Frequency-domain reverse time migration using the L1-norm

Lee, J., Kim, Y. and Shin, C., 2012. Frequency-domain reverse time migration using the L,-norm. Journal of Seismic Exploration, 21: 281-300. Waveform inversion algorithms generally use the L,-norm. However, previous work indicates that the L,-norm objective function can produce better results than the L,-norm objective function because the Li-norm is more robust against outliers. Moreover, because field data always contain some outliers, adopting the L,-norm objective function for waveform inversion would therefore be beneficial. Thus, we consider adopting the L,-norm for reverse time migration, since the algorithm structure of reverse time migration is identical to that of waveform inversion. Thus, we propose introducing the L,-norm into frequency domain reverse time migration for 2D acoustic media. To verify the effectiveness of our algorithm, we compare the results with those from the conventional algorithm. First, we apply both algorithms to synthetic data drawn from the Marmousi model. We also apply both algorithms to synthetic data on which we add artificial random outliers. Considering the data without outliers, both algorithms yield similar results regardless of the norm used. However, when we consider the data containing outliers, our algorithm using the L,-norm yields better results. We then apply the same algorithm to field data obtained from an area in the Gulf of Mexico. As expected from the synthetic test, our algorithm yields superior results. Through these experiments, we conclude that the newly proposed algorithm would be useful for performing reverse time migration on data containing considerable outliers, thus eliminating some preprocessing steps through the use of the L,-norm.
- Baysal, E., Kosloff, D.D. and Sherwood, J.W.C., 1983. Reverse time migration. Geophysics, 48:1514-1524.
- Chavent, G. and Plessix, R.E., 1999. An optimal true-amplitude least-squares prestackdepth-migration operator. Geophysics, 64: 508-515.
- Claerbout, J.F. and Muir, F., 1973. Robust modeling with erratic data. Geophysics, 38: 826-844.
- Clayton, R. and Enquist, B., 1977. Absorbing boundary conditions for acoustic and elastic waveequations. Bull. Seismol. Soc. Am., 67: 1529-1540.
- Crase, E., Pica, A., Noble, M., McDonald, J. and Tarantola, A., 1990. Robust elastic nonlinearwaveform inversion; application to real data. Geophysics, 55: 527-538.
- Dennis, J., 1997. Nonlinear least squares and equations. In: Jacobs, D. (Ed.), The State of the Artof Numerical Analysis. Academic Press, Inc., New York.
- Guitton, A., Kaelin, B. and Biondi, B., 2007. Least-squares attenuation of reverse-time-migrationartifacts. Geophysics, 72: 19-23.
- Ha, T., Chung, W. and Shin, C., 2009. Waveform inversion using a back-propagation algorithmand a Huber function norm. Geophysics, 74: 15-24.
- Jang, U., Min, D.-J. and Shin, C., 2009. Comparison of scaling methods for waveform inversion.Geophys. Prosp., 57: 49-59.
- Lailly, P., 1983. The seismic inverse problem as a sequence of before stack migrations. Conf. on
- Inverse Scattering, Theory and Applied Mathematics, Expanded Abstr.: 206-220.
- Loewenthal, D. and Mufti, I.R., 1983. Reverse time migration in spatial frequency domain.Geophysics, 48: 627-635.
- Marfurt, K.J., 1984. Accuracy of finite-difference and finite-element modeling of the scalar andelastic wave equation. Geophysics, 49: 533-549.
- Monteiller, V., Got, J.-L., Virieux, J. and Okubo, P.G., 2005. An efficient algorithm fordouble-difference tomography and location in heterogeneous media, with an application tothe Kilauea volcano. J. Geophys. Res., 110: B12306, doi:10.1029/2004JB003466
- Officer, C.B., 1958. Introduction to the Theory of Sound Transmission with Application to theOcean. McGraw-Hill, New York.
- Pratt, R.G., Shin, C. and Hicks, G.J., 1998. Gauss-Newton and full Newton methods infrequency-space seismic waveform inversion. Geophys. J. Internat., 133: 341-362.
- Pyun, S., Son, W. and Shin, C., 2009. Frequency-domain waveform inversion using an -normobjective function. Explor. Geophys., 40: 227-232.
- Shin, C. and Chung, S., 1999. Understanding CMP stacking hyperbola in terms of partial derivativewavefield. Geophysics, 64: 1774-1782.
- Shin, C., Jang, S. and Min, D.-J., 2001. Improved amplitude preservation for prestack depthmigration by inverse scattering theory. Geophys. Prosp., 49: 592-606.
- Shin, C., Min, D.-J., Yang, D. and Lee, $.K., 2003. Evaluation of poststack migration in termsof virtual source and partial derivative wavefields. J. Seismic Explor., 12: 17-37.
- Tarantola, A., 1984. Inversion of seismic reflection data in the acoustic approximation. Geophysics,49: 1259-1266.300 LEE, KIM & SHIN
- Whitmore, N.D., 1983. Iterative depth migration by backward time propagation. Expanded Abstr.,53rd Ann. Internat. SEG Mtg., Las Vegas.
- Zienkiewicz, O.C. and Taylor, R.L., 1991. The Finite Element Method, 4th ed. McGraw HillHigher Education, New York.