In this chapter I present a new approach for the Kirchhoff imaging of irregularly sampled 3D data. First, I discuss the discrete representation of integral operators as matrix-vector multiplication where each row of the matrix corresponds to a summation surface and each column corresponds to an impulse response. Due to irregularities in seismic coverage, the columns and rows are generally badly scaled. Therefore I apply a diagonal transformation to balance the rows of pull (sum) operators and the columns of push (spray) operators. The diagonal weighting is essentially a normalization by the response of a flat event. It calibrates the image for the effects of irregular coverage of the survey and varying illumination in the subsurface. Next, in the context of common azimuth processing I introduce a new ``true-amplitude'' sequence for processing wide-azimuth 3D surveys. The method employs the AMO operator to regularize the coverage of the survey and reduce the size of the prestack data by partial stacking. The AMO transformation organizes the data as common-azimuth (CA) and common-offset (CO) cubes and potentially enables reliable analysis of AVO-AZ (amplitude versus offset and azimuth) on the migrated data. Finally, in the last section of the chapter, I present the results of applying the imaging sequence to a 3D land survey from the Canadian Shorncliff region. I show the effectiveness of AMO in regularizing the geometry of the data, and the application of the normalization technique to reduce the effects of fold variations.

1/18/2001