Directivities of linear arrays and linear sources

From SEG Wiki
Jump to navigation Jump to search


Show that the directivity equations (8.6d) and (7.5d) are consistent.


Since equation (8.6d) applies to a discontinuous array of geophones whereas equation (7.5d) applies to a continuous source, we find the limit of equation (8.6d) as the number of geophones becomes infinite. We require that while in such a way that , being the same constant as in problem 7.5, thus keeping the array length equal to the source length. In the limit the numerator of equation (8.6d) becomes . To get the limit of the denominator, we replace the sine by its argument (because ) and get . Substituting these values in equation (8.6d), we obtain

Because the angles and are equivalent, equations (8.6d) and (7.5d) are equivalents.

Continue reading

Previous section Next section
Response of a linear array Tapered arrays
Previous chapter Next chapter
Seismic equipment Data processing

Table of Contents (book)

Also in this chapter

External links

find literature about
Directivities of linear arrays and linear sources
SEG button search.png Datapages button.png GeoScienceWorld button.png OnePetro button.png Schlumberger button.png Google button.png AGI button.png