Linear and parabolic τ-<i>p</i> transforms revisited

Zhou, Binzhong; Greenhalgh, Stewart

doi:10.1190/1.1443669

Cited by 66 publications

(26 citation statements)

References 28 publications

(54 reference statements)

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“…The LRT has various applications (TURNER, 1990;DUNNE and BERESFORD, 1995;ZHOU and GREENHALGH, 1994;LUIGIA and TATIANA, 2004;MAELAND, 2004;WILSON and GUITTON, 2007). After a temporal Fourier transformation, the LRT can be calculated for each temporal frequency component f :…”

Section: Standard Lrtmentioning

confidence: 99%

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

Luo

Xia

Miller

et al. 2008

Pure appl. geophys.

225

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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%.

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Section: Standard Lrtmentioning

confidence: 99%

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

Luo

Xia

Miller

et al. 2008

Pure appl. geophys.

225

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“…This effect is described in Dobbs et al (1990) as a filter in the 1-D waveform inversion. Zhou and Greenhalgh (1994) have suggested that a deconvolution in the p-direction of the transform domain may reduce the artifacts caused by the finite aperture. In the numerical calculation of the integral over x in equations (3) and (8), we simply use a truncated summation to approximate the infinite integral of the transform.…”

Section: Truncation Effectsmentioning

confidence: 99%

“…The τ -p transform clearly separates different reflection events that may be superposed in the t-x domain, as is illustrated in the example of Figures 1 and 2; thus the transform facilitates interpretation. Most of the examples of τ -p transformations in the literature (e.g., Schultz and Claerbout, 1978;McMechan and Ottolini, 1980;Stoffa et al, 1981;Zhou and Greenhalgh, 1994) are based on the 2-D slant stack or Radon transform, with the simple summation of the signal along lines of constant slope within the data and the possible addition of a semblance, or autocorrelation criterion to enhance noise rejection. This method is a sensitive means of velocity filtering for selecting waves with apparent slowness p and intercept time τ .…”

Section: Introductionmentioning

confidence: 99%

Point‐source τ‐p transform: A review and comparison of computational methods

Wang

Houseman

1997

GEOPHYSICS

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The τ -p transformation of reflection seismic data excited by a point source requires a cylindrical slant stack, which includes compensation for the phase shift and geometrical spreading associated with cylindrical geometry. Using a simple test model, we review and compare the different computational methods used for the cylindrical slant stack. The two major method types are the BesselFourier transform (BFT) method and a set of methods (TD2D, TDX, TDTC and TDTS) based on timedomain convolution. The stack integral in each of these approaches can be separated into two parts, with the part corresponding to the contribution of incoming waves being negligible for large ray parameter p. Neglecting the latter term for large p generally avoids a major problem caused by aliasing between time and space domains.The TDTS method introduced here has the advantage of being expressed in terms of a conventional 2-D slant stack (weighted by offset x) plus a correction term. This formulation facilitates a quantitative comparison of the 3-D cylindrical slant stack with a 2-D slant stack. The TDTS method compares favorably with the TD2D method, in which the cylindrical slant stack is expressed as a weighted integral of the 2-D slant stacks. TDTS avoids the singular weighting function needed in the integral for the TD2D method, and therefore has less problems with numerical noise. For all of the methods considered, the accuracy of the map transformation is limited by the spatial and temporal resolution of the test data set. Some corrections to previously published methods are also provided.

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“…Depending on the type of the integration path, several forms of the Radon transform have been introduced: the linear, the parabolic and the hyperbolic RT. The most popular is the linear RT, widely used in seismic data processing, where it is commonly known as slant-stack or -p transform (Durrani and Bisset, 1984;Beylkin, 1987;Yilmaz, 1987;Zhou and Greenhalgh, 1994). For the linear RT the integration path is a straight line with intercept and slope p in the x-t plane.…”

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confidence: 99%

Identification and removal of above‐ground spurious signals in GPR archaeological prospecting

Nuzzo

2005

Archaeological Prospection

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Ground-penetratingradar (GPR) isa shallowgeophysicalmethodincreasinglyusedinarchaeological prospecting to detect buried remains and to map the stratigraphy of the uppermost earth layers embodying the archaeological features.The GPR sections, however, can be contaminated by spurious correlated signals caused by above-ground obstacles (buildings, trees, fences, power lines) placed either in-line or off-line with respect to the profile (surface scattering).In the case study presented this problemis analysed fora 35 MHz GPR survey carried out for stratigraphicalpurposesin the archaeologicalsite ofthe Roman Shipsnear Pisa (Italy).Theinvestigationinsidethearchaeologicalexcavation, whenthelevelwasabout 5 mbelow thegroundsurface, producedaseveresurface scatteringproblem caused by the iron sheet-piling protecting the excavation walls and bordering some ofthe partly excavated boats. An attempt to interpret the profiles was carried out in a zone where the relatively simple geometry of the metallic enclosure allowed understanding of the possible origin of spurious events, also thanks to the high density of profiles acquired along two orthogonal directions. Migration at the air velocityand geometrical considerationshelped the identification of hyperbolic and slightly slanted featuresassurface scatteringphenomena from different sidesoftheiron sheet-piling.A simplebut original subtraction procedure was successful for the attenuation of some of the spurious reflections. After this partialremoval, other spurious signals could be recognized more easilyas well as two weak subhorizontal reflections of probable stratigraphical meaning. Subsequently, filtering procedures based on f-k and Radon transform methodswere tried to further reduce the spurious signals, thus enhancing the visibility of the interesting reflections

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Linear and parabolic τ-p transforms revisited

Cited by 66 publications

References 28 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

Point‐source τ‐p transform: A review and comparison of computational methods

Identification and removal of above‐ground spurious signals in GPR archaeological prospecting

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