Frequency‐wavenumber velocity filtering is often applied to prestack seismic data for the attenuation of coherent noise. Although the process often gives excellent results, it can sometimes result in signal smoothing and distortion and poor attenuation of coherent noise. A slowness adaptive f-k filter reduces signal distortion and improves the attenuation characteristics of the filter. The technique uses a time‐ and space‐variant narrow reject‐band f-k filter. Optionally, coherent noise is compressed before application of the filter. The apparent slowness of coherent noise events is estimated using local t-x slant stacks weighted by coherence. A two‐dimensional (2-D) window is moved across the shot record, and at each point on the record slant stacks are taken through the central sample of the window. The slowness value that produces the maximum stack is assigned to the central sample of the window. In this way, an instantaneous slowness image of the shot record is produced. A one‐dimensional (1-D), high‐pass, finite‐duration impulse‐response (FIR) filter is applied in a spatially and temporally varying way across the record on the basis of the instantaneous slowness values. Before filter application, trace‐to‐trace static and amplitude effects are estimated and removed from the data. This results in compression of coherent noise and improved attenuation after filtering. The filtering process has been applied to low‐fold prestack dynamite data from the Surat Basin, Australia. The results indicate that the technique has good attenuation characteristics and produces minimal distortion of seismic signal. The process, however, is computationally expensive.

Abctract Median filters may be used with seismic data to attenuate coherent wavefields. An example is the attenuation of the downgoing wavefield in VSP data processing. The filter is applied across the traces in the ‘direction’ of the wavefield. The final result is given by subtracting the filtered version of the record from the original record. This method of median filtering may be called ‘median filtering operated in subtraction’. The method may be extended by automatically estimating the slowness of coherent wavefields on a record. The filter is then applied in a time‐ and‐space varying manner across the record on the basis of the slowness values at each point on the record. Median filters are non‐linear and hence their behaviour is more difficult to determine than linear filters. However, there are a number of methods that may be used to analyse median filter behaviour: (1) pseudo‐transfer functions to specific time series; (2) the response of median filters to simple seismic models; and (3) the response of median filters to steps that simulate terminating wavefields, such as faults on stacked data. These simple methods provide an intuitive insight into the behaviour of these filters, as well as providing a semiquantitative measurement of performance. The performance degradation of median filters in the presence of trace‐to‐trace variations in amplitude is shown to be similar to that of linear filters. The performance of median filters (in terms of signal distortion) applied obliquely across a record may be improved by low‐pass filtering (in the t‐dimension). The response of median filters to steps is shown to be affected by background noise levels. The distortion of steps introduced by median filters approaches the distortion of steps introduced by the corresponding linear filter for high levels of noise.

Two‐dimensional median filters can be designed so that they have properties similar to f-k fan filters. This is done by using the coefficients of a truncated impulse response of an f-k filter as the weight coefficients for the weighted median process. The filter is called a median f-k filter and can be used to discriminate between events on the basis of apparent velocity. The filter appears suitable as a poststack coherency filter because it produces less distortion at wavefield terminations than conventional f-k fan filters. One‐dimensional weighted median filters that include negative coefficients are a logical starting point for the analysis of median f-k filters since simple numerical techniques may be used to analyze the behavior of these filters. We show that median filters with negative coefficients do not provide an unbiased estimate of the mean and can misplace the position of steps. Faults on a stacked section may be modeled by steps, and therefore applying a median f-k filter to stacked seismic data could change the position of faults. However, the distortion of steps introduced by median f-k filters is shown to be less than the distortion produced by the corresponding linear f-k filter, and the error in step placement is small. We present simple model examples and a seismic field data example to illustrate differences between linear f-k filters and median f-k filters.

Observation of azimuthal shear wave anisotropy can be useful for characterisation of fractures or stress field. Shear wave anisotropy is often estimated by measuring splitting of individual shear-wave events on VSP data; however this method may become unreliable for zero-offset (marine) VSP where the seismogram often contains no strong individual shear events but many low-amplitude PS conversions. In this paper we introduce a new approach to estimation of fast and slow shear wave velocities and orientation of polarization planes based on the multi-component velocity analysis. This technique is applicable to zero-offset VSP data and should take advantage of the presence of a large number of shear wave events with the same velocity. The main idea is to estimate the velocity for a given polarization direction by measuring the coherency of the seismic signal of a large number of events as a function of the apparent velocity. The algorithm was tested on marine 3C VSP acquired in the NorthWest Shelf of Australia. These tests show good agreement between anisotropy parameters (magnitude and orientation) derived from the VSP and cross-dipole sonic log data.