The Shuey-Radon transform

Geophysics ◽  
2019 ◽  
Vol 84 (3) ◽  
pp. V197-V206 ◽  
Author(s):  
Ali Gholami ◽  
Milad Farshad
Keyword(s):  
Radon Transform ◽  
Seismic Data ◽  
Matching Pursuit ◽  
Real Data ◽  
Transform Domain ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
Linear System Of Equations ◽  
Matching Pursuit Algorithm ◽  
Zero Offset

The traditional hyperbolic Radon transform (RT) decomposes seismic data into a sum of constant amplitude basis functions. This limits the performance of the transform when dealing with real data in which the reflection amplitudes include the amplitude variation with offset (AVO) variations. We adopted the Shuey-Radon transform as a combination of the RT and Shuey’s approximation of reflectivity to accurately model reflections including AVO effects. The new transform splits the seismic gather into three Radon panels: The first models the reflections at zero offset, and the other two panels add capability to model the AVO gradient and curvature. There are two main advantages of the Shuey-Radon transform over similar algorithms, which are based on a polynomial expansion of the AVO response. (1) It is able to model reflections more accurately. This leads to more focused coefficients in the transform domain and hence provides more accurate processing results. (2) Unlike polynomial-based approaches, the coefficients of the Shuey-Radon transform are directly connected to the classic AVO parameters (intercept, gradient, and curvature). Therefore, the resulting coefficients can further be used for interpretation purposes. The solution of the new transform is defined via an underdetermined linear system of equations. It is formulated as a sparsity-promoting optimization, and it is solved efficiently using an orthogonal matching pursuit algorithm. Applications to different numerical experiments indicate that the Shuey-Radon transform outperforms the polynomial and conventional RTs.

Traveltime and relative geometric spreading approximation in elastic orthorhombic medium

Geophysics ◽  
2020 ◽  
Vol 85 (5) ◽  
pp. C153-C162 ◽  
Author(s):  
Shibo Xu ◽  
Alexey Stovas ◽  
Hitoshi Mikada
Keyword(s):  
Seismic Data ◽  
Real Data ◽  
P Wave ◽  
Form Expression ◽  
Amplitude Variation ◽  
Rational Form ◽  
Amplitude Variation With Offset ◽  
Practical Applications ◽  
Numerical Tests ◽  
Geometric Spreading

Wavefield properties such as traveltime and relative geometric spreading (traveltime derivatives) are highly essential in seismic data processing and can be used in stacking, time-domain migration, and amplitude variation with offset analysis. Due to the complexity of an elastic orthorhombic (ORT) medium, analysis of these properties becomes reasonably difficult, where accurate explicit-form approximations are highly recommended. We have defined the shifted hyperbola form, Taylor series (TS), and the rational form (RF) approximations for P-wave traveltime and relative geometric spreading in an elastic ORT model. Because the parametric form expression for the P-wave vertical slowness in the derivation is too complicated, TS (expansion in offset) is applied to facilitate the derivation of approximate coefficients. The same approximation forms computed in the acoustic ORT model also are derived for comparison. In the numerical tests, three ORT models with parameters obtained from real data are used to test the accuracy of each approximation. The numerical examples yield results in which, apart from the error along the y-axis in ORT model 2 for the relative geometric spreading, the RF approximations all are very accurate for all of the tested models in practical applications.

Three-parameter Radon transform based on shifted hyperbolas

Geophysics ◽  
2018 ◽  
Vol 83 (1) ◽  
pp. V39-V48 ◽  
Author(s):  
Ali Gholami ◽  
Toktam Zand
Keyword(s):  
Radon Transform ◽  
Seismic Data ◽  
High Performance ◽  
Fourier Transforms ◽  
Real Data ◽  
Data Sets ◽  
Radon Transforms ◽  
Slice Theorem ◽  
Ground Roll ◽  
Zero Offset

The focusing power of the conventional hyperbolic Radon transform decreases for long-offset seismic data due to the nonhyperbolic behavior of moveout curves at far offsets. Furthermore, conventional Radon transforms are ineffective for processing data sets containing events of different shapes. The shifted hyperbola is a flexible three-parameter (zero-offset traveltime, slowness, and focusing-depth) function, which is capable of generating linear and hyperbolic shapes and improves the accuracy of the seismic traveltime approximation at far offsets. Radon transform based on shifted hyperbolas thus improves the focus of seismic events in the transform domain. We have developed a new method for effective decomposition of seismic data by using such three-parameter Radon transform. A very fast algorithm is constructed for high-resolution calculations of the new Radon transform using the recently proposed generalized Fourier slice theorem (GFST). The GFST establishes an analytic expression between the [Formula: see text] coefficients of the data and the [Formula: see text] coefficients of its Radon transform, with which a very fast switching between the model and data spaces is possible by means of interpolation procedures and fast Fourier transforms. High performance of the new algorithm is demonstrated on synthetic and real data sets for trace interpolation and linear (ground roll) noise attenuation.

scholarly journals A Broadband Spectrum Sensing Algorithm in TDCS Based on ICoSaMP Reconstruction

2018 ◽  
Vol 173 ◽  
pp. 03073
Author(s):  
Liu Yang ◽  
Ren Qinghua ◽  
Xu Bingzheng ◽  
Li Xiazhao
Keyword(s):  
Time Use ◽  
Matching Pursuit ◽  
Reconstruction Algorithm ◽  
Transform Domain ◽  
Low Snr ◽  
System Noise ◽  
Broadband Spectrum ◽  
Matching Pursuit Algorithm ◽  
The Mean ◽  
Occupancy Rates

In order to solve the problem that the wideband compressive sensing reconstruction algorithm cannot accurately recover the signal under the condition of blind sparsity in the low SNR environment of the transform domain communication system. This paper use band occupancy rates to estimate sparseness roughly, at the same time, use the residual ratio threshold as iteration termination condition to reduce the influence of the system noise. Therefore, an ICoSaMP(Improved Compressive Sampling Matching Pursuit) algorithm is proposed. The simulation results show that compared with CoSaMP algorithm, the ICoSaMP algorithm increases the probability of reconstruction under the same SNR environment and the same sparse degree. The mean square error under the blind sparsity is reduced.

An integrated broadband preprocessing method for towed-streamer seismic data

Geophysics ◽  
2020 ◽  
Vol 85 (2) ◽  
pp. V201-V221 ◽  
Author(s):  
Mehdi Aharchaou ◽  
Erik Neumann
Keyword(s):  
Seismic Data ◽  
High Frequency ◽  
Pressure Data ◽  
Amplitude Variation ◽  
Field Source ◽  
Amplitude Variation With Offset ◽  
Ringing Artifacts ◽  
Joint Application ◽  
Amplitude Compensation ◽  
Unified Method

Broadband preprocessing has become widely used for marine towed-streamer seismic data. In the standard workflow, far-field source designature, receiver and source-side deghosting, and redatuming to mean sea level are applied in sequence, with amplitude compensation for background [Formula: see text] delayed until the imaging or postmigration stages. Thus, each step is likely to generate its own artifacts, quality checking can be time-consuming, and broadband data are only obtained late in this chained workflow. We have developed a unified method for broadband preprocessing — called integrated broadband preprocessing (IBP) — which enables the joint application of all the above listed steps early in the processing sequence. The amplitude, phase, and amplitude-variation-with-offset fidelity of IBP are demonstrated on pressure data from the shallow, deep, and slanted streamers. The integration allows greater sparsity to emerge in the representation of seismic data, conferring clear benefits over the sequential application. Moreover, time sparsity, full dimensionality, and early amplitude [Formula: see text] compensation all have an impact on broadband data quality, in terms of reduced ringing artifacts, improved wavelet integrity at large crossline angles, and fewer residual high-frequency multiples.

2-D continuation operators and their applications

Geophysics ◽  
1996 ◽  
Vol 61 (6) ◽  
pp. 1846-1858 ◽  
Author(s):  
Claudio Bagaini ◽  
Umberto Spagnolini
Keyword(s):  
Seismic Data ◽  
Real Data ◽  
Integral Form ◽  
Amplitude Distribution ◽  
Velocity Model ◽  
Velocity Analysis ◽  
Seismic Data Processing ◽  
Analysis Method ◽  
Standard Tool ◽  
Zero Offset

Continuation to zero offset [better known as dip moveout (DMO)] is a standard tool for seismic data processing. In this paper, the concept of DMO is extended by introducing a set of operators: the continuation operators. These operators, which are implemented in integral form with a defined amplitude distribution, perform the mapping between common shot or common offset gathers for a given velocity model. The application of the shot continuation operator for dip‐independent velocity analysis allows a direct implementation in the acquisition domain by exploiting the comparison between real data and data continued in the shot domain. Shot and offset continuation allow the restoration of missing shot or missing offset by using a velocity model provided by common shot velocity analysis or another dip‐independent velocity analysis method.

Value of information analysis and Bayesian inversion for closed skew-normal distributions: Applications to seismic amplitude variation with offset data

Geophysics ◽  
2014 ◽  
Vol 79 (4) ◽  
pp. R151-R163 ◽  
Author(s):  
Javad Rezaie ◽  
Jo Eidsvik ◽  
Tapan Mukerji
Keyword(s):  
Seismic Data ◽  
Value Of Information ◽  
Bayesian Inversion ◽  
Information Analysis ◽  
Amplitude Variation ◽  
Mean Values ◽  
Amplitude Variation With Offset ◽  
Seismic Amplitude ◽  
Value Of Information Analysis ◽  
Skew Normal

Information analysis can be used in the context of reservoir decisions under uncertainty to evaluate whether additional data (e.g., seismic data) are likely to be useful in impacting the decision. Such evaluation of geophysical information sources depends on input modeling assumptions. We studied results for Bayesian inversion and value of information analysis when the input distributions are skewed and non-Gaussian. Reservoir parameters and seismic amplitudes are often skewed and using models that capture the skewness of distributions, the input assumptions are less restrictive and the results are more reliable. We examined the general methodology for value of information analysis using closed skew normal (SN) distributions. As an example, we found a numerical case with porosity and saturation as reservoir variables and computed the value of information for seismic amplitude variation with offset intercept and gradient, all modeled with closed SN distributions. Sensitivity of the value of information analysis to skewness, mean values, accuracy, and correlation parameters is performed. Simulation results showed that fewer degrees of freedom in the reservoir model results in higher value of information, and seismic data are less valuable when seismic measurements are spatially correlated. In our test, the value of information was approximately eight times larger for a spatial-dependent reservoir variable compared with the independent case.

AVA analysis after velocity-independent DMO and imaging

Geophysics ◽  
1998 ◽  
Vol 63 (2) ◽  
pp. 686-691 ◽  
Author(s):  
Gerald H. F. Gardner ◽  
Anat Canning
Keyword(s):  
Reflection Coefficient ◽  
Peak Amplitude ◽  
Angle Of Incidence ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
The Past ◽  
Reflectivity Function ◽  
Velocity Of Propagation ◽  
Zero Offset ◽  
Amplitude Versus

A common midpoint (CMP) gather usually provides amplitude variation with offset (AVO) information by displaying the reflectivity as the peak amplitude of symmetrical deconvolved wavelets. This puts a reflection coefficient R at every offset h, giving a function R(h). But how do we link h with the angle of incidence, θ, to get the reflectivity function, R(θ)? This is necessary for amplitude versus angle-of-incidence (AVA) analysis. One purpose of this paper is to derive formulas for this linkage after velocity-independent dip-moveout (DMO), done by migrating radial sections, and prestack zero-offset migration. Related studies of amplitude-preserving DMO in the past have dealt with constant-offset DMO but have not given the connection between offset and angle of incidence after processing. The results in the present paper show that the same reflectivity function can be extracted from the imaged volume whether it is produced using radial-trace DMO plus zero-offset migration, constant-offset DMO plus zero-offset migration, or directly by prestack, common-offset migration. The data acquisition geometry for this study consists of parallel, regularly spaced, multifold lines, and the velocity of propagation is constant. Events in the data are caused by an arbitrarily oriented 3-D plane reflector with any reflectivity function. The DMO operation transforms each line of data (m, h, t), i.e., midpoint, half-offset, and time, into an (m1, k, t1) space by Stolt-migrating each radial-plane section of the data, 2h = Ut, with constant velocity U/2. Merging the (m1, k, t1) spaces for all the lines forms an (x, y, k, t1) space, where the first two coordinates are the midpoint location, the third is the new half-offset, and the fourth is the time. Normal moveout (NMO) plus 3-D zero-offset migration of the subspace (x, y, t1) for each k creates a true-amplitude imaged volume (X, Y, k, T). Each peak amplitude in the volume is a reflection coefficient linked to an angle of incidence.

Amplitude preservation of Radon-based multiple-removal filters

Geophysics ◽  
2006 ◽  
Vol 71 (5) ◽  
pp. V123-V126 ◽  
Author(s):  
Ethan J. Nowak ◽  
Matthias G. Imhof
Keyword(s):  
Radon Transform ◽  
Seismic Data ◽  
Transform Domain ◽  
Multiple Reflections ◽  
Avo Analysis ◽  
Amplitude Versus Offset ◽  
Amplitude Preservation ◽  
Amplitude Versus

This study examines the effect of filtering in the Radon transform domain on reflection amplitudes. Radon filters are often used for removal of multiple reflections from normal moveout-corrected seismic data. The unweighted solution to the Radon transform reduces reflection amplitudes at both near and far offsets due to a truncation effect. However, the weighted solutions to the transform produce localized events in the transform domain, which minimizes this truncation effect. Synthetic examples suggest that filters designed in the Radon domain based on a weighted solution to the linear, parabolic, or hyperbolic transforms preserve the near- and far-offset reflection amplitudes while removing the multiples; whereas the unweighted solutions diminish reflection amplitudes which may distort subsequent amplitude-versus-offset (AVO) analysis.

Fracture detection via correlating P-wave amplitude variation with offset and azimuth analysis and well data in eastern central Saudi Arabia

2017 ◽  
Vol 5 (4) ◽  
pp. T531-T544
Author(s):  
Ali H. Al-Gawas ◽  
Abdullatif A. Al-Shuhail
Keyword(s):  
Saudi Arabia ◽  
Seismic Data ◽  
Production Data ◽  
Fracture Zones ◽  
Fracture Detection ◽  
Amplitude Variation ◽  
Data Set ◽  
Amplitude Variation With Offset ◽  
Well Data ◽  
Patch Geometry

The late Carboniferous clastic Unayzah-C in eastern central Saudi Arabia is a low-porosity, possibly fractured reservoir. Mapping the Unayzah-C is a challenge due to the low signal-to-noise ratio (S/N) and limited bandwidth in the conventional 3D seismic data. A related challenge is delineating and characterizing fracture zones within the Unayzah-C. Full-azimuth 3D broadband seismic data were acquired using point receivers, low-frequency sweeps down to 2 Hz, and 6 km patch geometry. The data indicate significant enhancement in continuity and resolution of the reflection data, leading to improved mapping of the Unayzah-C. Because the data set has a rectangular patch geometry with full inline offsets to 6000 m, using amplitude variation with offset and azimuth (AVOA) may be effective to delineate and characterize fracture zones within Unayzah-A and Unayzah-C. The study was undertaken to determine the improvement of wide-azimuth seismic data in fracture detection in clastic reservoirs. The results were validated with available well data including borehole images, well tests, and production data in the Unayzah-A. There are no production data or borehole images within the Unayzah-C. For validation, we had to refer to a comparison of alternative seismic fracture detection methods, mainly curvature and coherence. Anisotropy was found to be weak, which may be due to noise, clastic lithology, and heterogeneity of the reservoirs, in both reservoirs except for along the western steep flank of the study area. These may correspond to some north–south-trending faults suggested by circulation loss and borehole image data in a few wells. The orientation of the long axis of the anisotropy ellipses is northwest–southeast, and it is not in agreement with the north–south structural trend. No correlation was found among the curvature, coherence, and AVOA in Unayzah-A or Unayzah-C. Some possible explanations for the low correlation between the AVOA ellipticity and the natural fractures are a noisy data set, overburden anisotropy, heterogeneity, granulation seams, and deformation.

scholarly journals AVO analysis for high amplitude anomalies using 2D pre-stack seismic data

2022 ◽  
Author(s):  
Lamees N. Abdulkareem ◽  
Keyword(s):  
Seismic Data ◽  
High Amplitude ◽  
Rock Properties ◽  
Fluid Substitution ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
The Real ◽  
North West ◽  
Avo Analysis ◽  
Controlling Parameter

Amplitude variation with offset (AVO) analysis is an 1 efficient tool for hydrocarbon detection and identification of elastic rock properties and fluid types. It has been applied in the present study using reprocessed pre-stack 2D seismic data (1992, Caulerpa) from north-west of the Bonaparte Basin, Australia. The AVO response along the 2D pre-stack seismic data in the Laminaria High NW shelf of Australia was also investigated. Three hypotheses were suggested to investigate the AVO behaviour of the amplitude anomalies in which three different factors; fluid substitution, porosity and thickness (Wedge model) were tested. The AVO models with the synthetic gathers were analysed using log information to find which of these is the controlling parameter on the AVO analysis. AVO cross plots from the real pre-stack seismic data reveal AVO class IV (showing a negative intercept decreasing with offset). This result matches our modelled result of fluid substitution for the seismic synthetics. It is concluded that fluid substitution is the controlling parameter on the AVO analysis and therefore, the high amplitude anomaly on the seabed and the target horizon 9 is the result of changing the fluid content and the lithology along the target horizons. While changing the porosity has little effect on the amplitude variation with offset within the AVO cross plot. Finally, results from the wedge models show that a small change of thickness causes a change in the amplitude; however, this change in thickness gives a different AVO characteristic and a mismatch with the AVO result of the real 2D pre-stack seismic data. Therefore, a constant thin layer with changing fluids is more likely to be the cause of the high amplitude anomalies.

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