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Register a new userInterrogating probabilistic inversion results for subsurface structural information
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The goal of a scientific investigation is to find answers to specific questions. In geosciences this is typically achieved by solving an inference or inverse problem and interpreting the solution. However, the answer obtained is often biased because the solution to an inverse problem is nonunique and human interpretation is a biased process. Interrogation theory provides a systematic way to find optimal answers by considering their full uncertainty estimates, and by designing an objective function that defines desirable qualities in the answer. In this study we demonstrate interrogation theory by quantifying the size of a particular subsurface structure. The results show that interrogation theory provides an accurate estimate of the true answer, which cannot be obtained by direct, subjective interpretation of the solution mean and standard deviation. This demonstrates the value of interrogation theory. It also shows that fully nonlinear uncertainty assessments may be critical in order to address real-world scientific problems, which goes some way towards justifying their computational expense.
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We describe a novel framework for estimating subsurface properties, such as rock permeability and porosity, from time-lapse observed seismic data by coupling full-waveform inversion, subsurface flow processes, and rock physics models. For the inverse modeling, we handle the back-propagation of gradients by an intrusive automatic differentiation strategy that offers three levels of user control: (1) at the wave physics level, we adopted the discrete adjoint method in order to use our existing high-performance FWI code; (2) at the rock physics level, we used built-in operators from the $texttt{TensorFlow}$ backend; (3) at the flow physics level, we implemented customized PDE operators for the potential and nonlinear saturation equations. These three levels of gradient computation strike a good balance between computational efficiency and programming efficiency, and when chained together, constitute a coupled inverse system. We use numerical experiments to demonstrate that (1) the three-level coupled inverse problem is superior in terms of accuracy to a traditional decoupled inversion strategy; (2) it is able to simultaneously invert for parameters in empirical relationships such as the rock physics models; and (3) the inverted model can be used for reservoir performance prediction and reservoir management/optimization purposes.
Most of the seismic inversion techniques currently proposed focus on robustness with respect to the background model choice or inaccurate physical modeling assumptions, but are not apt to large-scale 3D applications. On the other hand, methods that are computationally feasible for industrial problems, such as full waveform inversion, are notoriously bogged down by local minima and require adequate starting models. We propose a novel solution that is both scalable and less sensitive to starting model or inaccurate physics when compared to full waveform inversion. The method is based on a dual (Lagrangian) reformulation of the classical wavefield reconstruction inversion, whose robustness with respect to local minima is well documented in the literature. However, it is not suited to 3D, as it leverages expensive frequency-domain solvers for the wave equation. The proposed reformulation allows the deployment of state-of-the-art time-domain finite-difference methods, and is computationally mature for industrial scale problems.
Sensitivity analysis plays an important role in searching for constitutive parameters (e.g. permeability) subsurface flow simulations. The mathematics behind is to solve a dynamic constrained optimization problem. Traditional methods like finite difference and forward sensitivity analysis require computational cost that increases linearly with the number of parameters times number of cost functions. Discrete adjoint sensitivity analysis (SA) is gaining popularity due to its computational efficiency. This algorithm requires a forward run followed by a backward run who involves integrating adjoint equation backward in time. This was done by doing one forward solve and store the snapshot by checkpointing. Using the checkpoint data, the adjoint equation is numerically integrated. The computational cost of this algorithm only depends on the number of cost functions and does not depend on the number of parameters. The algorithm is highly powerful when the parameter space is large, and in our case of heterogeneous permeability the number of parameters is proportional to the number of grid cells. The aim of this project is to implement the discrete sensitivity analysis method in parallel to solve realistic subsurface problems. To achieve this goal, we propose to implement the algorithm in parallel using data structures such as TSAdjoint and TAO. This paper dealt with large-scale subsurface flow inversion problem with discrete adjoint method. This method can effectively reduce the computational cost in sensitivity analysis.
The Hessian matrix plays an important role in correct interpretation of the multiple scattered wave fields inside the FWI frame work. Due to the high computational costs, the computation of the Hessian matrix is not feasible. Consequently, FWI produces overburden related artifacts inside the target zone model, due to the lack of the exact Hessian matrix. We have shown here that Marchenko-based target-oriented Full Waveform Inversion can compensate the need of Hessian matrix inversion by reducing the non-linearity due to overburden effects. This is achieved by exploiting Marchenko-based target replacement to remove the overburden response and its interactions with the target zone from residuals and inserting the response of the updated target zone into the response of the entire medium. We have also shown that this method is more robust with respect to prior information than the standard gradient FWI. Similarly to standard Marchenko imaging, the proposed method only requires knowledge of the direct arrival time from a focusing point to the surface and the reflection response of the medium.
The three electromagnetic properties appearing in Maxwells equations are dielectric permittivity, electrical conductivity and magnetic permeability. The study of point diffractors in a homogeneous, isotropic, linear medium suggests the use of logarithms to describe the variations of electromagnetic properties in the earth. A small anomaly in electrical properties (permittivity and conductivity) responds to an incident electromagnetic field as an electric dipole, whereas a small anomaly in the magnetic property responds as a magnetic dipole. Neither property variation can be neglected without justification. Considering radiation patterns of the different diffracting points, diagnostic interpretation of electric and magnetic variations is theoretically feasible but is not an easy task using Ground Penetrating Radar. However, using an effective electromagnetic impedance and an effective electromagnetic velocity to describe a medium, the radiation patterns of a small anomaly behave completely differently with source-receiver offset. Zero-offset reflection data give a direct image of impedance variations while large-offset reflection data contain information on velocity variations.
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