Full Waveform Inversion of Exponentially Damped Wavefield Using the Global-Correlation Norm
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Pure and Applied Geophysics
Full Waveform Inversion of Exponentially Damped Wavefield Using the Global-Correlation Norm YUNSEOK CHOI1 Abstract—Applying an exponential damping to seismic wavefield generates artificial low frequencies. Therefore, full waveform inversion (FWI) of such data has a potential to yield long wavelength structures using its artificial low frequencies. If we apply a shifted exponential damping to trace according to the offset distance, it is not trivial to implement the adjoint-state method for FWI. Applying a non-shifted exponential damping, or what I refer to as a stationary exponential damping, to all traces, we can accommodate the adjoint-state method; however, the time-domain FWI using the L2 norm of data misfit might fail in updating subsurface velocity model since a stationary exponential damping incurs an exponential-decrease of the amplitudes along offset axis. To nullify this adverse effect in retrieving subsurface velocity model, I suggest the global correlation objective function for FWI of exponentially damped wavefield instead of the L2 treatment. Keywords: Full waveform inversion, Exponential damping, Artificial low frequency, Global correlation, Amplitude.
1. Introduction Full waveform inversion (FWI) aims to reconstruct unknown model parameters (e.g. velocity, density, etc.) with high resolutions from recorded seismic data. To do so, FWI updates the background models with a quantity obtained by minimizing the residuals between the observed and modeled seismic data. Because of its potential, this subject has been widely studied for decades, especially to improve its poor success rate to a field data. However, its success primarily depends on the availability of low frequencies in the recorded seismic data (Bunks et al. 1995). Unfortunately, various factors such as mechanical limitations in acquisition equipment, poor
1 Petroleum and Marine Research Division, Korea Institute of Geoscience and Mineral Resources, Daejeon, South Korea. E-mail: [email protected]
signal-to-noise ratio and so on prevent us from recording low frequencies in the field seismic survey. Recently, many studies have been devoted to employing the artificial low frequencies in FWI framework, especially to retrieve a long wavelength model. Wu et al. (2014) considered the envelope only rather than the entire features of a seismic signal. Even if seismic trace has no low frequencies, its envelope induces the artificial low frequency components, and thus, its usage in FWI machinery is capable of providing long wavelength features. Jeon et al. (2014) and Choi and Kalita (2019) exploited the integral wavefield to formulate an objective function for FWI. The integral wavefield has a long wavelength feature in nature, thus it has a potential to provide long wavelength updates in FWI. Li et al. (2018) nonlinearly manipulated the wavefield (nonlinear wavefield such as the squared wavefield) to generate the artificial low frequencies and used them to yield long wavelength updates in FWI. On the other hand, Choi and A
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