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Fundamentals of data regularization

In this chapter, I develop a general theoretical framework for addressing the data regularization problem. The problem fundamentals are traced back to statistical estimation theory. Following Claerbout (1992, 1999), I formulate data regularization as a simple linear-estimation problem.

Statistical estimation
Representing covariance matrices by sparse operators
Data regularization as an optimization problem
- Model-space regularization
- Data-space regularization (model preconditioning)
Acknowledgments

Stanford Exploration Project
12/28/2000