# Seismic image mispositioning in the depth-angle domain

Ernesto Bonomi

Technical Report 06/17, CRS4, Center for Advanced Studies, Research and Development in Sardinia, Number 06/17 - september 2006

Download the publication :

From the 2D phase-shift extrapolation of two oriented waves, down-going and up-going, using the relation between $k_h$, the horizontal offset wavenumber, and $k_z$, the vertical one, I compute the true position of the image point lying on a reflecting surface with dip angle $alpha$. The resulting coordinates take into account the orientation of the slowness vectors $mathbfp_s$ and $mathbfp_r$ with scattering angle $2theta$, one describing the down-going wave and the other the up-going one. In this framework, I can show that a wrong estimate of the migration velocity causes the displacement and, then, the mispositioning of the image point along the normal to the reflector. I derive the well-known expression of the vertical residual moveout in the $(z,theta)$-domain with respect the true coordinate. Similarly, the image point displacement happens when the time of flight $t_0$ is not correctly identified as a primary echo. Assuming a planar reflector and substituting $t_0$ with $t_m$, the time of flight of a multiple event of order $m$, I derive in the $(z,theta)$-domain the general residual moveout expression.

## BibTex references

@TechReport{Bon06,
author = {Bonomi, E.},
title = {Seismic image mispositioning in the depth-angle domain},
institution = {CRS4, Center for Advanced Studies, Research and Development in Sardinia},
number = {06/17},
month = {september},
year = {2006},
address = {Cagliari, Italy},
type = {techreport},
keywords = {Seismic wavefield imaging, angle-domain common-image gathers, velocity analysis, multiple interface reflections},
url = {http://publications.crs4.it/pubdocs/2006/Bon06},
}

## Other publications in the database