Uncertainty quantification in rock physics full waveform inversion

Qi Hu, Tianze Zhang, Kristopher A. Innanen

Uncertainty quantification is a fundamental aspect of seismic analysis, enhancing the reliability of results obtained from seismic data. This practice enables a more informed and responsible approach to decision-making in various engineering and geoscience applications. We establish a recurrent neural network with rules that enforce the integration of rock physics modeling and elastic wave propagation. The network is then trained using the wavefield projected onto a measurement surface as labeled data, which is compared with observed seismic data. This training process involves the direct prediction of rock physics properties through Full Waveform Inversion (FWI). Utilizing the Automatic Differential method, we accurately and efficiently construct gradients through inspection and the use of the computational graph. The inverse Hessian, closely related to the posterior covariance operator, is then approximated using these gradients, providing uncertainty estimations for the rock physics variables. Our workflow is applied to address two geophysical inverse problems: seismic reservoir characterization and time-lapse CO₂ monitoring.