Stewart Trickett

Rank-Reduction-Based Trace Interpolation

Summary In previous papers we described a family of multidimensional filters to suppress random noise based on matrix-rank reduction of constant-frequency slices. Here we extend these filters to perform multidimensional trace interpolation. This requires rank reduction when some, perhaps most, of the matrix elements are unknown, a procedure called matrix completion or matrix imputation. We show how this new interpolator improves the spatial resolution of 3D data when applied prior to prestack migration.

F-xy Cadzow Noise Suppression

Summary Cadzow filtering has previously been applied along constant-frequency slices to remove random noise from 2-D seismic data. Here I extend Cadzow filtering to two or more spatial dimensions. The resulting method is superior to both f-xy prediction (deconvolution) and projection filtering, especially for very noisy data. In particular, it preserves signal better and can be made much harsher.

Prestack rank‐reducing noise suppression: Theory

Prestack random-noise suppression is an important but inadequately solved problem in land seismic processing. Two previously described techniques eigenimage and Cadzow filtering both use matrix-rank reduction on constant-frequency slices. These can be combined into a novel hybrid method with properties from both, forming a general class of noise suppressors that is powerful, versatile, and can be applied in any number of spatial dimensions. These methods can be shown to handle dipping data, irregularly spaced shots, AVO effects, and statics. A companion paper in this conference shows how to apply these techniques to prestack data and gives examples.

Reducing Acquisition Costs With Random Sampling And Multidimensional Interpolation

Seismic data must be migrated, preferably before stack. Prestack migration gives best results when traces are evenly and densely sampled in inline CMP, crossline CMP, offset, and azimuth (Vermeer, 2010). Otherwise one can generate artifacts such as lateral smearing, migration smiles, and acquisition footprint. Acquisition can not economically deliver such sampling. Recently, however, 5D prestack trace interpolation (in reality, interpolation in four spatial dimensions) has become commonplace (Abma, 2010; Trad 2009; Trickett et al., 2010). Its principle goal is to provide a data set to prestack migration which is well sampled in all spatial dimensions. Figure 1: Traces acquired and processed. On the left is the traditional situation, on the right is the current situation.

Maximum-likelihood-estimation Stacking

Common-midpoint (CMP) stacking is often done using the arithmetic mean. There are good reasons for this: it is simple, linear, and is optimal if the noise has a Gaussian distribution. Where the noise is not Gaussian, however, the mean does a poor job, resulting in a stacked section contaminated by erratic noise. By estimating the probability distribution of the noise as it varies with time and CMP, and stacking using a maximum-likelihood estimator for that distribution, we get a result that is identical to a normal stack where the noise is Gaussian, but is far cleaner where the noise is erratic.

The effect of stretch free stacking on a clastic exploration play in Alberta, Canada

A 3-D seismic survey was shot over a set of spatially complex channel leads that were thought to be charged with both gas and water. The prospects being investigated suffered from spatial and temporal reservoir resolution problems as well as fluid risks. In the attempt to address these challenges, the seismic data was processed using a new algorithm that promised to handle the long offset information advantageously. This algorithm is a new process that is meant to eliminate NMO stretch effects in the stack. Since fluid estimation was of such concern in this dataset, the algorithm was also used to create NMO stretch free gathers for AVO analysis. The results of this work seemed to be excellent. Numerous new prospects were identified on the 3-D survey, one of which could not have been identified without the stretch free stack process, or SFS (for brevity), and AVO analysis. As is sometimes the case, the most difficult and interesting task became that of understanding what the SFS process actually did to the data and why.

Prestack rank-reducing noise suppression: practice

Prestack random-noise suppression is a difficult problem in land seismic processing. A companion paper in this conference describes the theory behind a family of rankreduction methods applied in the constant-frequency domain. These methods, which include eigenimage, Cadzow, and hybrid filters, have properties which appear ideal for performing prestack noise suppression. Here we show how to apply these methods in practice to improve signal-to-noise and prepare data for AVO analysis.