2. Seismic/Geodetic Imaging Technologies
Comparison of Waveform Inversion: Amplitude Approach
Sukjoon Pyun(1), Changsoo Shin(2) and J. Bee Bednar(3)
(1) Computational Science & Technology Program, Seoul National University, Korea. (2) Division of Civil, Urban and Geosystem Engineering, Seoul National University, Korea. (3) Panorama Technologies, USA.
Abstract
In the first paper, "Comparison of waveform inversion: conventional wave field vs logarithmic wave field," of a series of three papers we investigated a logarithmic based approaches to full-waveform inversion of seismic data. Although formulated and implemented strictly in the frequency domain this in essence can be thought of as a "full" cepstrum based approach. We compared the conventional approach of Lailly (1983) and Tarantola (1984) with the logarithmic method of Shin and Min (2006) and demonstrated both theoretically and empirically that the logarithmic method was superior to the better known method. We observed that the logarithmic objective function was easily separated into amplitude and phase components which could be inverted simultaneously or individually. In the second paper, we studied the case of phase only approaches to this problem. Here we again take advantage of this separation and concentrate on deriving amplitude only approaches for both conventional and logarithmic based methods. Thus, we are after a comparison between two approaches that, at least in the optimization stage, ignore the kinematic aspects of the problem. One might conclude that this idea is doomed to failure and dismiss a study of this type out of hand. However, wavefield amplitudes are definitely sensitive to delicate velocity and impedance variations so it seemed to be worthy of investigation. Here we concentrate on velocity sensitivities, but other parameters which directly affect amplitudes would also be of interest. We define two amplitude only objective functions by simply assuming that the phase of the modeled wavefield is equal to that of the observed wavefield. We do this for both the conventional least squares approach and the logarithmic approach of Shin and Min. We show that these functions can be optimized using the same reverse-time-propagation algorithm of the full conventional methodology. Although the residuals in this case, are not really residual wavefields they can both be thought of and utilized in that sense. In contrast to the case for our phase only algorithm in the second paper of this series, we show through numerical tests that the conventional amplitude only inversion is superior to the logarithmic inversion.
Last modified: Mon May 15 13:14:34 2006