Introduction

An example of a migration artifact is the strong amplitude, low-frequency noise often seen on RTM images where a high velocity gradient exists. These crosstalk artifacts are usually produced by the unwanted cross-correlation of head waves, diving waves and back-scattered waves at the imaging step (Yoon et al., 2004), which severely contaminate the migration image. Various remedies have been proposed to suppress such migration artifacts, such as smoothing the velocity model before migration to reduce reflections (Loewenthal et al., 1987) or low-cut filtering (Mulder and Plessix, 2003) the migration image to reduce artifacts. Fletcher et al. (2005) attenuated reflections at boundaries by introducing a directional damping term to the nonreflection wave equation, while Guitton et al. (2006) reduced artifacts by using a least-squares filter. A physics based migration filter is the Poynting vector (Yoon and Marfurt, 2006) to improve the cross-correlation based imaging condition. Recently, Liu et al. (2007) and Liu et al. (2011) decomposed the full wavefield of the backpropagated data into their one-way components and applied the imaging condition to the appropriate parts. A similar procedure was used by Fei et al. (2010) where dip filtering was applied to vertical and horizontal slabs of the backpropagated data.

A difficulty with the above approaches is that the precise filtering of the back-projected data cannot distinguish data noise from operator noise. As an example, Kirchhoff migration images can have aliasing artifacts caused by both undersampling the data and the migration operator (Claerbout, 1992). In this case, the data are filtered separately from the migration operator to avoid loss of data information by aggressive filtering. In contrast, the filtered RTM approach of Liu et al. (2011) and Fei et al. (2011) extrapolates the data into the medium and the resulting wavefields are dip filtered at each time step. The back-projected data are hopelessly intertwined with the RTM operator, and so the dip filter simultaneously attacks both data and extrapolator noise. If the noise regime of the operator overlaps the signal of the data, then important data information can be needlessly lost. It is more desirable that the operator is filtered separately from the data.

I now propose a general dip filtering of the reverse-time extrapolation operator that is separate from the data filtering. The operator filtering can be performed using the generalized diffraction-stack migration (GDM) method proposed by Schuster (2002), which is mathematically equivalent to RTM, but its implementation is different. Unlike RTM which intertwines the extrapolation operator with the data at all depth levels, GDM separately computes the complete migration kernel and then applies it to the recorded data in the form of a dot-product to get the migration image. Unlike a Kirchhoff migration (KM) kernel which plots as a single hyperbola-like curve in the shot gather for a specified image point, all events are included in the generalized migration kernel such as direct waves, multiples, reflections, and diffractions. Similar to an antialiasing filter (Lumley et al., 1994) or a dip filter for the KM operator, a filter can be applied to the GDM operator.

This chapter is divided into four parts: an introduction, a theory section that describes the filtering methology, and an application section that applies filters to GDM for both synthetic data and a field data example. The filtering examples are similar to those in Liu et al. (2011) and Fei et al. (2011), except I apply the filter only to the migration kernel to avoid excessive filtering of both data and kernel. The final section is a summary of this work.