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We have addressed the problem of steep slope estimation by introducing a novel circle-interpolating method in plane-wave construction, which leads to omnidirectional plane-wave destruction. Frequency analysis demonstrates the ability of the proposed method to handle steep structures. We presented both synthetic and field data examples to show the performance of the omnidirectional dip estimation. The new estimation method can also be used in other applications that require slope fields for steep structures, such as attribute analysis on a migrated image or a time slice.

As a byproduct, we proved that the high-dimensional maxflat fractional delay filter is separable in all directions. A typical $ m-$ dimensional $ n-$ th order ($ n=2N+1$ in this paper) linear-phase approximating system is supported by $ n^m$ coefficients. Using the separability property, the maxflat linear-phase approximating system has only $ mn$ coefficients. It is useful in applications that require high-dimensional linear-phase approximations.