Project proposal

Comparison of seismic modelling algorithms

Milana Ayzenberg has just started her PhD studies at IPT, NTNU, on the project: Three-dimensional seismic diffraction modelling (see the enclosed PhD project description). It is part of the project to compare different approaches to seismic modelling. It is proposed to use diffractions and reflections from the ocean bottom above the Ormen Lange gas field in such a study.

Cooperation with SINTEF Petroleum (dr. Stig Hestholm) is planned on finite difference modelling (a separate project proposal exists). It is also possible to cooperate with NORSAR on Kirchhoff surface integral modelling. Cooperation with dr. K. Klem-Musatov and dr. A. Aizenberg in Novosibirsk will be related to the further development of surface integrals for anisotropic media.

Budget at IPT:

NOK 250 000 per year for expenses related to M. Ayzenberg’s PhD study and cooperation with Novosibirsk.

Ph.D. project

THREE-DIMENSIONAL SEISMIC DIFFRACTION MODELLING

In seismic survey planning and in the verification of seismic interpretation it is of great interest to model the seismic response from a complex geological structure. This involves a seismic source in the water or at the top of a heterogeneous isotropic or anisotropic overburden and hydrophones in the water and/or geophones at the top of the overburden. The top of the geological target is a piece-wise smooth surface representing a faulted reservoir.

Two-dimensional and three-dimensional modelling will be performed using the following numerical methods:

i. Finite-difference modelling

ii. Hybrid ray-tracing and finite-difference modelling

iii. Edge and tip-wave diffraction modelling (Klem-Musatov et al, 1994)

iv. Surface integral using the reflection/transmission transform

(Klem-Musatov et al, 2004)

v. The Kirchhoff surface integral (Schleicher et al, 2001)

vi. The Born-Helmholtz surface integral (Ursin and Tygel, 1997)

vii. A new reciprocal surface integral (Ursin, 2004)

viii. Asymptotic solution to the surface integrals (Tygel and Ursin, 1999). This involves the geometric ray approximation and edge and tip diffractions.

New theory will have to be developed for point iv. and viii. Available computer programs will be used whenever possible; otherwise it will be developed in the project. The result will be comparisons of accuracy and computer speed for the different methods.

References

Klem-Musatov, K., Aizenberg, A., Pajchel, J., and Helle, H.P., 1994, Edge and tip diffractions. Theory and applications in seismic prospecting. Lecture notes, Norsk Hydro, Bergen.

Klem-Musatov, K., Aizenberg, A., Helle, H.B., and Pajchel, J., 2004, Reflection and transmission at curvilinear interface in terms of surface integrals. Wave Motion, 39, 77-92.

Schleicher, J., Tygel, M., Ursin, B., and Bleistein, N., 2001, The Kirchoff-Helmholtz integral for anisotropic elastic media. Wave Motion, 34, 353-364.

Tygel, M., and Ursin, B., 1999, Weak-contrast edge and vertex diffractions in anisotropic elastic media. Wave Motion, 29, 363-373.

Ursin, B., 2004, Parameter inversion and angle migration in anisotropic elastic media. Geophysics, 69, 1125-1142.

Ursin, B., and Tygel, M., 1997, Reciprocal volume and surface scattering integrals for anisotropic elastic media. Wave Motion, 26, 31-42.