On the connection between artifact filtering in reverse-time migration and adjoint tomography

Finite-frequency sensitivity kernels in seismic tomographydefinethevolumesinsidetheearththatinfluenceseismic wavesastheytraversethroughit.Ithasrecentlybeennumerically observed that an image obtained using the impedance kernel is much less contaminated by low-frequency artifacts due to the presence of sharp wave-speed contrasts in the background model, than is an image obtained using reversetime migration. In practical reverse-time migration, these artifacts are routinely heuristically dampened by Laplacian filtering of the image. Here we show analytically that, for an isotropic acoustic medium with constant density, away from sources and receivers and in a smooth background medium, Laplacian imagefiltering is identical to imaging with the impedance kernel. Therefore, when imaging is pushed toward using background models with sharp wave-speed contrasts, the impedance kernel image is less prone to develop low-frequency artifacts than is the reverse-time migration image, due to the implicit action of the Laplacian that amplifies the higher-frequency reflectors relative to the low-frequency artifacts.Thus,theheuristicLaplacianfilteringcommonlyused in practical reverse-time migration is fundamentally rooted inadjointtomographyand,inparticular,closelyconnectedto theimpedancekernel.