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Book Chapter

Input-output Models

January 01, 2008


In this chapter, we present the basic mathematical framework for the study of input-output models, along with some simple examples that show various approaches to the description and analysis of those models. The mathematical tools are derived from the general field of operational calculus, so for the most part, we are limited to the consideration of linear systems. Linear digital systems are described by linear difference equations, whereas linear analog systems are described by linear differential equations. Fortunately, many cases occur in engineering and science in which the systems either are linear or can be approximated sufficiently closely by a linear representation.

Linear methods have been applied very successfully to the analysis of geophysical systems and the processing of geophysical data. The input and output of a system are related by a difference equation (digital case) or a differential equation (analog case), the solution of which gives the output for a given input. This equation provides a complete description of the system, but often it must be converted to other forms to be useful.

Other modes of description of the system are related to the outputs produced by special types of inputs. Thus, we have

  1. the impulse response of the system, which is the output produced by an impulse input

  2. the frequency response of the system, which relates the outputs produced by sinusoidal inputs

  3. the transfer function (or system function), which is a generalization of the frequency-response function

These modes of description are related to

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Society of Exploration Geophysicists Geophysical References Series

Digital Imaging and Deconvolution: The ABCs of Seismic Exploration and Processing

Enders A. Robinson
Enders A. Robinson
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Sven Treitel
Sven Treitel
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Society of Exploration Geophysicists
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January 01, 2008




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