The stabilization of high-order multistep schemes for the Laguerre one-way wave equation solver

Highlights: • The new finite difference algorithm for solving the one-way wave equation has been developed. • The method is based on the high order finite difference approximations including the predictor–corrector method. • For providing both the stability and high accuracy, the quintic spline-based stabilization procedure is proposed. This paper considers spectral-finite difference methods of a high-order of accuracy for solving the one-way wave equation using the Laguerre integral transform with respect to time as the base. In order to provide a high spatial accuracy and stability, the Richardson method can be employed. However such an approach requires high computer costs, therefore we consider alternative algorithms based on the Adams multistep schemes. To reach the stability for the one-way equation, the stabilizing procedures using the spline interpolation were developed. This made it possible to efficiently implement a predictor–corrector type method thus decreasing computer costs. The stability and accuracy of the procedures proposed have been studied, based on the implementation of the migration algorithm within a problem of seismic prospecting.