Recording Footprint Noise Removal by 3-D Least Squares Migration

Least squares migration (LSM) is applied to 3-D synthetic data in order to test the feasibility of removing the ”recording footprint” noise from migrated sections. The LSM algorithm is implemented with a conjugate gradient algorithm. Results for simple point scatterer and meandering stream channel models suggest that LSM can significantly attenuate the recording footprint noise. For comparison, the corresponding Kirchhoff migrated sections show noticeable artifacts due to a coarse sampling of the wavefield. The drawback with LSM is that it is at least an order of magnitude more computationally expensive than standard migration. It is therefore desirable to discover a means for accelerating the convergence of the conjugate gradient iterations. The next step is to apply LSM to field data where the associated migrated images contain a strong recording footprint. INTRODUCTION The recording footprint noise in migrated sections can be defined as artifacts that partly arise from improper spatial sampling of the wavefield. A mathematician would call these artifacts quadrature errors in approximating the Kirchhoff integral by a weighted sum of polynomials, where the weights are values of the integrand. These errors are exacerbated by coarse source/receiver sampling and aperture limitations, the later causing aliasing artifacts and the former leading to reduced lateral resolution. Moreover, the artifacts or deviations from the actual reflectivity also result from the assumption that the transpose L ̃̃ T to the forward modeling operator L ̃̃ is a good approximation to the inverse operator L ̃̃ .