The vertical-and horizontal-resolution limits Delta x(lossy) and Delta z(lossy) of post-stack migration and linearized waveform inversion images are derived for lossy data in the far-field approximation. Unlike the horizontal resolution limit Delta x proportional to lambda z/L in a lossless medium which linearly worsens in depth z, Delta x(lossy) proportional to z(2)/QL worsens quadratically with depth for a medium with small Q values. Here, Q is the quality factor, lambda is the effective wavelength, L is the recording aperture, and loss in the resolution formulae is accounted for by replacing lambda with z/Q. In contrast, the lossy vertical-resolution limit Delta z(lossy) only worsens linearly in depth compared to Delta z proportional to lambda for a lossless medium. For both the causal and acausal Q models, the resolution limits are linearly proportional to 1/Q for small Q. These theoretical predictions are validated with migration images computed from lossy data.
|Original language||English (US)|
|Number of pages||10|
|Journal||Geophysical Journal International|
|State||Published - Mar 14 2017|
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledgements: The research reported in this publication was supported by the King Abdullah University of Science and Technology (KAUST), Saudi Arabia. We are grateful to the sponsors of the Center for Subsurface Imaging and Modeling (CSIM) Consortium for their financial support. We also thank KAUST for providing funding by the CRG grant OCRF-14 2014-CRG3-2300. We thank the Editor Dr Lapo Boschi and the two anonymous reviewers for their helpful comments and suggestions.