A data adaptive interpolation method is designed and applied in the Fourier transform domain (f‐k or f‐kx‐ky for spatially aliased data. The method makes use of fast Fourier transforms and their cyclic properties, thereby offering a significant cost advantage over other techniques that interpolate aliased data. The algorithm designs and applies interpolation operators in the f‐k (or f‐kx‐ky domain to fill zero traces inserted in the data in the t‐x (or t‐x‐y) domain at locations where interpolated traces are needed. The interpolation operator is designed by manipulating the lower frequency components of the stretched transforms of the original data. This operator is derived assuming that it is the same operator that fills periodically zeroed traces of the original data but at the lower frequencies, and corresponds to the f‐k (or f‐kx‐ky domain version of the well‐known f‐x (or f‐x‐y) domain trace interpolators. The method is applicable to 2D and 3D data recorded sparsely in a horizontal plane. The most common prestack applications of the algorithm are common‐mid‐point domain shot interpolation, source‐receiver domain shot interpolation, and cable interpolation.

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A common practice in random noise reduction for 2-D data is to use pseudononcausal (PNC) 1-D prediction filters at each temporal frequency. A 1-D PNC filter is a filter that is forced to be two sided by placing a conjugate‐reversed version of a 1-D causal filter in front of itself with a zero between the two. For 3-D data, a similar practice is to solve for two 2-D (causal) one‐quadrant filters at each frequency slice. A 2-D PNC filter is formed by putting a conjugate flipped version of each quadrant filter in a quadrant opposite itself. The center sample of a 2-D PNC filter is zero. This paper suggests the use of 1-D and 2-D noncausal (NC) prediction filters instead of PNC filters for random noise attenuation, where an NC filter is a two‐sided filter solved from one set of normal equations. The number of negative and positive lags in the NC filter is the same. The center sample of the filter is zero. The NC prediction filters are more center loaded than PNC filters. They are conjugate symmetric as PNC filters. Also, NC filters are less sensitive than PNC filters to the size of the gate used in their derivation. They can handle amplitude variations along dip directions better than PNC filters. While a PNC prediction filter suppresses more random noise, it damages more signal. On the other hand, NC prediction filters preserve more of the signal and reject less noise for the same total filter length. For high S/N ratio data, a 2-D NC prediction filter preserves geologic features that do not vary in one of the spatial dimensions. In‐line and cross‐line vertical faults are also well preserved with such filters. When faults are obliquely oriented, the filter coefficients adapt to the fault. Spectral properties of PNC and NC filters are very similar.

The old technology [Formula: see text]-[Formula: see text] deconvolution stands for [Formula: see text]-[Formula: see text] domain prediction filtering. Early versions of it are known to create signal leakage during their application. There have been recent papers in geophysical publications comparing [Formula: see text]-[Formula: see text] deconvolution results with the new technologies being proposed. These comparisons will be most effective if the best existing [Formula: see text]-[Formula: see text] deconvolution algorithms are used. This paper describes common [Formula: see text]-[Formula: see text] deconvolution algorithms and studies signal leakage occurring during their application on simple models, which will hopefully provide a benchmark for the readers in choosing [Formula: see text]-[Formula: see text] algorithms for comparison. The [Formula: see text]-[Formula: see text] deconvolution algorithms can be classified by their use of data which lead to transient or transient-free matrices and hence windowed or nonwindowed autocorrelations, respectively. They can also be classified by the direction they are predicting: forward design and apply; forward design and apply followed by backward design and apply; forward design and apply followed by application of a conjugated forward filter in the backward direction; and simultaneously forward and backward design and apply, which is known as noncausal filter design. All of the algorithm types mentioned above are tested, and the results of their analysis are provided in this paper on noise free and noisy synthetic data sets: a single dipping event, a single dipping event with a simple amplitude variation with offset, and three dipping events. Finally, the results of applying the selected algorithms on field data are provided.