Patterns—with a Pinch of Salt *

Abstract

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.

3D Seismic Survey Design, Second edition

“…) This reasoning leads to the concept of array-based symmetric sampling, whereby (1) shot interval is equal to receiver interval and (2) length of shot arrays and length of receiver arrays equal shot and receiver interval. In the past, the use of weighted arrays was quite common; however, weighted arrays are hardly used anymore because the effect is often not as desired (Newman and Mahoney, 1973). Therefore, I consider nonweighted arrays only.…”

“…Energy in the flanks can be removed by filtering in the shot and receiver domains. Provided sampling is dense enough, filtering in the computer is better than in the field because of the limited control one has over the response of field arrays (Newman and Mahoney, 1973), whereas digital filter responses can be shaped as desired.…”

11. Measurement and Identification of 3-D Coherent Noise Generated from Irregular Surface Carbonates

“…A problem common to all high-performance arrays is the sensitivity of these arrays to variations in element spacing and weighting. Because earth-coupling effects may cause geophone-to-geophone amplitude variations within the array and because physical objects such as trees and bushes often get in the way, the desired weights and element spacing, and therefore, the desired attenuation levels are usually not achieved for field-implemented high-performance arrays (Newman and Mahoney, 1973).…”

Jointly Filtering and Regularizing Seismic Data Using Space-Varying FIR Filters

“…Usually the array weights are designed for a specific geometrical layout of the array elements. When this geometrical layout is violated, it can prove detrimental for the filtering capabilities of the array, as shown in [1]. Fortunately, advances in acquisition hardware have enabled us a) to record the output of each individual receiver and b) to know with high (but limited) accuracy the actual location of each receiver.…”

“…• Method A approximates the prototype filter in the spatial domain, which has been already designed, • Method B approximates the ideal response of the prototype filter in the wavenumber domain 1 . In other words, Method B also skips the intermediate step of designing the prototype filter.…”