Simulation and imaging with paraxial one-way wave equation in ray-centered coordinates

Prestack depth migration methods include two categories. One is kirchhoff method based on high-frequency approximate solution of wave equation, the other is differential method based on the finite difference solution or mixed-domain solution of wave equation. Gaussian beam method is between them and is used for wave propagation chracterization and imaging. The problem of Gaussian beam method is that too many approximations are introduced when characterizing the wave propagation in the ray-centered coordinates. In addition to high-frequency approximation, the amplitudes of wave field whose plane is perpendicular to any point of the ray path is merely derived from the amplitude Gauss attenuation of that point, which is too simple to characterize the complex wave phenomena. Therefore, we derived the one-way wave equation in ray-centered coordinates and used the equation to extrapolate wave field in ray beam to accurately characterize local wave field. The method preserves the flexibility of ray method and the accuracy of wave equation method to describe the wave field within certain ray beams. Compared with simple ray theory and complex wave equation theory, the method makes a compromise between the flexibility and accuracy. It can be used to complex subsurface structure imaging and tomography velocity estimation more conveniently. Numerical examples demonstrate the correctness of the method.