De‐aliased, high‐resolution radon transforms

Herrmann, P.; Mojesky, Todd; Magesan, M.; Hugonnet, P.

doi:10.1190/1.1815818

Cited by 96 publications

(27 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Formula (12) can be solved very efficiently by CG algorithm, and details of the strategy can be found in many literatures (TARANTOLA, 1987;MENKE, 1984;SACCHI and PORSANI, 1999;TRAD et al, 2002;JI, 2006). The weighting and the preconditioning matrices W d and W m at the i-th iteration of the CG algorithm are determined by using diagonal matrices: diag(W d ) i = |r i | -1/2 and diag(W m ) i = |m i | 1/2 , respectively, where m i is the Radon model at i-th iteration of the CG algorithm, r i is the standard deviation of residual r (HERRMANN et al, 2000;TRAD et al, 2002TRAD et al, , 2003JI, 2006).…”

Section: High Resolution Lrtmentioning

confidence: 99%

Rayleigh-Wave Dispersive Energy Imaging Using a High-Resolution Linear Radon Transform

Luo

Xia

Miller

et al. 2008

Pure appl. geophys.

232

View full text Add to dashboard Cite

Multichannel Analysis of Surface Waves (MASW) analysis is an efficient tool to obtain the vertical shear-wave profile. One of the key steps in the MASW method is to generate an image of dispersive energy in the frequency-velocity domain, so dispersion curves can be determined by picking peaks of dispersion energy. In this paper, we propose to image Rayleigh-wave dispersive energy by high-resolution linear Radon transform (LRT). The shot gather is first transformed along the time direction to the frequency domain and then the Rayleigh-wave dispersive energy can be imaged by high-resolution LRT using a weighted preconditioned conjugate gradient algorithm. Synthetic data with a set of linear events are presented to show the process of generating dispersive energy. Results of synthetic and real-world examples demonstrate that, compared with the slant stacking algorithm, high-resolution LRT can improve the resolution of images of dispersion energy by more than 50%.

show abstract

Section: High Resolution Lrtmentioning

confidence: 99%

Rayleigh-Wave Dispersive Energy Imaging Using a High-Resolution Linear Radon Transform

Luo

Xia

Miller

et al. 2008

Pure appl. geophys.

232

View full text Add to dashboard Cite

show abstract

“…If primaries and multiples show different moveout behavior, algorithms are available that allow separation of primaries and multiples in a transform domain. Successful moveout-based methods use the Radon transform ͑Hampson, 1986; Herrmann et al, 2000;Trad et al, 2003͒. A weak point of moveout algorithms is that they are less effective in the situation of complex wavefields ͑e.g., nonhyperbolic wavefronts͒.…”

Section: Introductionmentioning

confidence: 99%

Imaging of multiple reflections

2006

View full text Add to dashboard Cite

Current multiple-removal algorithms in seismic processing use either differential moveout or predictability. If the differential moveout between primaries and multiples is small, prediction is the only option available. In the last decade, multidimensional prediction-error filtering by weighted convolution, such as surface-related multiple elimination ͑SRME͒, have proved to be very successful in practice. So far, multiples have been considered as noise and have been discarded after the removal process. In this paper, we argue that multiple reflections contain a wealth of information that can be used in seismic processing to improve the resolution of reservoir images beyond current capability. In the near future, one may expect that the so-called weighted-crosscorrelation ͑WCC͒ concept may offer an attractive alternative in approaching the multiple problem. WCC creates an option to avoid the adaptive subtraction process as applied in prediction-error algorithms. Moreover, it allows the transformation of multiples into primaries. The latter means that seismic imaging with primaries and multiples ͑nonlinear process͒ can be implemented by a sequence of linear processes, including the transformation of multiples into primaries and the imaging of primaries.

show abstract

“…To speed up the computation, the Fourier image of the preceding frequency component can be used as the initial estimate of the Fourier image for the current frequency to set the weighting coefficients. This strategy was used by Herrmann et al (2000) in the parabolic Radon transform.…”

Section: The Constraint Matrixmentioning

confidence: 99%

“…The so-called SCLS inversion method has been applied to seismic signal processing, for example, in the Radon transform to overcome the difficulty caused by limited aperture of the input data set and to make the Radon transform image more focused (Thorson and Claerbout, 1985;Sacchi and Ulrych, 1995;Ulrych et al, 1999;Herrmann et al, 2000;Trad et al, 2003). With an improved (high-resolution) Radon transform image, one is able to separate the multiple reflections and the primary reflections in the Radon demultiple processing.…”

Section: Introductionmentioning

confidence: 99%

Sparseness‐constrained least‐squares inversion: Application to seismic wave reconstruction

Wang¹

2003

GEOPHYSICS

View full text Add to dashboard Cite

The spectrum of a discrete Fourier transform (DFT) is estimated by linear inversion, and used to produce desirable seismic traces with regular spatial sampling from an irregularly sampled data set. The essence of such a wavefield reconstruction method is to solve the DFT inverse problem with a particular constraint which imposes a sparseness criterion on the least-squares solution. A working definition for the sparseness constraint is presented to improve the stability and efficiency. Then a sparseness measurement is used to measure the relative sparseness of the two DFT spectra obtained from inversion with or without sparseness constraint. It is a pragmatic indicator about the magnitude of sparseness needed for wavefield reconstruction. For seismic trace regularization, an antialiasing condition must be fulfilled for the regularizing trace interval, whereas optimal trace coordinates in the output can be obtained by minimizing the distances between the newly generated traces and the original traces in the input. Application to real seismic data reveals the effectiveness of the technique and the significance of the sparseness constraint in the least-squares solution.

show abstract

De‐aliased, high‐resolution radon transforms

Cited by 96 publications

References 5 publications

Rayleigh-Wave Dispersive Energy Imaging Using a High-Resolution Linear Radon Transform

Rayleigh-Wave Dispersive Energy Imaging Using a High-Resolution Linear Radon Transform

Imaging of multiple reflections

Sparseness‐constrained least‐squares inversion: Application to seismic wave reconstruction

Contact Info

Product

Resources

About