Accurate 3-D DMO for Land and Patch Geometries: a Practical Approach and Application to Multi-Fold Field Data

It has been widely accepted for many years that constant velocity 3-D DMO cannot be accurately applied to multi-azimuth data acquired with typical 3-D recording geometries. This problem is particularly severe for many land and OBC geometries. Recent work by G.J.O. Vermeer and co-workers has provided a clear theoretical basis for the application of 3-D DMO to one class of data with varying shot-receiver azimuths. For the case of cross-spread geometry, the locus of contributing midpoints for a given output point is an hyperbola in the (x,y) plane passing through the output point. In practice, the input traces will not generally be located exactly on the appropriate hyperbola, implying that the DMO operator will not be correctly sampled at the output point. This gives rise to poor integration of DMO operators, leading to distortion of signal amplitudes, loss of frequency and a reduction in the signal-to-noise ratio.

Conventional ‘input-oriented’ 3-D DMO techniques operate by ‘smiling’ an input trace along the direction of the shot-receiver azimuth. The DMO operator is discretely sampled at regular intervals along the azimuth and the ‘smile traces’ collected into their respective CMP bins.

Since the input points do not, in general, lie along the required hyperbola in the (x,y) plane the operator at each output point is not well sampled and this results in DMO-generated noise and distortion of signal amplitudes.

Vermeer has pointed out that the ideal solution to this problem would be a fully output-oriented DMO implementation, computing input traces with regular and adequate spacing along the appropriate (x,y) hyperbola for each output point. The output-oriented approach ensures that input traces contribute exactly to a given output location (not merely to the output bin, as would be the case with the input-oriented approach). Also, the operator at the output point is well sampled. The drawback of this approach is that every output point requires a different hyperbola and therefore different input points so that a near continuum of recordings is required. This is an extremely expensive method.

This problem has been addressed by pre-conditioning the input data so that it more closely matches the correct hyperbolic loci. By recognising the pattern of the geometry in this way, an accurate 3-D DMO can be achieved for many multi-azimuth geometries. Significant improvements have been achieved for single-fold synthetic data and for multifold land and OBC field data.