Bayesian reverse time migration with quantified uncertainty

Abstract

Reverse time migration (RTM) has been proven capable of producing high-quality images of subsurface structures. However, limited subsurface illumination combined with inaccurate forward modeling and migration velocities all lead to uncertainty in the seismic images. We quantify the migration uncertainty of RTM using an iterative inversion method based on a Bayesian inference framework. The posterior covariance matrix, computed at the maximum a posteriori (MAP) model, provides the foundation for estimating uncertainty. In the Bayesian inference framework, we combine an explicit sensitivity matrix based on a Green's function representation with an iterative extended Kalman filter (IEKF) method. This enables us to determine the MAP solution of RTM as well as an estimate of its uncertainty. Numerical examples using synthetic data demonstrate how well the method can measure RTM uncertainty and produce reliable imaging results.