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 11.
Table 11. Response of the reflectivity sequence (1, 0, 1/2) to a zerodelay explosive impulse (1, 0).
Time of Onset

Reflectivity Sequence

Source

Response

0 
1 
0 
1/2 
1 
0 
1 
0 
1/2 
0

Table 12. Response of the reflectivity sequence (1, 0, 1/2) to a unitdelay 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 12.
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 13.
Table 13. Linear superposition of the two responses described in Tables 11 and 12.
Time of Onset 
Reflectivity Sequence 
Source 
Response

0 
1 
0 
${\frac {1}{2}}$ 
1 
0 
1 
0 
${\frac {1}{2}}$ 
0

1 
1 
0 
${\frac {1}{2}}$ 
0 
${\frac {1}{2}}$ 
0 
${\frac {1}{2}}$ 
0 
${\frac {1}{4}}$

Superposition: 
1 
${\frac {1}{2}}$ 
1 
${\frac {1}{2}}$ 
${\frac {1}{2}}$ 
${\frac {1}{4}}$

${\text{Expressed}}\ {\text{differently}}:\ \left(1,\ 0,\ {\frac {1}{2}}\right)*\left(1,\ {\frac {1}{2}}\right)=\left(1,\ {\frac {1}{2}},\ {\frac {1}{2}},\ {\frac {1}{4}}\right)$

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