Information-Based Inversion and Processing with Applications

Chapter 1 introduces basic concepts including: probability theory, elementary principles of parameter estimation, Fourier and z-transform essentials, and issues of orthogonality. In Chapter 2, the linear treatment of time series is provided. Particular attention is paid to Wold decomposition theorem and time series models (AR, MA, and ARMA) and their connection to seismic data analysis problems. Chapter 3 introduces concepts of Information and theories of synopsis. Examples are entropy, conditional entropy, Burg's maximum entropy, spectral estimator, and mutual information. Chapter 4 provides a description of the problem, then from a probabilistic one. Chapter 5 deals with methods to improve the signal-to-noise ratio of seismic records. Concepts from previous chapters are put in practice for the design of the noise filter for noise attenuation and high-resolution Radon operators. Chapter 6 deals with the topic of deconvolution and the inversion of acoustic impedance. The first part discusses band-limited extrapolation assuming a known wavelet and the issue of wavelet estimation. The second part deals with sparse deconvolution using various 'entropy' type norms. Finally, Chapter 7 introduces recent topics of interest to the authors.

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* Non-conventional approaches to data processing and inversion are presented
* Important problems in the area of seismic resolution enhancement are discussed
* Contains research material that could inspire graduate students and their supervisors to undertake new research directions in seismology and geophysical signal processing