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  • 1
    Electronic Resource
    Electronic Resource
    L-moments and C-moments (2000)
    Springer
    Stochastic environmental research and risk assessment 14 (2000), S. 50-68 
    Details
    ISSN: 1436-3259
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract  It is well known that the computation of higher order statistics, like skewness and kurtosis, (which we call C-moments) is very dependent on sample size and is highly susceptible to the presence of outliers. To obviate these difficulties, Hosking (1990) has introduced related statistics called L-moments. We have investigated the relationship of these two measures in a number of different ways. Firstly, we show that probability density functions (pdf ) that are estimated from L-moments are superior estimates to those obtained using C-moments and the principle of maximum entropy. C-moments computed from these pdf's are not however, contrary to what one may have expected, better estimates than those estimated from sample statistics. L-moment derived distributions for field data examples appear to be more consistent sample to sample than pdf 's determined by conventional means. Our observations and conclusions have a significant impact on the use of the conventional maximum entropy procedure which typically uses C-moments from actual data sets to infer probabilities.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s004770050004
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    Paper (German National Licenses)
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  • 2
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    In situ evidence for frequency dependence of near-surface Q (2016)
    Oxford University Press
    Details
    Publication Date: 2016-01-02
    Description: The frequency dependence of the quality factor Q has long been predicted by mathematical modelling and laboratory measurements; however, in situ evidence from seismic surveys is still lacking. We have conducted the cross-hole seismic surveys to investigate the near-surface seismic attenuation in the Daqing oilfield in northeastern China. The seismic waves were fired in a source hole of 40 m from the bottom to the surface at an interval of 1 m and were recorded in a receiver hole of 40 m by two geophones with one at the surface and the other one at the bottom. The direct waves were extracted to avoid the noise disturbance and the reflection interference, and the attenuations without the effects of the source signature and the receiver coupling were estimated by a method we proposed. The nonlinear attenuations were observed and fitted using the power-law-based Q . The reliability of Q estimate was verified by the high similarity between the real and the simulated attenuations. Therefore, the experiment we have conducted can be treated as a reliable evidence for the frequency dependence of near-surface  Q .
    Keywords: Seismology
    Print ISSN: 0956-540X
    Electronic ISSN: 1365-246X
    Topics: Geosciences
    Published by Oxford University Press on behalf of The Deutsche Geophysikalische Gesellschaft (DGG) and the Royal Astronomical Society (RAS).
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  • 3
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    Robust reduced-rank filtering for erratic seismic noise attenuation (2015)
    Society of Exploration Geophysicists (SEG)
    Details
    Publication Date: 2015-01-21
    Description: Singular spectrum analysis (SSA) or Cadzow reduced-rank filtering is an efficient method for random noise attenuation. SSA starts by embedding the seismic data into a Hankel matrix. Rank reduction of this Hankel matrix followed by antidiagonal averaging is utilized to estimate an enhanced seismic signal. Rank reduction is often implemented via the singular value decomposition (SVD). The SVD is a nonrobust matrix factorization technique that leads to suboptimal results when the seismic data are contaminated by erratic noise. The term erratic noise designates non-Gaussian noise that consists of large isolated events with known or unknown distribution. We adopted a robust low-rank factorization that permitted use of the SSA filter in situations in which the data were contaminated by erratic noise. In our robust SSA method, we replaced the quadratic error criterion function that yielded the truncated SVD solution by a bisquare function. The Hankel matrix was then approximated by the product of two lower dimensional factor matrices. The iteratively reweighed least-squares method was used to approximately solve for the optimal robust factorization. Our algorithm was tested with synthetic and real data. In our synthetic examples, the data were contaminated with band-limited Gaussian noise and erratic noise. Then, denoising was carried out by means of $$f\hbox{ - }x$$ deconvolution, the classical SSA method, and the proposed robust SSA method. The $$f\hbox{ - }x$$ deconvolution and the classical SSA method failed to properly eliminate the noise and to preserve the desired signal. On the other hand, the robust SSA method was found to be immune to erratic noise and was able to preserve the desired signal. We also tested the robust SSA method with a data set from the Western Canadian Sedimentary Basin. The results with this data set revealed improved denoising performance in portions of data contaminated with erratic noise.
    Print ISSN: 0016-8033
    Electronic ISSN: 1942-2156
    Topics: Geosciences , Physics
    Published by Society of Exploration Geophysicists (SEG)
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  • 4
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    A fast reduced-rank interpolation method for prestack seismic volumes that depend on four spatial dimensions (2013)
    Society of Exploration Geophysicists (SEG)
    Details
    Publication Date: 2013-02-07
    Description: Rank reduction strategies can be employed to attenuate noise and for prestack seismic data regularization. We present a fast version of Cadzow reduced-rank reconstruction method. Cadzow reconstruction is implemented by embedding 4D spatial data into a level-four block Toeplitz matrix. Rank reduction of this matrix via the Lanczos bidiagonalization algorithm is used to recover missing observations and to attenuate random noise. The computational cost of the Lanczos bidiagonalization is dominated by the cost of multiplying a level-four block Toeplitz matrix by a vector. This is efficiently implemented via the 4D fast Fourier transform. The proposed algorithm significantly decreases the computational cost of rank-reduction methods for multidimensional seismic data denoising and reconstruction. Synthetic and field prestack data examples are used to examine the effectiveness of the proposed method.
    Print ISSN: 0016-8033
    Electronic ISSN: 1942-2156
    Topics: Geosciences , Physics
    Published by Society of Exploration Geophysicists (SEG)
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  • 5
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    Microseismic source imaging in a compressed domain (2014)
    Oxford University Press
    Details
    Publication Date: 2014-07-03
    Description: Microseismic monitoring is an essential tool for the characterization of hydraulic fractures. Fast estimation of the parameters that define a microseismic event is relevant to understand and control fracture development. The amount of data contained in the microseismic records however, poses a challenge for fast continuous detection and evaluation of the microseismic source parameters. Work inspired by the emerging field of Compressive Sensing has showed that it is possible to evaluate source parameters in a compressed domain, thereby reducing processing time. This technique performs well in scenarios where the amplitudes of the signal are above the noise level, as is often the case in microseismic monitoring using downhole tools. This paper extends the idea of the compressed domain processing to scenarios of microseismic monitoring using surface arrays, where the signal amplitudes are commonly at the same level as, or below, the noise amplitudes. To achieve this, we resort to the use of an imaging operator, which has previously been found to produce better results in detection and location of microseismic events from surface arrays. The operator in our method is formed by full-waveform elastodynamic Green's functions that are band-limited by a source time function and represented in the frequency domain. Where full-waveform Green's functions are not available, ray tracing can also be used to compute the required Green's functions. Additionally, we introduce the concept of the compressed inverse, which derives directly from the compression of the migration operator using a random matrix. The described methodology reduces processing time at a cost of introducing distortions into the results. However, the amount of distortion can be managed by controlling the level of compression applied to the operator. Numerical experiments using synthetic and real data demonstrate the reductions in processing time that can be achieved and exemplify the process of selecting the compression rate that produces a tolerable amount of distortion into the results.
    Keywords: Seismology
    Print ISSN: 0956-540X
    Electronic ISSN: 1365-246X
    Topics: Geosciences
    Published by Oxford University Press on behalf of The Deutsche Geophysikalische Gesellschaft (DGG) and the Royal Astronomical Society (RAS).
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  • 6
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    Vector reconstruction of multicomponent seismic data (2013)
    Society of Exploration Geophysicists (SEG)
    Details
    Publication Date: 2013-07-13
    Description: A multicomponent seismic record was transformed to the frequency-wavenumber domain using the quaternion Fourier transform. This transform was integrated into the projection onto convex sets algorithm to allow for the reconstruction of vector signals. The method took advantage of the spectral overlap of components in the frequency-wavenumber domain. The results of the method were compared with standard component-by-component reconstruction. Results were found for synthetic and real data including an example of 5D reconstruction of a converted-wave data set acquired over a heavy oil reservoir. We found an improvement in reconstruction quality producing fully sampled radial and transverse offset-azimuth gathers with a preserved vector relationship.
    Print ISSN: 0016-8033
    Electronic ISSN: 1942-2156
    Topics: Geosciences , Physics
    Published by Society of Exploration Geophysicists (SEG)
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  • 7
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    Microseismic source imaging in a compressed domain (2014)
    Oxford University Press
    Details
    Publication Date: 2014-06-30
    Description: Microseismic monitoring is an essential tool for the characterization of hydraulic fractures. Fast estimation of the parameters that define a microseismic event is relevant to understand and control fracture development. The amount of data contained in the microseismic records however, poses a challenge for fast continuous detection and evaluation of the microseismic source parameters. Work inspired by the emerging field of Compressive Sensing has showed that it is possible to evaluate source parameters in a compressed domain, thereby reducing processing time. This technique performs well in scenarios where the amplitudes of the signal are above the noise level, as is often the case in microseismic monitoring using downhole tools. This paper extends the idea of the compressed domain processing to scenarios of microseismic monitoring using surface arrays, where the signal amplitudes are commonly at the same level as, or below, the noise amplitudes. To achieve this, we resort to the use of an imaging operator, which has previously been found to produce better results in detection and location of microseismic events from surface arrays. The operator in our method is formed by full-waveform elastodynamic Green's functions that are band-limited by a source time function and represented in the frequency domain. Where full-waveform Green's functions are not available, ray tracing can also be used to compute the required Green's functions. Additionally, we introduce the concept of the compressed inverse, which derives directly from the compression of the migration operator using a random matrix. The described methodology reduces processing time at a cost of introducing distortions into the results. However, the amount of distortion can be managed by controlling the level of compression applied to the operator. Numerical experiments using synthetic and real data demonstrate the reductions in processing time that can be achieved and exemplify the process of selecting the compression rate that produces a tolerable amount of distortion into the results.
    Keywords: Seismology
    Print ISSN: 0956-540X
    Electronic ISSN: 1365-246X
    Topics: Geosciences
    Published by Oxford University Press on behalf of The Deutsche Geophysikalische Gesellschaft (DGG) and the Royal Astronomical Society (RAS).
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  • 8
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    Elastic least-squares one-way wave-equation migration (2017)
    Society of Exploration Geophysicists (SEG)
    Details
    Publication Date: 2017-05-31
    Description: Least-squares migration seeks a reflectivity model that fits the observed data. It is used to compensate for acquisition noise, poor sampling of sources and receivers on the surface, as well as poor illumination of the subsurface. To date, least-squares migration has been mainly restricted to the imaging of acoustic wavefields. We have developed an extension of one-way wave-equation least-squares migration for elastic wavefields in isotropic media. Least-squares migration is an iterative method that requires a forward and an adjoint operator. In elastic least-squares one-way wave-equation migration, the forward operator generates data components from multiparameter images by recursive wavefield decomposition, extrapolation, and recomposition. Conversely, the adjoint operator generates multiparameter images from data components by recursively applying the adjoint of the wavefield recomposition, extrapolation, and wavefield decomposition operators. We use an extended imaging condition and regularize the inversion by applying a smoothing filter on the depth-angle axes of each common image point gather to reduce the effect of source/receiver sampling, noise, and crosstalk artifacts. Elastic least-squares migration is able to compensate for irregular subsurface illumination in elastic imaging and provides an alternative approach to interpolation and wavefield separation of multicomponent seismic data.
    Print ISSN: 0016-8033
    Electronic ISSN: 1942-2156
    Topics: Geosciences , Physics
    Published by Society of Exploration Geophysicists (SEG)
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  • 9
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    Restricted model domain time Radon transforms (2016)
    Society of Exploration Geophysicists (SEG)
    Details
    Publication Date: 2016-10-08
    Description: The coefficients that synthesize seismic data via the hyperbolic Radon transform (HRT) are estimated by solving a linear-inverse problem. In the classical HRT, the computational cost of the inverse problem is proportional to the size of the data and the number of Radon coefficients. We have developed a strategy that significantly speeds up the implementation of time-domain HRTs. For this purpose, we have defined a restricted model space of coefficients applying hard thresholding to an initial low-resolution Radon gather. Then, an iterative solver that operated on the restricted model space was used to estimate the group of coefficients that synthesized the data. The method is illustrated with synthetic data and tested with a marine data example.
    Print ISSN: 0016-8033
    Electronic ISSN: 1942-2156
    Topics: Geosciences , Physics
    Published by Society of Exploration Geophysicists (SEG)
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  • 10
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    L-moments and C-moments (2000)
    Springer
    Details
    Publication Date: 2000-01-01
    Print ISSN: 1436-3240
    Electronic ISSN: 1436-3259
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Published by Springer
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