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 seismologymethods used to process recorded data has been affected byGreen’s theorem.Among the seismic processes that can be relatedto, and/or have benefited from, Green’s theorem are waveletestimation, multiple elimination, regularization, redatuming, imaging,deghosting, and interferometry. This tutorial on variousseismic exploration methods derived from Green’s theorem emphasizesseismic data reconstruction including regularizationand redatuming and its relationship to interferometry as well asto wavelet estimation and wavefield separation. The last decadehas witnessed ever-increasing attention within the energy industryand its concomitant representation in the published literatureto methods dealing with wavefield reconstruction through interferometryor virtual-source techniques. The attention has renewedinterest in Green’s theorem because all different approachesto interferometry can be derived from it. This tutorialprovides a derivation and explication of the limitations of interferometrictechniques when interferometry is used to processmeasured data from marine surface seismic experiments withcontrolled sources as approximations to Green’s theorem. Thistutorial provides a definite statement of the comprehensiveframework given by Green’s theorem to wavefield reconstructionand shows how different techniques are directly understoodas specific mathematical forms and/or approximations to the theorem.The use of approximations can have shortcomings and createartifacts. These artifacts and errors are also analyzed and explained.All methods discussed in this tutorial recognize theirfoundation on Green’s theorem and have a secure mathematicalphysicscornerstone to recognize the assumptions behind distinctapproximate solutions and to guide the search for more accurate,effective techniques.