Arkady Aizenberg

3D diffraction modeling of singly scattered acoustic wavefields based on the combination of surface integral propagators and transmission operators

We present an improved method for modeling 3D acoustic wavefields scattered at smooth curved interfaces. The approach is based on a high-frequency approximation of surface integral propagators and a correct description of their boundary values in terms of transmission operators. The main improvement is a uniform local approximation of these operators in the form of effective reflection and transmission coefficients. We show that the effective coefficients represent a generalization of the plane-wave coefficients widely used in conventional seismic modeling, even for the case of curved reflectors, nonplanar wavefronts, and finite frequencies. The proposed method is capable of producing complex wave phenomenas, such as caustics, edge diffractions, and head waves. Seismograms modeled for even simple models reveal significant errors implicit in the plane-wave approximation. Comparison of modeling based on effective coefficients with the analytic solution reveals errors less than 4% in peak amplitude at seismic frequencies.

Effective reflection coefficients for curved interfaces in transversely isotropic media

Plane-wave reflection coefficients PWRCs are routinely used in amplitude-variation-with-offset analysis and for generating boundary data in Kirchhoff modeling. However, the geometrical-seismics approximation based on PWRCs becomes inadequate in describing reflected wavefields at near- and postcritical incidence angles. Also, PWRCs are derived for plane interfaces and break down in the presence of significant reflector curvature. Here, we discuss effective reflection coefficients ERCs designed to overcome the limitations of PWRCs for multicomponent data from heterogeneous anisotropic media. We represent the reflected wavefield in the immediate vicinity of a curved interface by a generalized plane-wave decomposition, which approximately reduces to the conventional Weyl-type integral computed for an apparent source location. The ERC then is obtained as the ratio of the reflected and incident wavefields at each point of the interface. To conduct diffraction modeling, we combine ERCs with the tip-wave superposition methodTWSM, extended to elastic media. This methodology is implemented for curved interfaces that separate an isotropic incidence half-space and a transversely isotropic TI medium with the symmetry axis orthogonal to the reflector. If the interface is plane, ERCs generally are close to the exact solution, sensitive to the anisotropy parameters and source-receiver geometry. Numerical tests demonstrate that the difference between ERCs and PWRCs for typical TI models can be significant, especially at low frequencies and in the postcritical domain. For curved interfaces, ERCs provide a practical approximate tool to compute the reflected wavefield. We analyze the dependence of ERCs on reflector shape and demonstrate their advantages over PWRCs in 3D diffraction modeling of PP and PS reflection data.

Tip-wave superposition method with effective reflection and transmission coefficients: A new 3D Kirchhoff-based approach to synthetic seismic modeling

Interest in synthetic modeling of seismic wavefields scattered in the subsurface is growing today due to its applicability in various forward and inverse problems of geophysics. It has been used extensively for general evaluation of the subsurface structure, in survey design and illumination studies, and also as the basis for imaging and inversion algorithms. Models with complex geological structures that contain strong-contrast or irregular reflectors and shadow zones and where conventional algorithms fail to simulate realistic wavefields present a particular challenge.

Effective Reflection Coefficients for Curved Interfaces in TI Media

We introduce so-called “effective” reflection coefficients (ERC) for curved interfaces in transversely isotropic media. If the reflector is plane, ERC describe the exact reflected wavefield for the full range of incidence angles, while plane-wave reflection coefficients become inadequate at near-critical and post-critical angles. For curved reflectors, ERC provide a practical way of computing the wavefield without using such time-consuming methods as finite differences. We analyze parameter dependence of ERC and evaluate the potential of using them in amplitude-versus-offset inversion and Kirchhoff-type modeling.

Analysis of Wave Scattering from a Viscoelastic Layer with Complex Shape

The Discretized Kirchhoff Integral method has been recently tested against laboratory experiments using a model with surface curvatures and sharp edges generating wave diffraction effects. Comparisons between numerical and laboratory data have exhibited a good quantitative fit in terms of time arrivals and amplitudes, except in the vicinity of secondary shadow boundaries created by the interaction of the edges of some topographical structures. Following this work, the effect of multiple scattering and the surface curvatures on the wavefield is studied here, using the so-called diffraction attenuation coefficient, in order to define the cases where these effects may be neglected in the numerical modeling without loss of accuracy.

Single-diffraction Approximation of the Feasible Green’s Function in Geometrical Shadow Zones

The subsurface image is often generated by applying an imaging condition, which implies the knowledge of the conventional Greens function satisfying the Fermats principle. The presence of geometrical shadow zones in the model limits its applicability and requires a Greens function satisfying the generalized Fermats (Hadamard’s) principle for complex subsurface geometries. We show that the feasible Greens function in the vicinity of geological discontinuities (salt domes, reef edges, pinchouts, etc.) contains a cascade diffraction which corrects the conventional Greens function. We provide numerical examples for an acoustic model with a concave boundary, which illustrate the dependence of the single-diffraction approximation of the feasible Greens function on the curvature of boundary in a vicinity of the line of ray tangency.

3-D Acoustic Green's Function Modeling in Multilayered Overburden

P293 3-D Acoustic Green’s Function Modeling in Multilayered Overburden M. Ayzenberg* (Norwegian University of Science & Technology) A. Aizenberg (Institute of Petroleum Geology and Geophysics) H. Helle (Odin Petroleum) K. Klem-Musatov (Institute of Petroleum Geology and Geophysics) J. Pajchel (Norsk Hydro) & B. Ursin (Norwegian University of Science & Technology) SUMMARY We present an analytic approach to the description and modeling of the 3-D acoustic waves in complex multilayered overburden. The total scattered wavefield is split into a branching sequence of multiply reflected/transmitted wavefields which can be directly identified with the intermediate reflectors generating them. Each wavefield is represented by

Modeling of seismic waves in layers with shadow boundaries in terms of unsparse propagation-absorption matrices: realization and optimization

The conventional Greens 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 Greens 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 Greens function has been introduced as the superposition of the conventional Greens function and cascade diffraction. Cascade diffraction compensates for the unfeasible parts of the conventional Greens 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.

Modeling of Cascade Diffraction in Terms of Propagation-absorption Matrices - Realization and Optimization for GPU

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 algorithm for modeling the single-diffraction approximation of thecascade 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.

3D Seismic Diffraction Modeling in Multilayered Media in Terms of Surface Integrals

SUMMARY We present an improved multiple tip wave superposition method (MTWSM) for the 3-D seismic modeling in multilayered media in terms of the Kirchhoff type integrals. The main improvement consists in correct description of their boundary values by the reflection/transmission operators. The high-frequency approximation of the operators (effective coefficients) generalizes the plane-wave coefficients used in the conventional seismics and allows adequate reproduction of multiple reflections and transmissions accounting for the nearcritical effects. To show the potential of the MTWSM we give results of the Greens function modeling for a strong-contrast curvilinear interface in two-layered acoustic medium.