Nonlinear impedance inversion for attenuating media

摘要

Applications of seismic impedance inversion normally assumethe data are free of multiples and transmission effects,requiring knowledge of the seismic pulse that is assumed tobe stationary. An alternative formulation for impedance inversionis based on an exact frequency-domain, zero-offsetreflectivity function for a 1D medium. Analytical formulasfor the Fréchet derivatives are derived for efficient implementationof an iterative nonlinear inversion. The exact zerooffsetreflectivity accounts for internal multiples and transmissioneffects in the data.Absorption and dispersion are alsoconveniently handled if a reasonable estimate for the qualityQ factor of the medium is available.Aseries of convenientfeatures are included in the inversion algorithm: an automaticestimation of the amplitude spectrum of the seismic pulse, animpedance transform that makes the inversion independentfrom the initial smooth model, and a practical approach to estimatethe regularization weight. Numerical tests using syntheticand real data show that the method is stable and needsonly a few iterations to converge.