Introduction

In recent reports I introduced the concept of a steering filter Clapp et al. (1997). Since then it has been used to regularize a wide variety of geophysical problems including interpolation Crawley (2000), multiple attenuation Clapp and Brown (1999, 2000), missing data problems Clapp et al. (1997), migration Prucha et al. (2000) , and tomography Clapp and Biondi (1998, 1999, 2000).

Each of these problems used a 2-D steering filter. Fomel (1999) introduced a method to construct a 3-D steering filter. Fomel formed a 3-D steering filter operator by first convolving two 2-D operators. To obtain a minimum-phase filter he performed spectral factorization for each dip component (p_x , p_y) pair in the data, significantly increasing the cost of constructing the operator. In order for the resulting filter to spread information over significant distances, a large number of filter coefficients must be used, increasing the cost of each iteration.

In this paper I present an alternative construction method. I show how a 3-D steering filter can be produced by cascading two 2-D steering filters. The cascaded approach does not provide as accurate a dip discrimination as that in Fomel's approach but it does not require the expensive spectral factorization, and the resulting filters are much smaller and less expensive to apply. I show how this method can accurately characterize a large range of dips and that it is accurate enough for a wide class of applications. In addition, I apply it to a simple synthetic missing data problem with very encouraging results.