A multisource least-squares migration algorithm is proposed to efficiently produce high quality images. This algorithm is implemented with Kirchhoff migration method and tested with 320 synthetic shot gathers for the 2D SEG/EAGE salt model. An accurate image is obtained by migrating a supergather composite of all these 320 shot gathers after 60 iterations. Compared to conventional Kirchhoff migration image, the I/O cost of MLSM with static encoding is reduced by 320 times. The MLSM image is much more resolved than conventional Kirchhoff migration image, because the migration artifacts are suppressed, the reflector amplitudes are balanced, the image resolution is enhanced and the crosstalk noise is reduced. According to the signal-to-noise ratio analysis, an acceptable number of iterations are needed to achieve high enough SNR. This suggests that high quality images can be produced with less cost than conventional migration method, if the MLSM algorithm is implemented with the wave-equation migration method.
Two encoding strategies are discussed in this chapter. The MLSM algorithm with static encoding enjoys lower I/O cost compared to the MLSM with dynamic encoding, but the empirical results show that the MLSM with dynamic encoding, on the other hand, is more effective in reducing crosstalk noise introduced by blended sources. Compared to the iterative stacking method, the MLSM algorithm improves the image quality by suppressing the migration artifacts, balancing the reflector amplitudes and enhancing the image resolution, although the MLSM algorithm requires more iterations to reduce crosstalk than the iterative stacking method. For example, the measured SNR of the 60-iteration MLSM image with dynamic encoding is comparable with the SNR of the 20-fold stacked image.
Future research is needed to address following questions. Firstly, the MLSM has only been tested with fixed-spread acquisition geometry. The extension to marine acquisition will be significant. Secondly, the least-square migration seeks a model that optimally fits the data. This process is sensitive to the velocity model, and it is important to reduce this sensitivity for real applications. A third interesting research topic is to look for model dependent efficient encoding functions.