1887
Volume 21 Number 2
  • E-ISSN: 1365-2478

Abstract

A

The time‐honoured method of attenuating coherent noise in the seismic record is by the use of source and geophone arrays. In theory, and using methods familiar in the synthesis of digital frequency filters, arrays can be designed having virtually any desired response in the wavenumber spectrum.

In practice, arrays cannot be implemented with the same precision that is applied in design. The response actually achieved must be compromized by a number of factors. These include inaccuracies in the effectiveness or positioning of individual array elements, variations in ground coupling, and the effect of local heterogenities in the environment of the array. We have no reliable way of knowing how well a particular array will perform from one location to the next.

Statistical modelling methods have been applied to examine the effects of implementation errors. Experimental results, supported by statistical theory, show that errors are expected to impose a limit upon the rejection capabilities of an array. The expected limiting value of attenuation due to errors in element weights is inversely proportional to the standard deviation of errors and directly proportional to the square root of the number of array elements. Position errors exert a limiting influence which is wavenumber dependent such that attenuation decreases with increasing wavenumber. For arrays of common dimensions, Gaussian random errors of 10% standard deviation in element weights and positions result in an expected attenuation limit of about 30 dB.

It follows that the more ambitious array designs are less tolerant of errors, and must be implemented with greater care and precision in the field. The present work enables us to specify tolerances for any particular array design.

Ultimately, the degree of pattern refinement which may be effectively employed in any area is determined by errors which are associated with the array environment. Complex arrays are expensive to operate. In order to avoid over‐design it would be useful to establish the magnitude of errors to be expected under different terrain conditions.

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2006-04-27
2020-05-27
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References

  1. Galbraith, J. N.Jr., Harter, R., and Steinhart, E. R., 1968. The effect of non‐ideal sensor configurations on array response: paper read at the 38th Annual International Meeting of the SEG, Denver , Colorado , November 1968.
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  • Article Type: Research Article
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