1. The Morlet Wavelets Jo Ann Lee MAP 4413 March 22, 2006

2. Who was Jean Morlet? French geophysicist Graduated from the �cole Polytechnique Worked at Elf Aquitaine � an oil company

3. What does OIL have to do with it? standard way to look for underground oil is to send vibrations into the earth and analyze the echoes that return PROBLEM: abrupt changes in the wave as it passes from one rock layer to another limits of Fourier --- Fourier analysis spreads that spatial information out

4. The Morlet Wavelet (1981) Morlet wanted to analyze brief changes in signals SOLUTION: �wavelets of constant shape� his own way of analyzing the seismic signals to create components that were localized in space Defined by

5. The Morlet Wavelet (1981) Decomposed into real and imaginary parts Real Imaginary

6. It works but how? Alex Grossman � physicist at Centre de Physique Th�orique in Marseilles Grossman and Morlet confirmed that waves could be reconstructed Joint paper in 1984, brings �wavelet� into math lexicon Why wavelets worked better than Fourier: much less sensitive to small errors in the computation