Post stack least squares migration and migration deconvolution with different weightening functions

The seismic migration process, which is the last and most important step of the seismic data processing steps, is widely used to obtain the correct image of the subsurface structure by moving the reflection amplitudes to the actual reflection positions. In this scope, least square migration (LSM) is recently used a linearized inversion process which improve spatial resolution of post-stack seismic data, but also represents blurred images of earth's reflectivity distribution because of migration artifacts. To partly alleviate this blurring, Migration Deconvolution (MD) are proposed and applied to migrated images. The main disadvantage of the method is that it increases the computational time cost. In this study, in addition to the deblurring function which is derived from migration operator (L), it is tried to decrease processing cost by using different deblurring functions which are derived from input data (d). According to the applications on models, the deblurring functions which have the least error rate are cov((d d^T))^(-1) and cov ((L^T L)^(-1)), and it is seen that cov(dd^T )^(-1) deblurring function reduces processing time %60 (for MD %80, for LSMD %40) respect to cov (L^T L)^(-1). Besides, (d d^T )^(-1) has been found to have the same error rates as the traditional deblurring function (L^T L)^(-1) at a cost of %45 (for MD %18, for LSMD %65). It was also found that the LSMD procedure reduced the error rates by about 15% compared to the MD procedure.