Chapter 1
Fourier Analysis
1.1
Introduction
In this part of the course we will review some fundamental aspects of Fourier Analysis.
We will rst study some aspects of orthogonal expansions. We will also study Fourier
series, and the Fourier transform. Alon
Chapter 2
Z-transform and Convolution
In this chapter we will introduce a new concept that is very useful at the time of dealing
with discrete signals and linear systems. The transform permits one to do what the
Fourier transform to continuous signals. La
Chapter 3
Discrete Fourier Transform
In this Chapter will present the transition from the Z transform to the DFT (Discrete
Fourier Transform). The DFT is used to compute the Fourier transform of discrete data.
3.1
The Z transform and the DFT
We have alrea
Chapter 4
Deconvolution of reectivity series
4.1
Modeling normal incidence seismograms
In this chapter we will study the problem of computing reection and transmition coefcients for a layered media when plane waves propagate in the earth with angle of
inc
Chapter 5
Signal-to-noise-ratio Enhancement
5.1
lters
Signal-to-noise-ratio enhancemnet in the
domain has been proposed by Canales
(1994) as a method for random noise attenuation. The technique is widely accepted
and used in the industry. The method is ve
Chapter 6
The KL transform and eigenimages
In this chapter we will discuss another technique to improve the information content
of seismic data. The application of eigenimage analysis in seismology was proposed
by Hemon and Mace (1978). In their approach
Chapter 7
Radon Transforms
In this chapter we deal with the numerical implementation of the Radon transform. We
will analyze the problem using the inverse problem formalism and study the problem
of designing a high resolution Parabolic Radon transform for