Wave pulses

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Digital Imaging and Deconvolution: The ABCs of Seismic Exploration and Processing
Series Geophysical References Series
Title Digital Imaging and Deconvolution: The ABCs of Seismic Exploration and Processing
Author Enders A. Robinson and Sven Treitel
Chapter 1
DOI http://dx.doi.org/10.1190/1.9781560801610
ISBN 9781560801481
Store SEG Online Store

Up to this point, we have pictured a wave as a periodic function. In other words, we have pictured a wave as a repeating train involving a succession of crests and troughs, all of the same shape. In subsequent chapters, we shall see that this is not at all necessary. In fact, in seismic exploration, innumerable situations occur in which we picture a single isolated pulse of a seismic disturbance as it propagates from one point to the next. Such pulses can be created by taking a stretched string and producing a local deformation in it by pulling one end and then holding it still. Consider the subsequent behavior of such a pulse as it travels at constant speed along the string. At any instant in time, only a limited region of the string is disturbed. The remaining string segments are undisturbed. The pulse travels in this way until it reaches the far end of the string, where it is reflected. However, as long as the pulse moves uninterrupted, it preserves its same shape. How can we relate the behavior of a pulse to what we already have learned about sinusoidal waves? We find the answer to this question with Fourier analysis, about which we will have much to say in later chapters.

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