Analysis of the Effects of First-Arrival Traveltime, Multiples, and Velocity Errors on Subsalt Kirchhoff Images
Authors: Lewis Gary G. 
Published: October 2008

Abstract
One of the common techniques used to form depth images of subsalt structure from seismic data is Kirchhoff migration based on first-arrival traveltimes, Three of the most common factors blamed for poor results using this approach are limitations in the first-arrival traveltime approximation, multiples, and migration velocity model errors1,2. A 2-D seismic model study was conducted to assess the impact of each of these factors on our ability to form structural images from a realistic 2-D synthetic dataset. This work demonstrates that, even in the presence of these factors, Kirchhoff migration is capable of generating useful images of subsalt structure.

Introduction
In this study, I show that the use of first-arrival traveltimes, the presence of multiples, and the presence of reasonable errors in the migration velocity model do not appear sufficient to impair our ability to form useful images of subsalt structure using Kirchhoff prestack depth migration. The impact of each of these factors was analyzed individually by applying 2-D Kirchhoff prestack depth migration to a realistic synthetic dataset generated using 2-D acoustic finite-difference modeling. This study did not investigate the combined effects of velocity model errors and the presence of strong noise such as surface-related multiples in the input data. There are recognizable artifacts due to the first-arrival approximation on common-offset images, common reflection point gathers, and depth slices extracted from the prestack migrated synthetic data volume. Multiples also produce strong coherent noise in all of these types of migrated images. However, both the first-arrival artifacts and multiples vary strongly with offset, and stacking the individual common offset images produced a high-quality structural image of the subsalt section. One of the more interesting aspects of this work is the analysis of the effect of velocity errors on prestack depth migrated images. This work shows that typical velocity errors (those that do not significantly degrade the focus at the top of salt) do not significantly degrade subsalt images, and, in fact, that prestack depth migration is relatively robust with respect to the velocity errors one would typically expect to make. There are several important limitations of the methodology used in this study. Because the analysis 2-D, it cannot address the effects of limited azimuth or 3-D effects in the data. Also, since seismic energy decays more rapidly with propagation distance in 3-D than in 2-D, one would expect the multiples in real data to be stronger relative to subsalt primaries than predicted by 2-D modeling. Finally, since the data is acoustic, the relative amplitude of the signal versus source generated noise is only crudely approximated. Further work should be done to include these effects in the analysis.

Modeling
This model study was designed to test the hypothesis that first arrival travel times are insufficient to produced useful structural images for an actual Gulf of Mexico salt body. To test this hypothesis, a velocity model that preserved the kinematic properties of the migration velocity field used to image the salt body was generated (Fig. I). To produce artifacts in the model images representative of those in field data, it was also important that the model generate a realistic set of reflections.