Green’s theorem as a comprehensive framework for data reconstruction, regularization, wavefield separation, seismic interferometry, and wavelet estimation: A tutorial

摘要

Almost every link in the chain of exploration seismology methods used to process recorded data has been affected by Green’s theorem.Among the seismic processes that can be related to, and/or have benefited from, Green’s theorem are wavelet estimation, multiple elimination, regularization, redatuming, imaging, deghosting, and interferometry. This tutorial on various seismic exploration methods derived from Green’s theorem emphasizes seismic data reconstruction including regularization and redatuming and its relationship to interferometry as well as to wavelet estimation and wavefield separation. The last decade has witnessed ever-increasing attention within the energy industry and its concomitant representation in the published literature to methods dealing with wavefield reconstruction through interferometry or virtual-source techniques. The attention has renewed interest in Green’s theorem because all different approaches to interferometry can be derived from it. This tutorial provides a derivation and explication of the limitations of interferometric techniques when interferometry is used to process measured data from marine surface seismic experiments with controlled sources as approximations to Green’s theorem. This tutorial provides a definite statement of the comprehensive framework given by Green’s theorem to wavefield reconstruction and shows how different techniques are directly understood as specific mathematical forms and/or approximations to the theorem. The use of approximations can have shortcomings and create artifacts. These artifacts and errors are also analyzed and explained. All methods discussed in this tutorial recognize their foundation on Green’s theorem and have a secure mathematicalphysics cornerstone to recognize the assumptions behind distinct approximate solutions and to guide the search for more accurate, effective techniques.