Integral (Kirchhoff-style) methods for dip moveout (DMO), while possessing several advantages over Fourier transform methods, are prone to problems of spatial aliasing. DMO methods with spatially aliased operators yield significant processing errors, even when applied to data that are not spatially aliased. In particular, such DMO methods may alter the amplitude and phase of horizontal reflections, to which DMO should do nothing.A simple test can be used to detect spatial aliasing in a DMO implementation. First, compute the responses of DMO to an impulse for several source-receiver offsets and recording times. Second, sum the traces in each of these impulse responses to obtain the corresponding horizontal-reflection responses. These horizontal-reflection responses should be identical to the original impulse for all offsets and times. Integral DMO methods with spatial aliasing problems fail this test.Integral DMO methods typically apply a sequence of time compressions to an input seismogram so that each input sample forms an elliptical impulse response. These methods typically yield horizontal-reflection responses with significant errors in amplitude and phase that vary with source-receiver offset and recording time. Perhaps surprisingly, the worst errors may occur for small offsets and late times, for which DMO action should be inconsequential.The integral DMO method proposed in this paper applies a sequence of time shifts to each input seismogram. These shifted input traces are mapped to output traces along curved trajectories that enable each sample to form the appropriate elliptical impulse response. The proposed method, by design, passes the test described above. Even the most approximate, highly efficient implementation of this method will improve the imaging of dipping reflections without altering horizontal reflections.

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