Efficient calculation of the steepest descent direction for source-independent seismic waveform inversion

In seismic waveform inversion, if we have no information on source signature, we need to invert seismic data and source signature either simultaneously or successively. In order to avoid the iterative update of the source signature in waveform inversion based on classical, local optimization techniques, we propose two source-independent objective functions using amplitude spectra of Fourier-transformed wavefields. One is constructed by normalizing the amplitude spectra of observed data and modeled data with respect to the respective reference amplitudes. The other is achieved by cross-multiplying the amplitude spectra of observed data and modeled data with the respective reference amplitudes. In the computation of the steepest descent direction, we circumvent explicitly computing the Jacobian by employing a matrix formalism of the wave equation in the frequency domain. Through numerical examples for the Marmousi model, we demonstrate that our inversion algorithms can reproduce the subsurface velocity structure without estimating source signature.

[1]  G. Chavent,et al.  Inversion of normal incidence seismograms , 1982 .

[2]  Albert Tarantola,et al.  The Non-Linear Inversion of Seismic Waveforms can BE Performed either by Time Extrapolation or by Depth EXTRAPOLATION1 , 1988 .

[3]  Gerard T. Schuster,et al.  Wave-equation traveltime inversion , 1991 .

[4]  A. Tarantola.  A strategy for nonlinear elastic inversion of seismic reflection data , 1986 .

[5]  G. McMechan,et al.  3-D prestack full-wavefield inversion , 1995 .

[6]  Wafik B. Beydoun,et al.  A simultaneous inversion for background velocity and impedance maps , 1990 .

[7]  G. Schuster,et al.  Acoustic wave-equation traveltime and waveform inversion of crosshole seismic data , 1995 .

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

[9]  R. Shipp,et al.  Seismic waveform inversion in the frequency domain, Part 2: Fault delineation in sediments using crosshole data , 1999 .

[10]  Full-wavefield inversion of wide-aperture SH and Love wave data , 1991 .

[11]  C. H. Chapman,et al.  Crosshole seismic tomography , 1989 .

[12]  Understanding CMP stacking hyperbola in terms of partial derivative wavefield , 1999 .

[13]  Hicks,et al.  Gauss–Newton and full Newton methods in frequency–space seismic waveform inversion , 1998 .

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

[15]  G. McMechan,et al.  2‐D full‐wavefield inversion for wide‐aperture, elastic, seismic data , 1992 .

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

[17]  S. Greenhalgh,et al.  Crosshole seismic inversion with normalized full‐waveform amplitude data , 2003 .

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

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

[20]  K. Marfurt.  Accuracy of finite-difference and finite-element modeling of the scalar and elastic wave equations , 1984 .

[21]  J. Harris,et al.  Elastic wave equation traveltime and waveform inversion of crosswell data , 1997 .

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

[23]  P. Lailly,et al.  Pre-stack inversion of a 1-D medium , 1986, Proceedings of the IEEE.

[24]  C. Shin,et al.  An optimal 9-point, finite-difference, frequency-space, 2-D scalar wave extrapolator , 1996 .