Migrated Exploding Reflectors in Evaluation of Finite Difference Solution for Inhomogeneous Seismic Models

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Earth is inhomogeneous, which means its elastic characteristics change with depth. The seismic method employs the propagation of waves throughout the earth to locate different structures and stratigraphy. Understanding the wave propagation is an important matter in exploration seismology; therefore modeling of seismic wave is an important tool. To validate the interpreted earth model out of the seismic data, seismic synthetic seismograms should be generated in a process named “seismic forward modeling”. Finite difference method is used as one of the most common numerical modeling techniques. In this paper the accuracy of finite difference method in seismic section modeling is explored on different modeled data set of heterogeneous earth. It is shown that finite difference method completes with migration to reposition the events in their correct location. Two different migration methods are used and various velocities are also tested to determine an appropriate migration velocity. Finally the validly of finite difference modeling is examined using a 2D structural similarity index technique.

References

[1] K. Zoeppritz, “Erdbebenwellen VII. VIIb. über Reflexion und Durchgang Seismischer Wellen durch Unstetigkeitsfl?chen. Nachrichten von der K?niglichen Gesellschaft der Wissenschaften zu G?ttingen,” Mathematisch-Physikalische Klasse, 1919, pp. 66-84.

[2] R. E. Sheriff and L. P. Geldart, “Exploration Seismology,” 2nd Edition, Cambridge University Press, Cambridge, 1995. doi:10.1017/CBO9781139168359

[3] M. Zaitian, “Seismic Imaging Technology: The Finite Difference Migration,” China Petroleum Industry Press, Beijing, 1989.

[4] J. E. Vidale, “Finite-Difference Calculation of Traveltimes in Three Dimensions,” Geophysics, Vol. 55, No. 5, 1990, pp. 521-526. doi:10.1190/1.1442863

[5] R. T. Coates and M. Schoenberg, “Finite-Difference Modeling of Faults and Fractures,” Geophysics, Vol. 60, 1995, pp. 1514-1526. doi:10.1190/1.1443884

[6] A. Pitarka, “3D Elastic Finite-Difference Modeling of Seismic Motion Using Staggered Grids with Nonuniform Spacing,” Bulletin of the Seismological Society of America, Vol. 89, 1999, pp. 54-68.

[7] C. F. Youzwishen and G. F. Margrave, “Finite Difference Modelling of Acoustic Waves in Matlab,” Crewes Report, Vol. 11, 1999, pp. 1-19.

[8] J. M. Carcione, G. B?hm and A. Marchetti, “Simulation of a CMP Seismic Section,” Journal of Seismic Exploration, Vol. 3, 1994, pp. 381-396.

[9] D. Loewenthal, L. Lu, R. Roberson and J. W. C. Sherwood, “The Wave Equation Applied to Migration,” Geophysical Prospecting, Vol. 24, 1976, pp. 380-399.

[10] J. F. Claerbout, “Basic Earth Imaging: Stanford Exploration Project,” Preliminary, 1993.
http://sepwww.stanford.edu/sep/prof/index.html

[11] Z. Wang, A. C. Bovik, H. R. Sheikh and E. P. Simoncelli, “Image Quality Assessment: From Error Visibility to Structural Similarity,” IEEE Transactions on Image Processing, Vol. 13, No. 4, 2004, pp. 600-612.
doi:10.1109/TIP.2003.819861