2. Seismic/Geodetic Imaging Technologies
Comparison of Waveform Inversion: Phase Approach
J. Bee Bednar(1), Changsoo Shin(2) and Sukjoon Pyun(3)
(1) Panorama Technologies, USA. (2) Division of Civil, Urban and Geosystem Engineering, Seoul National University, Korea. (3) Computational Science & Technology Program, Seoul National University, Korea.
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 approach 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. Here we take advantage of this separation and concentrate on deriving phase only approaches for both conventional and logarithmic based methods. Thus, we are after a comparison between two approaches to what might be called full waveform kinematic inversion. We show that both of these new techniques, although different in implementation style, share the same methodology for computation of the steepest descent directions. In fact, we show that the residual for our new logarithmic method can be considered to be a simple scaling by the a phase difference which confirms the reverse-time formulation of the required gradients. Again, we show that our phase based method is more robust than its conventional phase-only counterpart.
Last modified: Mon May 15 13:11:58 2006