Amplitude-compensated Laplacian filtering of reverse time migration and its application

Reverse time migration is an advanced seismic migration imaging method. When the source wavefield and the receiver wavefield are cross-correlated, the cross-correlations of direct arrivals, backscattered waves and overturned waves will produce a lot of low-frequency noise, which will mask the final imaging results. Laplacian filtering, as a common method to suppress low-frequency noise, can adapt to any complex media, just adding a little computational cost. However, simple direct Laplacian filtering will destroy the characteristics of the useful signals. Therefore, the amplitude needs to be compensated before filtering when using the Laplacian filtering method. Zhang and Sun proposed an improved Laplacian filtering method and gave a simple calculation formula and explanation. This method can effectively suppress the low-frequency noise in reverse time migration while retaining the useful signal characteristics, but lacks detailed and strict mathematical derivation. Therefore, this paper gives a detailed and rigorous mathematical derivation of the amplitude-compensated Laplace filtering method from the point of view of amplitude-preserved filtering. The source wavelet is used instead of the source wavefield to compensate amplitude, just adding a little calculation cost. Finally, the amplitude-compensated Laplace filtering method is verified by two theoretical models and compared with the direct Laplacian filtering method.