Ray‐tracing‐based prediction and subtraction of water‐layer multiples

Geophysics ◽  
1990 ◽  
Vol 55 (4) ◽  
pp. 443-451 ◽  
Author(s):  
Andrew J. Calvert
Keyword(s):  
Ray Tracing ◽  
Seismic Data ◽  
Computational Cost ◽  
Water Layer ◽  
Computational Effort ◽  
Lateral Variation ◽  
Multiple Reflections ◽  
Seafloor Topography ◽  
Arrival Times ◽  
Data Matching

Many methods of multiple suppression break down when the structure that produces the reverberation possesses significant lateral variation; a common example of this situation occurs in marine data with the multiple reflections that are generated by seafloor topography. Such multiples may be suppressed by techniques based upon wave‐equation extrapolation; the recorded seismic data are mathematically propagated through a simulated water layer to generate a set of multiple arrivals which may, after data matching, be subtracted. However, the computational effort required to propagate prestack data to a laterally varying datum is very large. In this paper, a method of suppressing selected multiples with arbitrary moveout is presented. In order to reduce the computational cost, prediction of the multiple arrival times is performed by ray tracing through a model of the laterally varying water layer and, possibly, the subsurface. An estimate of the multiple waveform on each trace is obtained by stacking a window of data about the calculated arrival times. The multiple arrival can then be attenuated by subtracting this wavelet from each trace in the prestack gather from which the estimate is derived. In practice, calculations of the variation in multiple amplitude and of any errors in the moveout correction require the multiple reflections to be of comparable, or higher, amplitude than contemporary primary events, a situation that is often the case where multiple contamination is a problem.

Deep‐water peg legs and multiples: Emulation and suppression

Geophysics ◽  
1986 ◽  
Vol 51 (12) ◽  
pp. 2177-2184 ◽  
Author(s):  
J. R. Berryhill ◽  
Y. C. Kim
Keyword(s):  
Wave Equation ◽  
Seismic Data ◽  
Water Layer ◽  
Original Data ◽  
Equation Method ◽  
Multiple Reflections ◽  
Step Method ◽  
Arrival Times ◽  
Sea Floor ◽  
Water Bottom

This paper discusses a two‐step method for predicting and attenuating multiple and peg‐leg reflections in unstacked seismic data. In the first step, an (observed) seismic record is extrapolated through a round‐trip traversal of the water layer, thus creating an accurate prediction of all possible multiples. In the second step, the record containing the predicted multiples is compared with and subtracted from the original. The wave‐equation method employed to predict the multiples takes accurate account of sea‐floor topography and so requires a precise water‐bottom profile as part of the input. Information about the subsurface below the sea floor is not required. The arrival times of multiple reflections are reproduced precisely, although the amplitudes are not accurate, and the sea floor is treated as a perfect reflector. The comparison step detects the similarities between the computed multiples and the original data, and estimates a transfer function to equalize the amplitudes and account for any change in waveform caused by the sea‐floor reflector. This two‐step wave‐equation method is effective even for dipping sea floors and dipping subsurface reflectors. It does not depend upon any assumed periodicity in the data or upon any difference in stacking velocity between primaries and multiples. Thus it is complementary to the less specialized methods of multiple suppression.

SOME CHARACTERISTICS OF MARINE SPARKER SEISMIC DATA

Geophysics ◽  
1972 ◽  
Vol 37 (3) ◽  
pp. 462-470 ◽  
Author(s):  
F. T. Allen
Keyword(s):  
Seismic Data ◽  
Water Layer ◽  
Seismic Survey ◽  
Multiple Reflections ◽  
Time Profiles ◽  
Survey Technique ◽  
Recording Conditions ◽  
Single Detector ◽  
Marine Seismic ◽  
The Relationship

The marine seismic survey technique of frequent recordings with a single detector group can provide intricate details valuable to relatively shallow investigations. Velocities may be computed from time anomalies, under certain circumstances. The extent of multiple energy response is an indication that the 100,000-joule source is strong enough for the purpose. Recognizable minor details in primary reflections are important clues in identifying related multiple reflections. Bounces off the underside of the water layer are rarely found. The pattern and character of reflections are influenced by recording conditions; thus, the relationship between recorded events and sedimentary beds is not simple. Seismic time profiles frequently give wrong impressions of structural attitudes because of the horizontal‐to‐vertical exaggeration, time anomalies, and multiple reflections, as well as the usual effects of velocity differences. The interpreted cross‐section gives a reasonably correct (even if velocities are assumed) impression of structure; the profile often does not.

WATER REVERBERATIONS—THEIR NATURE AND ELIMINATION

Geophysics ◽  
1959 ◽  
Vol 24 (2) ◽  
pp. 233-261 ◽  
Author(s):  
Milo M. Backus
Keyword(s):  
Seismic Data ◽  
Structural Information ◽  
Water Layer ◽  
Original Data ◽  
Present Form ◽  
Linear Filtering ◽  
Inverse Filtering ◽  
Multiple Reflections ◽  
Filtering Techniques

In offshore shooting the validity of previously recorded seismic data has been severely limited by multiple reflections within the water layer. The magnitude of this problem is dependent on the thickness and the nature of the boundaries of the water layer. The effect of the water layer is treated as a linear filtering mechanism, and it is suggested that most apparent water reverberation records probably contain some approximate subsurface structural information, even in their present form. The use of inverse filtering techniques for the removal or attenuation of the water reverberation effect is discussed. Examples show the application of the technique to conventional magnetically recorded offshore data. It has been found that the effectiveness of the method is strongly dependent on the instrumental parameters used in the recording of the original data.

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.

LONG-PERIOD SURFACE-RELATED MULTIPLE SUPPRESSION IN 2D MARINE SEISMIC DATA USING PREDICTIVE DECONVOLUTION AND COMBINATION OF SURFACE-RELATED MULTIPLE ELIMINATION AND PARABOLIC RADON FILTERING

2021 ◽  
Author(s):  
Pimpawee Sittipan ◽  
Pisanu Wongpornchai
Keyword(s):  
Seismic Data ◽  
Seismic Reflection ◽  
Petroleum Reservoirs ◽  
The United States ◽  
Multiple Reflections ◽  
Long Period ◽  
Predictive Deconvolution ◽  
Short Period ◽  
Marine Seismic ◽  
Multiple Elimination

Some of the important petroleum reservoirs accumulate beneath the seas and oceans. Marine seismic reflection method is the most efficient method and is widely used in the petroleum industry to map and interpret the potential of petroleum reservoirs. Multiple reflections are a particular problem in marine seismic reflection investigation, as they often obscure the target reflectors in seismic profiles. Multiple reflections can be categorized by considering the shallowest interface on which the bounces take place into two types: internal multiples and surface-related multiples. Besides, the multiples can be categorized on the interfaces where the bounces take place, a difference between long-period and short-period multiples can be considered. The long-period surface-related multiples on 2D marine seismic data of the East Coast of the United States-Southern Atlantic Margin were focused on this research. The seismic profile demonstrates the effectiveness of the results from predictive deconvolution and the combination of surface-related multiple eliminations (SRME) and parabolic Radon filtering. First, predictive deconvolution applied on conventional processing is the method of multiple suppression. The other, SRME is a model-based and data-driven surface-related multiple elimination method which does not need any assumptions. And the last, parabolic Radon filtering is a moveout-based method for residual multiple reflections based on velocity discrimination between primary and multiple reflections, thus velocity model and normal-moveout correction are required for this method. The predictive deconvolution is ineffective for long-period surface-related multiple removals. However, the combination of SRME and parabolic Radon filtering can attenuate almost long-period surface-related multiple reflections and provide a high-quality seismic images of marine seismic data.

Comparative Analysis of Methodologies for Uncertainty Propagation and Quantification

2017 ◽  
Author(s):  
Alessandra Cuneo ◽  
Alberto Traverso ◽  
Shahrokh Shahpar
Keyword(s):  
Engineering Design ◽  
Polynomial Chaos ◽  
Epistemic Uncertainty ◽  
Uncertainty Propagation ◽  
Computational Cost ◽  
Computational Effort ◽  
Optimization Under Uncertainty ◽  
Design Parameters ◽  
Test Case ◽  
Aleatory And Epistemic Uncertainty

In engineering design, uncertainty is inevitable and can cause a significant deviation in the performance of a system. Uncertainty in input parameters can be categorized into two groups: aleatory and epistemic uncertainty. The work presented here is focused on aleatory uncertainty, which can cause natural, unpredictable and uncontrollable variations in performance of the system under study. Such uncertainty can be quantified using statistical methods, but the main obstacle is often the computational cost, because the representative model is typically highly non-linear and complex. Therefore, it is necessary to have a robust tool that can perform the uncertainty propagation with as few evaluations as possible. In the last few years, different methodologies for uncertainty propagation and quantification have been proposed. The focus of this study is to evaluate four different methods to demonstrate strengths and weaknesses of each approach. The first method considered is Monte Carlo simulation, a sampling method that can give high accuracy but needs a relatively large computational effort. The second method is Polynomial Chaos, an approximated method where the probabilistic parameters of the response function are modelled with orthogonal polynomials. The third method considered is Mid-range Approximation Method. This approach is based on the assembly of multiple meta-models into one model to perform optimization under uncertainty. The fourth method is the application of the first two methods not directly to the model but to a response surface representing the model of the simulation, to decrease computational cost. All these methods have been applied to a set of analytical test functions and engineering test cases. Relevant aspects of the engineering design and analysis such as high number of stochastic variables and optimised design problem with and without stochastic design parameters were assessed. Polynomial Chaos emerges as the most promising methodology, and was then applied to a turbomachinery test case based on a thermal analysis of a high-pressure turbine disk.

High-resolution imaging: An approach by incorporating stationary-phase implementation into deabsorption prestack time migration

Geophysics ◽  
2016 ◽  
Vol 81 (5) ◽  
pp. S317-S331 ◽  
Author(s):  
Jianfeng Zhang ◽  
Zhengwei Li ◽  
Linong Liu ◽  
Jin Wang ◽  
Jincheng Xu
Keyword(s):  
Stationary Phase ◽  
Fresnel Zone ◽  
Computational Cost ◽  
Computational Effort ◽  
Propagation Path ◽  
Time Migration ◽  
Resolution Imaging ◽  
Prestack Time Migration ◽  
Dip Angle ◽  
Absorption And Dispersion

We have improved the so-called deabsorption prestack time migration (PSTM) by introducing a dip-angle domain stationary-phase implementation. Deabsorption PSTM compensates absorption and dispersion via an actual wave propagation path using effective [Formula: see text] parameters that are obtained during migration. However, noises induced by the compensation degrade the resolution gained and deabsorption PSTM requires more computational effort than conventional PSTM. Our stationary-phase implementation improves deabsorption PSTM through the determination of an optimal migration aperture based on an estimate of the Fresnel zone. This significantly attenuates the noises and reduces the computational cost of 3D deabsorption PSTM. We have estimated the 2D Fresnel zone in terms of two dip angles through building a pair of 1D migrated dip-angle gathers using PSTM. Our stationary-phase QPSTM (deabsorption PSTM) was implemented as a two-stage process. First, we used conventional PSTM to obtain the Fresnel zones. Then, we performed deabsorption PSTM with the Fresnel-zone-based optimized migration aperture. We applied stationary-phase QPSTM to a 3D field data. Comparison with synthetic seismogram generated from well log data validates the resolution enhancements.

Subsurface reflectivity estimation from imaging of primaries and multiples using amplitude-normalized separated wavefields

Geophysics ◽  
2016 ◽  
Vol 81 (3) ◽  
pp. S101-S117 ◽  
Author(s):  
Alba Ordoñez ◽  
Walter Söllner ◽  
Tilman Klüver ◽  
Leiv J. Gelius
Keyword(s):  
Integral Equation ◽  
Fredholm Integral Equation ◽  
Computational Cost ◽  
Image Point ◽  
Point Location ◽  
Multiple Reflections ◽  
Frequency Space ◽  
Propagation Effects ◽  
The Matrix ◽  
Spatial Domains

Several studies have shown the benefits of including multiple reflections together with primaries in the structural imaging of subsurface reflectors. However, to characterize the reflector properties, there is a need to compensate for propagation effects due to multiple scattering and to properly combine the information from primaries and all orders of multiples. From this perspective and based on the wave equation and Rayleigh’s reciprocity theorem, recent works have suggested computing the subsurface image from the Green’s function reflection response (or reflectivity) by inverting a Fredholm integral equation in the frequency-space domain. By following Claerbout’s imaging principle and assuming locally reacting media, the integral equation may be reduced to a trace-by-trace deconvolution imaging condition. For a complex overburden and considering that the structure of the subsurface is angle-dependent, this trace-by-trace deconvolution does not properly solve the Fredholm integral equation. We have inverted for the subsurface reflectivity by solving the matrix version of the Fredholm integral equation at every subsurface level, based on a multidimensional deconvolution of the receiver wavefields with the source wavefields. The total upgoing pressure and the total filtered downgoing vertical velocity were used as receiver and source wavefields, respectively. By selecting appropriate subsets of the inverted reflectivity matrix and by performing an inverse Fourier transform over the frequencies, the process allowed us to obtain wavefields corresponding to virtual sources and receivers located in the subsurface, at a given level. The method has been applied on two synthetic examples showing that the computed reflectivity wavefields are free of propagation effects from the overburden and thus are suited to extract information of the image point location in the angular and spatial domains. To get the computational cost down, our approach is target-oriented; i.e., the reflectivity may only be computed in the area of most interest.

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