2D Laplace-Domain Waveform Inversion of Field Data Using a Power Objective Function
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Pure and Applied Geophysics
2D Laplace-Domain Waveform Inversion of Field Data Using a Power Objective Function EUNJIN PARK,1 WANSOO HA,1 WOOKEEN CHUNG,2 CHANGSOO SHIN,1 and DONG-JOO MIN1 Abstract—The wavefield in the Laplace domain has a very small amplitude except only near the source point. In order to deal with this characteristic, the logarithmic objective function has been used in many Laplace domain inversion studies. The Laplacedomain waveform inversion using the logarithmic objective function has fewer local minima than the time- or frequency domain inversion. Recently, the power objective function was suggested as an alternative to the logarithmic objective function in the Laplace domain. Since amplitudes of wavefields are very small generally, a power \1 amplifies the wavefields especially at large offset. Therefore, the power objective function can enhance the Laplacedomain inversion results. In previous studies about synthetic datasets, it is confirmed that the inversion using a power objective function shows a similar result when compared with the inversion using a logarithmic objective function. In this paper, we apply an inversion algorithm using a power objective function to field datasets. We perform the waveform inversion using the power objective function and compare the result obtained by the logarithmic objective function. The Gulf of Mexico dataset is used for the comparison. When we use a power objective function in the inversion algorithm, it is important to choose the appropriate exponent. By testing the various exponents, we can select the range of the exponent from 5 9 10-3 to 5 9 10-8 in the Gulf of Mexico dataset. The results obtained from the power objective function with appropriate exponent are very similar to the results of the logarithmic objective function. Even though we do not get better results than the conventional method, we can confirm the possibility of applying the power objective function for field data. In addition, the power objective function shows good results in spite of little difference in the amplitude of the wavefield. Based on these results, we can expect that the power objective function will produce good results from the data with a small amplitude difference. Also, it can partially be utilized at the sections where the amplitude difference is very small. Key words: Power objective function, field data, inverse theory.
1
Department of Energy Systems Engineering, Seoul National University, Gwanak-ro 1, Gwanak-gu, 151-744 Seoul, South Korea. E-mail: [email protected] 2 Department of Energy and Resources Engineering, Korea Maritime University, 727 Taejong-ro, Yeongdo-gu, 606-791 Busan, South Korea.
1. Introduction Since LAILLY (1983) and TARANTOLA (1984) suggested the back-propagation technique for waveform inversion, many studies on waveform inversion have been performed in the time domain (MORA 1987; BUNKS et al. 1995; SHIPP and SINGH 2002) and in the frequency domain (GELLER and HARA 1993; PRATT et al. 1998; OPERTO et al. 2004; SHIN and MIN 2006; SHIN et
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