Pure and Applied Geophysics

, Volume 170, Issue 12, pp 2075–2085 | Cite as

2D Laplace-Domain Waveform Inversion of Field Data Using a Power Objective Function

  • Eunjin Park
  • Wansoo HaEmail author
  • Wookeen Chung
  • Changsoo Shin
  • Dong-Joo Min


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 Laplace-domain 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 Laplace-domain 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 × 10−3 to 5 × 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.


Power objective function field data inverse theory 



This work was supported financially by the Energy Efficiency & Resources (No. 2010T100200376) and Human Resources Development program (No. 20124010203200) of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) grant funded by the Korea government Ministry of Knowledge Economy. We thank GX Technology for providing us with the field data.


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Copyright information

© Springer Basel 2013

Authors and Affiliations

  • Eunjin Park
    • 1
  • Wansoo Ha
    • 1
    Email author
  • Wookeen Chung
    • 2
  • Changsoo Shin
    • 1
  • Dong-Joo Min
    • 1
  1. 1.Department of Energy Systems EngineeringSeoul National UniversitySeoulSouth Korea
  2. 2.Department of Energy and Resources EngineeringKorea Maritime UniversityBusanSouth Korea

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