Least‐Squares Reverse Time Migration in Visco‐Acoustic Media

Abstract

As the subsurface medium is widely viscous, it is necessary to compensate absorption and to correct dispersion of seismic waves in true-amplitude pre-stack imaging. The instability problem encountered in conventional inverse-Q migration hinders the application of the method. In this work, imaging was treated as a linear inverse problem named least-squares reverse time migration (LSRTM). Firstly, we linearized the wave equation and defined the cost function. Then based on the derived equations of the adjoint wave propagation operator, iterative solution was derived using the adjoint-state method. At last dynamical phase encoding technology was used to reduce computation cost. This method breaks a new way for imaging in visco-acoustic media while avoiding the instability problem. The true-amplitude imaging results can be obtained while compensating absorption and correcting dispersion automatically. It is also a good way to suppress the imaging noise and correct amplitude unbalance caused by geometrical spreading or weak illumination. Compared with conventional reverse time migration (RTM), this method can yield results with higher resolution and lower imaging noise. The validity of the method was demonstrated by the numerical test on synthetic seismic data.