Response of a triangular array

ADVERTISEMENT
From SEG Wiki
Jump to: navigation, search

Problem 8.10a

The tapered array [1, 2, 3, 3, 2, 1] =[1, 1, 1, 1] * [1, 1, 1] is called a triangular array. Use this fact to sketch the array response.

Background

We use the notation to represent a continuous function of the variable while the notation denotes a digital function, that is, the result of sampling a continuous function at a fixed sampling interval (see problem 9.4).

The triangular array is also used to approximate a cosine array where successive elements are weighted as equally spaced samples of the first half-cycle of a cosine function.

Figure 8.10a.  Response of tapered array.

The notation denotes the convolution of and (see problem 9.2). The convolution is given by the summation in equation (9.2b), namely


(8.10a)

Solution

We get for the convolution:

The response of this array to a harmonic signal is shown in Figure 8.10a.

Problem 8.10b

How could three strings of geophones, each having four equally spaced elements, be laid out to yield a triangular array?

Solution

Number six geophone locations 1 through 6 and lay the first string (see problem 8.13) of four geophones from position 1 to position 4, the second string from 2 to 5, and the third string from 3 to 6. This give the array 1, 2, 3, 3, 2, 1.

Problem 8.10c

How could a smoother tapered array be approximated?

Solution

We could achieve a smoother array by spacing the geophones unequally such that each represents an equal portion of the area under the desired array response curve, as illustrated in Figure 8.10c.

Figure 8.10c.  Approximating smooth array with unequal geophone spacing.

Continue reading

Previous section Next section
Directivity of marine arrays Noise tests
Previous chapter Next chapter
Seismic equipment Data processing

Table of Contents (book)

Also in this chapter

External links

find literature about
Response of a triangular array
SEG button search.png Datapages button.png GeoScienceWorld button.png OnePetro button.png Schlumberger button.png Google button.png AGI button.png