FREQUENCY‐SELECTIVE DESIGN OF THE KIRCHHOFF MIGRATION OPERATOR1

Abstract

AbstractIntegral migration techniques perform a sum over an aperture of input traces to obtain output at a single point. The length of the aperture is limited by a spatial Nyquist criterion, which typically prohibits imaging very steep dips at very high frequencies without generating severe migration artifacts (migration operator aliasing). For time‐domain Kirchhoff migration, this can be a fatal shortcoming. The standard way to address this problem is to interpolate traces spatially before migration. This reduces the trace spacing, thereby increasing the frequency content which can be migrated without aliasing at steep dips.An alternative remedy to the operator aliasing problem is to modify the phase response of the Kirchhoff migration operator. This operator is frequency‐selective across the migration aperture: it passes all temporal frequencies of the input traces in the innermost portion of the aperture (referring to the shallow dips), and gradually cuts out the higher frequencies as it approaches the outer portion of the aperture. Thus, while all frequencies of the input data contribute to the shallow‐dip portion of the migrated image, only the permissible low frequencies of the input data contribute to imaging the steepest dips.Using a simple realization of a frequency‐selective Kirchhoff migration operator, this technique is illustrated on a synthetic data set involving greater than vertical dips.