Migration for velocity and attenuation perturbations

Migration maps seismic data to reflectors in the Earth. Reflections are not only caused by small‐scale variations of the velocity and density but also of the quality factor that describes attenuation. We investigated scattering due to velocity and attenuation perturbations by computing the resolution function or point‐spread function in a homogeneous background model. The resolution function is the migration image of seismic reflection data generated by a point scatterer. We found that the resolution function mixes velocity and attenuation parameter perturbations to the extent that they cannot be reconstructed independently. This is true for a typical seismic setting with sources and receivers at the surface and a buried scatterer. As a result, it will be impossible to simultaneously invert for velocity and attenuation perturbations in the scattering approach, also known as the Born approximation. We proceeded to investigate other acquisition geometries that may resolve the ambiguity between velocity and attenuation perturbations. With sources and receivers on a circle around the scatterer, in 2D, the ambiguity disappears. It still shows up in a cross‐well setting, although the mixing of velocity and attenuation parameters is less severe than in the surface‐to‐surface case. We also consider illumination of the target by diving waves in a background model that has velocity increasing linearly with depth. The improvement in illumination is, however, still insufficient to remove the ambiguity.