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Application of facies constraints and machine learning to full-waveform inversion for anisotropic media
Singh, Sagar
Singh, Sagar
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2022
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2023-09-30
Abstract
The nonlinearity of seismic full-waveform inversion (FWI) and parameter trade-offs can prevent convergence toward the actual model, especially for elastic anisotropic media. The problems with parameter updating become particularly severe if ultra-low-frequency seismic data are unavailable and the initial model is not sufficiently accurate. In this thesis, I develop an efficient FWI framework to incorporate prior geologic information with the goal of mitigating the issues mentioned above. In addition to deterministic inversion strategies, I employ stochastic schemes, including Bayesian deep-learning models. I design parallelized algorithms (on both CPU and GPU) to efficiently simulate the wavefield for inversion-gradient computation and for training machine-learning models.
First, I develop a Bayesian framework for FWI of multicomponent seismic data from isotropic elastic media and investigate the impact of significantly distorted initial model and of the absence of low frequencies in the data. The unconstrained FWI algorithm suffers from trade-offs between the model parameters that substantially distort the inversion results. By stochastically incorporating prior geologic (or facies) information into the inversion, it is possible to reduce the trade-offs and produce the high-resolution velocity and, potentially, density models without using ultra-low frequencies. This methodology is successfully applied to 2D and 3D elastic models.
Next, this technique is extended to transversely isotropic models with a vertical axis of symmetry (VTI media). An image-guided interpolation algorithm is employed to create the spatial distribution of facies from sparse borehole locations, some of which may be far from the target reservoir. The facies-constrained algorithm substantially reduces the nonlinearity of FWI and guides the inversion toward the global minimum of the objective function for realistic levels of noise in the data. Although including multicomponent data improves the spatial resolution of the inverted parameters, the facies-based FWI of more common pressure recordings yields an adequate reconstruction of most VTI parameter fields.
Transverse isotropy adequately describes the elastic properties of unfractured shale formations and finely layered sequences in typical sedimentary basins. However, the presence of natural fracture sets and/or non-hydrostatic stresses reduces the medium symmetry to at least orthorhombic. Analyzing the radiation (scattering) patterns of the parameters of orthorhombic media yields valuable insights into potential trade-offs and the types of data required for reliable parameter estimation. To evaluate the sensitivity of the objective function to the model parameters, I derive the Frechet kernels and radiation patterns for arbitrary anisotropic symmetry by using the Born approximation and asymptotic Green’s functions. Then the radiation patterns are obtained for perturbations in the parameters of orthorhombic media embedded in a homogeneous VTI background. The results of the sensitivity analysis provide valuable insight into elastic FWI for orthorhombic media.
Then, I implement 3D elastic FWI for orthorhombic media to simultaneously estimate all pertinent model parameters. Because the locations of the available well logs are sparse, a supervised machine-learning (ML) technique (Support Vector Machine) is employed to account for lateral heterogeneity in building the lithologic constraints. The developed algorithm, which operates with wide-azimuth multicomponent surface data, achieves a much higher spatial resolution than unconstrained FWI, even in the absence of recorded frequencies below 2 Hz. The method also produces a high-resolution facies model, which should be instrumental in reservoir characterization. The facies-based FWI is successfully tested on 2D ocean-bottom data from the North Sea using a tilted transversely isotropic model (TTI). This case study demonstrates the effectiveness of adequately employed geologic constraints in elastic FWI for anisotropic media.
To automate and improve the process of facies picking, I also develop supervised and semisupervised Bayesian deep-learning methodologies, which are employed depending on the scope of the labeled data. The developed networks not only reliably predict facies distribution using seismic reflection data, but also estimate the corresponding uncertainty. Therefore, these networks provide more consistent and meaningful information for seismic interpretation than conventional deterministic approaches. The proposed deep-learning methodologies are applied to field data from the North Sea to demonstrate the generalized-prediction capabilities of the devised ML model.
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