Extended waveform inversion globalizes the convergence of seismic waveform inversion by adding nonphysical degrees of freedom to the model, thus permitting it to fit the data well throughout the inversion process. These extra degrees of freedom must be curtailed at the solution, for example, by penalizing them as part of an optimization formulation. For separable (partly linear) models, a natural objective function combines a mean square data residual and a quadratic regularization term penalizing the nonphysical (linear) degrees of freedom. The linear variables are eliminated in an inner optimization step, leaving a function of the outer (nonlinear) variables to be optimized. This variable projection method is convenient for computation, but it requires that the penalty weight be increased as the estimated model tends to the (physical) solution. We describe an algorithm based on discrepancy, that is, maintaining the data residual at the inner optimum within a prescribed range, to control the penalty weight during the outer optimization. We evaluate this algorithm in the context of constant density acoustic waveform inversion, by recovering background model and perturbation fitting bandlimited waveform data in the Born approximation.

Subsurface-offset extended full-waveform inversion (FWI) may converge to kinematically accurate velocity models without the low-frequency data accuracy required for standard data-domain FWI. However, this robust alternative approach to waveform inversion suffers from a very high computational cost resulting from its use of nonlocal wave physics: The computation of strain from stress involves an integral over the subsurface offset axis, which must be performed at every space-time grid point. We found that a combination of data-fit driven offset limits, grid coarsening, and low-pass data filtering can reduce the cost of extended inversion by one to two orders of magnitude.

Distributed acoustic sensing (DAS) has emerged as a transformational technology for seismic data acquisition. However, noise remains a major impediment, necessitating advanced denoising techniques. This study pioneers the application of diffusion models, a type of generative model, for DAS vertical seismic profile (VSP) data denoising. The diffusion network is trained on a new generated synthetic dataset that accommodates variations in the acquisition parameters. The trained model is applied to suppress noise in synthetic and field DAS-VSP data. The results demonstrate the model’s effectiveness in removing various noise types with minimal signal leakage, outperforming conventional methods. This research signifies diffusion models’ potential for DAS processing.

Seismic data is the primary way to study the subsurface structure and properties. A conventional seismic sensor like geophone or accelerometer measures particle velocity or acceleration at a local point only, while Distributed Acoustic Sensing (DAS) measures dynamic strain along the fiber optic cable at densely spaced sample points where strain rate is obtained over certain gauge length interval. Therefore, DAS measures subsurface properties with high sampling resolution and large coverage. When an optical fiber is installed in a well, DAS can provide continuous, dense downhole recording. However, currently most of the seismic processing, imaging and inversion techniques are developed for geophone data. These well-established techniques can be readily and properly utilized if DAS data is transformed into geophone measurements such as particle velocity. In this study, we present a recurrent neural network framework to perform this transformation. This effectiveness of the deep learning-based mapping is then demonstrated with a field measurement data, showing that DAS data can be transformed into particle velocity accurately and robustly using the proposed deep-learning approach.

Well logs are processed and interpreted to estimate in-situ reservoir properties, which are essential for reservoir modeling, reserve estimation, and production forecasting. While the traditional methods are mostly based on multimineral physics or empirical formulae, machine learning provides an alternative data-driven approach that requires much less a-priori geological or petrophysical information. From October 2021 to March 2022, the Petrophysical Data-Driven Analytics Special Interest Group (PDDA SIG) of the Society of Petrophysicists and Well Log Analysts (SPWLA) hosted a machine-learning contest aiming to develop data-driven models for estimating reservoir properties, including shale volume, porosity, and fluid saturation, based on a common set of well logs, including gamma ray, bulk density, neutron porosity, resistivity, and sonic. Log data from nine wells from the same field, together with the interpreted reservoir properties by petrophysicists, were provided as training data, and five additional wells were provided as blind test data. During the contest, various data-driven models were developed by the contestants to predict the three reservoir properties with the provided training data set. The top five performing models from the contest, on average, beat the performance of the benchmarked Random Forest model by 45% in the root-mean-square error (RMSE) score. In the paper, we will review these top-performing solutions, including their preprocessing techniques, feature engineering, and machine-learning models, and summarize their advantages and conditions.