Potentially Reducing Seismic Acquisition Costs by Dealiasing DMO Processing
Authors: Ronen Shuki , Nichols Dave , Geco-Prakta Ronen , Griffiis Ed 
Published: October 2008

Abstract
Three dimensional seismic surveys have coverage irregularities due to obstacles, cable feathering. and other field conditions. Often acquisition footprints are obvious. At other times, subtle irregularities degrade the quality and may lead to erroneous interpretation and to poor estimates of rock and fluid properties. Dense acquisition geometry and in-fill data provide costly solutions.
The required acquisition geometry and the amount of in-fill data depend on the processing. Minor irregularities can be handled by conventional processing. Major irregularities will always require fill data. Moderate irregularities can sometimes be handled by advanced processing methods. One of these methods is Dealiasing DMO.
Dealiasing is a constrained inversion &signed to handle data with irregular geometry. Unlike conventional DMO and Prestack Pull Migration Dealiasing DMO is not based on extrapolating irregularly sampled data. Instead, it is based on a constrained iterative-inversion of a modeling operator which does not suffer from irregular data geometry. Therefore it has an advantage over conventional DMO and even Prestack Full Migration, if the acquiahion geometry is irregular.
Them is a substantial coat involved in inverting wave-field extrapolation operators. To keep a reasonable turn-around time. we implemented Dealiasing DMO in parallel and used optimization techniques such as Bresenham rasterization in the calculation of the offset-extrapolation operator.
As an example, we apply the method to k dimensional North Sea data with a moderately irregular acquisition geometry including cross-line gaps of up to 50 meters. The gaps adversely affect the image generated by conventional DMO processing and costly in-fill data would be required. Dealiasing DMO produces an acceptable image without usage of in-fill data.

Introduction
Conventional DMO and preastack full migration often fail to produce correct amplitude and phase when one attempts to extrapolate irregularly sampled wave-fields. preastack full migration extrapolates such wave-fields downward in depth; DMO extrapolates them inward in the offset direction (Ref. 1). To handle minor sampling irregularities, the extrapolation operators are derived from the wave equation in the form of Kirchhoff integrals. The integrals are then approximated bydiscrete summations. We have excellent non-abed approximation designed for regularly sampled data (Ref. 2). The approximation, however, is based on the assumption of regular sampled input data. When applied to irregular data, evennon-aliased DMO would produce compromised quality, unless equalized (Ref. 3), or dealiased. Likewise, Prestack full Migration is based on depth-extraexpolotion and requires equalization, normalization, or dealiasing when applied to irregular data. Processing is therefore based on a problematic approximation of integrals by discrete summations.
Unlike processing, generating data from a given model does not suffer from the problem of extrapolating irregularly sampled input. We control the sampling of the model. and we can set it to satisfy any requirement. Therefore, once a candidate model is proposed, we can measure its quality using a reliable modeling operator to generate data at the geometry of the field data, and compute the diffence between the modeled data and the field data; the smaller the difference, the better the model.