# Seismic well tie theory

Well to seismic ties is a fundamental step in seismic interpretation. It relates subsurface measurements obtained at a wellbore measured in depth and seismic data measured in time. A time-depth relationship is typically computed by integrating the slowness function measured at a wellbore. Mis-ties are often present and adjustments to the time-depth relationship are typically fine-tuned by stretching and squeezing of the well logs. However, the validity of stretching and squeezing is sometimes questioned and the question of how much stretching and squeezing is acceptable remains a topic of debate.

In this study, we investigate the idea of using a Backus averaged well log that accounts for dispersion resulting from layer induced long wave elastic attenuation to compute a time-depth relationship. We review the theory to compute a local Q function that results in both positive and negative Q values, which imply that a mandatory stretch and squeeze is required when dispersion is present. We illustrate with an example from Western Canada where the presence of low velocity coals results in large errors in the well to seismic tie. We show that these mis-ties can be reduced by using a Backus averaged well log to compute the time-depth relationship, which accounts for velocity differences between the logging and seismic frequencies. In addition, the ratio of the logging and seismic velocities provides an indication of how much stretching and squeezing is justifiable.