Reverse time migration using pseudo spectral method based on Jacobi-Anger expansion for the acoustic wave equation

Abstract

In the petroleum industry, seismic survey which is the one of geophysical survey methods is implemented to discover the subsurface structure. After obtaining the subsurface media velocity values which are gained from the Full Waveform Inversion, it is able to operating the numerical acoustic waveform simulation. Forward wavefield which is simulated wave field from the source and backward wavefield which is simulated wavefield from the receiver wavefield are convoluted to obtain the reverse time migration image. In full waveform Inversion and reverse time migration calculation process, the numerical wavefield result causes the significant condition of the result. In this paper, the pseudo spectral method which is based on the Jacobi-Anger expansion is implemented as the solution of Hyperbolic type PDE(Partial Differential Equation). By using the method, several problems of numerical solution-stability and dispersion- are effectively solved and the error between the numerical result and analytic result is considerably diminished at the same time. Still there are several problems of reverse time migration result caused by the low wavenumber contamination that the inherent problem of RTM and unclear image condition on the image pixel boundary, by using the above effective numerical wave equation solution as the method of reverse time migration process. To solve above problems, this research uses the method of Poynting vector decomposition to eliminate the low wavenumber contamination and Laplacian filtering which is equal to the second derivative of image value to illuminate the pixel boundary. The result is verified in two numerical examples, the one is the Marmousi synthetic velocity model which contains the complicate geological structure such as fault, folds and salt dome intrusion, the other one is the BP salt dome synthetic velocity model which low wavenumber contamination effect severely occurs on the salt dome. Marmousi model result shows the complicate geological structure image is clearly shown by Laplacian filtering and BP salt dome model result presents the result that low wavenumber contamination image values are eliminated.