Estimation of multiple scattering by iterative inversion, Part I: Theoretical considerations

Geophysics ◽  
1997 ◽  
Vol 62 (5) ◽  
pp. 1586-1595 ◽  
Author(s):  
A. J. Berkhout ◽  
D. J. Verschuur
Keyword(s):  
Numerical Experiments ◽  
Velocity Model ◽  
Neumann Series ◽  
Related Method ◽  
Feedback Model ◽  
Iterative Inversion ◽  
Internal Multiples ◽  
Surface Operator ◽  
Theoretical Considerations ◽  
Upper Boundary

A review has been given of the surface‐related multiple problem by making use of the so‐called feedback model. From the resulting equations it has been concluded that the proposed solution does not require any properties of the subsurface. However, source‐detector and reflectivity properties of the surface need be specified. Those properties have been quantified in a surface operator and this operator is estimated as part of the multiple removal problem. The surface‐related multiple removal algorithm has been formulated in terms of a Neumann series and in terms of an iterative equation. The Neumann formulation requires a nonlinear optimization process for the surface operator; while the iterative formulation needs a number of linear optimizations. The iterative formulation also has the advantage that it can be integrated easily with another multiple removal method. An algorithm for the removal of internal multiples has been proposed as well. This algorithm is an extension of the surface‐related method. Removal of internal multiples requires knowledge of the macro velocity model between the surface and the upper boundary of the multiple generating layer. In part II (also published in this issue) the success of the proposed algorithms has been demonstrated on numerical experiments and field data examples.

scholarly journals Removal of internal multiples with the common-focus-point (CFP) approach: Part 2 — Application strategies and data examples

Geophysics ◽  
2005 ◽  
Vol 70 (3) ◽  
pp. V61-V72 ◽  
Author(s):  
D. J. Verschuur ◽  
A. J. Berkhout
Keyword(s):  
Physical Model ◽  
Field Data ◽  
Velocity Model ◽  
Data Sets ◽  
Removal Method ◽  
The Past ◽  
Feedback Model ◽  
The Common ◽  
Internal Multiples ◽  
Focus Point

In the past, the surface-multiple-removal method based on the feedback model has been successfully applied to many different field data sets. The extension of surface to internal multiples can be made by replacing shot records with common-focus-point (CFP) gathers, a CFP gather representing focused data with one source in the subsurface and all receivers at the surface (or vice versa for a receiver gather). The internal-multiple-removal algorithm can be formulated in terms of boundary-related and layer-related versions. In the boundary-related version, the internal multiples are removed for one downward-scattering reflector at a time. In the layer-related version, the internal multiples are removed for a sequence of downward-scattering reflectors at a time. An exact velocity model is not required, but proper muting is critical; muting becomes straightforward in the CFP domain. The strategy for applying the two versions of the multiple-removal algorithm is demonstrated on physical-model and field data. One can conclude that the layer-related version is the most appropriate in most situations because it requires less user action and does not need exact knowledge of the multiple-generating boundary.

scholarly journals Data-driven wavefield focusing and imaging with multidimensional deconvolution: Numerical examples for reflection data with internal multiples

Geophysics ◽  
2014 ◽  
Vol 79 (3) ◽  
pp. WA107-WA115 ◽  
Author(s):  
Filippo Broggini ◽  
Roel Snieder ◽  
Kees Wapenaar
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Imaging Techniques ◽  
Velocity Model ◽  
Single Scattering ◽  
Data Driven ◽  
Multiple Reflections ◽  
Prestack Migration ◽  
Reflection Data ◽  
Internal Multiples

Standard imaging techniques rely on the single scattering assumption. This requires that the recorded data do not include internal multiples, i.e., waves that have bounced multiple times between reflectors before reaching the receivers at the acquisition surface. When multiple reflections are present in the data, standard imaging algorithms incorrectly image them as ghost reflectors. These artifacts can mislead interpreters in locating potential hydrocarbon reservoirs. Recently, we introduced a new approach for retrieving the Green’s function recorded at the acquisition surface due to a virtual source located at depth. We refer to this approach as data-driven wavefield focusing. Additionally, after applying source-receiver reciprocity, this approach allowed us to decompose the Green’s function at a virtual receiver at depth in its downgoing and upgoing components. These wavefields were then used to create a ghost-free image of the medium with either crosscorrelation or multidimensional deconvolution, presenting an advantage over standard prestack migration. We tested the robustness of our approach when an erroneous background velocity model is used to estimate the first-arriving waves, which are a required input for the data-driven wavefield focusing process. We tested the new method with a numerical example based on a modification of the Amoco model.

Reflector spectrum for relating seismic arrivals to reflectors

Geophysics ◽  
2012 ◽  
Vol 77 (6) ◽  
pp. T239-T246
Author(s):  
Hong Liang ◽  
Yi Luo ◽  
Panos G. Kelamis ◽  
Arthur B. Weglein
Keyword(s):  
Seismic Data ◽  
Velocity Model ◽  
Forward Modeling ◽  
Modeling Method ◽  
Relative Contribution ◽  
Sonic Log ◽  
Minimum Number ◽  
Internal Multiples ◽  
Seismic Images

When interpreting seismic images or suppressing multiples in seismic data, it is important to identify the reflectors from which the multiples, especially the internal multiples, originated. We evaluated a method to relate all seismic arrivals, including primaries and multiples, to their originating reflectors. We used the reflectivity forward modeling method to isolate reflectors and determine the contribution of an individual reflector to arrivals in a seismic trace. Repeating this process for all reflectors produced a reflector spectrum, which shows quantitatively the relative contribution of each reflector to all arrivals in a trace. Then we modified the reflector spectrum to relate seismic arrivals only to their shallowest reflectors. We applied the reflector spectrum and the modified reflector spectrum to a velocity model constructed from a field sonic log. We provided an indication of the minimum number of reflectors responsible for multiples and demonstrated that internal multiples originate from many reflectors distributed throughout the model, rather than from a few major ones.

scholarly journals Stratification effects on shoaling Internal Solitary Waves

2021 ◽  
Author(s):  
Sam Hartharn-Evans ◽  
Magda Carr ◽  
Marek Stastna ◽  
Peter Davies
Keyword(s):  
Density Gradient ◽  
Solitary Waves ◽  
Numerical Experiments ◽  
Lower Layer ◽  
Internal Solitary Waves ◽  
Topographic Slope ◽  
Numerical Studies ◽  
The World ◽  
Upper Boundary ◽  
Mixing And Transport

<p>Shoaling is a key mechanism by which Internal Solitary Waves (ISWs) dissipate energy, induce mixing, and transport sediment. Past studies of shoaling ISWs in a three-layer stratification (with homogeneous upper and lower layers separated by a thin pycnocline layer) have identified a classification system where waves over the shallowest slopes undergo fission, whilst over steeper slopes, the breaking type changes from surging, through collapsing to plunging as a function of increasing internal Irribaren number (Ir) defined with the topographic slope, s, and the incident wave’s amplitude and wavelength, A<sub>w</sub> and L<sub>w </sub>respectively, as <img src="https://contentmanager.copernicus.org/fileStorageProxy.php?f=gnp.9fb46536f70067154311161/sdaolpUECMynit/12UGE&app=m&a=0&c=d84eaf790c6586a46ed8fca09040fcd7&ct=x&pn=gnp.elif&d=1" alt="" width="117" height="24">. Here, a combined numerical and laboratory study extends this prior work into new stratifications, representing the diversity of ocean structures across the world. Numerical results were able to successfully reproduce past studies in the three-layer stratification, and those in the two-layer stratification in the laboratory. Where a linear stratified layer overlays a homogeneous lower layer (two-layer stratification), it is found that plunging dynamics are inhibited by the density gradient throughout the upper layer, instead forming collapsing-type breakers. In numerical experiments, where the density gradient is continuous throughout the full water column (linear stratification), not only are the plunging dynamics inhibited, but the density gradient at the bottom boundary also prevents the formation of collapsing dynamics, instead all waves in this stratification either fission, or form surging breakers. Where the wave steepness is particularly high in the linear stratification, the upslope bolus formed by surging was unstable, and Kelvin-Helmholtz instabilities were observed on the upper boundary of the bolus, dynamics not previously observed in the literature. These results indicate the importance of using representative stratifications in laboratory and numerical studies of ISW behaviours.</p>

Practical aspects and applications of 2D stereotomography

Geophysics ◽  
2003 ◽  
Vol 68 (3) ◽  
pp. 1008-1021 ◽  
Author(s):  
Frederic Billette ◽  
Soazig Le Bégat ◽  
Pascal Podvin ◽  
Gilles Lambaré
Keyword(s):  
Estimation Method ◽  
Synthetic Data ◽  
Velocity Model ◽  
Velocity Estimation ◽  
Common Source ◽  
Depth Migration ◽  
Reflection Seismic ◽  
Velocity Models ◽  
Automatic Picking ◽  
Iterative Inversion

Stereotomography is a new velocity estimation method. This tomographic approach aims at retrieving subsurface velocities from prestack seismic data. In addition to traveltimes, the slope of locally coherent events are picked simultaneously in common offset, common source, common receiver, and common midpoint gathers. As the picking is realized on locally coherent events, they do not need to be interpreted in terms of reflection on given interfaces, but may represent diffractions or reflections from anywhere in the image. In the high‐frequency approximation, each one of these events corresponds to a ray trajectory in the subsurface. Stereotomography consists of picking and analyzing these events to update both the associated ray paths and velocity model. In this paper, we describe the implementation of two critical features needed to put stereotomography into practice: an automatic picking tool and a robust multiscale iterative inversion technique. Applications to 2D reflection seismic are presented on synthetic data and on a 2D line extracted from a 3D towed streamer survey shot in West Africa for TotalFinaElf. The examples demonstrate that the method requires only minor human intervention and rapidly converges to a geologically plausible velocity model in these two very different and complex velocity regimes. The quality of the velocity models is verified by prestack depth migration results.

The Stop-Loss Start-Gain Strategy Modification With Tilt Deadband Research

2019 ◽  
Vol 09 (4) ◽  
pp. 46-56
Author(s):  
S.A. Zubov
Keyword(s):  
Mathematical Model ◽  
Monte Carlo Simulation ◽  
Numerical Experiments ◽  
Top Down ◽  
Slope Coefficient ◽  
Pricing Process ◽  
Nonzero Mean ◽  
Stop Loss ◽  
The Given ◽  
Upper Boundary

In this article The stop-loss start-gain strategy modification with tilt deadband is studied. The top line of this band is tilted. During the research mathematical model with discrete pricing process was examined. The increments of this process have a normal distribution with a constant nonzero mean and constant dispersion. The article considers the distribution of the number of intersections of a nonrectilinear strip by a discrete Gaussian walk. Formulas that allow to specify the distribution of the number of intersections of the strip in the directions “bottomup” and “top-down” were deduced. An algorithm was developed to calculate the number of these intersections and evaluate the conditional probability of the transition. In addition, the dependence of the average hedger losses while using this strategy on the slope coefficient of the upper boundary of the dead band and the band width was considered. Using the Monte Carlo simulation, an algorithm was developed to find the optimal width and slope of the strip. During the numerical experiments, the dependence was revealed and the optimal slope coefficient was determined for the given parameters. Experimental work confirmed the correctness of the proposed algorithms and proved the effectiveness of this modification in comparison with the use of a strategy with a straight strip.

Least-squares reverse time migration in the presence of velocity errors

Geophysics ◽  
2019 ◽  
Vol 84 (6) ◽  
pp. S567-S580 ◽  
Author(s):  
Jizhong Yang ◽  
Yunyue Elita Li ◽  
Arthur Cheng ◽  
Yuzhu Liu ◽  
Liangguo Dong
Keyword(s):  
Least Squares ◽  
Velocity Model ◽  
Migration Velocity ◽  
Resolution Limit ◽  
Reverse Time ◽  
Reverse Time Migration ◽  
Time Migration ◽  
Large Velocity ◽  
Iterative Inversion ◽  
Inversion Procedure

Least-squares reverse time migration (LSRTM), which aims to match the modeled data with the observed data in an iterative inversion procedure, is very sensitive to the accuracy of the migration velocity model. If the migration velocity model contains errors, the final migration image may be defocused and incoherent. We have used an LSRTM scheme based on the subsurface offset extended imaging condition, least-squares extended reverse time migration (LSERTM), to provide a better solution when large velocity errors exist. By introducing an extra dimension in the image space, LSERTM can fit the observed data even when significant errors are present in the migration velocity model. We further investigate this property and find that after stacking the extended migration images along the subsurface offset axis within the theoretical lateral resolution limit, we can obtain an image with better coherency and fewer migration artifacts. Using multiple numerical examples, we demonstrate that our method provides superior inversion results compared to conventional LSRTM when the bulk velocity errors are as large as 10%.

STABILITY AND ACCURACY OF LATTICE BOLTZMANN SCHEMES FOR ANISOTROPIC ADVECTION-DIFFUSION EQUATIONS

2009 ◽  
Vol 20 (04) ◽  
pp. 633-650 ◽  
Author(s):  
SHINSUKE SUGA
Keyword(s):  
Lattice Boltzmann ◽  
Numerical Experiments ◽  
Numerical Solutions ◽  
Velocity Model ◽  
Diffusion Equations ◽  
Benchmark Problems ◽  
Relaxation Parameters ◽  
Advection Diffusion ◽  
The Stability ◽  
Stability And Accuracy

The stability of the numerical schemes for anisotropic advection-diffusion equations derived from the lattice Boltzmann equation with the D2Q4 particle velocity model is analyzed through eigenvalue analysis of the amplification matrices of the scheme. Accuracy of the schemes is investigated by solving benchmark problems, and the LBM scheme is compared with traditional implicit schemes. Numerical experiments demonstrate that the LBM scheme produces stable numerical solutions close to the analytical solutions when the values of the relaxation parameters in x and y directions are greater than 1.9 and the Courant numbers satisfy the stability condition. Furthermore, the numerical solutions produced by the LBM scheme are more accurate than those of the Crank–Nicolson finite difference scheme for the case where the Courant numbers are set to be values close to the upper bound of the stability region of the scheme.

scholarly journals RIVERBED EVOLUTION OF YANGTZE ESTUARY AND ITS RESPONSE TO THE HYDRODYNAMIC CHANGES AT UPSTREAM

2012 ◽  
Vol 1 (33) ◽  
pp. 92
Author(s):  
Yongping Chen ◽  
Ninglin Jiang ◽  
Changkuan Zhang
Keyword(s):  
Cross Sections ◽  
Water Depth ◽  
River Discharge ◽  
Numerical Experiments ◽  
Yangtze Estuary ◽  
Main Channel ◽  
Depth Profiles ◽  
Discharge Ratio ◽  
Upper Boundary

The riverbed evolution of upper part of Yangtze estuary, Chengtong reach, is analyzed by comparison of 6 sets of bathymetry data during 1977~2011. The significant changes of water depth profiles along 6 representative cross-sections indicate the reach is still in the process of development. In order to get a better understanding of the effect of river discharge at upstream on the riverbed evolution of Chengtong reach, a series of numerical experiments are implemented by specifying different river discharge conditions at the upper boundary. The corresponding discharge ratio at main sub-reaches is compared to reveal the response of the riverbed evolution to the hydrodynamic changes at upstream. The results show that with the increase of river discharge, the discharge ratio in the main channels of Fujiangsha sub-reach and Rugaosha sub-reach increases, but it changes to decrease when the upstream river discharge becomes very large; however, the discharge ratio in the main channel of Tongzhousha sub-reach always decreases with the increase of river discharge at upstream.

scholarly journals A parallel preconditioner based on the approximation of an inverse matrix by power series for solving sparse linear systems on graphics processors

2019 ◽  
pp. 444-456
Author(s):  
А.В. Юлдашев ◽  
Н.В. Репин ◽  
В.В. Спеле
Keyword(s):  
Power Series ◽  
Linear Systems ◽  
Numerical Experiments ◽  
Computing System ◽  
Neumann Series ◽  
Inverse Matrix ◽  
Reservoir Modeling ◽  
Sparse Linear Systems ◽  
Graphics Processors ◽  
Tridiagonal Matrices

Рассмотрена применимость метода AIPS, аппроксимирующего обратную матрицу на основе степенного разложения в ряд Неймана, в рамках двухступенчатого предобусловливателя CPR. Предложен ориентированный на архитектуру CUDA параллельный алгоритм решения линейных систем с трехдиагональной матрицей, состоящей из независимых блоков различного размера. Показано, что реализация предложенного алгоритма может более чем в 2 раза превосходить по быстродействию функции решения трехдиагональных систем из библиотеки cuSPARSE. Проведено тестирование метода BiCGStab с предобусловливателем CPRAIPS на современных GPU, в том числе на гибридной вычислительной системе с 4 GPU NVIDIA Tesla V100, показавшее приемлемую масштабируемость данного предобусловливателя, а также возможность ускорить решение линейных систем, характерных для задачи гидродинамического моделирования нефтегазовых месторождений, по сравнению с CPRAMG. The applicability of the AIPS method approximating an inverse matrix using Neumann series is considered in the framework of the CPR two stage preconditioner. A parallel CUDAoriented algorithm is proposed for solving linear systems with tridiagonal matrices consisting of independent blocks of different sizes. It is shown that the implementation of the proposed algorithm can be more than twice the speed of the similar functions from the cuSPARSE library. Experimental evaluation of the BiCGStab method with the CPRAIPS preconditioner on modern GPUs, including a hybrid computing system with 4 GPU NVIDIA Tesla V100, is performed. Numerical experiments show an adequate scalability of this preconditioner as well as the possibility (compared to the CPRAMG) to accelerate the solution of linear systems being typical for the reservoir modeling problems.

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