Time-domain operations

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Seismic Data Analysis
Seismic-data-analysis.jpg
Series Investigations in Geophysics
Author Öz Yilmaz
DOI http://dx.doi.org/10.1190/1.9781560801580
ISBN ISBN 978-1-56080-094-1
Store SEG Online Store


Consider a reflectivity sequence represented by the time series (1, 0, 1/2). Also consider an impulsive source that causes an explosion at t = 0 with an amplitude of 1. The response of the reflectivity sequence to an impulse is called the impulse response. This physical process can be described as in Table 1-1.

Table 1-1. Response of the reflectivity sequence (1, 0, 1/2) to a zero-delay explosive impulse (1, 0).
Time of Onset Reflectivity Sequence Source Response
0 1 0 1/2 1 0 1 0 1/2 0
Table 1-2. Response of the reflectivity sequence (1, 0, 1/2) to a unit-delay implosive impulse (0, -  1/2).
Time of Onset Reflectivity Sequence Source Response
1 1 0 1/2 0 -  1/2 0 -  1/2 0 -  1/4

One unit time later, suppose that the impulsive source generates an implosion with an amplitude of -  1/2. This response is described in Table 1-2.

Note that the response in each case is the reflectivity sequence scaled by the impulse strength and delayed by the impulse onset. Since a general source function is considered to be a sequence of explosive and implosive impulses, the individual impulse responses are added to obtain the combined response. This process is called linear superposition and is described in Table 1-3.

Table 1-3. Linear superposition of the two responses described in Tables 1-1 and 1-2.
Time of Onset Reflectivity Sequence Source Response
0 1 0 1 0 1 0 0
1 1 0 0 0 0
Superposition: 1 1

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Time-domain operations
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