Full Waveform Inversion (FWI) is a technique used to visualize and analyze wave propagation through a medium in order to infer its physical properties. This method relies on computational models and algorithms to simulate and interpret the behavior of waves—such as sound, electromagnetic, or seismic waves—as they travel through different materials. By analyzing how these waves are reflected, refracted, or absorbed by the medium, FWI can provide detailed information about the medium’s internal structure, composition, and physical properties, such as density, elasticity, or internal defects. The traditional process typically involves: 1) Wave Simulation: Using physics-based models to simulate how waves propagate through a medium. This may involve solving complex differential equations that describe wave behavior in different contexts. 2) Data Acquisition: Collecting data on wave interactions with the medium using sensors or other measurement devices. This could include data on wave speed, direction, amplitude, and phase changes. 3) Image Reconstruction: Applying computational techniques, such as inverse problems or tomographic reconstruction, to create images or maps of the medium based on the acquired wave data. 4) Analysis: Interpreting the reconstructed images to deduce the physical properties of the medium. This can involve identifying features like boundaries, interfaces, or anomalies within the medium.

Full-waveform inversion (FWI) plays a vital role in geoscience to explore the subsurface. It utilizes the seismic wave to image the subsurface velocity map. As the machine learning (ML) technique evolves, the data-driven approaches using ML for FWI tasks have emerged, offering enhanced accuracy and reduced computational cost compared to traditional physics-based methods. However, a common challenge in geoscience --- the unprivileged data --- severely limits ML effectiveness. The issue becomes even worse during model pruning, a step essential in geoscience due to environmental complexities. To tackle this, we introduce the EdGeo toolkit, which employs a diffusion-based model guided by physics principles to generate high-fidelity velocity maps. The toolkit uses the acoustic wave equation to generate corresponding seismic waveform data, facilitating the fine-tuning of pruned ML models. Our results demonstrate significant improvements in SSIM scores and reduction in both MAE and MSE across various pruning ratios. Notably, the ML model fine-tuned using data generated by EdGeo yields superior quality of velocity maps, especially in representing unprivileged features, outperforming other existing methods.

Ultrasound computed tomography (USCT) is an emerging imaging modality that holds great promise for breast imaging. Full-waveform inversion (FWI)-based image reconstruction methods leverage accurate wave physics to generate high spatial resolution quantitative images of the breast tissue’s acoustic properties, such as speed of sound, from USCT measurement data. However, the significant computational demand for FWI reconstruction poses a considerable challenge to its widespread adoption in clinical settings. Data-driven machine learning approaches offer a faster and more efficient means of translating waveform data into images. Yet, the effectiveness of machine learning methods is constrained by the diversity and quality of the training data. Given the heterogeneous distribution of breast tissue characteristics, such as fat content and size, the performance of machine learning varies across different sizes. This variability is problematic, particularly in medical diagnostics, where precision is crucial. In response to the limited data in certain categories, we propose utilizing generative AI to augment data samples, thereby enhancing FWI’s performance on limited-sample data and addressing issues of AI fairness.

In the study of subsurface seismic imaging, solving the acoustic wave equation is a pivotal component in existing models. The advancement of deep learning enables solving partial differential equations, including wave equations, by applying neural networks to identify the mapping between the inputs and the solution. This approach can be faster than traditional numerical methods when numerous instances are to be solved. Previous works that concentrate on solving the wave equation by neural networks consider either a single velocity model or multiple simple velocity models, which is restricted in practice. Instead, inspired by the idea of operator learning, this work leverages the Fourier neural operator (FNO) to effectively learn thefrequency domainseismic wavefields under the context ofvariable velocity models. We also propose a new frameworkparalleled Fourier neural operator(PFNO) for efficiently training the FNO-based solver given multiple source locations and frequencies. Numerical experiments demonstrate the high accuracy of both FNO and PFNO with complicated velocity models in the OpenFWI datasets. Furthermore, the cross-dataset generalization test verifies that PFNO adapts to out-of-distribution velocity models. Finally, PFNO admits higher computational efficiency on large-scale testing datasets than the traditional finite-difference method. The aforementioned advantages endow the FNO-based solver with the potential to build powerful models for research on seismic waves.

Full waveform inversion (FWI) is widely used in geophysics to reconstruct high-resolution velocity maps from seismic data. The recent success of data-driven FWI methods results in a rapidly increasing demand for open datasets to serve the geophysics community. We present OpenFWI, a collection of large-scale multi-structural benchmark datasets, to facilitate diversified, rigorous, and reproducible research on FWI. In particular, OpenFWI consists of $12$ datasets ($2.1$TB in total) synthesized from multiple sources. It encompasses diverse domains in geophysics (interface, fault, CO$_2$ reservoir, etc.), covers different geological subsurface structures (flat, curve, etc.), and contain various amounts of data samples (2K - 67K). It also includes a dataset for 3D FWI. Moreover, we use OpenFWI to perform benchmarking over four deep learning methods, covering both supervised and unsupervised learning regimes. Along with the benchmarks, we implement additional experiments, including physics-driven methods, complexity analysis, generalization study, uncertainty quantification, and so on, to sharpen our understanding of datasets and methods. The studies either provide valuable insights into the datasets and the performance, or uncover their current limitations. We hope OpenFWI supports prospective research on FWI and inspires future open-source efforts on AI for science. All datasets and related information can be accessed through our website at https://openfwi-lanl.github.io/

The microseismic monitoring technique is widely applied to petroleum reservoirs to understand the process of hydraulic fracturing. Geophones continuously record the microseismic events triggered by fluid injection on the Earth’s surface or in monitoring wells. The microseismic event localization precision has a large impact on the performance of the technique. Deep learning has achieved significant progress in computer vision and natural language processing in recent years. We propose to use a deep convolutional neural network (CNN) to directly map the field records to their event locations. The biggest advantage of deep learning methods over conventional methods is that they can efficiently predict the characteristics of a huge amount of recorded data without human intervention. Thus, we use a CNN to predict the event location of field microseismic data that were recorded during a hydraulic fracturing process of a shale gas play in Oklahoma, the United States. We use synthetic data with extracted field noise from the records to train CNN. The synthetic training data allow us to produce the corresponding labels, and the extracted noise from the field data reduces the difference between the field and synthetic data. We use a correlation preprocessing step to avoid the need for event detection and picking of arrivals. We demonstrate that the proposed approach provides accurate microseismic event locations at a much faster speed than traditional imaging methods, such as time-reversal imaging. Comparison with an existing study on the same data is presented to evaluate the performance of the trained neural network.