Reverse time migration for vertical transversely isotropic media
Abstract
One of the main assumptions for solving wave equation either numerically or analytically is to compensate the anisotropic properties which are usually observed in the earth materials. Consequently, most conventional prestack depth migration techniques based on wave equation solution are not sufficient for these anisotropic media.
Asymptotic analysis of wave propagation in vertical transversely isotropic (VTI) media yields a dispersion relation of couple P- and SV wave modes that can be converted to a fourth order scalar partial differential equation (PDE). By setting the shear wave velocity equal 0 and defining the auxiliary function, the fourth order PDE acoustic wave equation for VTI media can be reduced to a system of coupled second order PDEs and then can be solved numerically by finite difference method (FDM). The result of this P wavefi eld simulation is kinematically similar to the one of elastic VTI wavefield simulation.
Since the FDM approach can simulate the wavefield propagation in the VTI media, and reverse time migration (RTM) images the reflectors by using time extrapolation to synthesise source and receiver wavefield in the subsurface by FDM, the RTM technique is then promptly suggested to image the subsurface. The accuracy of subsurface imaging of the proposed algorithm has been verified by VTI Marmousi synthetic example.
References
K.Aki, P.G.Rechards. Quantitative seismology: theory and methods. 1980.
T.Alkhalifah. An anisotropic Marmousi model. SEP report. 1997: p. 265 - 283.
T.Alkhalifah. An acoustic wave equation for anisotropic media. Geophysics. 2000; 65: p. 1239 - 1250.
T.Alkhalifah, K.Larner. Migration error in transversely isotropic media. Geophysics. 1994; 59: p. 1405 - 1418.
E.Baysal. Modelling and migration by the Fourier transform method. PhD thesis, University of Houston. 1982.
W.F.Chang, G.A.M.Mechan. Reverse time migration in of offset vertical seismic data profiling data using the excitation time imaging condition. Geophysics. 1986; 51: p. 1514 - 1524.
J.Etgen, S.H.Grey, Y.Zhang. An overview of depth imaging in exporation geophysics. Geophysics. WCA5-WCA17. 2009; 74.
J.H.Isaac, D.C.Lawton. Imaging mispositioning due to dipping TI media: A physical seismic modeling study. Geophysics. 1999; 64: p. 1230 - 1238.
S.Jang. Imaging of the earth interior using cross correlation. PhD thesis, Hanyang University. 1996.
K.Larner, J.K.Cohen. Migration error in transversely isotropic media with linear velocity variation in depth. Geophysics. 1993; 58: p. 1454 - 1467.
K.J.Marfurt. Accuracy of finte difference and finite element modeling of scalar and elastic wave equation. Geophysics. 1984; 49: p. 533 - 549.
G.A.McMechan. Migration by extrapolation of time-dependent boundary values. Geophysical Prospecting. 1983; 31: p. 413 - 420.
C.Shin, S.Jang, D.Min. Improved amplitude preservation for prestack depth migration by inverse scattering theory. Geophysical Prospecting. 2001; 49: p. 592 - 606.
C.Shin, S.Chung. Understanding CMP stacking hyperpola in terms of partial derivative wavefield. Geophysics. 1999; 64: p. 1774 - 1782.
L.Thomsen. Weak elastic anisotropy. Geophysics. 1986; 51: p. 1954 - 1966.
1. The Author assigns all copyright in and to the article (the Work) to the Petrovietnam Journal, including the right to publish, republish, transmit, sell and distribute the Work in whole or in part in electronic and print editions of the Journal, in all media of expression now known or later developed.
2. By this assignment of copyright to the Petrovietnam Journal, reproduction, posting, transmission, distribution or other use of the Work in whole or in part in any medium by the Author requires a full citation to the Journal, suitable in form and content as follows: title of article, authors’ names, journal title, volume, issue, year, copyright owner as specified in the Journal, DOI number. Links to the final article published on the website of the Journal are encouraged.
