Tapered arrays

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Problem

Array tapering can be achieved by

  1. increasing the number of elements at some locations,
  2. weighting equally spaced elements either
    1. within the elements, or
    2. in a mixing box, or
  3. using unequal spacing of elements.

What arguments are there for/against each of these approaches?

Background

In Figure 8.6b the main lobe is the lobe centered on the origin while its replica to the right is the alias lobe. The region between these lobes is the reject region, so-called because of the high attenuation in this region.

Tapered arrays are used to broaden the main and alias lobes while decreasing the response in the reject region. Compare parts (i) and (iii) of Figure 8.6b.

Solution

1) Increasing the number of elements at some locations improves geophone coupling to the ground and does not require special instrumentation. However, this requires more geophones and more connections, and increases the possibility of adding the extra geophones at the wrong locations or connecting some geophones incorrectly.

2,a) Weighting equally spaced elements within the elements requires fewer geophones. However, it requires specially designed geophones and increases the possiblity of using the wrong geophone at a location.

2,b) Weighting equally spaced elements in a mixing box easily achieves tapering and permits the tapering to be varied easily. However, it involves the cost of the mixing box and possible errors in connecting the geophones to the box or adjusting the weights.

3) Spacing elements unequally does not require special equipment. However, it is inconvenient and expensive to determine accurately the individual geophone locations.

Method 1 is the one almost always used.

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