In the workflow of Full-Waveform Inversion (FWI), we often tune the parameters of the inversion to help us avoid cycle skipping and obtain high resolution models. For example, typically start by using objective functions that avoid cycle skipping, like tomographic and image based or using only low frequency, and then later, we utilize the least squares misfit to admit high resolution information. We also may perform an isotropic (acoustic) inversion to first update the velocity model and then switch to multi-parameter anisotropic (elastic) inversions to fully recover the complex physics. Such hierarchical approaches are common in FWI, and they often depend on our manual intervention based on many factors, and of course, results depend on experience. However, with the large data size often involved in the inversion and the complexity of the process, making optimal choices is difficult even for an experienced practitioner. Thus, as an example, and within the framework of reinforcement learning, we utilize a deep-Q network (DQN) to learn an optimal policy to determine the proper timing to switch between different misfit functions. Specifically, we train the state-action value function (Q) to predict when to use the conventional L2-norm misfit function or the more advanced optimal-transport matching-filter (OTMF) misfit to mitigate the cycle-skipping and obtain high resolution, as well as improve convergence. We use a simple while demonstrative shifted-signal inversion examples to demonstrate the basic principles of the proposed method.
King Abdullah University of Science and Technology（阿卜杜拉国王科技大学）
Most of the available advanced misfit functions for full waveform inversion (FWI) are hand-crafted, and the performance of those misfit functions is data-dependent. Thus, we propose to learn a misfit function for FWI, entitled ML-misfit, based on machine learning. Inspired by the optimal transport of the matching filter misfit, we design a neural network (NN) architecture for the misfit function in a form similar to comparing the mean and variance for two distributions. To guarantee the resulting learned misfit is a metric, we accommodate the symmetry of the misfit with respect to its input an…
We consider the high-resolution seismic imaging method called full-waveform inversion (FWI). FWI is a data fitting method aimed at inverting for subsurface mechanical parameters. Despite the large adoption of FWI by the academic and industrial communities, and many successful results, FWI still suffers from severe limitations. From a mathematical standpoint, FWI is a large scale PDE-constrained optimization problem. The misfit function that is used, which measures the discrepancy between observed seismic data and data calculated through the solution of a wave propagation problem, is non-convex…
Conventional full waveform inversion (FWI) using least square distance (LSD) between the observed and predicted seismograms suffers from local minima. Recently, earth mover's distance (EMD) has been introduced to FWI to compute the misfit between two seismograms. Instead of comparisons bin by bin, EMD allows to compare signal intensities across different coordinates. This measure has great potential to account for time and space shifts of events within seismograms. However, there are two main challenges in application of EMD to FWI. The first one is that the compared signals need to satisfy no…
We have formulated elastic seismic full waveform inversion (FWI) within a deep learning environment. In our formulation, a recurrent neural network is set up with rules enforcing elastic wave propagation, with the wavefield projected onto a measurement surface acting as the synthetic data to be compared with observed seismic data. Gradients for iterative updating of an elastic model, with a variety of parameterizations and misfit functionals, can be efficiently constructed within the network through the automatic differential method. With this method, the inversion based on complex misfits can…
Full-waveform inversion is a cutting-edge methodology for recovering high-resolution subsurface models. However, one of the main conventional full-waveform optimization problems challenges is cycle-skipping, usually leading us to an inaccurate local minimum model. A highly investigated track to alleviate this challenge involves designing a more global measure of misfit between the observed and modelled data beyond the sample-to-sample comparison. However, most of these approaches admit relatively smooth inversion results. Here, we introduce a novel misfit function based on the Fourier-based me…
Non-invasive subsurface imaging using full waveform inversion (FWI) has the potential to fundamentally change engineering site characterization by enabling the recovery of high resolution 2D/3D maps of subsurface stiffness. Yet, the accuracy of FWI remains quite sensitive to the choice of the initial starting model due to the complexity and non-uniqueness of the inverse problem. In response, we present the novel application of convolutional neural networks (CNNs) to transform an experimental seismic wavefield acquired using a linear array of surface sensors directly into a robust starting mode…
Full waveform inversion (FWI) is a powerful yet computationally expensive technique that can yield subsurface models at high resolution. Randomly selected shots ("mini-batches") can be used to approximate the misfit and the gradient of FWI, thereby reducing its computational cost. Here, we present a methodology to perform mini-batch FWI using the Adam algorithm, an adaptive optimization scheme based on stochastic gradient descent. It provides for stable model updates by smoothing the gradient across iterations and can also account for the curvature of the optimization landscape. We describe em…
Full-Waveform Inversion (FWI) has now become a widely accepted tool to obtain high-resolution velocity models from seismic data. Typically, the velocity model in its discrete form is represented on a rectangular grid, and we solve for the elastic properties at these grid points. FWI is mostly solved employing a local optimization method, where one obtains a velocity update by minimizing the misfit between the observed and the calculated seismograms. Note also that FWI is a highly non-linear problem which is known to be prone to non-uniqueness. The convergence to a globally optimum solution is …
A new practical and effective source-independent full-waveform inversion with a velocity-distribution supported deep image prior: Applications to two real datasets
Jilin University（吉林大学）；King Abdullah University of Science and Technology (KAUST)（阿卜杜拉国王科技大学）；King Fahd University of Petroleum and Minerals（法赫德国王石油与矿业大学）
Application of Optimal Transport and the Quadratic Wasserstein Metric to Full-Waveform Inversion
The University of Texas at Austin（德克萨斯大学奥斯汀分校）；Bureau of Economic Geology, John A. and Katherine G. Jackson School of Geosciences, The University of Texas at Austin（德克萨斯大学奥斯汀分校杰克逊地球科学学院经济地质局）；New Jersey Institute of Technology（新泽西理工学院）
Full-waveform inversion (FWI) is an accurate imaging approach for modeling velocity structure by minimizing the misfit between recorded and predicted seismic waveforms. However, the strong non-linearity of FWI resulting from fitting oscillatory waveforms can trap the optimization in local minima. We propose a neural-network-based full waveform inversion method (NNFWI) that integrates deep neural networks with FWI by representing the velocity model with a generative neural network. Neural networks can naturally introduce spatial correlations as regularization to the generated velocity model, wh…
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…
Full-waveform inversion (FWI) is a widely used technique in seismic processing to produce high resolution Earth models that fully explain the recorded seismic data. FWI is a local optimisation problem which aims to minimise in a least-squares sense the misfit between recorded and modelled data. The inversion process begins with a best-guess initial model which is iteratively improved using a sequence of linearised local inversions to solve a fully non-linear problem. Deep learning has gained widespread popularity in the new millennium. At the core of these tools are Neural Networks (NN), in pa…
The quantitative reconstruction of sub-surface Earth properties from the propagation of waves follows an iterative minimization of a misfit functional. In marine seismic exploration, the observed data usually consist of measurements of the pressure field but dual-sensor devices also provide the normal velocity. Consequently, a reciprocity-based misfit functional is specifically designed, and defines the Full Reciprocity-gap Waveform Inversion (FRgWI ) method. This misfit functional provides additional features compared to the more traditional least-squares approaches with, in particular, that …
Reliability-calibrated deep residual full-waveform inversion using geometry-invariant physics encoding: synthetic validation and zero-shot Marmousi-2 testing
Institute of Geophysics, Polish Academy of Sciences（波兰科学院地球物理研究所）；University of Allahabad（阿拉哈巴德大学）；CSIR–National Geophysical Research Institute（印度科学工业研究理事会国家地球物理研究所）
