Pythagoras (c. 580-c. 500 B.C.) taught that “all is number.” Pythagoras realized that numbers were hidden in everything, from the harmonies of music to the orbits of the planets. In other words, number and the nature of number make a thing clear either in itself or in its relation to other things. Today's world, with its digital computers, digital pictures, digital animation, digital television, digital telephones, digital regulators, and digital processing, attests to the foresight of Pythagoras. Pythagoras was instrumental in the development of the language of mathematics, which enabled him and others to describe the nature of the universe.
In additional ways unforeseen by Pythagoras, everything is number. The great mathematician Carl Friedrich Gauss (1777–1855) once said, “Mathematics is the queen of science and number theory the queen of mathematics.” While he was still a teenager, Gauss was intrigued with numbers. At the age of 18, he thought up and justified the numerical method of least squares.
Gauss's love for numerical calculations stirred his interest in astronomy. On New Year's Eve 1800–1801, Giuseppe Piazzi had discovered what he thought was a new planet (it was the asteroid Ceres). Because observers soon would lose sight of such a small object, it was important to calculate its elliptical orbit as soon as possible. Using only the few observations that had been made of the asteroid, Gauss calculated its orbit (reputedly by least squares) so accurately that astronomers could locate it again late in 1801 and early in 1802.
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Digital Imaging and Deconvolution: The ABCs of Seismic Exploration and Processing
Digital Imaging and Deconvolution: The ABCs of Seismic Exploration and Processing (SEG Geophysical References Series No. 15), covers the basic ideas and methods used in seismic processing, concentrating on the fundamentals of seismic imaging and deconvolution. Most chapters are followed by problem sets. Some exercises supplement textual material; others are meant to stimulate classroom discussions. Text and exercises deal mostly with simple examples that can be solved with nothing more than pencil and paper. The book covers wave motion; digital imaging; digital filtering; various visualization aspects of the seismic reflection method; sampling theory; the frequency spectrum; synthetic seismograms; wavelets and wavelet processing; deconvolution; the need for continuing interaction between the seismic interpreter and the computer; seismic attributes; phase rotation; and seismic attenuation. The last of the 15 chapters gives a detailed mathematical overview. Digital Imaging and Deconvolution, nominated for the Association of Earth Science Editors award for best geoscience publication of 2008–2009, will interest professional geophysicists, graduate students, and upper-level undergraduates in geophysics. The book also will be helpful to scientists and engineers in other disciplines who use digital signal processing to analyze and image wave-motion data in remote-detection applications. The methods described are important in optical imaging, video imaging, medical and biological imaging, acoustical analysis, radar, and sonar.