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NASA NTRS2018

Affine Generalized Inverse for Optimal Control Allocation

This research is a follow on to the "Optimal Control Prediction Method for Control Allocation" paper in which the Prediction Method iterative algorithm was introduced. Previously, the Prediction Method was shown to provide optimal control allocation solutions over the entire Attainable Moment Set for the Moore-Penrose and the generalized (weighted) inverse. As an extension to the Prediction Method, this paper introduces a family of Moore Penrose Affine Generalized Inverses, applicable for all moments, which compute control allocation solutions using a constant matrix and fixed null-space vector. The Moore-Penrose Affine Generalized Inverse is proven to yield equivalent solutions to those of the Prediction Method and therefore is guaranteed to yield Moore-Penrose optimal control allocation solutions. While the Prediction Method is applicable for any moment along an a priori specified moment direction, the Affine Generalized Inverse is shown to yield optimal control allocation solutions in a neighborhood of the given moment which is not restricted to a specified moment direction. Furthermore, the Affine Generalized Inverse is shown to provide the time derivative of optimal control allocation solutions and to facilitate maintaining solutions within control effector rate limitations. The Moore-Penrose Affine Generalized Inverse is broadened to encompass any arbitrary (weighted) Affine Generalized Inverse. Finally, a method of creating a moment lookup table is outlined to utilize the Affine Generalized Inverse as an offline control allocation solution for all moments in the Attainable Moment Set.

Acheson, Michael J.↗

NASA NTRS2004

Bayesian Approach to the Joint Inversion of Gravity and Magnetic Data, with Application to the Ismenius Area of Mars

This viewgraph presentation reviews a Bayesian approach to the inversion of gravity and magnetic data with specific application to the Ismenius Area of Mars. Many inverse problems encountered in geophysics and planetary science are well known to be non-unique (i.e. inversion of gravity the density structure of a body). In hopes of reducing the non-uniqueness of solutions, there has been interest in the joint analysis of data. An example is the joint inversion of gravity and magnetic data, with the assumption that the same physical anomalies generate both the observed magnetic and gravitational anomalies. In this talk, we formulate the joint analysis of different types of data in a Bayesian framework and apply the formalism to the inference of the density and remanent magnetization structure for a local region in the Ismenius area of Mars. The Bayesian approach allows prior information or constraints in the solutions to be incorporated in the inversion, with the "best" solutions those whose forward predictions most closely match the data while remaining consistent with assumed constraints. The application of this framework to the inversion of gravity and magnetic data on Mars reveals two typical challenges - the forward predictions of the data have a linear dependence on some of the quantities of interest, and non-linear dependence on others (termed the "linear" and "non-linear" variables, respectively). For observations with Gaussian noise, a Bayesian approach to inversion for "linear" variables reduces to a linear filtering problem, with an explicitly computable "error" matrix. However, for models whose forward predictions have non-linear dependencies, inference is no longer given by such a simple linear problem, and moreover, the uncertainty in the solution is no longer completely specified by a computable "error matrix". It is therefore important to develop methods for sampling from the full Bayesian posterior to provide a complete and statistically consistent picture of model uncertainty, and what has been learned from observations. We will discuss advanced numerical techniques, including Monte Carlo Markov

data analysis↗

DOE OSTI2022

The Influence of Temperature Inversion on the Vertical Distribution of Aerosols

Temperature inversion plays an important role in the accumulation and diffusion of aerosols. In this study, the relationship between temperature inversion and the vertical distribution of aerosols is investigated based on Raman lidar observations taken from January 2010 to September 2015 at the Atmospheric Radiation Measurement site in the Southern Great Plains, USA. First, the diurnal and seasonal variations of the surface-based inversion (SBI) and elevated temperature inversion (EI) are investigated. The results indicate that the occurrence frequency of SBI and EI have different seasonal trends. SBI has the highest frequency in summer, while EI has the highest frequency in winter. The diurnal variation of SBI is obvious, with a higher frequency in nighttime and a lower frequency in daytime. The inversion intensity (ΔT) and inversion depth (ΔZ) of SBI and EI have consistent diurnal and seasonal trends. The effects of SBI and EI on the vertical distribution of aerosols are then analyzed. The mean aerosol optical depth (AOD) below the SBI height shows a clear seasonal variation, which is consistent with the seasonal trends of ΔT and ΔZ. This phenomenon also occurs on the AOD below EI top height. The sensitivity analysis shows that the mean AOD below SBI height or EI top height increases with an increase of the ΔT and ΔZ of SBI (EI). It indicates that ΔT and ΔZ are the key factors affecting the vertical distribution of aerosols. In addition, the variation of AOD below and above EI top height is opposite to that of AOD below and above EI bottom height under different ΔT and ΔZ conditions. The correlation coefficients between ΔT (ΔZ) of EI with AOD in EI were 0.62 (0.65). These results indicate that the space between EI bottom height and EI top height can store aerosols. The larger the ΔZ of EI, the more aerosols are stored. These findings contribute to our understanding of the effect of temperature inversion on the vertical distribution of aerosols.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Generative Adversarial Networks and Mixture Density Networks-Based Inverse Modeling for Microstructural Materials Design

Abstract There are two broad modeling paradigms in scientific applications: forward and inverse. While forward modeling estimates the observations based on known causes, inverse modeling attempts to infer the causes given the observations. Inverse problems are usually more critical as well as difficult in scientific applications as they seek to explore the causes that cannot be directly observed. Inverse problems are used extensively in various scientific fields, such as geophysics, health care and materials science. Exploring the relationships from properties to microstructures is one of the inverse problems in material science. It is challenging to solve the microstructure discovery inverse problem, because it usually needs to learn a one-to-many nonlinear mapping. Given a target property, there are multiple different microstructures that exhibit the target property, and their discovery also requires significant computing time. Further, microstructure discovery becomes even more difficult because the dimension of properties (input) is much lower than that of microstructures (output). In this work, we propose a framework consisting of generative adversarial networks and mixture density networks for inverse modeling of structure–property linkages in materials, i.e., microstructure discovery for a given property. The results demonstrate that compared to baseline methods, the proposed framework can overcome the above-mentioned challenges and discover multiple promising solutions in an efficient manner.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Diagnosing the pedestal magnetic field and magnetohydrodynamics radial structure with pedestal–scrape of layer electron cyclotron emission radiation inversion in H-mode plasma (invited)

Forward modeling is used to interpret inversion patterns of the pedestal–Scrape of Layer (SOL) Electron Cyclotron Emission (ECE) in DIII-D H-mode experiments. The modeling not only significantly improves the ECE data interpretation quality but also leads to the potential measurements of (1) the magnetic field strength |B| at the separatrix, (2) the pedestal |B| evolution during an inter-Edge Localized Mode (ELM) period, and (3) the pedestal Magnetohydrodynamics (MHD) radial structure. The ECE shine-through effect leads to three types of pedestal–SOL radiation inversions that are discussed in this paper. The first type of inversion is the non-monotonic T e,rad profile with respect to the major radius. Using the ECE frequency at the minimum T e,rad , the inversion can be applied to measure the magnetic field |B| at the separatrix and calibrate the mapping of the ECE channels with respect to the separatrix. The second type of inversion refers to the opposite phase between the radiation fluctuations δT e,rad at the pedestal and SOL. This δT e,rad phase inversion is sensitive to density and temperature fluctuations at the pedestal foot and, thus, can be used to qualitatively measure the MHD radial structure. The third type of inversion appears when the pedestal and SOL T e,rad evolve in an opposite trend, which can be used to infer the pedestal |B| field change during an inter-ELM period. Finally, the bandwidth effect on measuring δT e,rad due to pedestal MHD is also investigated in the radiation modeling.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Bayesian Neural Network Variational Autoencoder Inverse Mapper (BNN-VAIM) and its application in Compton Form Factors extraction

Abstract We extend the Variational Autoencoder Inverse Mapper (VAIM) framework for the inverse problem of extracting Compton Form Factors (CFFs) from deeply virtual exclusive reactions, such as the unpolarized Deeply virtual exclusive scattering (DVCS) cross section. VAIM is an end-to-end deep learning framework to address the solution ambiguity issue in ill-posed inverse problems, which comprises of a forward mapper and a backward mapper to simulate the forward and inverse processes, respectively. In particular, we incorporate Bayesian Neural Network (BNN) into the VAIM architecture (BNN-VAIM) for uncertainty quantification. By sampling the weights and biases distributions of the BNN in the backward mapper of the VAIM, BNN-VAIM is able to estimate prediction uncertainty associated with each individual solution obtained for an ill-posed inverse problem. We first demonstrate the uncertainty quantification capability of BNN-VAIM in a toy inverse problem. Then, we apply BNN-VAIM to the inverse problem of extracting 8 CFFs from the unpolarized DVCS cross section.

Instruments & Instrumentation↗

DOE OSTI2026

3D Deep Learning Joint Inversion of Active Seismic Full Waveform and Passive Seismic Traveltime Data for Reservoir Imaging and Uncertainty Quantification

Here, we present deep learning (DL) networks for three-dimensional (3D) joint inversion of active seismic full waveform and passive seismic traveltime data to image reservoirs and their properties and quantify imaging uncertainties. Active seismic full-waveform data can provide high-resolution monitoring images but are collected only intermittently because of their high acquisition cost. In contrast, passive seismic data can be gathered at relatively low cost between regular active surveys, although their imaging quality can be compromised by factors such as low signal-to-noise ratios and limited ray coverage of the target. Although these datasets are routinely acquired together at CO 2 storage sites, their combined inversion within a 3D DL framework has not been previously demonstrated. To our knowledge, this is the first study to address this gap, combining the strength of both data types. For efficient data storage and DL training with large 3D seismic datasets, we use a 3D data matrix in which a random number of passive seismic traveltime data are stored as parabolic envelopes using one-hot encoding and a 3D full-waveform data matrix in which multiple shot gathers are summed. Two network architectures are evaluated: a single-encoder U-Net for single-data type inversion and a dual-encoder U-Net for joint inversion of active and passive seismic data. We also evaluate the single-encoder U-Net for joint inversion by concatenating full-waveform data and traveltime data. We propose a systematic approach for selecting an optimal dropout rate that balances regularization during training and Monte Carlo dropout-based uncertainty quantification during prediction by examining the correlation coefficient between standard deviation and prediction error, along with the training misfit, across a range of dropout rates. 3D DL inversion experiments include five different network configurations, with evaluations under ideal, noisy and dropout-enabled conditions. Both model and data uncertainties are assessed, as well as their combined effects. Across all conditions, the networks consistently predict accurate CO 2 saturation models with low prediction errors, such as a structural similarity index of 0.993 and CO 2 difference of 1.1%. Uncertainty estimates show strong spatial correlation with prediction errors, confirming the effectiveness of the proposed dropout selection approach. The results demonstrate that our DL approach, utilizing compact data representations and appropriate uncertainty quantification, yields accurate subsurface images under various inversion conditions and provides valuable insights into the reliability of predictions.

Um, Evan Schankee [Lawrence Berkeley National Labo↗

DOE OSTI2026

Robust Optimal Experimental Design of Infinite-Dimensional Bayesian Nonlinear Inverse Problems

Abstract. We consider robust optimal experimental design (ROED) for nonlinear Bayesian inverse problems governed by partial differential equations (PDEs). An optimal design is one that maximizes some utility quantifying the quality of the solution of an inverse problem. However, the optimal design is dependent on elements of the inverse problem such as the simulation model, the prior, or the measurement error model. ROED aims to produce an optimal design that is aware of the additional uncertainties encoded in the inverse problem and remains optimal even after variations in them. We follow a worst-case scenario approach to develop a new framework for robust optimal design of nonlinear Bayesian inverse problems. The proposed framework (a) is scalable and designed for infinite-dimensional Bayesian nonlinear inverse problems constrained by PDEs; (b) develops efficient approximations of the utility, namely the expected information gain; (c) employs eigenvalue sensitivity techniques to develop analytical forms and efficient evaluation methods of the gradient of the utility with respect to the uncertainties against which we wish to be robust; and (d) employs a probabilistic optimization paradigm that properly defines and efficiently solves the resulting combinatorial max-min optimization problem. The effectiveness of the proposed approach is illustrated for optimal sensor placement problem in an inverse problem governed by an elliptic PDE.

Chowdhary, Abhijit↗

DOE OSTI2023

Massively parallel modeling and inversion of electrical resistivity tomography data using PFLOTRAN

Abstract. Electrical resistivity tomography (ERT) is a broadly accepted geophysical method for subsurface investigations. Interpretation of field ERT data usually requires the application of computationally intensive forward modeling and inversion algorithms. For large-scale ERT data, the efficiency of these algorithms depends on the robustness, accuracy, and scalability on high-performance computing resources. In this regard, we present a robust and highly scalable implementation of forward modeling and inversion algorithms for ERT data. The implementation is publicly available and developed within the framework of PFLOTRAN, an open-source, state-of-the-art massively parallel subsurface flow and transport simulation code. The forward modeling is based on a finite-volume discretization of the governing differential equations, and the inversion uses a Gauss–Newton optimization scheme. To evaluate the accuracy of the forward modeling, two examples are first presented by considering layered (1D) and 3D earth conductivity models. The computed numerical results show good agreement with the analytical solutions for the layered earth model and results from a well-established code for the 3D model. Inversion of ERT data, simulated for a 3D model, is then performed to demonstrate the inversion capability by recovering the conductivity of the model. To demonstrate the parallel performance of PFLOTRAN's ERT process model and inversion capabilities, large-scale scalability tests are performed by using up to 131 072 processes on a leadership class supercomputer. These tests are performed for the two most computationally intensive steps of the ERT inversion: forward modeling and Jacobian computation. For the forward modeling, we consider models with up to 122 ×106 degrees of freedom (DOFs) in the resulting system of linear equations and demonstrate that the code exhibits almost linear scalability on up to 10 000 DOFs per process. On the other hand, the code shows superlinear scalability for the Jacobian computation, mainly because all computations are fairly evenly distributed over each process with no parallel communication.

58 GEOSCIENCES↗

NASA NTRS1992

Sources of unbounded priority inversions in real-time systems and a comparative study of possible solutions

In the design of real-time systems, tasks are often assigned priorities. Preemptive priority driven schedulers are used to schedule tasks to meet the timing requirements. Priority inversion is the term used to describe the situation when a higher priority task's execution is delayed by lower priority tasks. Priority inversion can occur when there is contention for resources among tasks of different priorities. The duration of priority inversion could be long enough to cause tasks to miss their dead lines. Priority inversion cannot be completely eliminated. However, it is important to identify sources of priority inversion and minimize the duration of priority inversion. In this paper, a comprehensive review of the problem of and solutions to unbounded priority inversion is presented.

Davari, Sadegh↗

NASA NTRS2013

Inverse Modeling of Texas NOx Emissions Using Space-Based and Ground-Based NO2 Observations

Inverse modeling of nitrogen oxide (NOx) emissions using satellite-based NO2 observations has become more prevalent in recent years, but has rarely been applied to regulatory modeling at regional scales. In this study, OMI satellite observations of NO2 column densities are used to conduct inverse modeling of NOx emission inventories for two Texas State Implementation Plan (SIP) modeling episodes. Addition of lightning, aircraft, and soil NOx emissions to the regulatory inventory narrowed but did not close the gap between modeled and satellite observed NO2 over rural regions. Satellitebased top-down emission inventories are created with the regional Comprehensive Air Quality Model with extensions (CAMx) using two techniques: the direct scaling method and discrete Kalman filter (DKF) with Decoupled Direct Method (DDM) sensitivity analysis. The simulations with satellite-inverted inventories are compared to the modeling results using the a priori inventory as well as an inventory created by a ground-level NO2 based DKF inversion. The DKF inversions yield conflicting results: the satellite based inversion scales up the a priori NOx emissions in most regions by factors of 1.02 to 1.84, leading to 3-55% increase in modeled NO2 column densities and 1-7 ppb increase in ground 8 h ozone concentrations, while the ground-based inversion indicates the a priori NOx emissions should be scaled by factors of 0.34 to 0.57 in each region. However, none of the inversions improve the model performance in simulating aircraft-observed NO2 or ground-level ozone (O3) concentrations.

Nitrogen dioxide↗

DOE OSTI2025

Robust A-Optimal Experimental Design for Sensor Placement in Bayesian Linear Inverse Problems

Optimal design of experiments for Bayesian inverse problems has recently gained wide popularity and attracted much attention, especially in the computational science and Bayesian inversion communities. An optimal design maximizes a predefined utility function that is formulated in terms of the elements of an inverse problem, an example being optimal sensor placement for parameter identification. The state-of-the-art algorithmic approaches following this simple formulation generally overlook misspecification of the elements of the inverse problem, such as the prior or the measurement uncertainties. This work presents an efficient algorithmic approach for designing optimal experimental design schemes for Bayesian linear inverse problems such that the optimal design is robust to misspecification of elements of the inverse problem. Specifically, we consider a worst-case scenario approach for the uncertain or misspecified parameters, formulate robust objectives, and propose an algorithmic approach for optimizing such objectives. Furthermore, both relaxation and stochastic solution approaches are discussed with detailed analysis and insight into the interpretation of the problem and the proposed algorithmic approach. Extensive numerical experiments to validate and analyze the proposed approach are carried out for sensor placement in a parameter identification problem.

Bayesian inverse problems↗

DOE OSTI2022

Multi-variance replica exchange SGMCMC for inverse and forward problems via Bayesian PINN

Physics-informed neural network (PINN) has been successfully applied in solving a variety of nonlinear non-convex forward and inverse problems. However, the training is challenging because of the non-convex loss functions and the multiple optima in the Bayesian inverse problem. In this work, we propose a multi-variance replica exchange stochastic gradient Langevin dynamics method to tackle the challenge of the multiple local optima in the optimization and the challenge of the multiple modal posterior distribution in the inverse problem. Replica exchange methods are capable of escaping from the local traps and accelerating the convergence; two chains with different temperatures are designed where the low temperature chain aims for the local convergence, and the target of the high temperature chain is to travel globally and explore the whole loss function entropy landscape. However, it may not be efficient to solve mathematical inversion problems by using the vanilla replica method directly since the method doubles the computational cost in evaluating the forward solvers (likelihood functions) in the two chains. To address this issue, we propose to make different assumptions on the energy function estimation and this facilities one to use solvers of different fidelities in the likelihood function evaluation. More precisely, one can use a solver with low fidelity in the high temperature chain while using a solver with high fidelity in the low temperature chain. Our proposed method significantly lowers the computational cost in the high temperature chain, meanwhile preserving the accuracy and converging very fast. Here we give an unbiased estimate of the swapping rate and give an estimation of the discretization error of the scheme. To verify our idea, we design and solve four inverse problems which have multiple modes. The proposed method is also employed to train the Bayesian PINN to solve the forward and inverse problems; faster and more accurate convergence has been observed when compared to the stochastic gradient Langevin dynamics (SGLD) method and vanilla replica exchange methods.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Deep inverse photonic design: A tutorial

Deep learning (DL) has been used to design deep neural networks (DNNs) which have recently been applied to solving inverse problems in artificial electromagnetic materials (AEMs). Although inverse problems are often ill-posed, and therefore are difficult to solve, deep inverse models (DIMs) have achieved impressive results often surpassing capabilities possible with other approaches. We overview the process of deep inverse learning applied to AEM problems, including the building of data sets, design of a forward model, and comparison of inverse approaches including limitations. We conclude by detailing some important outstanding issues of deep inverse design of AEMs, and present an outlook of this exciting field.

42 ENGINEERING↗

DOE OSTI2022

Real-time deep-learning inversion of seismic full waveform data for CO 2 saturation and uncertainty in geological carbon storage monitoring

Deep-learning inversion has recently drawn attention in geological carbon storage research due to its potential of imaging and monitoring carbon storage in real time, significantly improving efficiency and safety of carbon storage operations. We present a deep-learning full waveform inversion method that after the neural network has been trained can image CO 2 saturation and its uncertainty in real time. Our deep-learning inversion method is based on the U-Net architecture with the neural network trained on pairs of synthetic seismic data and CO 2 saturation models. Accordingly, our training establishes a mapping relationship between seismic data and CO 2 saturation models and once fully trained directly estimates CO 2 saturation as a function of subsurface location. We further quantify uncertainties of CO 2 saturation estimates using the Monte Carlo dropout method and a bootstrap aggregating method. For this proof-of-concept study, the CO 2 training models and data are derived from the Kimberlina 1.2 model, a hypothetical 3D geological carbon storage model that is constructed based on various geological and hydrological data from the Southern San Joaquin Basin, California. We perform deep-learning inversion experiments using noise-free and noisy training and test data sets and compare the results. Our modelling experiments show that (1) the deep-learning inversion can estimate 2D distributions of CO 2 fairly well even in the presence of Gaussian random noise and (2) both CO 2 saturation imaging and uncertainty quantification can be done in real time. Our results suggest that the deep-learning inversion method can serve as a robust real-time monitoring tool for geological carbon storage and/or other time-varying reservoir/aquifer properties that result from injection, extraction, and/or other subsurface transport phenomena.

58 GEOSCIENCES↗

DOE OSTI2025

Identifying Band Inversions in Topological Materials Using Diffusion Monte Carlo

Topological insulators are characterized by insulating bulk states and robust metallic surface states. Band inversion is a hallmark of topological insulators. At time-reversal invariant points in the Brillouin zone, spin–orbit coupling (SOC) induces a swapping of orbital character at the bulk band edges. Reliably detecting band inversion in solid-state systems with many-body methods would aid in identifying possible candidates for spintronics and quantum computing applications and improve our understanding of the physics behind topologically nontrivial systems. Density functional theory (DFT) methods are a well-established means of investigating these interesting materials due to their favorable balance of computational cost and accuracy but often struggle to accurately model the electron–electron correlations present in the many materials containing heavier elements. In this work, we develop a novel method to detect band inversion within continuum quantum Monte Carlo (QMC) methods that can accurately treat the electron correlation and spin–orbit coupling that are crucial to the physics of topological insulators. Our approach applies a momentum-space-resolved atomic population analysis throughout the first Brillouin zone utilizing the Löwdin method and the one-body reduced density matrix produced with diffusion Monte Carlo (DMC). We integrate this method into QMCPACK, an open source ab initio QMC package, so that these ground-state methods can be used to complement experimental studies and validate prior DFT work on predicting the band structures of correlated topological insulators. Here, we demonstrate this new technique on the topological insulator bismuth telluride, which displays band inversion between its Bi-p and Te-p states at the Γ-point. We show an increase in charge on the bismuth-p orbital and a decrease in charge on the tellurium-p orbital when comparing band structures with and without SOC. Additionally, we use our method to compare the degree of band inversion present in monolayer Bi 2 Te 3 , which has no interlayer van der Waals interactions, to that seen in the bilayer and bulk. The method presented here will enable future many-body studies of band inversion that can shed light on the delicate interplay between correlation and topology in correlated topological materials.

Band structure↗

DOE OSTI2023

Physics-embedded inverse analysis with algorithmic differentiation for the earth’s subsurface

Abstract Inverse analysis has been utilized to understand unknown underground geological properties by matching the observational data with simulators. To overcome the underconstrained nature of inverse problems and achieve good performance, an approach is presented with embedded physics and a technique known as algorithmic differentiation. We use a physics-embedded generative model, which takes statistically simple parameters as input and outputs subsurface properties (e.g., permeability or P-wave velocity), that embeds physical knowledge of the subsurface properties into inverse analysis and improves its performance. We tested the application of this approach on four geologic problems: two heterogeneous hydraulic conductivity fields, a hydraulic fracture network, and a seismic inversion for P-wave velocity. This physics-embedded inverse analysis approach consistently characterizes these geological problems accurately. Furthermore, the excellent performance in matching the observational data demonstrates the reliability of the proposed method. Moreover, the application of algorithmic differentiation makes this an easy and fast approach to inverse analysis when dealing with complicated geological structures.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Probabilistic inversion of circular phase spectra: application to two-station phase-velocity dispersion estimation in western Canada

SUMMARY Periodic directional and temporal measurements are common in seismology, and necessitate specific statistical analyses that are appropriate for circular quantities. In this work, we explore the use of a von Mises distribution as a representation of errors on circular seismological observations. Specifically, we automate the estimation of surface-wave phase-velocity dispersion for the teleseismic two-station method, which generally suffers from a 2π phase ambiguity. The use of Bayesian inverse techniques, which aim to rigorously quantify model parameter uncertainty, have become widespread throughout seismology over the last decade. Here, we apply Bayesian inversion to measurements of surface-wave phase spectra in order to estimate 1-D, path-averaged Earth structure between station pairs. The dispersion curve and associated uncertainties are additional results of the inversion, which can then be used as input for subsequent analyses (e.g. tomography). We demonstrate this technique through application to surface-wave recordings from long-running seismic stations throughout western Canada. Our results for over 10 000 station pairs reveal first-order tectonic features consistent with previous studies, which provides confidence in our approach as well as an initial step towards resolving a full 3-D seismic velocity model for the region. This work also presents a foundation for the inversion of surface-wave phase spectra to estimate 3-D Earth structure directly. Finally, the ideas presented in this work are not limited to the inversion of surface-wave phase spectra, but can also be considered for Bayesian geophysical inversion of any circular quantities.

Gosselin, Jeremy M. (ORCID:0000000203754102)↗