Least-Squares Reverse Time Migration of Primary and Internal Multiple Predicted by the High-Order Born Modeling Method

Multiples can cause artifacts in imaging; however, they contain information about underground structures. If the internal multiples are removed as a noise, the information contained by the internal multiple will also be removed. This will cause loss of some useful structures in the image. If the multiples and the primary can be separated from the recorded seismic data for imaging, the information contained by the multiples can be used and the artifacts can be attenuated. Here we developed a method to separate the primary and internal multiples and use them in least squares reverse time migration (LSRTM). This method first separates the primary and the internal multiples in the data residual and predicts the wavefield of the primary and internal multiples in a forward- propagated wavefield. We use the high-order Born modeling method to predict the internal multiples. In this method, the internal multiples can be achieved by forward modeling of three times in the time domain. In the internal multiple prediction process, we get the wavefield of the primary and internal multiples in the forward-propagated wavefield. Then, by introducing the weighting matrix, we established the objective function for imaging of the primary and the internal multiples separately. In the calculation of gradient, we use the correlation of primary in the forward-propagated wavefield with the backward-propagated wavefield of the primary in the data residual, and internal multiples in the forward-propagated with the backward-propagated wavefield of internal multiples in the data residual. In this method, the multiple prediction process provided the internal multiples to suppress the artifacts, and LSRTM constructed the model for the multiple prediction process. Finally, we performed numerical tests using synthetic data, and the results indicated that the LSRTM without the internal multiple can suppress not only the artifacts of internal multiples but also some useful structures below the salt dome. LSRTM with primary and internal multiples can suppress the artifact of internal multiples, and the useful structures below the salt dome are compensated in the image.