Source-independent least-squares reverse time migration using student's t distribution

Compared to the conventional migration method, the least-squares reverse time migration (LSRTM) has a lot of advantages, such as higher imaging resolution, amplitude preservation and amplitude balance. It is the focus of current research. However, the source wavelet estimation for LSRTM is a very difficult task. The challenge of determining source strength, which can vary from source to source, is even greater. In this paper, we developed a source-independent LSRTM using convolved wavefields. The misfit function consists of the convolution of the observed wavefields with a reference trace from the modeled wavefields, plus the convolution of the modeled wavefields with a reference trace from the observed wavefield. In this case, the source wavelet of the observed and the modeled wavefields are equally convolved with both terms in the misfit function, and thus, the effects of the source wavelets are eliminated. In addition, the field data often contain a lot of noise. The L2 norm based LSRTM algorithm is very sensitive to noise, especially when the data contains outliers. In this case, the conventional LSRTM result is seriously contaminated by noise. Compared to L2 norm, Student's t distribution has better robustness. We extend the Student's t distribution to the SILSRTM algorithm. Theoretical models and field data processing verify the effectiveness of the algorithm and suitability for complex models.