Forward interpolation |

**Sergey Fomel**

As I will illustrate in later chapters, the crucial part of data
regularization problems is in the choice and implementation of the
regularization operator or the corresponding
preconditioning operator . The choice of the forward
modeling operator is less critical. In this chapter, I
discuss the nature of forward interpolation, which has been one of the
traditional subjects in computational mathematics. Wolberg (1990)
presents a detailed review of different conventional approaches. I
discuss a simple mathematical theory of interpolation from a regular
grid and derive the main formulas from a very general idea of function
bases.

Forward interpolation plays only a supplementary role in this dissertation, but it has many primary applications, such as trace resampling, NMO, Kirchhoff and Stolt migrations, log-stretch, and radial transform, in seismic data processing and imaging. Two simple examples appear at the end of this chapter.

- Interpolation theory
- Function basis
- Solution
- Interpolation with Fourier basis

- Continuous case and seismic imaging

- Interpolation with convolutional bases

- Seismic applications of forward interpolation
- Acknowledgments
- Bibliography
- About this document ...

Forward interpolation |

2014-02-21