Transformation of 3‐D prestack data by azimuth moveout (AMO)

Abstract

We introduce a new partial-migration operator, named Azimuth Moveout (AMO), that rotates the azimuth and modifies the offset of 3-D prestack data. AMO can be effectively applied to improve the accuracy and to reduce the computational cost of 3-D prestack imaging. For example, a 3-D prestack dataset can be drastically reduced in size by coherent partial-stacking after AMO. The reduced dataset can be then imaged by prestack depth migration, a process that would have been too expensive to apply to the original dataset. AMO can also be effectively used for regularizing data geometries (e.g. correct for cable feather) and for interpolating unevenly sampled data. AMO is defined as the cascade of DMO and inverse DMO at different offsets and azimuths. We derive the time-space domain formulation of the AMO operator by first deriving its Fourier domain representation, and then analytically evaluating the stationaryphase approximation. The impulse response of AMO is a surface in the time-midpoint space; the shape of the surface is a skewed saddle, and its spatial extent is determined by the amount of azimuth rotation and offset continuation to be applied to the data. When the azimuth rotation is small (≤ 20 •), the AMO operator is compact and inexpensive to apply in the time-space domain. We successfully tested AMO by coherently stacking traces with similar offsets and azimuths from a synthetic land survey.

Theory of differential offset continuation

“…Expression (70) for the summation path of the OC operator was obtained previously by Stovas and Fomel (1996) and Biondi and Chemingui (1994). A somewhat different form of it is proposed by Bagaini and Spagnolini (1996).…”

Amplitude preserving azimuth moveout

“…We define Azimuth Moveout as an operator that transforms 3-D prestack data with a given offset and azimuth to equivalent data with different offsets and azimuths (Biondi and Chemingui, 1994). Figure 1 shows a graphical representation of this offset transformation; the input data with offset = sin is transformed into data with offset = AMO is not a single-trace to singletrace transformation, but moves events across midpoints according to their dip.…”

“…A stationary-phase approximation of (1) yields a time-space representation of the AMO operator where the equation for the kinematics of the impulse response is (Biondi and Chemingui, 1994) = (2) while the amplitudes are given by…”

“…Previously, Biondi and Chemingui (1994) introduced a partial-migration operator named Azimuth-Offset Moveout (AMO) that rotates the data azimuth and changes the data absolute offset. The AM0 operator can be defined as the cascade of an imaging operator that acts on data with a given offset and azimuth, followed by a forward modeling operator that reconstructs the data at a different offset and azimuth.…”

Asymptotic pseudounitary stacking operators

“…If the data are continued from half-offset h 1 to a larger offset h 2 , the summation path of the post-NMO integral offset continuation has the following form (Biondi and Chemingui, 1994;Stovas and Fomel, 1996;Fomel, 2001b): , and x and y are the midpoint coordinates before and after the continuation. The summation path of the reverse continuation is found from inverting (73) to be θ(y; z, x) = z h 2 2…”