Multiscale frequency-domain seismic inversion for fracture weakness

Abstract

Amplitude variation with offset and azimuth (AVOAz) inversion is an effective tool to invert the azimuthal seismic reflection data for fracture weaknesses, which play an important role in seismic characterization of fractures. Conventional AVOAz inversion is implemented in the time domain, which simultaneously uses full-frequency components of the seismic data causing an unstable and inaccurate inversion result in the case of noisy seismic data. Here we propose a novel multiscale frequency-domain seismic inversion approach to improve resolution and accuracy of fracture weakness estimates. Based on new derived frequency-domain expression of azimuthal seismic amplitude difference for a horizontal transversely isotropic (HTI) medium, we build the kernel function incorporated with the Fourier operator, which avoids the Fourier inverse transform in the frequency-domain inversion. Low frequency information in seismic data is often missing or contaminated with noises, thus we establish an inversion objective function combining low frequency regularization term and Cauchy sparse regularization term in the Bayesian framework. We adopt the multiscale strategy and perform inversion successively from low to high frequency group utilizing a limited number of frequency components with a high signal-to-noise (S/N) ratio. In addition, we compare the multiscale frequency-domain inversion approach, the frequency-domain simultaneous inversion approach, and the time-domain inversion approach using synthetic data and field data. Synthetic example demonstrates that the cross-correlation coefficients (CCs) between the true fracture weaknesses and the inversion results obtained by multiscale frequency-domain inversion approach are above 0.83 even with a S/N of 2. Compared to the time-domain inversion approach and the frequency-domain simultaneous inversion approach, the inversion results with multiscale frequency-domain inversion approach have higher resolution and accuracy. Field data example further validates the feasibility and superiority of the proposed multiscale frequency-domain inversion approach.