Scattering‐angle migration of ocean‐bottom seismic data in weakly anisotropic media

Geophysics ◽  
2003 ◽  
Vol 68 (2) ◽  
pp. 641-655 ◽  
Author(s):  
Anders Sollid ◽  
Bjørn Ursin
Keyword(s):  
Seismic Data ◽  
Large Angle ◽  
Computational Cost ◽  
Synthetic Data ◽  
Transversely Isotropic ◽  
Real Data ◽  
Image Point ◽  
Ocean Bottom ◽  
Weak Anisotropy ◽  
Scattering Angle

Scattering‐angle migration maps seismic prestack data directly into angle‐dependent reflectivity at the image point. The method automatically accounts for triplicated rayfields and is easily extended to handle anisotropy. We specify scattering‐angle migration integrals for PP and PS ocean‐bottom seismic (OBS) data in 3D and 2.5D elastic media exhibiting weak contrasts and weak anisotropy. The derivation is based on the anisotropic elastic Born‐Kirchhoff‐Helmholtz surface scattering integral. The true‐amplitude weights are chosen such that the amplitude versus angle (AVA) response of the angle gather is equal to the Born scattering coefficient or, alternatively, the linearized reflection coefficient. We implement scattering‐angle migration by shooting a fan of rays from the subsurface point to the acquisition surface, followed by integrating the phase‐ and amplitude‐corrected seismic data over the migration dip at the image point while keeping the scattering‐angle fixed. A dense summation over migration dip only adds a minor additional cost and enhances the coherent signal in the angle gathers. The 2.5D scattering‐angle migration is demonstrated on synthetic data and on real PP and PS data from the North Sea. In the real data example we use a transversely isotropic (TI) background model to obtain depth‐consistent PP and PS images. The aim of the succeeding AVA analysis is to predict the fluid type in the reservoir sand. Specifically, the PS stack maps the contrasts in lithology while being insensitive to the fluid fill. The PP large‐angle stack maps the oil‐filled sand but shows no response in the brine‐filled zones. A comparison to common‐offset Kirchhoff migration demonstrates that, for the same computational cost, scattering‐angle migration provides common image gathers with less noise and fewer artifacts.

Depth-consistent reflection tomography using PP and PS seismic data

Geophysics ◽  
2005 ◽  
Vol 70 (5) ◽  
pp. U51-U65 ◽  
Author(s):  
Stig-Kyrre Foss ◽  
Bjørn Ursin ◽  
Maarten V. de Hoop
Keyword(s):  
Seismic Data ◽  
Optimization Procedure ◽  
Transversely Isotropic ◽  
Data Depth ◽  
Image Point ◽  
Ocean Bottom ◽  
Data Set ◽  
Scattering Angle ◽  
Velocity Models ◽  
Reflection Tomography

We present a method of reflection tomography for anisotropic elastic parameters from PP and PS reflection seismic data. The method is based upon the differential semblance misfit functional in scattering angle and azimuth (DSA) acting on common-image-point gathers (CIGs) to find fitting velocity models. The CIGs are amplitude corrected using a generalized Radon transform applied to the data. Depth consistency between the PP and PS images is enforced by penalizing any mis-tie between imaged key reflectors. The mis-tie is evaluated by means of map migration-demigration applied to the geometric information (times and slopes) contained in the data. In our implementation, we simplify the codepthing approach to zero-scattering-angle data only. The resulting measure is incorporated as a regularization in the DSA misfit functional. We then resort to an optimization procedure, restricting ourselves to transversely isotropic (TI) velocity models. In principle, depending on the available surface-offset range and orientation of reflectors in the subsurface, by combining the DSA with codepthing, the anisotropic parameters for TI models can be determined, provided the orientation of the symmetry axis is known. A proposed strategy is applied to an ocean-bottom-seismic field data set from the North Sea.

Regularization and datuming of seismic data by weighted, damped least squares

Geophysics ◽  
2006 ◽  
Vol 71 (5) ◽  
pp. U67-U76 ◽  
Author(s):  
Robert J. Ferguson
Keyword(s):  
Least Squares ◽  
Seismic Data ◽  
Synthetic Data ◽  
Real Data ◽  
Structural Data ◽  
Irregular Sampling ◽  
Data Set ◽  
Near Surface ◽  
Damped Least Squares ◽  
Wavefield Extrapolation

The possibility of improving regularization/datuming of seismic data is investigated by treating wavefield extrapolation as an inversion problem. Weighted, damped least squares is then used to produce the regularized/datumed wavefield. Regularization/datuming is extremely costly because of computing the Hessian, so an efficient approximation is introduced. Approximation is achieved by computing a limited number of diagonals in the operators involved. Real and synthetic data examples demonstrate the utility of this approach. For synthetic data, regularization/datuming is demonstrated for large extrapolation distances using a highly irregular recording array. Without approximation, regularization/datuming returns a regularized wavefield with reduced operator artifacts when compared to a nonregularizing method such as generalized phase shift plus interpolation (PSPI). Approximate regularization/datuming returns a regularized wavefield for approximately two orders of magnitude less in cost; but it is dip limited, though in a controllable way, compared to the full method. The Foothills structural data set, a freely available data set from the Rocky Mountains of Canada, demonstrates application to real data. The data have highly irregular sampling along the shot coordinate, and they suffer from significant near-surface effects. Approximate regularization/datuming returns common receiver data that are superior in appearance compared to conventional datuming.

Restricted model domain time Radon transforms

Geophysics ◽  
2016 ◽  
Vol 81 (6) ◽  
pp. A17-A21 ◽  
Author(s):  
Juan I. Sabbione ◽  
Mauricio D. Sacchi
Keyword(s):  
Inverse Problem ◽  
Seismic Data ◽  
Computational Cost ◽  
Synthetic Data ◽  
Model Space ◽  
Radon Transforms ◽  
Iterative Solver ◽  
Hard Thresholding ◽  
Restricted Model ◽  
Marine Data

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.

Geometrical spreading in a layered transversely isotropic medium with vertical symmetry axis

Geophysics ◽  
2003 ◽  
Vol 68 (6) ◽  
pp. 2082-2091 ◽  
Author(s):  
Bjørn Ursin ◽  
Ketil Hokstad
Keyword(s):  
Ray Tracing ◽  
Seismic Data ◽  
Symmetry Axis ◽  
Transversely Isotropic ◽  
Analytical Approximation ◽  
Geometrical Spreading ◽  
S Wave ◽  
Weak Anisotropy ◽  
P Waves ◽  
Amplitude Versus

Compensation for geometrical spreading is important in prestack Kirchhoff migration and in amplitude versus offset/amplitude versus angle (AVO/AVA) analysis of seismic data. We present equations for the relative geometrical spreading of reflected and transmitted P‐ and S‐wave in horizontally layered transversely isotropic media with vertical symmetry axis (VTI). We show that relatively simple expressions are obtained when the geometrical spreading is expressed in terms of group velocities. In weakly anisotropic media, we obtain simple expressions also in terms of phase velocities. Also, we derive analytical equations for geometrical spreading based on the nonhyperbolic traveltime formula of Tsvankin and Thomsen, such that the geometrical spreading can be expressed in terms of the parameters used in time processing of seismic data. Comparison with numerical ray tracing demonstrates that the weak anisotropy approximation to geometrical spreading is accurate for P‐waves. It is less accurate for SV‐waves, but has qualitatively the correct form. For P waves, the nonhyperbolic equation for geometrical spreading compares favorably with ray‐tracing results for offset‐depth ratios less than five. For SV‐waves, the analytical approximation is accurate only at small offsets, and breaks down at offset‐depth ratios less than unity. The numerical results are in agreement with the range of validity for the nonhyperbolic traveltime equations.

Relative time seislet transform

Geophysics ◽  
2020 ◽  
Vol 85 (2) ◽  
pp. V223-V232 ◽  
Author(s):  
Zhicheng Geng ◽  
Xinming Wu ◽  
Sergey Fomel ◽  
Yangkang Chen
Keyword(s):  
Seismic Data ◽  
Computational Cost ◽  
Lifting Scheme ◽  
Real Data ◽  
Data Sets ◽  
Relative Time ◽  
New Approach ◽  
New Formulation ◽  
Wavelet Lifting ◽  
Seismic Images

The seislet transform uses the wavelet-lifting scheme and local slopes to analyze the seismic data. In its definition, the designing of prediction operators specifically for seismic images and data is an important issue. We have developed a new formulation of the seislet transform based on the relative time (RT) attribute. This method uses the RT volume to construct multiscale prediction operators. With the new prediction operators, the seislet transform gets accelerated because distant traces get predicted directly. We apply our method to synthetic and real data to demonstrate that the new approach reduces computational cost and obtains excellent sparse representation on test data sets.

scholarly journals Seismic AVOA Inversion for Weak Anisotropy Parameters and Fracture Density in a Monoclinic Medium

2020 ◽  
Vol 10 (15) ◽  
pp. 5136 ◽  
Author(s):  
Zijian Ge ◽  
Shulin Pan ◽  
Jingye Li
Keyword(s):  
Fractured Rock ◽  
Synthetic Data ◽  
Transversely Isotropic ◽  
P Wave ◽  
Inversion Method ◽  
Fracture Density ◽  
Weak Anisotropy ◽  
Amplitude Versus Offset ◽  
Porosity And Permeability ◽  
Transverse Isotropic

In shale gas development, fracture density is an important lithologic parameter to properly characterize reservoir reconstruction, establish a fracturing scheme, and calculate porosity and permeability. The traditional methods usually assume that the fracture reservoir is one set of aligned vertical fractures, embedded in an isotropic background, and estimate some alternative parameters associated with fracture density. Thus, the low accuracy caused by this simplified model, and the intrinsic errors caused by the indirect substitution, affect the estimation of fracture density. In this paper, the fractured rock of monoclinic symmetry assumes two non-orthogonal vertical fracture sets, embedded in a transversely isotropic background. Firstly, assuming that the fracture radius, width, and orientation are known, a new form of P-wave reflection coefficient, in terms of weak anisotropy (WA) parameters and fracture density, was obtained by substituting the stiffness coefficients of vertical transverse isotropic (VTI) background, normal, and tangential fracture compliances. Then, a linear amplitude versus offset and azimuth (AVOA) inversion method, of WA parameters and fracture density, was constructed by using Bayesian theory. Tests on synthetic data showed that WA parameters, and fracture density, are stably estimated in the case of seismic data containing a moderate noise, which can provide a reliable tool in fracture prediction.

Colored and linear inversions to relative acoustic impedance

Geophysics ◽  
2019 ◽  
Vol 84 (2) ◽  
pp. N15-N27 ◽  
Author(s):  
Carlos A. M. Assis ◽  
Henrique B. Santos ◽  
Jörg Schleicher
Keyword(s):  
Seismic Data ◽  
Acoustic Impedance ◽  
Computational Cost ◽  
Synthetic Data ◽  
Seismic Source ◽  
Alternative Methods ◽  
Well Log ◽  
Linear Inversion ◽  
Amplitude Inversion ◽  
Band Limited

Acoustic impedance (AI) is a widely used seismic attribute in stratigraphic interpretation. Because of the frequency-band-limited nature of seismic data, seismic amplitude inversion cannot determine AI itself, but it can only provide an estimate of its variations, the relative AI (RAI). We have revisited and compared two alternative methods to transform stacked seismic data into RAI. One is colored inversion (CI), which requires well-log information, and the other is linear inversion (LI), which requires knowledge of the seismic source wavelet. We start by formulating the two approaches in a theoretically comparable manner. This allows us to conclude that both procedures are theoretically equivalent. We proceed to check whether the use of the CI results as the initial solution for LI can improve the RAI estimation. In our experiments, combining CI and LI cannot provide superior RAI results to those produced by each approach applied individually. Then, we analyze the LI performance with two distinct solvers for the associated linear system. Moreover, we investigate the sensitivity of both methods regarding the frequency content present in synthetic data. The numerical tests using the Marmousi2 model demonstrate that the CI and LI techniques can provide an RAI estimate of similar accuracy. A field-data example confirms the analysis using synthetic-data experiments. Our investigations confirm the theoretical and practical similarities of CI and LI regardless of the numerical strategy used in LI. An important result of our tests is that an increase in the low-frequency gap in the data leads to slightly deteriorated CI quality. In this case, LI required more iterations for the conjugate-gradient least-squares solver, but the final results were not much affected. Both methodologies provided interesting RAI profiles compared with well-log data, at low computational cost and with a simple parameterization.

scholarly journals Nonequispaced curvelet transform for seismic data reconstruction: A sparsity-promoting approach

Geophysics ◽  
2010 ◽  
Vol 75 (6) ◽  
pp. WB203-WB210 ◽  
Author(s):  
Gilles Hennenfent ◽  
Lloyd Fenelon ◽  
Felix J. Herrmann
Keyword(s):  
Seismic Data ◽  
First Generation ◽  
Second Generation ◽  
Synthetic Data ◽  
Curvelet Transform ◽  
Real Data ◽  
Sampled Data ◽  
Regularized Inversion ◽  
Irregularly Sampled Data ◽  
Fast Discrete Curvelet Transform

We extend our earlier work on the nonequispaced fast discrete curvelet transform (NFDCT) and introduce a second generation of the transform. This new generation differs from the previous one by the approach taken to compute accurate curvelet coefficients from irregularly sampled data. The first generation relies on accurate Fourier coefficients obtained by an [Formula: see text]-regularized inversion of the nonequispaced fast Fourier transform (FFT) whereas the second is based on a direct [Formula: see text]-regularized inversion of the operator that links curvelet coefficients to irregular data. Also, by construction the second generation NFDCT is lossless unlike the first generation NFDCT. This property is particularly attractive for processing irregularly sampled seismic data in the curvelet domain and bringing them back to their irregular record-ing locations with high fidelity. Secondly, we combine the second generation NFDCT with the standard fast discrete curvelet transform (FDCT) to form a new curvelet-based method, coined nonequispaced curvelet reconstruction with sparsity-promoting inversion (NCRSI) for the regularization and interpolation of irregularly sampled data. We demonstrate that for a pure regularization problem the reconstruction is very accurate. The signal-to-reconstruction error ratio in our example is above [Formula: see text]. We also conduct combined interpolation and regularization experiments. The reconstructions for synthetic data are accurate, particularly when the recording locations are optimally jittered. The reconstruction in our real data example shows amplitudes along the main wavefronts smoothly varying with limited acquisition imprint.

Estimation of primaries by sparse inversion with scattering-based multiple predictions for data with large gaps

Geophysics ◽  
2016 ◽  
Vol 81 (3) ◽  
pp. V183-V197 ◽  
Author(s):  
Tim T.Y. Lin ◽  
Felix J. Herrmann
Keyword(s):  
Free Surface ◽  
Computational Cost ◽  
Estimation Method ◽  
Synthetic Data ◽  
Real Data ◽  
Memory Efficiency ◽  
Forward Prediction ◽  
Primary Model ◽  
Estimated Green’S Function ◽  
Sparse Inversion

We have solved the estimation of primaries by sparse inversion problem for a seismic record with large near-offset gaps and other contiguous holes in the acquisition grid without relying on explicit reconstruction of the missing data. Eliminating the unknown data as an explicit inversion variable is desirable because it sidesteps possible issues arising from overfitting the primary model to the estimated data. Instead, we have simulated their multiple contributions by augmenting the forward prediction model for the total wavefield with a scattering series that mimics the action of the free surface reflector within the area of the unobserved trace locations. Each term in this scattering series involves convolution of the total predicted wavefield once more with the current estimated Green’s function for a medium without the free surface at these unobserved locations. It is important to note that our method cannot by itself mitigate regular undersampling issues that result in significant aliases when computing the multiple contributions, such as source-receiver sampling differences or crossline spacing issues in 3D acquisition. We have investigated algorithms that handle the nonlinearity in the modeling operator due to the scattering terms, and we also determined that just a few of the terms can be enough to satisfactorily mitigate the effects of near-offset data gaps during the inversion process. Numerical experiments on synthetic data found that the final derived method can significantly outperform explicit data reconstruction for large near-offset gaps, with a similar computational cost and better memory efficiency. We have also found on real data that our scheme outperforms the unmodified primary estimation method that uses an existing Radon-based interpolation of the near-offset gap.

Seismic signal band estimation by interpretation of f-x spectra

Geophysics ◽  
1999 ◽  
Vol 64 (1) ◽  
pp. 251-260 ◽  
Author(s):  
Gary F. Margrave
Keyword(s):  
Seismic Data ◽  
Synthetic Data ◽  
Real Data ◽  
Seismic Signal ◽  
Radial Component ◽  
Resolving Power ◽  
Random Fluctuation ◽  
Corner Frequency ◽  
Potential Signal ◽  
Signal Band

The signal band of reflection seismic data is that portion of the temporal Fourier spectrum which is dominated by reflected source energy. The signal bandwidth directly determines the spatial and temporal resolving power and is a useful measure of the value of such data. The realized signal band, which is the signal band of seismic data as optimized in processing, may be estimated by the interpretation of appropriately constructed f-x spectra. A temporal window, whose length has a specified random fluctuation from trace to trace, is applied to an ensemble of seismic traces, and the temporal Fourier transform is computed. The resultant f-x spectra are then separated into amplitude and phase sections, viewed as conventional seismic displays, and interpreted. The signal is manifested through the lateral continuity of spectral events; noise causes lateral incoherence. The fundamental assumption is that signal is correlated from trace to trace while noise is not. A variety of synthetic data examples illustrate that reasonable results are obtained even when the signal decays with time (i.e., is nonstationary) or geologic structure is extreme. Analysis of real data from a 3-C survey shows an easily discernible signal band for both P-P and P-S reflections, with the former being roughly twice the latter. The potential signal band, which may be regarded as the maximum possible signal band, is independent of processing techniques. An estimator for this limiting case is the corner frequency (the frequency at which a decaying signal drops below background noise levels) as measured on ensemble‐averaged amplitude spectra from raw seismic data. A comparison of potential signal band with realized signal band for the 3-C data shows good agreement for P-P data, which suggests the processing is nearly optimal. For P-S data, the realized signal band is about half of the estimated potential. This may indicate a relative immaturity of P-S processing algorithms or it may be due to P-P energy on the raw radial component records.

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