Papers by Arkady Aizenberg
Geophysics, 2009
Three-dimensional seismic modeling is an important tool widely used in many areas of exploration.... more Three-dimensional seismic modeling is an important tool widely used in many areas of exploration. Geologically complex areas with strong reflectors, shadow zones and diffracting edges still impose challenges to conventional modeling techniques. To overcome some of the existing limitations, we have been developing a new approach to the theoretical description and numerical modeling of three-dimensional acoustic wavefields scattered in layered media. This approach belongs to the group of analytical approaches which merge the methods based on the surface integral representation and the wavenumber-domain decomposition. The approach is based on an explicit representation of the scattered wavefield as the superposition of events multiply reflected and transmitted in accordance with the wavecode, which allows modeling of selected events independently. Each event is formed by the sequential action of classical surface integral propagators and convolutional reflection and transmission operators. We use a high-frequency approximation of the propagators in the form of a multiple tip-wave superposition method. Also, we reduce the reflection and transmission operators to effective reflection and transmission coefficients. The effective coefficients represent a generalization of the plane-wave coefficients widely used in the conventional seismic modeling for curved reflectors, non-planar wavefronts and finite frequencies. As we demonstrate in the paper, the new method is capable of reproducing complex wave phenomena, such as caustics, edge diffractions and head waves. We believe that the proposed approach has a strong potential for improving the seismic image resolution, in particular by a better description of the Green's function in geologically complex media. 1 form. In Appendix C, we explain how the propagators and reflection and transmission operators can be combined in order to obtain the transmission-propagation operators. In Appendix D, we derive an approximation for these operators, which is convenient for computational purposes. Thus we validate the MTWSM-approach.
71st EAGE Conference and Exhibition incorporating SPE EUROPEC 2009, 2009
ABSTRACT
Analysis of seismic reflection amplitudes versus offset (AVO) is one of common techniques widely ... more Analysis of seismic reflection amplitudes versus offset (AVO) is one of common techniques widely exploited in the industry for reservoir characterization. For the last two decades a lot of approaches to analysis, inversion and interpretation of AVO data have been developed. Existing modifications valid for weak-contrast interfaces were successfully employed for conventional reservoirs. The growing interest of the industry to unconventional reservoirs, such as stiff-carbonate reservoirs, heavy oil traps and reservoirs close to salts domes - associated with strong-contrast interfaces and critical angles - implies the development of AVO techniques valid prior and beyond the critical angle. It has been reported in literature that near- and post-critical reflections have a potential to be employed as an additional source of information about the media. However, the use of these reflections is limited by the inability of well-known Zoeppritz equations to explain phenomena observed around and beyond the critical angle. The aim of the thesis is to investigate phenomena observed at the reflected data around and beyond the critical angle, understand their potential from the AVO analysis and inversion point of view and develop a long-offset AVO inversion approach valid for strong-contrast interfaces. The theory of effective reflection coefficients is exploited as a mathematical apparatus providing an adequate description of phenomena observed at near- and post-critical reflections. The thesis consists of five papers, where four major issues are addressed. The sensitivity of the reflection coefficient to isotropic and HTI media parameter changes prior to and beyond the critical angle is studied. The long-offset AVO inversion approach valid prior to and beyond the critical angle, strong-contrast and curved interfaces is developed and tested on synthetic data obtained for models with a single interface of various curvatures. Frequency effects in pre- near- and post-critical domains observed on the data of physical modeling are studied from the point of view of potential exploiting. Finally, the sensitivity of long-offset AVO inversion to errors related to overburden velocity misinterpretation is analyzed.
Abstract Plane-wave reflection coefficients (PWRC) are routinely used in amplitude- variation-wit... more Abstract Plane-wave reflection coefficients (PWRC) are routinely used in amplitude- variation-with-offset (AVO) analysis and for generating boundary data in Kirch- hoff modeling. However, the geometrical-seismics approximation based on PWRC becomes,inadequate in describing reflected wavefields at near- and post-critical incidence angles. Also, PWRC are derived for plane interfaces and break down in the presence of significant reflector curvature. Here, we dis- cuss so-called effective reflection coefficients (ERC) designed to overcome the limitations of PWRC for multicomponent data from heterogeneous anisotropic media. We show that the reflected wavefield in the immediate vicinity of a curved interface can be represented by a generalized plane-wave decomposition, which approximately reduces to the conventional Weyl-type integral computed,for an “apparent” source location. The ERC is then obtained as the ratio of the reflected and incident wavefields at each point of the interface. T...
Proceedings of the 2012 Joint International Conference on Human-Centered Computer Environments - HCCE '12, 2012
ABSTRACT The conventional Green's function introduced for an unbounded medium and applied... more ABSTRACT The conventional Green's function introduced for an unbounded medium and applied in domains with complex boundaries may contain physically unfeasible components. These components would not be observed in an experimental study and thus lead to misinterpretation of the wave-field structure. The feasible Green's function that does not contain unfeasible components satisfies the principle of absorption of the part of the wavefield which penetrate the shadow zones formed by the concave parts of layer boundaries [9, 7]. Recently the feasible Green's function has been introduced as the superposition of the conventional Green's function and cascade diffraction. Cascade diffraction compensates for the unfeasible parts of the conventional Green's function and takes into account the actual shape of the boundaries. We represent a new algorithm for modelling the single-diffraction approximation of the cascade diffraction in terms of unsparse propagation-absorption matrices and provide numerical examples for an acoustic half-space with a wedge-shaped boundary, which illustrate the accuracy and efficiency of the algorithm.
The Leading Edge, 2009
ABSTRACT
London 2013, 75th eage conference en exhibition incorporating SPE Europec, 2013
ABSTRACT The conventional Green’s function introduced for an unbounded medium and applied in doma... more ABSTRACT The conventional Green’s function introduced for an unbounded medium and applied in domains with complex boundaries may contain physically unfeasible components. These components would not be observed in an experimental study and thus lead to misinterpretation of the wavefield structure. Recently the feasible Green’s function has been introduced as the superposition of the conventional Green’s function and cascade diffraction. Cascade diffraction compensates for the unfeasible parts of the conventional Green’s function and takes into account the actual shape of the boundaries. We represent a new highly-optimized TWSM algorithm for modeling the double-diffraction approximation of the cascade diffraction in terms of unsparse propagation-absorption matrices. Accuracy, stability and efficiency of the algorithm are illustrated by numerical examples for an acoustic half-space with a W-shaped boundary.
London 2013, 75th eage conference en exhibition incorporating SPE Europec, 2013
ABSTRACT The synthetic wavefield is often generated by applying an illuminating condition which i... more ABSTRACT The synthetic wavefield is often generated by applying an illuminating condition which implies the knowledge of the conventional Green's function satisfying the Fermat's principle. The presence of geometrical shadow zones in the model restricts its applicability and requires a Green's function satisfying the generalized Fermat's (Hadamard’s) principle. We show that the feasible Green's function in the vicinity of geological obstacles (salt domes, reef edges, pinchouts, etc.) includes a cascade diffraction term that improves the conventional Green's function. We provide numerical examples for an acoustic model with a concave boundary which illustrate wave structure of the double-diffraction approximation of the feasible Green's function.
Proceedings, 2014
ABSTRACT We consider a salt overhang model with salt body covered by sediments. The problem of mo... more ABSTRACT We consider a salt overhang model with salt body covered by sediments. The problem of modeling of the wavefield below salt body is solved with help of the cascade diffraction method. The near-front wavefield is a superposition of the feasible double-transmitted wavefield and the feasible direct wave which is a conventional direct wave corrected by the diffraction correction. We provide numerical examples which illustrate the structure of the wavefield.
Wave Motion, 2015
h i g h l i g h t s • We consider the multiphysics wave equation in arbitrary inhomogeneous domai... more h i g h l i g h t s • We consider the multiphysics wave equation in arbitrary inhomogeneous domains. • We introduce new integral absorption condition at the boundary of a homogeneous domain. • We derive feasible fundamental solution in the homogeneous domain using new condition. • Feasible fundamental solution in the inhomogeneous domain accounts for the above solution. • We determine surface and volume propagation integrals with the feasible kernels.
PAMM, 2007
We schematically derive rigorous transmission and reflection operators at a curved interface betw... more We schematically derive rigorous transmission and reflection operators at a curved interface between heterogeneous acoustic media. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
EAGE/SPE Workshop on Subsalt Imaging, 2014
ABSTRACT The presence of geometrical shadow zones in the model requires a feasible Green'... more ABSTRACT The presence of geometrical shadow zones in the model requires a feasible Green's function satisfying the generalized Fermat's (Hadamard's) principle. We show that this function in the vicinity of geological obstacles (salt domes, reef adges, pinchouts, etc.) includes a cascade diffraction term that improves the conventional Green's function. We provide numerical examples of the double-diffraction approximation of the feasible Green's function and its wave components in a sub-salt zone.
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Papers by Arkady Aizenberg