Smoothing imaging condition for shot-profile migration

Amplitudes in shot-profile migration can be improved if the imaging condition incorporates a division deconvolution in the time domain of the upgoing wavefield by the downgoing wavefield. This division can be enhanced by introducing an optimal Wienerfilterwhichassumesthatthenoisepresentinthedatahas a white spectrum. This assumption requires a damping parameter, related to the signal-to-noise ratio, often chosen by trial and error. In practice, the damping parameter replaces the small valuesofthespectrumofthedowngoingwavefieldandavoidsdivision by zero. The migration results can be quite sensitive to the damping parameter, and in most applications, the upgoing and downgoing wavefields are simply multiplied. Alternatively, the division can be made stable by filling the small values of the spectrumwithanaverageoftheneighboringpoints.Thisaveraging is obtained by running a smoothing operator on the spectrum ofthedowngoingwavefield.Thisoperationcalledthesmoothing imaging condition. Our results show that where the spectrum of the downgoing wavefield is high, the imaging condition with dampingandsmoothingyieldssimilarresults,thuscorrectingfor illumination effects. Where the spectrum is low, the smoothing imaging condition tends to be more robust to the noise level present in the data, thus giving better images than the imaging condition with damping. In addition, our experiments indicate that the parameterization of the smoothing imaging condition, i.e., choice of window size for the smoothing operator, is easy and repeatable from one data set to another, making it a valuable additiontoourimagingtoolbox.