Kai Gao

Summary: Seismic wave modeling and full-waveform inversion (FWI) are important tools for investigating subsurface structures and properties. Open-source seismic modeling and inversion tools enable researchers to test new methods, reproduce published results, and use waveform data to characterize the subsurface. However, building flexible FWI workflows still requires substantial effort to integrate wave solvers, misfit functions, and inversion algorithms. We introduce the Open Wave Library (OWL), an open-source framework that integrates these capabilities for local- to exploration-scale modeling and FWI. We implement high-order finite-difference solvers for 2D and 3D isotropic acoustic, isotropic elastic, and general anisotropic elastic media. We combine curvilinear meshes and local refinement to represent topographic elastic free surfaces, and use complex-frequency-shifted multi-axial perfectly matched layers to support stable simulations in strongly anisotropic media. For FWI, we implement conventional waveform, correlation, and adaptive waveform misfits to accommodate different waveform characteristics and degrees of cycle skipping. We also develop two objectives based on generalized dynamic time warping: one penalizes the estimated time shifts, while the other measures amplitude differences after warping. We regularize the time-shift estimates and use a common warping function across components for multi-component data. We compute adjoint-state gradients using source wavefields reconstructed from stored boundary values. We accelerate modeling and inversion through shot-level parallelism, distributed-memory domain decomposition for 3D models, and OpenMP shared-memory parallelism. We assess solver accuracy and numerical consistency through unit tests and comparisons with spectral-element solutions. Through sensitivity-kernel studies and synthetic and field data examples, we demonstrate the complementary behavior of the misfit functions and the applicability of OWL to heterogeneous, anisotropic, and topographic models. OWL assumes negligible Earth curvature and is not intended for regional- or global-scale simulations. Our current implementation runs on central processing units (CPUs); support for heterogeneous computing architectures, viscoelasticity, and coupled acoustic–elastic media remains for future development. With OWL, we provide an extensible platform for methodological research and reproducible seismic modeling and inversion.

SUMMARY: The central United States has experienced a surge in induced seismicity linked to wastewater injection, with Oklahoma as a key study area. While the broader effects of large-scale injection are well documented, the relationship between local injection activities and short-term seismicity fluctuations is less understood. Using deep learning and dense seismic monitoring, we developed an enhanced earthquake catalogue and identified four persistent, low-magnitude (${{M}_\mathrm{ L}} = \ - 0.69\ \rm to\ 2.83)$ seismic clusters within an active saltwater-disposal region. These clusters, several located near mapped faults, exhibit near-daily activity and provide case studies for examining local injection–seismicity dynamics. We find that injection histories for wells within approximately 8–10 km of the clusters generally exhibit stronger temporal correspondence with seismicity than those aggregated over larger spatial scales. Analysis of individual wells further identifies injection histories exhibiting comparatively strong short-term temporal correspondence with observed seismicity, independent of average injection rate or well distance. These relationships are interpreted as statistical associations within a pre-existing regional stress and pore-pressure state rather than evidence of direct hydraulic causality. Compared with higher-moment induced-seismicity cases, the detected clusters exhibit comparable patterns of cumulative seismic moment growth but at predominantly lower magnitudes. These low-moment sequences demonstrate how deep learning-augmented, high-resolution earthquake catalogues can reveal short-term variations in seismic response that are poorly resolved by conventional regional catalogues. Our results suggest that temporal similarity metrics may complement established injection rate and distance criteria by identifying individual wells for further evaluation in induced-seismicity monitoring and mitigation strategies.

Generating high-fidelity geological models is essential for advancing machine learning (ML) methods in automated seismic interpretation. For instance, seismic images paired with corresponding fault labels are foundational for ML-based fault detection from seismic migration sections. While several open-access datasets of random geological models exist, open-source tools specifically designed to produce large volumes of such models for ML applications remain scarce. To address this gap, we present RGM (Random Geological Model), an open-source software package for efficiently generating 2D and 3D synthetic geological models tailored for ML workflows. RGM supports the creation of diverse model components, including medium property distributions (P-/S-wave velocities and density), seismic reflectivity images (i.e., synthetic migration sections), relative geological time, and discrete fault attributes such as probability, dip, strike, rake, and displacement. It also accommodates the creation of complex geological features such as salt bodies and unconformities. The model generation algorithm employs a multi-randomization strategy, yielding an effectively infinite-dimensional model space that encompasses a wide range of geological scenarios and associated seismic features. Furthermore, RGM incorporates a method to generate synthetic elastic migration images using analytical elastic reflection coefficients combined with frequency-dependent scaling. This functionality enables the creation of training datasets for ML models that leverage elastic seismic images. RGM is implemented in modern object-oriented Fortran, allowing users to flexibly control statistical parameters governing model variability. We demonstrate the capability, performance, and geological realism of the package through comprehensive 2D and 3D examples.

SUMMARY: Traveltime-based tomography and source location are fundamental approaches for imaging subsurface structures and understanding the spatiotemporal distribution of seismicity from local to global scales. We present an open-source, high-performance framework integrating eikonal equation solvers and adjoint-state theory for traveltime computation, velocity tomography, source location and joint tomography-location in 2-D/3-D acoustic and elastic media. We introduce novel regularization schemes based on total generalized p-variation, structural similarity and multitask machine learning to enhance the fidelity and interpretability of inverted models and source locations. Key features of our implementation also include the ability to leverage both absolute-difference and double-difference traveltime misfits for high-fidelity velocity tomography and source parameter estimation; support for traveltime computation and inversion in diverse 2-D/3-D scenarios with arbitrary source and receiver distributions; and a perturbation-based optimal step-size estimation method to reduce computational costs. In addition, our implementation employs shared-memory and distributed-memory parallelization to provide an efficient solution for traveltime computation, tomography, and source location. We validate the efficacy and accuracy of our approach through multiple synthetic data examples.

Geological fault detection and characterization from geophysical data have been one of the center challenges in geophysics and seismology as it holds the key to understanding subsurface dynamics ranging from borehole, reservoir, to regional scales. While paradigms of auto or semi-auto fault delineation either based on seismicity location analysis or on seismic migration image reflector discontinuity identification have been well established, a systematic method that can integrate both seismic image and seismicity location information is still missing. We develop a novel machine learning (ML) model that integrates seismic reflector image and seismicity location information into a unified model to automatically identify geological faults and characterize their geometrical properties. We detail the architecture of this neural network, the strategy and procedure of high-quality training data-label generation, as well as the validation results on the trained models. Specially, we also use two field data examples to validate the efficacy and accuracy of our ML model. The results demonstrate that by integrating seismicity location information and seismic migration image in a unified framework, the end-to-end neural network provides notably higher fidelity in delineating subsurface faults and its geometrical properties compared with image-only fault detection methods.