Of the various factors which influence reflection amplitudes in a seismic recording, divergence effects are possibly of least direct interest to the interpreter. Nevertheless, proper compensation for these effects is mandatory if reflection amplitudes are to be of diagnostic value. For an earth model consisting of horizontal, isotropic layers, and assuming a point source, we apply ray theory to determine an expression for amplitude correction factors in terms of initial incidence, source‐receiver offset, and reflector depth. The special case of zero offset yields an expression in terms of two‐way traveltime, velocity in the initial layer, and the time‐weighted rms velocity which characterizes reflections. For this model it follows that information which is needed for divergence compensation in the region of normal incidence is available from the customary analysis of normal moveout (NMO). It is hardly surprising that NMO and divergence effects are intimately related when one considers the expanding wavefront situation which is responsible for both phenomena. However, it is evident that an amplitude correction which is appropriate for the primary reflection sequence cannot in general be appropriate for the multiples. At short offset distances the disparity in displayed amplitude varies as the square of the ratio of primary to multiple rms velocities, and favors the multiples. These observations are relevant to a number of concepts which are founded upon plane‐wave theory, notably multiple attenuation processes and record synthesis inclusive of multiples.

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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.

NEWMAN, P.J. and WORTHINGTON, M.H. 1982, In-situ Investigation of Seismic Body Wave Attenuation in heterogeneous Media, Geophysical Prospecting 30, 377-400.Field experiments have been carried out to study the nature and magnitude of seismic wave attenuation for a variety of lithologies. In each survey two three-component sets of geophones with wall clamping mechanisms were lowered down boreholes and signals originating from surface compressional and shear-wave sources were recorded. The data collected were corrected for spherical divergence and analyzed to determine intrinsic attenuation. For situations of anomalous wavefront expansion and in cases where multiple reflection losses may be significant, corrections were supplied by a synthetic seismogram programme to improve the estimates of intrinsic attenuation.Values of attenuation were obtained for pure sandstone, sandstone-mar1 sequences and fissured-unfissured chalk sequences. These formations were all near surface and relatively porous. Significant differences in the relative values of compressional and shear-wave attenuation in the various lithologies were noted. In particular compressional absorption in the fissured zones of chalk was twice the absorption associated with the seismic velocities and the absorption of shear waves fluctuated much less. A large contrast in P-wave attenuation was also observed between pure Bunter Sandstone and the sandstone-marl sequence (absorption was over three times as small in the former). A smaller contrast was noted for shear attenuation.The results obtained suggest that, for the relatively homogeneous formations such as pure sandstone and " unfissured " chalk, " shear " absorption was dominant over " bulk " absorption. In contrast bulk absorption was larger than shear absorption for other formations, e.g. the ' I fissured " chalk sequences and a "partially saturated" chalk section. Attenuation was found to be approximately proportional to frequency in all experiments.