Finite-frequency sensitivity kernels in seismic tomography define the volumes inside the earth that influence seismic waves as they traverse through it. It has recently been numerically 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 reverse-time 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 image filtering 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, the heuristic Laplacian filtering commonly used in practical reverse-time migration is fundamentally rooted in adjoint tomography and, in particular, closely connected to the impedance kernel.

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