11th Applied Inverse Problems Conference
September 4 - 8, 2023 | Göttingen, Germany
Conference Agenda
Overview and details of the sessions of this conference. Please select a date or location to show only sessions at that day or location. Please select a single session for detailed view (with abstracts and downloads if available).
|
|
|
Session Overview | |
| Location: VG1.102 |
| Date: Monday, 04/Sept/2023 | |
| 1:30pm - 3:30pm | MS15 1: Experimental and Algorithmic Progress in Photoemission Orbital Imaging Location: VG1.102 Session Chair: Russell Luke Session Chair: Stefan Mathias |
|
|
Imaging valence and excited states of fullerenes in momentum space 1University of Mainz, Germany; 2University of Kaiserslautern-Landau
One of the key milestones in advancing the performance of molecular electronic and photonic devices is to gain a comprehensive understanding of the electronic properties and rich excited state dynamics of this class of materials. In this context, momentum-resolved photoemission in combination with photoemission orbital tomography (POT) has been established as a powerful tool to study the band structure of molecular films and to reveal the degree of localization of molecular valence orbitals by their characteristic emission pattern in momentum space.
In this contribution, we exploit these capabilities of POT to study the valence and excited states of fullerenes grown on noble metal surfaces. For the most prototypical fullerene, the buckyball C$_{60}$, we will show that the valence states show signatures of an atomic crystal-like band structure with delocalized $\pi$- and localized $\sigma$-orbitals [1]. This observation differ significantly from our results for thin films of the endohedral fullerene Sc$_3$N@C$_{80}$, where the valence states are strongly localized on the carbon cage of the molecules.
Finally, we provide a first insight into the momentum space signatures of the excited state dynamics of C$_{60}$ thin films obtained by time-resolved two-photon momentum microscopy. For an optical excitation with $3.1\,$eV photons, we are able to identify three characteristic emission patterns even in the small momentum space range accessible by our experiment. These signatures are discussed in the context of the recently proposed charge transfer and Frenkel exciton character of these states [2].
[1] N. Haag, D. Lüftner, F. Haag, J. Seidel, L. Kelly, G. Zamborlini, M. Jugovac, V. Feyer, M. Aeschlimann, P. Puschnig, M. Cinchetti, B. Stadtmüller. Signatures of an atomic crystal in the band structure of a C60 thin film, Phys. Rev. B 101, 2020.
[2] B. Stadtmüller, S. Emmerich, D. Jungkenn, N. Haag, M. Rollinger, S. Eich, M. Maniraj, M. Aeschlimann, M. Cinchetti, S. Mathias. Strong modification of the transport level alignment in organic materials after optical excitation, Nat. Commun. 10, 2019.
Imaging molecular wave functions with photoemission orbital tomography: An introduction Forschungszentrum Jülich, Germany
The photoemission orbital tomography (POT) technique, a variant of angle-resolved photoemission spectroscopy, has been very useful in the characterization of the electronic properties of molecular films. It is a combined experimental and theoretical approach that is based on the interpretation of the photoelectron angular distribution in terms of a one-electron initial state. This includes the unambiguous assignment of emissions to specific molecular orbitals, their reconstruction to real space orbitals in two and three dimensions, the deconvolution of complex spectra into individual orbital contributions beyond the limits of energy resolution, the extraction of detailed geometric information such as molecular orientations, twists and bends, the precise description of the charge balance and transfer at interface, and the detection of momentum-selective hybridization with the substrate, to name only a few examples. In its simplest form, POT relies on the plane-wave approximation for the final state. While this works surprisingly well in many cases, this approximation does have its limitations, most notably for small molecules and with respect to the photon-energy dependence of the photoemission intensity. Regarding the latter, a straightforward extension of the plane wave final state leads to a much-improved description while preserving the simple and intuitive connection between the photoelectron distribution and the initial state.
Time-resolved photoemission orbital tomography of organic interfaces Philipps-Universität Marburg, Germany
Charge transfer across molecular interfaces is reflected in the population of electronic orbitals. For ordered organic layers, time-resolved photoemission orbital tomography (tr-POT) is capable of spectroscopically identifying the involved orbitals and deducing their population from the measured angle-resolved photoemission intensity with high temporal resolution [1]. As examples, I will present recent results obtained for PTCDA and CuPc adsorbed on Cu(100)-2O. We observe two distinct excitation pathways with visible light. While the parallel component of the electric field makes a direct HOMO-LUMO transition, the perpendicular component can transfer a substrate electron into the molecular LUMO. The experimental data are modelled by a density matrix description of the excitation and photoemission process. We find similar LUMO lifetimes for both excitation pathways, whereas the true dephasing times differ by two orders of magnitude.
Future tr-POT experiments will employ a two-pulse coherent control excitation scheme to steer the charge transfer. In some cases, this scheme will allow us to deduce the relative phase of the involved orbitals directly from the experiment. Furthermore, the combination with strong THz excitation and subcycle time resolution will make it possible to monitor charge transfer processes and hybridization during surface bond formation with POT.
[1] R. Wallauer, M. Raths, K. Stallberg, L. Münster, D. Brandstetter, X. Yang, J. Güdde, P. Puschnig, S. Soubatch, C. Kumpf, F. C. Bocquet, F. S. Tautz, U. Höfer. Tracing orbital images on ultrafast time scales, Science 371: 1056-1059, 2021.
https://doi.org/10.1126/science.abf3286
Exciton Photoemission Orbital Tomography: Probing the electron and the hole contributions I. Physical Institute, University of Goettingen, Germany
Time-resolved photoemission orbital tomography is a promising technique for the characterization of light-matter interaction in organic semiconductors. However, its state-of-the-art analysis approach based on density functional theory and the plane-wave model of photoemission cannot account for the correlated many-body nature of excitonic wavefunctions, which nevertheless represent the dominant optoelectronic response of organic semiconductors. Building on the many-body interaction formalisms of the $GW$ approach and the Bethe-Salpeter equation, we present a complete description of the angle-resolved exciton photoemission spectrum, and apply this model to the exemplary exciton relaxation cascade in multilayer C$_{60}$ crystals to investigate an intriguing property of the excitonic wavefunction: In C$_{60}$, and more generally in organic semiconductors, excitons can be of multiorbital nature, with both the electron and hole spread over multiple orbitals. We elucidate how photoemission orbital tomography is uniquely sensitive to this multiorbital nature and exploit it to directly access the hole part of the excitonic wavefunction in addition to its electron counterpart. With this capability, exciton photoemission orbital tomography provides a versatile probe of key exciton properties such as localization, charge transfer, and relaxation dynamics.
|
| 4:00pm - 6:00pm | MS15 2: Experimental and Algorithmic Progress in Photoemission Orbital Imaging Location: VG1.102 Session Chair: Russell Luke Session Chair: Stefan Mathias |
|
|
A minimalist approach to 3D photoemission orbital tomography: how many measurements are enough? University of Göttingen, Germany
Photoemission orbital tomography provides a unique access to the real-space molecular orbitals of well-ordered organic semiconductor layers. Specifically, the application of phase retrieval algorithms to photon-energy- and angle-resolved photoemission patterns enables the reconstruction of full 3D molecular orbitals independent of density functional theory calculations. However, until now this procedure has remained challenging due to the need for densely-sampled, well-calibrated 3D photoemission data. Here, we present an iterative projection algorithm that completely eliminates this challenge: For the benchmark case of the Pentacene frontier orbitals, we demonstrate reconstruction of the full orbital based on a data set containing only seven photoemission momentum maps. Based upon application to simulated data, we discuss the algorithm performance, sampling requirements with respect to the photon energy, optimal measurement strategies and the accuracy of orbital images that can be achieved.
Experimental progress towards time-resolved three-dimensional orbital tomography 1I. Physikalisches Institut, Georg-August-Universität Göttingen; 2Institut für Numerische und Angewandte Mathematik, Georg-August-Universität Göttingen
Photoemission Orbital Tomography (POT) is a powerful tool for probing the full electronic structure of oriented molecular thin films which allows a direct comparison of angle-resolved photoemission spectroscopy (ARPES) data with density functional theory calculations. Moreover, the application of numerical phase retrieval algorithms in the POT framework has enabled a complete recovery of the initial molecular orbital independent of theoretical calculations [1, 2]. In combination with ultrafast pump-probe spectroscopy this approach promises to image excited state wavefunctions with Angstrom-level spatial and femtosecond temporal resolution.
However, most POT experiments to date have been restricted to a single probe photon energy, providing only a two-dimensional view of the initial wavefunction. This has limited the access to the full three-dimensional wavefunction to specialized, synchrotron-based facilities, where the implementation of femtosecond time-resolved experiments is challenging. At the same time, a time-resolved access to the third dimension is highly desirable, as it would enable the study of light-induced charge-transfer processes at hybrid molecular interfaces.
We overcome this limitation by implementing an EUV monochromator into the existing high harmonic generation beamline of our femtosecond photoemission setup with the ultimate goal of performing time-resolved three-dimensional orbital tomography. In this talk, I will report on our newly built-up setup and present our first energy-dependent photoemission data of molecules.
[1] P. Puschnig, S. Berkebile, A.J. Fleming, G. Koller, K. Emtsev, T. Seyller, J.D. Riley, C. Ambrosch-Draxl, F.P. Netzer, M.G. Ramsey. Reconstruction of Molecular Orbital Densities from Photoemission Data, Science 326: 702-706, 2009.
[2] G.S.M. Jansen, M. Keunecke, M. Düvel, C. Möller, D. Schmitt, W. Bennecke, F.J.S. Kappert, D. Steil, D.R. Luke, S. Steil, S. Mathia. Efficient orbital imaging based on ultrafast momentum microscopy and sparsity-driven phase retrieval, New J. Phys. 22, 2020.
Element-Selective Structural Information by Hard X-ray Photoelectron Diffraction Johannes Gutenberg-University Mainz, Germany
X-ray photoelectron diffraction (XPD) is a powerful technique that yields detailed structural information of solids and thin films that complements electronic structure measurements. Among the strongholds of XPD we can identify dopant sites, track structural phase transitions, and perform holographic reconstruction. High-resolution imaging of momentum-distributions (momentum microscopy) presents a new approach to core-level photoemission. It yields full-field XPD patterns with unprecedented acquisition speed and richness in details. Beyond the pure intensity-related diffraction information, XPD patterns exhibit pronounced circular dichroism in the angular distribution (CDAD) with asymmetries up to 80%. Experimental results for a number of examples prove that core-level CDAD is a general phenomenon that is independent of atomic number. Calculations using both the Bloch-wave approach and one-step photoemission reveal the origin of the fine structure that represents the signature of Kikuchi diffraction. Comparison to theory allow to disentangle the roles of photoexcitation and diffraction.
[1] O. Fedchenko, A. Winkelmann, K. Medjanik, S. Babenkov, D. Vasilyev, S. Chernov, C. Schlueter, A. Gloskovskii, Yu. Matveyev, W. Drube, B. Schönhense, H.J. Elmers, G. Schönhense. High-resolution hard-x-ray photoelectron diffraction in a momentum microscope – The model case of graphite, New. J. Phys. 21, 2019.
[2] K. Medjanik, O. Fedchenko, O. Yastrubchak, J. Sadowski, M. Sawicki, L. Gluba, D. Vasilyev, S.
Babenkov, S. Chernov, A. Winkelmann, H.J. Elmers, G. Schönhense. Site-specific atomic order and band structure tailoring in the diluted magnetic semiconductor (In, Ga, Mn) As, Phys. Rev. B 103, 2021.
Imaging molecular wave functions with photoemission orbital tomography: Recent developments University of Graz, Austria
This contribution will concentrate on three recent applications of photoemission orbital tomography (POT). First, results of an on-surface synthesized molecular layer will be presented, show-casing how the imaging of molecular orbitals using POT sheds light on surface chemical reactions. Second, it will be demonstrated how POT can be generalized to extended two-dimensional systems. On the example of a strongly-hybridising molecular overlayer on a Cu(110) surface, deep insights into the complicated interplay of bulk states, surface states, and molecular orbitals can be gained from the orbital imaging. Finally, experimental and theoretical results for monolayer graphene will be presented. Here, the photon energy dependence of photoemission intensities indicate limitations of the plane-wave final state approximation which is at the heart of POT. Validated by real-time time-dependent density functional calculations, we develop a simple and intuitive model which accounts for final state scattering, which should allow for the inversion of experimental data to real-space orbital images, thereby going beyond the plane-wave paradigm of POT.
|
| Date: Tuesday, 05/Sept/2023 | |
| 1:30pm - 3:30pm | MS02 1: Advances in regularization for some classes of nonlinear inverse problems Location: VG1.102 Session Chair: Bernd Hofmann Session Chair: Robert Plato |
|
|
Deautoconvolution in the two-dimensional case 1Chemnitz University of Technology, Germany; 2University of Würzburg
There is extensive mathematical literature on the inverse problem of deautoconvolution for a function with support in the unit interval $[0,1] \subset \mathcal{R}$, but little is known about the multidimensional situation. We try to fill this gap with analytical and numerical studies on the reconstruction of a real function of two real variables over the unit square from observations of its autoconvolution on $[0,2]^2 \subset \mathcal{R}^2$ (full data case) or on $[0,1]^2$ (limited data case). In an $L^2$-setting, twofoldness and uniqueness assertions are presented for the deautoconvolution problem in 2D. Moreover, its ill-posedness is characterized and illustrated. Extensive numerical
case studies give an overview of the behaviour of stable approximate solutions to the two-dimensional deautoconvolution problem obtained by Tikhonov-type regularization with different penalties and the iteratively regularized Gauss-Newton method.
Efficient minimization of variational functionals via semismooth* Newton methods 1Johann Radon Institue Linz, Austria; 2Johannes Kepler University Linz, Austria
In this talk, we consider the efficient numerical minimization of variational functionals as they appear for example in $L_{p}$ or TV regularization of nonlinear inverse problems. For this, we consider so-called semismooth* Newton methods, which are a class of optimization methods for non-differentiable and set-valued mappings. Based on the concept of (limiting) normal cones, which are a purely geometrical generalization of derivatives, these methods can be shown to converge locally superlinearly under suitable assumptions. Furthermore, we show how they can be applied to efficiently minimize variational functionals with general convex and in some special cases even non-convex penalty terms.
Convergence Nestorov acceleration for linear ill-posed problems Johannes Kepler University Linz, Austria
We show that Nesterov acceleration is an optimal-order iterative regularization method for linear ill-posed problems provided that a parameter is chosen accordingly to the smoothness of the solution.
The central result is a representation of the iteration residual polynomials via Gegenbauer polynomials. This also explains the observed semi-saturation effect of Nesterov iteration.
Analysis of the discrepancy principle for Tikhonov regularization under low order source conditions Universität Siegen, Germany
We study the application of Tikhonov regularization to ill-posed nonlinear operator equations. The objective of this work is to prove low order convergence rates for the discrepancy principle under low order source conditions of logarithmic type. We work within the framework of Hilbert scales and extend existing studies on this subject to the oversmoothing case. The latter means that the exact solution of the treated operator equation does not belong to the domain of definition of the penalty term. As a consequence, the Tikhonov functional fails to have a finite value.
|
| 4:00pm - 6:00pm | MS02 2: Advances in regularization for some classes of nonlinear inverse problems Location: VG1.102 Session Chair: Bernd Hofmann Session Chair: Robert Plato |
|
|
New results for variational regularization with oversmoothing penalty term in Banach spaces 1Chemnitz University of Technology, Germany; 2University of Siegen, Germany; 3University of Siegen, Germany
In this talk on variational regularization for ill-posed nonlinear problems, we discuss the impact of utilizing an oversmoothing penalty term. This means that the searched-for solution of the considered nonlinear operator equation does not belong to the domain of definition of the penalty functional. In the past years, such variational regularization has been investigated comprehensively in Hilbert scales. Our present results extents those results to Banach scales. This new study includes convergence rates results for a priori and a posteriori choices of the regularization parameter, both for H\"older-type smoothness and low order-type smoothness. An illustrative example intends to indicate the specific characteristics of non-reflexive Banach spaces.
Iterative regularization methods for non-linear ill-posed operator equations in Banach spaces Visvesvaraya National institute of Technology, Nagpur, India
In this talk, we will introduce few simplified iterative regularization methods, in a Banach space setting, to obtain stable approximate solution of nonlinear ill-posed operator equation. We will discuss convergence analysis of these methods under suitable non linearity conditions. Numerical examples will be demonstrated to show applicability of these methods to practical problems.
An Abstract Framework for Stochastic Elliptic Inverse Problems. Rochester Institute of Technology, United States of America
Motivated by the necessity to identify stochastic parameters in a wide range of stochastic partial differential equations, this talk will focus on an abstract inversion framework for stochastic inverse problems. The stochastic inverse problem will be posed as a convex stochastic optimization problem. The essential properties of the solution maps and the solvability of the inverse problem will be discussed. Convergence rates for the stochastic inverse problem without requiring the so-called smallness condition will be presented. We will discuss an application of the abstract framework to estimate stochastic Lam\'e parameters in the system of linear elasticity. We will present numerical results to show the feasibility and efficacy of the developed framework.
|
| Date: Wednesday, 06/Sept/2023 | |
| 9:00am - 11:00am | MS01: Machine Learning for Inverse Problems in Medical Imaging Location: VG1.102 Session Chair: Christian Fiedler Session Chair: Jens Flemming |
|
|
Chances and limitations of machine learning approaches to inverse problems Zwickau University of Applied Sciences, Germany
Machine learning techniques, especially artificial neural networks, share many ideas and features with classical (that is, non-ML) methods for solving inverse problems. Examples are underlying Tikhonov-type optimization problems and the interpretation of deep neural networks as iterative methods structured like typical forward-backward splitting.
In the talk we discuss those similarities and draw conclusions on possible directions for future research. Chances and limitations of ML techniques are discussed in the context of inverse problems from medical imaging. Of particular interest will be susceptibility weighted MR imaging (SWI).
From Manual to Automatic: Streamlining MRI Marker Detection and Localization for Surgical Planning Zwickau University of Applied Sciences, Germany
The accurate detection and localization of natural or artificial structures in medical images is essential for effective diagnostics and surgical planning.
In particular, determining the pose of artificial markers in MRI images is a foundational step for subsequent spatial adjustments, such as the registration between imaging modalities and with surgical devices.
Manual detection and localization of these markers can be tedious and time-consuming, which has prompted the exploration of reliable, and highly automated approaches that can significantly reduce the need for human interaction.
In recent years, automatic approaches based on neural networks have shown remarkable success in the detection and semantic segmentation of natural, anatomical structures.
In contrast to these structures, the geometry of artificial markers is typically known, which enables the development of relatively simple algorithms that can perform well without the need for complex neural network architectures.
The challenge often lies in the incomplete and inhomogeneous representation of the markers within the MRI images, due to noise, distortions, artifacts and further image defects.
In this talk, we will explore different automatic approaches to MRI marker localization from a practical perspective, including conventional image processing pipelines utilizing basic methods such as convolution filters or connected component analysis and labeling as well as approaches based on neural networks.
By addressing the benefits and challenges of using these methods, we gain a better understanding of their potential applications and impact on clinical image processing workflows.
Approaches on Feature and Model Selection for high-dimensional data in Medical Research and Analysis Leipzig University Medicine, Germany
In recent years the availability of multi-omics data, had a great impact on medical research. Such high-dimensional data-sets contain molecular as well as radiological variables from genomics, epigenomics, transcriptomics, proteomics, metabolomics, microbiomics and radiomics. The challenge when working with this kind of data is to find a subset of meaningful variables in order to deduce disease specific characteristics or make predictions on clinical endpoint variables. The process of eliminating non-informative and redundant features is called feature selection. Feature selection can be considered a necessary pre-processing for the actual modeling step in which statistical or machine-learning models are built in order to conduct classification tasks or time-to-event-data analysis.
Given the pre-selected subset of features and a variety of candidate models, finding the most accurate as well as informative model is thereafter the remaining challenge also referred to as model selection. The goal of model selection is eliciting a parsimonious model, which uses only a small set of explanatory variables, which can then be considered as clinical covariates or biomarkers and in turn provide information how the treatment of the disease can be improved. Further, model selection is a step to prevent misleading conclusions due to possible over-fitting of the data inherent noise.
In this talk, we present recent methodologies in feature and model selection. An introduction of rather simple feature selection techniques like statistical filter and classifier performance focused methods is followed by a description of more sophisticated regularization and shrinkage methods as well as the utilization of decision tree analysis algorithms. Finally we discuss how statistical as well as machine-learning models can benefit from the application of various information criteria for model selection.
Deceptive performance of artificial neural networks in semantic segmentation tasks on the example of lung delineation Westsächsische Hochschule Zwickau, Germany
The presentation focuses on a critical analysis of the performance of artificial neural networks (ANNs) in the context of semantic segmentation of organs as reported in scientific reports.
In recent years, extensive research has been performed on combining loss functions and developing non-trainable layers for ANNs in order to optimize the boundary regions of semantic segmentation.
These boundaries are particularly crucial for various segmentation tasks such as the detection of water retention in the lungs for COVID-19 diagnosis, the localization of organs at risk in radiotherapy treatment planning or the identification of white matter hyperintensities in the brain.
With the U-Net, Ronneberger et al. have designed a powerful network architecture for any type of segmentation task.
With a reported IOU (intersection over union) of $92\%$ and $77.5\%$ for the datasets used in the original work, respectively, it was far superior to the follow-up network.
On this basis, U-Net was used for many segmentation tasks in the following years.
In the field of semantic organ segmentation, the U-Net and U-Net-like artificial neural networks achieved very high accuracies. Since then, the reported accuracy has hardly improved.
However, the underlying calculation of accuracy is misleading, as the improvements in recent years have been aimed at improving boundary regions, but these are usually unfavourably proportionate to the inner area.Hence, improvements in boundary segmentation accuracy has only a marginal impact on the overall accuracy.
To illustrate this, we will look at the reported performance and improvements of artificial neural networks in both single-task and multi-task applications, using lung segmentation as an example.
Typical evaluation methods, specifically Dice coefficient or Hausdorff distance, will be presented with current values and improvements.
An overview of new evaluation methods and a discussion of the current way of reporting will also be addressed.
|
| Date: Thursday, 07/Sept/2023 | |
| 1:30pm - 3:30pm | MS37 1: Passive imaging in terrestrial and extra-terrestrial seismology Location: VG1.102 Session Chair: Florian Faucher Session Chair: Damien Fournier |
|
|
Source-free seismic imaging with reciprocity-gap misfit criterion. Inria Bordeaux, France
We consider the quantitative inverse problem of recovering sub-surface Earth’s parameters from measurements obtained near surface. The reconstruction procedure uses the iterative minimization of a misfit criterion that evaluates the discrepancy between the observed and simulated signals, following the principles of Full Waveform Inversion. In the context of passive imaging, the position and characterization of the source signature are unknown, hence increasing the difficulty of inversion. In this work, we propose a new misfit criterion based upon reciprocity formulas, and that allows for source-free inversion, such that no information regarding the probing sources is required, making it an interesting candidate for ambient noise imaging. Our misfit criterion relies on the deployment of new sensing devices such as dual-sensors and distributed acoustic sensing technology, that offer the perspective of measuring different wave fields. It is the combination of these wave fields that makes the essence of our Full Reciprocity-gap Waveform Inversion method,
[1, 2]. with two and three-dimensional reconstructions of acoustic and elastic media.
[1] F. Faucher, G. Alessandrini, H. Barucq, M. V. de Hoop, R. Gaburro, E. Sincich. Full Reciprocity-Gap Waveform Inversion, enabling sparse-source acquisition, Geophysics, 85 (6), 2020. https://dx.doi.org/10.1190/geo2019-0527.1
[2] F. Faucher, M. V. de Hoop, O. Scherzer. Reciprocity-gap misfit functional for Distributed Acoustic Sensing, combining data from active and passive sources , Geophysics, 86 (2), 2021. https://doi.org/10.1190/geo2020-0305.1
Improving our Understanding of Jupiter’s and Saturn’s Interior Structure University of Califonia, Berkeley, United States of America
Traditionally models for the interior structure of giant planets are constrained by spacecraft measurements that fly by a planet at close range and measure its gravitational field with high precision. Still with increasing depth, it becomes more and more difficult with such measurements to uniquely determine what type of layers exist in a giant planet. This is especially true for the cores of giant planets that harbor valuable information on how the planet formed and what the early solar system looked like. Measurements of normal modes on the other hand offer an alternate potentially powerful approach to probing much deeper into a giant planet. While such dynamic measurements are very challenging, a number of such observations have already been reported. Here we review ring seismological measurements of spiral density waves in Saturn’s rings, radial velocity measurements of Jupiter’s atmosphere as well as a recent analysis of time dependent variations in Jupiter’s gravity field. We then compare results from these measurements with predictions from models for the interiors of Jupiter and Saturn that were constrained by gravity measurements alone. We conclude by discussing Jupiter’s dilute core and a recent study that explains how Saturn’s ring formed.
Full-Waveform Inversion and Reverse-Time Migration in Earthquake and Exploration Seismology 1Princeton University, United States of America; 2Ocean University of China; 3Massachusetts Institute of Technology, United States of America; 4Chinese Academy of Sciences; 5The University of Bristol
In this presentation I will gather an overview of various inverse problems that have arisen in the context of (passive) terrestrial imaging—including but not limited to earthquakes, that is. At the smallest scale, I will discuss a source-encoded crosstalk-free Laplace-domain elastic Full Waveform Inversion (FWI) method that uses time- domain solvers, which cuts down drastically on computation time even for very data rich environments. This technique has been used in medical ultrasound, but also at the scale of the globe, and is now actively being developed for applications in the oil industry. At the regional scale, I will discuss full-waveform centroid moment tensor (CMT) inversion of passive seismic data acquired at the reservoir scale, for a field application in Tajikistan. At the largest scale, I will show how receiver function techniques are being supplemented by new technology to image mantle transition zone (MTZ) discontinuities in three-dimensional (3-D) heterogeneous background Earth models, and I will show new seismic evidence for a 1000 km mid-mantle discontinuity under the Pacific obtained by imaging via full-waveform reverse-time migration of precursors to surface-reflected seismic body waves, and its interpretation.
Passive seismic body waves imaging for the deep Earth. Universite Grenoble Alpes, France
The ambient seismic noise has been widely used for surface wave tomography. We present examples of imaging of geological structures of interest at different depths and different scales: the region of the core-mantle boundary and an active fault in the crust. In both cases, we use continuous data from large arrays of sensors. We discuss the global spatial correlation properties of seismic ambient vibrations and their relations with body waves [1-2]. We show the signature of the heterogeneity of the lowermost mantle in contrast to the almost transparent upper core [3]. For the case of the fault systems, a major issue is the strong lateral variations of seismic velocity in the first kilometers that degrade the quality of the imaging. In this case an aberration correction is performed to the data of a dense array through the reflection matrix framework [4].
[1] P. Boué, P. Poli, M. Campillo, P. Roux. Reverberations, coda waves and ambient noise : correlations at the global scale and retrieval of the deep phases, Earth and Planetary Science Let. 391, 137-145, 2014.
[2] L. Li, P. Boué, M. Campillo. Observation and explanation of spurious seismic signals emerging in teleseismic noise correlations Solid Earth 11, 173-184, 2020.
[3] L. Retailleau, P. Boué, L. Li, M. Campillo. Ambient seismic noise imaging of the lowermost mantle beneath the North Atlantic Ocean Geophysical J. Int. 222 (2), 1339-1351, 2020.
[4] R. Touma, T. Blondel, A. Derode, M. Campillo, A. Aubry. A Distortion Matrix Framework for High-Resolution Passive Seismic 3D Imaging: Application to the San Jacinto Fault Zone, California Geophysical J. Int., 226, 780–794, 2021.
|
| 4:00pm - 6:00pm | MS37 2: Passive imaging in terrestrial and extra-terrestrial seismology Location: VG1.102 Session Chair: Florian Faucher Session Chair: Damien Fournier |
|
|
Reduced order model approach for active and passive imaging with waves 1University of Michigan, USA; 2Ecole polytechnique, France; 3University of Houston, USA; 4Uppsala University, Sweden
We consider the velocity estimation problem for the scalar wave equation using the array response matrix of sensors. In the active configuration, the sensors probe the unknown medium to be imaged with a pulse and measure the backscattered waves which gives directly the array response matrix. In the passive configuration, the sensors are passive receivers that record the signals transmitted by unknown, ambient noise or opportunistic sources and the array response matrix can be obtained by cross correlating the recorded signals. Under such circumstances, conventional Full Waveform Inversion (FWI) is carried out by nonlinear least-squares fitting of the array response matrix. It turns out that the FWI misfit function is high-dimensional and non-convex with many local minima. A novel approach to FWI based on a data driven reduced order model (ROM) of the wave equation operator is introduced and it is shown that the minimization of ROM misfit function performs much better.
Three-dimensional random wave coupling along a boundary with scaling representative of Mars' crust, and an associated inverse problem Rice University, United States of America
We consider random wave coupling along a flat boundary in dimension three, where the coupling is between surface and body modes and is induced by scattering by a randomly heterogeneous medium. In an appropriate, anisotropic scaling regime we obtain a system of radiative transfer equations which are satisfied by the mean Wigner transform of the mode amplitudes. Interestingly, seismograms recently acquired with SEIS on Mars (InSight mission) show a behavior that fits the hypotheses of our analysis about the properties of its crust. We provide a rigorous probabilistic framework for describing solutions to the mentioned system using that it has the form of a Kolmogorov equation for some Markov process. We then prove statistical stability of the smoothed Wigner transform under the Gaussian approximation. We conclude with analyzing the nonlinear inverse problem for the radiative transfer equations and establish the unique recovery of phase and group velocities as well as power spectral information for the medium fluctuations from the observed smoothed Wigner transform.
Frequency-Difference Backprojection of Earthquakes 1University of Michigan, Ann Arbor, USA; 2Scripps Institution of Oceanography, USA
Backprojection has proven useful in imaging large earthquake rupture processes. The method is generally robust and requires relatively simple assumptions about the fault geometry or the Earth velocity model. It can be applied in both the time and frequency domain. Backprojection images are often obtained from records filtered in a narrow frequency band, limiting its ability to uncover the whole rupture process. Here, we develop and apply a novel frequency-difference backprojection (FDBP) technique to image large earthquakes, which imitates frequencies below the bandwidth of the signal. The new approach originates from frequency-difference beamforming, which was initially designed to locate acoustic sources. Our method stacks the phase-difference of frequency pairs, given by the autoproduct, and is less affected by scattering and -time errors from 3-D Earth structures. It can potentially locate sources more accurately, albeit with lower resolution. We validated the FDBP algorithm with synthetic tests and benchmarked it against conventional backprojection. We successfully applied the method to the 2015 M7.8 Gorkha earthquake, and tested two stacking approaches - Band Width Averaged Autoproduct and its counterpart (BWAP and non-BWAP). The FDBP method shows promise in resolving complex earthquake rupture processes in tectonically complex regions.
Quantitative passive imaging in helioseismology MPI für Sonnensystemforschung, Germany
In helioseismology one studies cross-correlations of line-of-sight velocities at the solar surface in order to invert for parameters in the solar interior. In the frequency domain the cross-correlation data takes the form $C(\pmb{r_1}, \pmb{r_2}, \omega)=\psi(\pmb{r_1}, \omega)^* \psi(\pmb{r_2}, \omega)$ with freqeuency $\omega$ and two points $\pmb{r_1}, \pmb{r_2}$ on the solar surface. This data set is of immense size and unfeasible to store, such that it is in need of an apriori averaging in space in frequency. Helioseismic holography is a physically motivated averaging scheme, which is based on backpropagation of surface fluctuations [1]. In this talk we show that the traditional holograms can be understood as the first step of an iterative inversion procedure [2]. This way we can extend traditional helioseismic holography to a full quantitative regularization method, which has two main advantages compared to traditional helioseismic inversions:
By changing the order of backpropagation and local correlation we can use the whole cross-correlation data implicitly by avoiding the computation explicitly. Furthermore the iterative setup allows us to tackle nonlinear problems, which are only rarely studied in helioseismology. We validate iterative helioseismic holography on synthetics of large-scale axisymmetric flows like solar differential rotation and meridional flows. Finally we show some interesting future applications of iterative helioseismic holography which can not be studied with traditional helioseismology so far.
[1] C. Lindsey, D. Braun. Helioseismic Holography, Astrophysical Journal 485(2), p.895-903, 1997. doi:10.1086/304445
[2] T. Hohage, H. Raumer, C. Spehr. Uniqueness of an inverse source problem in experimental aeroacoustics, Inverse Problems 36(7), 2020. doi:10.1088/1361-6420/ab8484
|
| Date: Friday, 08/Sept/2023 | |
| 1:30pm - 3:30pm | MS09: Forward and inverse domain uncertainty quantification Location: VG1.102 Session Chair: Vesa Kaarnioja Session Chair: Claudia Schillings |
|
|
Isogeometric multilevel quadrature for forward and inverse random acoustic scattering 1University of Bonn, Germany; 2University of Basel, Switzerland; 3USI Lugano, Switzerland; 4Universidad Adolfo Ibáñez, Santiago, Chile
We study the numerical solution of forward and inverse time-harmonic acoustic scattering problems by randomly shaped obstacles in three-dimensional space using a fast isogeometric boundary element method. Within the isogeometric framework, realizations of the random scatterer can efficiently be computed by simply updating the NURBS mappings which represent the scatterer. This way, we end up with a random deformation field. In particular, we show that it suffices to know the deformation field’s expectation and covariance at the scatterer’s boundary to model the surface’s Karhunen–Loève expansion. Leveraging on the isogeometric framework, we employ multilevel quadrature methods to approximate quantities of interest such as the scattered wave’s expectation and variance. By computing the wave’s Cauchy data at an artificial, fixed interface enclosing the random obstacle, we can also directly infer quantities of interest in free space. Adopting the Bayesian paradigm, we finally compute the expected shape and variance of the scatterer from noisy measurements of the scattered wave at the artificial interface. Numerical results for the forward and inverse problems validate the proposed approach.
Evolving surfaces driven by stochastic PDEs Chalmers & University of Gothenburg, Sweden
Motivated by evolving shapes such as moving cells, we construct examples of evolving stochastic surfaces by transformation of solutions to stochastic PDEs on spheres. We focus on the stochastic heat equation and its approximation to understand the transformation and simulation methods for the surfaces.
Multilevel domain UQ in computational electromagnetics 1Universität Heidelberg; 2Universidad Adolfo Ibáñez; 3ETH Zürich
In this talk, we focus on the numerical approximation of time-harmonic electromagnetic fields for the Maxwell lossy cavity problem on uncertain domains. To deal with the different problem geometries, a shape parametrization framework that maps physical domains to a fixed polyhedral nominal domain is adopted. We discuss multilevel Monte Carlo sampling and multilevel sparse-grid quadrature for computing the expectation of the solutions with respect to uncertain domain ensembles. In addition, we analyze sparse-grid interpolation to compute surrogates of the domain-to-solution mappings. A rigorous fully discrete error analysis is provided, and we prove that dimension-independent algebraic convergence is achieved.
Advantages of locality in random field representations for shape uncertainty quantification Radboud University, Netherlands, The
We consider the solution to an elliptic partial differential equation on a domain which is subject to uncertain changes in its shape.
When representing uncertain shape variations, using localized basis functions can be appealing from a modeling point of view, as they offer more geometrical flexibility compared to globally supported basis functions. In this talk, we will see that locality of basis functions can also be convenient in terms of approximation properties with respect to the uncertain parameter. Extending ideas from [1,2], it is indeed possible to prove, using pointwise summability bounds, that sparse polynomial approximations to the parameter-to-solution map may converge faster if localized functions are used in the shape representation. We will also see that this approximability result goes beyond shape uncertainty, and it applies in fact to many other parameter-to-solution maps, as long as they are smooth and have some given sparsity properties.
[1] M. Bachmayr, A. Cohen, G. Migliorati. Sparse polynomial approximation of parametric elliptic PDEs. Part I: affine coefficients, ESAIM: Mathematical Modelling and Numerical Analysis 51(1): 321-339, 2017.
[2] M. Bachmayr, A. Cohen, R. DeVore, G. Migliorati, Sparse polynomial approximation of parametric elliptic PDEs. Part II: lognormal coefficients, ESAIM: Mathematical Modelling and Numerical Analysis 51(1): 341-363, 2017
|
Contact and Legal Notice · Contact Address:  Privacy Statement · Conference: AIP 2023 |
Conference Software: ConfTool Pro 2.8.101+TC © 2001–2024 by Dr. H. Weinreich, Hamburg, Germany |
