Cross-correlation least-squares reverse time migration in the pseudo-time domain

The least-squares reverse time migration (LSRTM) method with higher image resolution and amplitude is becoming increasingly popular. However, the LSRTM is not widely used in field land data processing because of its sensitivity to the initial migration velocity model, large computational cost and mismatch of amplitudes between the synthetic and observed data. To overcome the shortcomings of the conventional LSRTM, we propose a cross-correlation least-squares reverse time migration algorithm in pseudo-time domain (PTCLSRTM). Our algorithm not only reduces the depth/velocity ambiguities, but also reduces the effect of velocity error on the imaging results. It relieves the accuracy requirements on the migration velocity model of least-squares migration (LSM). The pseudo-time domain algorithm eliminates the irregular wavelength sampling in the vertical direction, thus it can reduce the vertical grid points and memory requirements used during computation, which makes our method more computationally efficient than the standard implementation. Besides, for field data applications, matching the recorded amplitudes is a very difficult task because of the viscoelastic nature of the Earth and inaccuracies in the estimation of the source wavelet. To relax the requirement for strong amplitude matching of LSM, we extend the normalized cross-correlation objective function to the pseudo-time domain. Our method is only sensitive to the similarity between the predicted and the observed data. Numerical tests on synthetic and land field data confirm the effectiveness of our method and its adaptability for complex models.