We discover that the adjoint system of the second-order pseudoacoustic anisotropic wave equations can have unstable solutions and present a possible alternative system. The unstable solutions have magnitude that grows linearly with time and do not propagate spatially. This is not the kind of numerical instability that occurs when the propagation timestep does not satisfy the CFL condition. This instability is inherent to this particular type of wave equations. In fact, there is a family of unstable wave equations that all describe the same kinematics. A necessary condition for stability of this type of pseudoacoustic anisotropic wave equations is that it reduces to the scalar wave equation in isotropic media. We also find out that the time-reversed forward equations can substitute the correct adjoint equations in the back propagation step of full waveform inversion without loss in convergence.
Presentation Date: Wednesday, September 18, 2019
Session Start Time: 8:30 AM
Presentation Time: 9:45 AM
Location: 221C
Presentation Type: Oral
