We have extended the method of stationary spiking deconvolution of seismic data to the context of nonstationary signals in which the nonstationarity is due to attenuation processes. As in the stationary case, we have assumed a statistically white reflectivity and a minimum-phase source and attenuation process. This extension is based on a nonstationary convolutional model, which we have developed and related to the stationary convolutional model. To facilitate our method, we have devised a simple numerical approach to calculate the discrete Gabor transform, or complex-valued time-frequency decomposition, of any signal. Although the Fourier transform renders stationary convolution into exact, multiplicative factors, the Gabor transform, or windowed Fourier transform, induces only an approximate factorization of the nonstationary convolutional model. This factorization serves as a guide to develop a smoothing process that, when applied to the Gabor transform of the nonstationary seismic trace, estimates the magnitude of the time-frequency attenuation function and the source wavelet. By assuming that both are minimum-phase processes, their phases can be determined. Gabor deconvolution is accomplished by spectral division in the time-frequency domain. The complex-valued Gabor transform of the seismic trace is divided by the complex-valued estimates of attenuation and source wavelet to estimate the Gabor transform of the reflectivity. An inverse Gabor transform recovers the time-domain reflectivity. The technique has applications to synthetic data and real data.

Coherent noise is a persistent problem in seismic imaging, and a number of techniques have been developed to attenuate it. The radial trace (RT) transform, a simple seismic data mapping algorithm, can be used as the basis for a particularly flexible and effective method for attenuating coherent noise on both prestack and poststack seismic data. Described here are the principles and some practical application details for attenuating coherent noise in the RT domain. A comparison between frequency–wavenumber (f–k) and RT domain filtering on a synthetic model is presented, and some of the differences and advantages of RT methods are identified. Next, RT coherent noise attenuation is demonstrated using a set of good‐quality field data; it is then applied to a very noisy data set. The results obtained with this last set prove to be as good as, or better than, those produced using f–k filtering.

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The radial trace transform, a simple geometric re-mapping of a seismic trace gather, can be used to separate overlapping coherent events on seismic trace panels in such a way that bandpass filtering or spectral editing will very effectively eliminate undesired events or enhance desired ones. Filtering in the radial trace domain can be more effective than F-K filtering for certain kinds of coherent noise: specific examples include dispersive linear noise such as the ice wave in arctic settings and some instances of ground roll; various direct, refracted, or waveguide modes; and any coherent filtering of 3D data, since no re-gridding of data is required. The simple transform described in early literature can be made much more general and useful by allowing the coordinates of its origin to be placed anywhere in the x-t plane, and by allowing bending or curving of the traces themselves. Examples are shown of various radial trace applications.