Pre-stack and post-stack noise attenuation using the diversity t-p transform

Abstract

A new method for attenuating seismic noise, the diversity t-p transform (DTPT), is presented and illustrated with synthetic and field data examples. This method can be used either with pre-stack or post-stack data. Furthermore, the method can also be used for trace interpolation. In the pre-stack case, the DTPT is implemented exploiting the benefits provided by the classical t-p transform using hyperbolic velocity filtering during the transform procedure and diversity scaling applied to the data prior to the t-p transformation. This approach permits attenuation of complex noise ? for example, aliased noise, non-linear noise trends, noise bursts, spikes, etc. Conventional f-k and f-x modelling techniques do not cope well with these types of noise. Most importantly, with the use of the DTPT technique, the useful signal does not suffer distortion in any part of the frequency spectrum at any offset. In the post-stack case, the DTPT method is performed using the local slant stack concept. A discrete t-p representation of the data can be determined which minimises the presence of random noise and compresses the t-p response of linear events so that aliasing effects are much reduced. The DTPT technique used as a post-stack noise attenuator has significant benefits when compared with conventional approaches to noise attenuation. It attenuates noisy isolated traces (spikes, noise bursts, etc.) and does not demand uniform spatial sampling (as required by f-k and f-x prediction techniques). In addition, by exploiting the DTPT characteristics mentioned above, the DTPT technique may be utilised for trace interpolation purposes ? thus improving the lateral resolution of the seismic data prior to the migration process. Trace interpolation is achieved during the inverse t-p transform by outputting traces at a finer spatial sampling than the original input data. In addition, the output spatial sample interval may be uniform even though the input interval may not be.