Frequency-domain waveform inversion using an l1-norm objective function

In general, seismic waveform inversion adopts an objective function based on the l2-norm. However, waveform inversion using the l2-norm produces distorted results because the l2-norm is sensitive to statistically invalid data such as outliers. As an alternative, there have been several studies applying l1-norm-based objective functions to waveform inversion. Although waveform inversion based on the l1-norm is known to produce robust inversion results against specific outliers in the time domain, its effectiveness and characteristics are yet to be studied in the frequency domain. The present study proposes an algorithm for l1-norm-based waveform inversion in the frequency domain. The proposed algorithm employs a structure identical to those used in conventional frequency-domain waveform inversion algorithms that exploit the back-propagation technique, but displays robustness against outliers, which has been confirmed based on inversion of the synthetic Marmousi model. The characteristics and advantages of the l1-norm were analysed by comparing it with the l2-norm. In addition, inversion was performed on data containing outliers to examine the robustness against outliers. The effectiveness of removing outliers was verified by using the l1-norm to calculate the residual wavefield and its spectrum for the data containing outliers.

[1]  R. Pratt.  Inverse theory applied to multisource cross-hole tomography, Part2 : Elastic wave-equation method , 1990 .

[2]  R. Pratt.  Seismic waveform inversion in the frequency domain; Part 1, Theory and verification in a physical scale model , 1999 .

[3]  C. Shin,et al.  Improved amplitude preservation for prestack depth migration by inverse scattering theory , 2001 .

[4]  Jean Virieux,et al.  Crustal seismic imaging from multifold ocean bottom seismometer data by frequency domain full waveform tomography: Application to the eastern Nankai trough , 2006 .

[5]  Jean Virieux,et al.  Multiscale imaging of complex structures from multifold wide-aperture seismic data by frequency-domain full-waveform tomography: application to a thrust belt , 2004 .

[6]  Z. M. Song,et al.  Frequency-domain acoustic-wave modeling and inversion of crosshole data; Part II, Inversion method, synthetic experiments and real-data results , 1995 .

[7]  P. Mora.  Nonlinear two-dimensional elastic inversion of multioffset seismic data , 1987 .

[8]  Mark Noble,et al.  Robust elastic nonlinear waveform inversion: Application to real data , 1990 .

[9]  A. Tarantola.  Inversion of seismic reflection data in the acoustic approximation , 1984 .

[10]  A. Pica,et al.  Nonliner inversion of seismic reflection data in a laterally invariant medium , 1990 .

[11]  Changsoo Shin,et al.  Comparison of waveform inversion, part 1: conventional wavefield vs logarithmic wavefield , 2007 .

[12]  Roelof Versteeg,et al.  The Marmousi experience; velocity model determination on a synthetic complex data set , 1994 .

[13]  Changsoo Shin,et al.  Waveform inversion using a logarithmic wavefield , 2006 .

[14]  A. Tarantola,et al.  Two‐dimensional nonlinear inversion of seismic waveforms: Numerical results , 1986 .

[15]  A. Tarantola,et al.  Nonlinear Inversion of Seismic Reflection Data , 1984 .

[16]  R. Gerhard Pratt,et al.  Efficient waveform inversion and imaging: A strategy for selecting temporal frequencies , 2004 .

[17]  J. Claerbout,et al.  Robust Modeling With Erratic Data , 1973 .

[18]  Albert Tarantola,et al.  Multiparameter l 1 norm waveform fitting; interpretation of Gulf of Mexico reflection seismograms , 1999 .