One-way wave-equation migration in log-polar coordinates

We obtained acoustic wave and wavefield extrapolation equations in log-polar coordinates (LPCs) and tried to enhance the imaging. To achieve this goal, it was necessary to decrease the angle between the wavefield extrapolation axis and wave propagation direction in the one-way wave-equation migration (WEM). If we were unable to carry it out, more reflection wave energy would be lost in the migration process. It was concluded that the wavefield extrapolation operator in LPCs at low frequencies has a large wavelike region, and at high frequencies, it can mute the evanescent energy. In these coordinate systems, an extrapolation operator can readily lend itself to high-order finite-difference schemes; therefore, even with the use of inexpensive operators, WEM in LPCs can clearly image varied (horizontal and vertical) events in complex geologic structures using wide-angle and turning waves. In these coordinates, we did not encounter any problems with reflections from opposing dips. Dispersion played important roles not only as a filter operator but also as a gain function. Prestack and poststack migration results were obtained with extrapolation methods in different coordinate systems, and it was concluded that migration in LPCs can image steeply dipping events in a much better way when compared with other methods.