Viscoelastic time-reversal imaging

The time invariance of wave equations, an essential precondition for time-reversal (TR) imaging, is no longer valid when introducing attenuation. I evaluated a viscoelastic (VE) TR imaging algorithm based on a novel VE wave equation. By reversing the sign of the P-and S-wave loss operators, the VE wave equation became time invariant for the TR operation. Attenuation effects were thus compensated for during TR wave propagation. I developed the formulations of VE forward modeling and TR imaging. I tested my imaging approach in three numerical experiments. The first experiment used a 2D homogeneous model with full-aperture receivers to examine the time invariance of the VE TR imaging equation. Using the same model, the second experiment was used to demonstrate the method's ability to characterize a point source. In the third experiment, I applied this method to characterize a complex source using borehole geophones. Numerical results illustrated that the VE TR imaging improved our knowledge of the source location, radiation pattern, and amplitude.