is computed by solving the eikonal equations. On the basis of above techniques, a prestack reverse-time depth migration algorithm is developed. The processing examples of synthetic data show that the method can remove unwanted internal reflections and decrease the migration noise. The method also has the advantage of fidelity and is applicable of dip angle reflector imaging.