3D interpolation of irregular data with a POCS algorithm

Geophysics ◽  
2006 ◽  
Vol 71 (6) ◽  
pp. E91-E97 ◽  
Author(s):  
Ray Abma ◽  
Nurul Kabir
Keyword(s):  
Seismic Data ◽  
Convex Sets ◽  
Fourier Transforms ◽  
Higher Dimensions ◽  
Seismic Surveys ◽  
Projection Onto Convex Sets ◽  
Irregular Data ◽  
Restoration Method ◽  
The Cost

Seismic surveys generally have irregular areas where data cannot be acquired. These data should often be interpolated. A projection onto convex sets (POCS) algorithm using Fourier transforms allows interpolation of irregularly populated grids of seismic data with a simple iterative method that produces high-quality results. The original 2D image restoration method, the Gerchberg-Saxton algorithm, is extended easily to higher dimensions, and the 3D version of the process used here produces much better interpolations than typical 2D methods. The only parameter that makes a substantial difference in the results is the number of iterations used, and this number can be overestimated without degrading the quality of the results. This simplicity is a significant advantage because it relieves the user of extensive parameter testing. Although the cost of the algorithm is several times the cost of typical 2D methods, the method is easily parallelized and still completely practical.

scholarly journals Low-Dose Computed Tomography Filtering Using Geodesic Distances

2020 ◽  
Author(s):  
Daniel A. Góes ◽  
Nelson D. A. Mascarenhas
Keyword(s):  
Computed Tomography ◽  
Low Dose ◽  
Convex Sets ◽  
Projection Onto Convex Sets ◽  
Local Means ◽  
Gamma Distributions ◽  
Non Local ◽  
Geodesic Distances ◽  
Low Dose Computed Tomography

Due to the concerns related to patient exposure to X-ray, the dosage used in computed tomography must be reduced (Low-dose Computed Tomography - LDCT). One of the effects of LDCT is the degradation in the quality of the final reconstructed image. In this work, we propose a method of filtering LDCT sinograms that are subject to signal-dependent Poisson noise. To filter this type of noise, we use a Bayesian approach, changing the Non-local Means (NLM) algorithm to use geodesic stochastic distances for Gamma distribution, the conjugate prior to Poisson, as a similarity metric between each projection point. Among the geodesic distances evaluated, we found a closed solution for the Shannon entropy for Gamma distributions. We compare our method with the following methods based on NLM: PoissonNLM, Stochastic Poisson NLM, Stochastic Gamma NLM and the original NLM after Anscombe transform. We also compare with BM3D after Anscombe transform. Comparisons are made on the final images reconstructed by the Filtered-Back Projection (FBP) and Projection onto Convex Sets (POCS) methods using the metrics PSNR and SSIM.

Imaging the near surface using velocity inversions of ultra-high-density 3D seismic data

2021 ◽  
Vol 40 (8) ◽  
pp. 584-589
Author(s):  
Tim Dean ◽  
Margarita Pavlova ◽  
Matthew Grant ◽  
Martin Bayly ◽  
Denis Sweeney ◽  
...  
Keyword(s):  
Seismic Data ◽  
Coal Industry ◽  
High Density ◽  
Rock Properties ◽  
3D Seismic ◽  
Near Surface ◽  
Seismic Surveys ◽  
Weathered Layer ◽  
History Of ◽  
The Cost

Within the coal industry, there is a rich history of the use of the surface seismic method, principally for exploration and employing sparse 2D lines for broad resource delineation and structural modeling. However, the acquisition of 3D seismic surveys adjacent to open-cut mines (from which the majority of coal is extracted) for superior resource definition ahead of their expansion has been explored only recently. Although the reflection results are extremely useful and enable the mapping of faults with sub-5 m throws, there is still interest in determining if the seismic data can be used to image both structures and rock properties in the near surface. In addition to mapping near-surface structures that have geotechnical implications, the ability to map the overburden properties (which can be quite heterogeneous) is desired. Before mining activities can take place, the overburden needs to be removed. The cost of the removal method employed is directly affected by the depth of the weathered layer and rock properties. In particular, hardness can vary significantly. In this paper, we demonstrate how high-density seismic data originally acquired for reflection processing can be processed to generate high-resolution velocity (both VS and VP) depth volumes, which enable the successful identification of shallow structures and the creation of highly detailed near-surface rock-property volumes.

RECENT DEVELOPMENTS IN BOREHOLE SEISMIC SURVEYS, OFFSHORE NORTHERN AUSTRALIA

1991 ◽  
Vol 31 (1) ◽  
pp. 250
Author(s):  
A. Sutherland ◽  
P.M. Smith
Keyword(s):  
Shear Wave ◽  
Seismic Data ◽  
Seismic Energy ◽  
Hard Water ◽  
Main Body ◽  
Northern Australia ◽  
Seismic Surveys ◽  
Sensor Module ◽  
Borehole Seismic

Offshore northern Australia has long been recognised as a region where the quality of seismic data is frequently adversely affected by several factors which include the following.The presence of a hard water bottom.The presence of carbonate units in the Eocene and Paleocene which are highly reflective and reduce the amount of seismic energy which penetrates to the deeper target horizons. These also produce interbedded multiples which are difficult to remove from the seismic data.Complex shallow faulting which causes ray path distortion and disperses the seismic energy.The confidence with which well data can be tied to the poor quality seismic data through well velocity surveys is further reduced by the complicated deeper faulting associated with the structures drilled and the low acoustic impedance contrast at the target horizon.Borehole seismic surveys provide the most reliable link between the subsurface intersected by a well and seismic data. The recent introduction of a new borehole seismic tool has improved the quality of Vertical Seismic Profiles (VSPs) acquired. This tool has three component geophones mounted in a sensor module which is isolated from the main body of the tool by springs which minimise the effect of source-generated noise.This reduction in sensitivity to the source-generated noise has allowed the introduction of more powerful source arrays to improve the signal to noise ratio. The use of source arrays has increased the bandwidth of the seismic impulse and decreased the effect of the bubble pulse.The quality of the horizontal component VSP data recorded using the new tool has also improved significantly and this has increased the possibility of detecting mode converted reflected and transmitted shear wave energy and the more accurate measurement of shear wave velocities.

Compressive sensing for seismic data reconstruction via fast projection onto convex sets based on seislet transform

2016 ◽  
Vol 130 ◽  
pp. 194-208 ◽  
Author(s):  
Shuwei Gan ◽  
Shoudong Wang ◽  
Yangkang Chen ◽  
Xiaohong Chen ◽  
Weiling Huang ◽  
...  
Keyword(s):  
Compressive Sensing ◽  
Seismic Data ◽  
Convex Sets ◽  
Data Reconstruction ◽  
Projection Onto Convex Sets ◽  
Seismic Data Reconstruction
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