In recent years, full-waveform inversion (FWI) has been extensively used to derive high-resolution subsurface velocity models from seismic data. However, due to the nonlinearity and ill-posed nature of the problem, FWI requires a good starting model to avoid producing non-physical solutions (i.e. being trapped in local minima). Moreover, traditional optimization methods often struggle to effectively quantify the uncertainty associated with the recovered solution, which is critical for decision-making processes. Bayesian inference offers an alternative approach as it directly or indirectly evaluates the posterior probability density function using Bayes' theorem. For example, Markov Chain Monte Carlo (MCMC) methods generate multiple sample chains to characterize the solution's uncertainty. Despite their ability to theoretically handle any form of distribution, MCMC methods require many sampling steps; this limits their usage in high-dimensional problems with computationally intensive forward modelling, as is the FWI case. Variational inference (VI), on the other hand, approximates the posterior distribution in the form of a parametric or non-parametric proposal distribution. Among the various algorithms used in VI, Stein Variational Gradient Descent (SVGD) is characterized for its ability to iteratively refine a set of samples (commonly referred to as particles) to approximate the target distribution through an optimization process. However, mode and variance-collapse issues affect SVGD in high-dimensional inverse problems. In this study, we propose to improve the performance of SVGD within the context of FWI by combining an annealed variant of the SVGD algorithm with a multiscale strategy, a common practice in deterministic FWI settings. Additionally, we demonstrate that principal component analysis (PCA) can help us to evaluate the performance of the optimization process and gain insights into the behaviour of the output particles and their overall distribution. Clustering techniques are also employed to provide more rigorous and meaningful statistical analysis of the particles in the presence of multimodal distributions (as is usually the case in FWI). Numerical tests, performed on a portion of the acoustic Marmousi model using both single and multiple frequency ranges, reveal the benefits of annealed SVGD compared to vanilla SVGD to enhance uncertainty estimation using a limited number of particles and thus address the challenges of dimensionality and computational constraints.

SUMMARY Full-waveform inversion (FWI) relies on low-frequency data to succeed if a good initial model is unavailable. However, field seismic data excited by active sources are typically band-limited above 3 Hz. By extrapolated FWI, we can start inversion from computational low frequencies extrapolated from band-limited data. However, low-frequency extrapolation with deep learning is challenging for field data since a neural network trained on synthetic data usually generalizes poorly on real seismic data. Here we use a semi-supervised learning method to extrapolate low frequencies for field data by training with real data without real labels. Specifically, by training CycleGAN with unpaired images of field 4–10 Hz band-limited and synthetic 0–4 Hz low-frequency shot gathers, we can extrapolate the 0–4 Hz low frequencies for the field data band-limited above 4 Hz. The source wavelet for the simulation of synthetic low-frequency data is used as the source in FWI using the extrapolated data. The inverted velocity model using only the extrapolated low frequencies is comparable to the tomography model. Our method strengthens the ability of FWI for mapping fine Earth structures by mitigating the cycle-skipping problem effectively.

SUMMARY Surface wave dispersion curves are useful to characterize shallow subsurface structures while accurately picking them is typically laborious. To make these approaches more efficient and practical, it is important to automate the picking process. We propose a convolutional neural network (CNN) based ML method to automatically pick multimode surface wave dispersion curves. We modify the typical U-net architecture to convert the conventional 2-D image segmentation problem into direct multimode curve fitting and subsequent picking. A variety of attributes of the data amplitude (A) in the (f, k) domain, such as frequency (F), wavenumber (K), maximum coherency (Coh) and Power weighted amplitude (Pwa), are combined to constrain the picking more accurately than a single attribute does. The effects of two different loss functions on the final picking results are compared; the one that combines conventional wavenumber residuals and curve slope residuals produces more continuous curves. Pre-training the network with synthetic data, and thus using transfer learning, improves the efficiency of the algorithm when the data set is large. To determine the frequency band of each dispersive mode (effective frequency band) in the picked curves, the CNN outputs are post-processed by using measurements such as long/short moving average ratios of squared picked wavenumbers, posterior uncertainty of picked wavenumbers and wavenumbers in the picked curves or the power attribute. We demonstrate the effectiveness of this automatic picking by applying it to a 2-D line and a 3-D subset from a field ocean bottom node data set, where the fundamental and first higher modes of Scholte waves are accurately picked.

Uncertainty quantification (UQ) is important for geophysical inversion because it measures the confidence in the results and allows one to assess the value of information in data. However, the cost of accepted methods for UQ ranges from high to prohibitive and it is often difficult to estimate noise levels and insert prior information. Here, we investigate the properties of a Machine Learning-based UQ tool, the Invertible neural network (INN). This appears perfectly suited for UQ but in practice is limited by its memory requirements. We therefore propose a strategy to enable INN to perform tomographic inversion of a realistically sized velocity model within a complex foothills context. We use two variational autoencoders to compress both the model and data and apply the INN in the compressed (latent) domain. We further use the deep ensemble method to incorporate the epistemic uncertainties. We demonstrate that this strategy allows us to perform tomographic inversion of a realistically-scaled velocity model at highly accurate mean and plausible estimates of uncertainty. Research continues on better understanding the quantitative nature of these estimates.

Noise removal is a standard part of seismic data processing; however, deterministic workflows may require specific adaptations and parameter tuning for each dataset. Conventional ground-roll noise attenuation methods involving domain transform or decomposition can be timeconsuming. Recent studies have demonstrated that machine learning (including supervised, self-supervised and unsupervised approaches) can be an effective tool for seismic noise removal. However, in most applications, the proposed method targets one or other of coherent or incoherent noise. In this study, we propose a workflow for a field dataset containing both coherent (ground-roll) and incoherent noise components. The workflow is built by sequentially combining supervised and self-supervised methods. For the incoherent noise, we train a neural network directly with field data in a self-supervised approach; however, by careful design and selection of the training data, we can also target noise that is coherent over a short range For the coherent, ground-roll noise, we train a second neural network with supervised learning using synthetic data; we found that this can be directly applied to field data without any additional training which makes this approach very computationally efficient. The synthetic training data need to be thoughtfully augmented to include the key features of the target field test sets. We demonstrate that the proposed workflow can effectively and efficiently remove multiple types of noise from seismic data.

Inversion velocity analysis (IVA) is an image-domain method built upon the spatial scale separation of the model. Accordingly, the IVA method is performed with an iterative process composed of two minimization steps consisting of migration (inner loop) and tomography (outer loop), respectively, with each step accounting for its Hessian or not. The migration part provides the common-image gathers (CIGs) with extension in the horizontal subsurface offset. Then, the differential semblance optimization (DSO) misfit measures the focusing of the events in the CIGs, which indicates the quality of the velocity model. Commonly, the velocity updates are obtained from the DSO gradient. IVA is a modified version in which the approximate inverse replaces the adjoint of the inner loop process; in that case, the migration Hessian is approximately diagonal in the high-frequency regime. In this work, we report on implementation of the tomographic Hessian (i.e., the second derivative of the DSO misfit with respect to the background model) for the estimation of the background velocity model. We apply the second-order adjoint-state method to obtain the application of the tomographic Hessian on a vector. Then, we use the truncated-Newton (TN) method to obtain the update directions by computing approximately the application of the inverse of the tomographic Hessian on the descent direction. We also make a theoretical comparison between tomography in the IVA and full-waveform inversion contexts. Two numerical examples are used to compare, in terms of geophysical results and computational costs, the TN method with different gradient-based optimization methods applied to the IVA. A small model allows us to evaluate the eigenvalues of the tomographic Hessian, which explains the large damping needed in the TN case.

Summary Inversion velocity analysis (IVA) alternates between migration and tomography steps. It uses the pseudo-inverse of the extended Born operator to compute an improved extended reflectivity in comparison to migration velocity analysis (MVA) based on the adjoint of the extended Born operator. One important feature of the pseudo-inverse formula is that it is defined such that the migration Hessian is approximately diagonal. In this work, we report our first evaluation of the tomographic Hessian of IVA for the estimation of the background velocity model. We apply the second-order adjoint-state method to obtain the action of the tomographic Hessian on a vector. Then, improved update directions are obtained by computing approximately the action of the inverse of the tomographic Hessian on the descent direction. One numerical example demonstrates the potential of the tomographic Hessian-based IVA.

Passive source location is a fundamental problem in earthquake seismology and reservoir characterization with fluid injection. It has been shown that geometric-mean reverse time migration (GmRTM) can produce source images with improved resolution and fewer migration artifacts than conventional time-reversal imaging in acoustic media. However, the acoustic assumption often requires data windowing and polarity correction when we apply it to the elastic data which involves manual efforts and introduces uncertainties. Therefore, we have extended this cross-correlation-based GmRTM imaging method to elastic media. Back-propagation and Helmholtz decomposition are conducted individually for each receiver wavefield, after which we apply zero-lag cross-correlations over the decoupled P or/and S wavefields to obtain the corresponding P-, S-, and PS-source images. Considering the influences of random noise, anisotropy, and interferences from multiple sources, we test the proposed elastic GmRTM method on a synthetic example with a layered model and determine its advantages over other imaging conditions (e.g., time-reversal imaging). The method is further validated using another synthetic test based on the elastic Marmousi model and a field-data example from Oklahoma.

Geometric-mean reverse time migration (GmRTM), a powerful crosscorrelation-based imaging method, generates higher resolution source images and is more robust to noise compared with conventional time-reversal imaging. The price to pay is the higher computational costs. Alternatively, we can adopt hybrid strategies by dividing the receivers into different groups. Conventional time reversal (i.e., wavefield summation) is performed inside each group, followed by the application of crosscorrelation imaging condition among different groups. Such hybrid strategies can retain the advantages of GmRTM and time reversal and are often more practical than pure GmRTM. Yet, designing appropriate grouping strategy is not trivial. Here, we have developed two grouping strategies (adjacent and scattered) and used synthetic and field-data examples to evaluate their performance with various group numbers. In addition to the spatial resolution of the source image, robustness to random noise is another important assessment criterion, for which we consider two distribution patterns, such as concentrated and scattered, of traces contaminated with strong random noise. We also evaluated their effectiveness to visualize events (in the image domain) that are not completely recorded by all receivers. Our comprehensive tests illustrate the respective advantages of the two grouping strategies.

SUMMARY Passive seismic inversion at the reservoir scale offers the advantages of low cost, negligible environmental impact and the ability to probe a target area with low-frequency energy not afforded by even the most modern active-source seismic technology. In order to build starting models suitable for full-waveform wave speed tomography, characterization of earthquake sources is an indispensable first step. We present a workflow for the centroid moment tensor (CMT) inversion of seismic events identified in a passive seismic data set acquired by a large and dense array of three-component broad-band seismic sensors in a mountainous setting in the Himalayan foothills. The data set comprised 256 instruments operating for 2×4 months over an area of 8000 km2. An initial 3-D wave speed model was determined for the region via the analysis of first-arriving traveltime picks. Of the 2607 identified seismic events that were well recorded at frequencies between 0.2–50 Hz, 86 with magnitudes 1.3 ≤ M ≤ 3.0 initially had their CMT focal mechanisms determined by a waveform fitting procedure built on a Green’s function approach in a 1-D layered average wave speed model, for stations within an offset of 10 km, in the frequency range 0.2–1.4 Hz. Here, we obtain updated CMT mechanisms for the 86 events in that catalogue via multicomponent full-waveform inversion in the 3-D wave speed model. Our workflow includes automated data- and model-driven data selection using a combination of different metrics derived from signal-to-noise considerations and waveform-fitting criteria, and relies upon spectral-element simulations of elastic wave propagation in the 3-D wave speed model, honouring topography. Starting from the initial CMT solutions, we seek improvement to the data fit within the frequency band 0.5–2.5 Hz by minimizing the waveform difference between observed and synthetic data, while accommodating wave speed-model errors by allowing for small time-shifts. We balance uneven data coverage and tune their contributions via data-space weighting functions. We quantify the improvements to the data fit in terms of different metrics. We summarize the changes to the CMT solutions, and present and analyse the resulting catalogue for the region, including their breakdown into double-couple and non-double couple components, and their relation to mapped faults.

In the early 1970s, urbanisation shifted towards counterurbanisation in most developed countries. In contrast, there is little evidence that developing countries will experience counterurbanisation due to the complexity of their historical, economic, and social conditions. To examine the transition process, Geyer and Kontuly (1993) introduced differential urbanisation theory to explain the concentration and deconcentration of populations in urban systems (from urbanisation to polarisation reversal to counterurbanisation). Most studies have applied this theory in developed country settings, but few have done so for developing countries and none have done so in the Malaysian context. This paper tested the theory in the Malaysian setting to consider the extent to which the theoretical assumptions are supported or challenged. In addition, compared to previous papers, this paper focuses far more on the nature of migration flows leading to urbanisation in terms of the relative contributions of net migration and natural increase to population change, as well as origin-destination migration flows in total and according to age structures. The results show that natural increase, rather than migration flows, was the dominant cause of urbanisation in all settlement types. This was due to the population momentum effect of high fertility levels, primarily after the Second World War, which resulted in the birth of a large number of females who later grew to childbearing age. Malaysia experienced the second stage of urbanisation (Intermediate Primate City) after 1980 but had shifted towards the final stage (Advanced Primate City) by 2000. This analysis of three decades (1980-2010), however, shows clear evidence of urbanisation but no evidence of polarisation reversal or counterurbanisation. Due to the continuous rapid urban development and growth in the largest city, the capital metropolitan area, and if the current migration trends persist in the future, Malaysia may never experience polarisation reversal or counterurbanisation.

A hybrid optimization framework is proposed for full waveform inversion (FWI) problems by incorporating derivative information into the model update rule of a global optimization method called Very Fast Simulated Annealing (VFSA). The proposed optimization framework tackles the local minima issue of non‐linear inverse problems. Additionally, it can converge to the close neighborhood of the global solution from different starting points with an improved convergence speed compared to traditional global optimization methods. Applied to large‐scale FWI problems, the proposed framework greatly relaxes the issue of the dependence of FWI on starting models. Given a proper tuning and sufficient number of iterations, hybrid optimization based FWI can render a good background model, which is a good approximation to the ground truth, even with uninformative prior constraints and poor starting models. The output of hybrid optimization based FWI can be used as the starting model for a subsequent local optimization based FWI run to improve the spatial resolution of the result. The proposed hybrid optimization framework is very general, and can be applied to other linear and non‐linear problems that need optimization loops.

Regional seismic networks typically monitor and locate seismic sources using only kinematic (i.e., traveltime) observations. We propose an automated “sliding box” procedure to improve source locations by leveraging dynamic (e.g., full waveform) information via Geometric-mean Reverse-Time Migration (GmRTM). We demonstrate the proposed method’s efficacy by selecting and relocating some of the cataloged tectonic earthquakes recorded by a network of ∼250 three-component seismic sensors deployed across 8,000 km2 of mountainous terrain in Central Asia. Each event is recorded with sufficient signal-to-noise ratio (≥4) by at least 8 sensors inside a 20 km × 20 km box centered on the cataloged location. For each event, we extract a local 3-D velocity model, multiply the waveform data by their corresponding STA/LTA ratios to suppress coda waves and other coherent noise, and apply GmRTM to reconstruct high-resolution source images. The automatic procedure reasonably relocates 280 earthquakes.

High-quality seismic imaging strongly relies on spatially well-sampled input data. However, due to budgetary or physical constraints during the acquisition process, seismic data are often irregularly and/or sparsely sampled in at least one dimension. We have investigated Deep-learning (DL) interpolation to assess its ability to transcend aliasing limits without the computational effort of going to a full 5D interpolation process. In particular we consider the problem of interpolating between streamers, in marine acquisitions. We started with a “standard”, 3D convolutional neural network (CNN) architecture: while computationally intense, a 3D NN is required to optimize interpolation performance. This already outperforms sinc interpolation. We then enhanced the network training by adding a second label – the data transformed into the frequency-wavenumber domain; this requires the addition of a Fourier Transform layer to the architecture, which can be denoted a Frequency-Constrained NN (FC-NN). Tests show that FC-NN outperforms CNN on both structural similarity index (SSIM) and peak signal-to-noise ratio (PSNR) evaluation metrics. Adding inception blocks to FC-NN to capture features at multiple scales further improves the prediction accuracy. We demonstrate that the proposed architecture can provide high accuracy interpolated results for both synthetic and field data. For real data, we also test the hypothesis that an FC-NN trained to interpolate the streamers at a given spacing can also be used to further interpolate the streamers at a finer spacing.

Seismic full waveform inversion (FWI) has been widely applied in different geophysical applications. By fitting both the phase and the amplitude of the observed seismic data using computational modeling engine, FWI can render high resolution subsurface model estimations compared to travel-time based inversion methods. Although FWI applications typically require a modeling engine that accurately approximate the physics that produces the observed data, acoustic FWI in the elastic world might still be able to provide valuable information in many circumstances, especially in marine cases, if proper methodology is adapted. Here, we study acoustic FWI for acoustic and elastic data with a recently introduced hybrid optimization method. The hybrid optimization based FWI is much less sensitive to the starting model, and is able to explore the parameter space to find possible solutions. We use a synthetic model that simulates the geology of deep-water salt province to demonstrate the behaviour of acoustic FWI based on hybrid optimization method when inverting acoustic and elastic data. Even though, the numerical tests illustrate some limitations of such implementation, the inversion results are very promising, the acoustic FWI based on hybrid optimization using the elastic pressure data can generate a reasonably good background Vp model without an accurate starting model, and the result does not degrade too much compared to the FWI result generated using the acoustic data.

Low fertility is set to worsen economic problems in many developed countries, and maternity, paternity, and parental leave have emerged as key pro-natal policies. Gender inequity in the balance of domestic and formal work has been identified as a key driver of low fertility, and leave can potentially equalise this balance and thereby promote fertility. However, the literature contends that evidence for the effect of leave on fertility is mixed. We conduct the first systematic review on this topic. By applying a rigorous search protocol, we identify and review empirical studies that quantify the impact of leave policies on fertility. We focus on experimental or quasi-experimental studies that can identify causal effects. We identify 11 papers published between 2009 and 2019, evaluating 23 policy changes across Europe and North America from 1977 to 2009. Results are a mixture of positive, negative, and null impacts on fertility. To explain these apparent inconsistencies, we extend the conceptual framework of Lalive and Zweimüller (2009), which decomposes the total effect of leave on fertility into the “current-child” and “future-child” effects. We decompose these into effects on women at different birth orders, and specify types of study design to identify each effect. We classify the 23 studies in terms of the type of effect identified, revealing that all the negative or null studies identify the current-child effect, and all the positive studies identify the future-child or total effect. Since the future-child and total effects are more important for promoting aggregate fertility, our findings show that leave does in fact increase fertility when benefit increases are generous. Furthermore, our extensions to Lalive and Zweimüller’s conceptual framework provide a more sophisticated way of understanding and classifying the effects of pro-natal policies on fertility. Additionally, we propose ways to adapt the ROBINS-I tool for evaluating risk of bias in pro-natal policy studies.

Landslides in the Thompson River Valley, British Columbia, Canada, threaten the serviceability of two railway lines that connect Vancouver to the rest of Canada and the US. To minimise the impact of slope instability on vital transport infrastructure, as well as on terrestrial and aquatic ecosystems, public safety, communities, local heritage, and the economy, and to better inform decision making, there is a need for monitoring. Since 2013, the Ripley Landslide – a small, slow-moving, translational landslide – has been the focus of monitoring efforts in the Thompson River Valley transportation corridor. In November 2017, a novel Electrical Resistivity Tomography (ERT) monitoring system was installed on the site, providing near-real-time data collection via a telemetric link. 4-Dimensional resistivity models are presented in the context of moisture content and soil suction, two parameters known to influence slope stability in the Thompson River Valley. Here, we discuss the development of laboratory-based petrophysical relationships that relate electrical resistivity to moisture content and soil suction directly, building on relationships developed in the field. The 4-D ERT models were calibrated using these petrophysical relationships to provide insights into the complex spatial and temporal variations in moisture content and soil suction. This study highlights the utility of geoelectrical monitoring for assessing slope stability in the context of moisture-driven landslides.

The success of hydrocarbon exploration and production imaging projects relies heavily on the accuracy of the velocity model. The standard methodology for model building is computationally expensive and requires extensive human interpretation and quality control. Several deep learning (DL) approaches have been proposed to reduce both computational and labor costs, but they are all confronted with the challenge of limited available pertinent training data. In this paper, we propose a hybrid workflow to tackle the generalization issue in DL-driven velocity model building frameworks with two major components: 1) Generative Adversarial Network (GAN) to enrich the training dataset and 2) Transfer Learning to improve the alignment of the predictions with the target output population. The results show that trained GANs can generate synthetic models which contain similar features to the targeted Gulf of Mexico (GOM) velocity models. Using the SASI evaluation metric we demonstrate that GAN-generated velocity models have similar data distribution for salt geometries as GOM models. To reconstruct velocity models, U-Net-like architectures are first trained with pseudo-randomly-generated velocity models and then, with transfer learning, re-trained with GAN-generated synthetic velocity models. Afterwards, the trained model is tested with synthetic data from velocity models representative of real GOM geological settings. The results demonstrate that the prediction accuracies for both salt geometries (IoU increased from 0.646 to 0.801) and background velocities (MAE decreased from 359.3 to 158.2 m/s) can be largely improved with the proposed hybrid workflow.

PreviousNext No AccessFirst International Meeting for Applied Geoscience & Energy Expanded AbstractsWaveform inversion for shear velocity and attenuation via the spectral-element adjoint methodAuthors: Fan V. WuDmitry BorisovFrederik J. SimonsPaul WilliamsonFan V. WuPrinceton University and Kansas Geological Survey.Search for more papers by this author, Dmitry BorisovPrinceton University and Kansas Geological Survey.Search for more papers by this author, Frederik J. SimonsPrinceton University.Search for more papers by this author, and Paul WilliamsonTotal EP Research and Technology.Search for more papers by this authorhttps://doi.org/10.1190/segam2021-3581151.1 SectionsSupplemental MaterialAboutPDF/ePub ToolsAdd to favoritesDownload CitationsTrack CitationsPermissions ShareFacebookTwitterLinked InRedditEmail AbstractIntrinsic attenuation affects both amplitude and phase behavior of the seismic wavefield. Its three-dimensional distribution in the subsurface needs to be robustly estimated to make earth models accurate. Full Waveform Inversion (FWI) has become the technique of choice for recovering high-resolution velocity structure, but its ability to reliably recover attenuation variations remains challenging. Multistage and hierarchical approaches offer promise to control the delicate trade-off between resolving elastic and anelastic structure in inversions for the shear velocity VS and quality factor Qµ, in regimes with strong surface waves prone to cycle skipping. We present a procedure for their joint reconstruction via spectral-element adjoint-based full-waveform modeling. Starting from a checkerboard example, we develop a frequency and offset continuation strategy for onshore active-source acquisition. In the early stages of our algorithm, the inversion targets the refinement of the shear-wave speed model by gradually widening the frequency band and increasing the offset range. The shear quality factor is of major consideration only in the final stage of the inversion. Our procedure is robust, competitive, and practical.Keywords: attenuation, tomography, viscoelastic, full-waveform inversion, inversionPermalink: https://doi.org/10.1190/segam2021-3581151.1FiguresReferencesRelatedDetails First International Meeting for Applied Geoscience & Energy Expanded AbstractsISSN (print):1052-3812 ISSN (online):1949-4645Copyright: 2021 Pages: 3561 publication data© 2021 Published in electronic format with permission by the Society of Exploration GeophysicistsPublisher:Society of Exploration Geophysicists HistoryPublished: 01 Sep 2021 CITATION INFORMATION Fan V. Wu, Dmitry Borisov, Frederik J. Simons, and Paul Williamson, (2021), "Waveform inversion for shear velocity and attenuation via the spectral-element adjoint method," SEG Technical Program Expanded Abstracts : 697-701. https://doi.org/10.1190/segam2021-3581151.1 Plain-Language Summary Keywordsattenuationtomographyviscoelasticfull-waveform inversioninversionPDF DownloadLoading ...

Multi-mode dispersion curve picking is required by many approaches for shallow-subsurface characterization using surface waves, but is typically a labor-intensive process. Previously we automated the picking procedure using convolutional neural network (CNN) based machine learning (ML) method, which made industry-scale application possible in terms of efficiency. This study improves the picking algorithm in three ways: (1) it is more stable by using a new loss function which combines the conventional wavenumber differences and the wavenumber slope differences; (2) it is more efficient because we pretrain with synthetic data and then use transfer learning; (3) it is more complete because we estimate uncertainties in the picking using random dropout. These improvements make the picking algorithm more mature technically.