Extended full-waveform inversion (FWI) has shown promising results for accurate estimation of subsurface parameters when the initial models are not sufficiently accurate. Frequency-domain applications have shown that the augmented Lagrangian (AL) method solves the inverse problem accurately with a minimal effect of the penalty parameter choice. Applying this method in the time domain, however, is limited by two main factors: (1) The challenge of data-assimilated wavefield reconstruction due to the lack of an explicit time-stepping and (2) The need to store the Lagrange multipliers, which is not feasible for the field-scale problems. We show that these wavefields are efficiently determined from the associated data (projection of the wavefields onto the receivers space) by using explicit time stepping. Accordingly, based on the augmented Lagrangian, a new algorithm is proposed which performs in "data space" (a lower dimensional subspace of the full space) in which the wavefield reconstruction step is replaced by reconstruction of the associated data, thus requiring optimization in a lower dimensional space (convenient for handling the Lagrange multipliers). We show that this new algorithm can be implemented efficiently in the time domain with existing solvers for the FWI and at a cost comparable to that of the FWI while benefiting from the robustness of the extended FWI formulation. The results obtained by numerical examples show high-performance of the proposed method for large scale time-domain FWI.
This paper concerns the Time-Domain Full Waveform Inversion (FWI) for dispersive and dissipative poroelastic materials. The forward problem is an initial boundary value problem (IBVP) of the poroelastic equations with a memory term; the FWI is formulated as a minimization problem of a least-square misfit function with the (IBVP) as the constraint. In this paper, we derive the adjoint problem of this minimization problem, whose solution can be applied to computed the direction of steepest descent in the iterative process for minimization. The adjoint problem has a similar numerical structure as…
Full waveform inversion (FWI) is one of a family of methods that allows the reconstruction of earth subsurface parameters from measurements of waves at or near the surface. This is a numerical optimization problem that uses the whole waveform information of all arrivals to update the subsurface parameters that govern seismic wave propagation. We apply FWI in the multi-scale approach on two well-known benchmarks: Marmousi and 2004 BP velocity model. For the forward modeling, we use an RBF-FD solver on hexagonal grids and quasi-optimal shape parameters.
Seismic full-waveform inversion tries to estimate subsurface medium parameters from seismic data. Areas with subsurface salt bodies are of particular interest because they often have hydrocarbon reservoirs on their sides or underneath. Accurate reconstruction of their geometry is a challenge for current techniques. This paper presents a parametric level-set method for the reconstruction of salt-bodies in seismic full-waveform inversion. We split the subsurface model in two parts: a background velocity model and the salt body with known velocity but undetermined shape. The salt geometry is repr…
Full waveform inversion (FWI) is an important and popular technique in subsurface earth property estimation. However, using the least-squares norm in the misfit function often leads to the local minimum solution of the optimization problem, and this phenomenon can be explained with the cycle-skipping artifact. Several methods that apply optimal transport distances to mitigate the cycle-skipping artifact have been proposed recently. The optimal transport distance is designed to compare two probability measures. To overcome the mass equality limit, we introduce an unbalanced optimal transport (U…
Understanding the causes of sinkholes and determining the earth's subsurface properties will help Engineering Geologists in designing and constructing different kinds of structures. Also, determining subsurface properties will increase possibilities of preventing expensive structural damages as well as a loss of life. Among the available health monitoring techniques, non-destructive methods play an important role. Full-waveform inversion together with the Gauss-Newton method, which we called as the regular method, able to determine the properties of the subsurface data from seismic data. Howev…
Recently, the Wasserstein loss function has been proven to be effective when applied to deterministic full-waveform inversion (FWI) problems. We consider the application of this loss function in Bayesian FWI so that the uncertainty can be captured in the solution. Other loss functions that are commonly used in practice are also considered for comparison. Existence and stability of the resulting Gibbs posteriors are shown on function space under weak assumptions on the prior and model. In particular, the distribution arising from the Wasserstein loss is shown to be quite stable with respect to …
This paper presents a novel numerical method for the Newton seismic full-waveform inversion (FWI). The method is based on the full-space approach, where the state, adjoint state, and control variables are optimized simultaneously. Each Newton step is formulated as a PDE-constrained optimization problem, which is cast in the form of the Karush-Kuhn-Tucker (KKT) system of linear algebraic equitations. The KKT system is solved inexactly with a preconditioned Krylov solver. We introduced two preconditioners: the one based on the block-triangular factorization and its variant with an inexact block …
We introduce a novel approach to waveform inversion, based on a data driven reduced order model (ROM) of the wave operator. The presentation is for the acoustic wave equation, but the approach can be extended to elastic or electromagnetic waves. The data are time resolved measurements of the pressure wave gathered by an acquisition system which probes the unknown medium with pulses and measures the generated waves. We propose to solve the inverse problem of velocity estimation by minimizing the square misfit between the ROM computed from the recorded data and the ROM computed from the modeled …
This paper proposes a new method that combines check-pointing methods with error-controlled lossy compression for large-scale high-performance Full-Waveform Inversion (FWI), an inverse problem commonly used in geophysical exploration. This combination can significantly reduce data movement, allowing a reduction in run time as well as peak memory. In the Exascale computing era, frequent data transfer (e.g., memory bandwidth, PCIe bandwidth for GPUs, or network) is the performance bottleneck rather than the peak FLOPS of the processing unit. Like many other adjoint-based optimization problems, F…
PDE-constrained optimization problems are often treated using the reduced formulation where the PDE constraints are eliminated. This approach is known to be more computationally feasible than other alternatives at large scales. However, the elimination of the constraints forces the optimization process to fulfill the constraints at all times. In some problems this may lead to a highly non-linear objective, which is hard to solve. An example to such a problem, which we focus on in this work, is Full Waveform Inversion (FWI), which appears in seismic exploration of oil and gas reservoirs, and me…
Center for Energy and Geo Processing (CeGP) at Georgia Tech and KFUPM（乔治亚理工学院与法赫德国国石油矿物大学能源与地球处理中心）
Full waveform inversion (FWI) delivers high-resolution images of the subsurface by minimizing iteratively the misfit between the recorded and calculated seismic data. It has been attacked successfully with the Gauss-Newton method and sparsity promoting regularization based on fixed multiscale transforms that permit significant subsampling of the seismic data when the model perturbation at each FWI data-fitting iteration can be represented with sparse coefficients. Rather than using analytical transforms with predefined dictionaries to achieve sparse representation, we introduce an adaptive tra…
