High Resolution Seismic Imaging using Least Squares Migration

Abdolnaser Yousefzadeh

High resolution seismic imaging methods are getting increasing attention in the exploration and development industry. Regularized Least Squares Prestack Migration (LSPSM) is one of these methods.

Of the various methods of seismic migration, due to its low cost and flexibility of handling acquisition and topography irregularities, Kirchhoff migration has been the most frequently used method of migration in the industry for decades. LSPSM based on Kirchhoff migration is an effective method to attenuate acquisition footprint that result from sparseness or irregularities of seismic data sampling.

LSPSM is a costly choice when compared to a conventional Kirchhoff migration. As shown in this study, the LSPSM equation cannot be solved efficiently using a standard multigrid method as it requires an explicit form of the corresponding Hessian matrix which needs to be diagonally dominant. It is shown that the Hessian of the LSPSM equation is a very large, dense, and diagonally non-dominant matrix.

The performance of LSPSM is highly sensitive to the accuracy of the velocity model. Without a reasonably accurate velocity model, LSPSM cannot improve the quality of the migration image or do proper data reconstruction. This property provides a method to quantify the accuracy of the velocity model. Velocity analysis that is based on the migration CIGs can be extended to LSPSM CIGs. A coherency spectrum measured from LSPSM CIGs provides a velocity model that is accurate enough to give a high resolution image using LSPSM, and good data reconstruction in a few iterations.

In a complementary study, the application of LSPSM in time lapse seismic analyses is investigated. Separate and joint LSPSM inversion of time lapse data gives a high resolution time lapse image which is less affected by different acquisition geometries of the baseline and monitor surveys. Data reconstruction of old and new surveys into a consistent new geometry will provide comparable prestack time lapse data sets.

In conclusion, LSPSM is an effective method for high resolution imaging, with its advantages possibly outweighing its high cost.