Potentials of Distributed Acoustic Sensing in Seismic Imaging

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(1)Diss. ETH No. 27319. P o t e n t i a l s o f D i s t r i b u t e d Ac o u s t i c S e n s i n g i n S e i s m i c I m ag i n g. A thesis submitted to attain the degree of. Doctor of Sciences of ETH Zurich [D r . s c . E T H Z u r i c h]. presented by. Pat r i c k Pa i t z MSc. in Applied Geophysics, ETH Zurich MSc. in Applied Geophysics, RWTH Aachen MSc. in Applied Earth Sciences, TU Delft born on 17.05.1990 citizen of Germany. accepted on the recommendation of Prof. Dr. Andreas Fichtner Dr. Cédric Schmelzbach Dr. Pascal Edme Prof. Dr. Heiner Igel 2021.

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(3) Diss. ETH No. 27319. P o t e n t i a l s o f D i s t r i b u t e d Ac o u s t i c S e n s i n g i n S e i s m i c I m ag i n g. A thesis submitted to attain the degree of. Doctor of Sciences of ETH Zurich [D r . s c . E T H Z u r i c h]. presented by. Pat r i c k Pa i t z MSc. in Applied Geophysics, ETH Zurich MSc. in Applied Geophysics, RWTH Aachen MSc. in Applied Earth Sciences, TU Delft born on 17.05.1990 citizen of Germany. accepted on the recommendation of Prof. Dr. Andreas Fichtner Dr. Cédric Schmelzbach Dr. Pascal Edme Prof. Dr. Heiner Igel 2021.

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(5) "A laser is a solution seeking a problem" - Theodor Maiman, inventor of the laser, 1960.

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(7) Abstract. This thesis investigates the potentials of Distributed Acoustic Sensing in seismology. Distributed Acoustic Sensing (DAS) is an emerging method to measure strain along optical fibers. DAS systems are capable of measuring acoustic and elastic waves propagating along the fiber, and hence can be used as a seismological receiver, where its measurements are related to the symmetric part of the displacement gradient tensor. To investigate the potentials of DAS in seismic imaging, this thesis first establishes the properties of DAS measurements in an extensive instrument response study utilizing data from a wide range of experiments conducted as part of this thesis. Confirming the suitability of DAS measurements for seismological applications from the instrument response study, this thesis then connects strain to rotational measurements, related to the anti-symmetric part of the displacement gradient tensor, and introduces the concept of obtaining rotational observations from DAS recordings. This thesis then extends the existing theory of generalized ambient noise interferometry from displacements to gradient measurements. We show the potential to combine different seismic observables within the framework of interferometry, accounting for the observational effect on the interferometric wavefield due to spatial gradients. With the extended formulation of interferometry, we use adjoint-based methods to incorporate spatial gradient observations into full waveform ambient noise inversion. Based on theoretical investigations, numerical simulations and real-world examples, this thesis ultimately aims to incorporate gradient observations into existing geophysical workflows and to develop new methods utilizing such gradient observations, expanding the fields of theoretical, numerical and observational seismology.. i.

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(9) Zusammenfassung. Die vorliegende Arbeit untersucht das Potenzial von Distributed Acoustic Sensing (DAS) in der Seismologie. DAS ist eine neue Methode um Dehnungen entlang einer Glasfaser zu messen. Solche DAS Systeme sind in der Lage akustische und elastische Wellen zu messen, die sich entlang der Glasfaser fortbewegen und können somit als seismologische Messgeräte genutzt werden. Um die Potenziale von DAS in der seismischen Bildgebung zu untersuchen, werden zunächst die Eigenschaften von DAS-Messungen in einer umfangreichen empirischen Studie zur Instrumentenantwort analysiert. Basierend auf verschiedenen Messungen, die im Rahmen dieser Arbeit durchgeführt wurden, können wir eine Reihe an Instrumentantworten bestimmen. Nachdem die Eignung von DAS-Messungen für seismologische Anwendungen anhand der Studie zur Instrumentenantwort bestätigt werden konnte, verbindet diese Arbeit Dehnungsmessungen und Rotationsmessungen, und stellt ein Konzept vor um Rotationsmessungen von DAS-Messungen zu erhalten. Daraufhin erweitert diese Arbeit die Theorie zu generalized ambient noise interferometry (ein Interferenzmessverfahren basierend auf Aufzeichnungen von Bodenunruhe) von Verschiebungs- zu Gradientenmessungen. Wir zeigen die Möglichkeit auf, verschiedene seismische Beobachtungsgrössen in einem gemeinsamen theoretischen Rahmen der Interferometrie zu kombinieren. Diese erweiterte Formulierung der Interferometrie ermöglicht es uns unter Zuhilfenahme von adjungierten Methoden, die räumlichen Ableitungen in das Feld der full waveform ambient noise inversion (eine spezielle Methode der Wellenforminversion) aufzunehmen. Aufbauend auf theoretischen Untersuchungen, numerischen Simulationen und praktischen Messungen, strebt diese Arbeit letztendlich ebenso an, Messungen von Gradienten in existierende geophysikalische Workflows aufzunehmen, wie auch neue Methoden basierend auf Gradientenmessungen zu entwickeln - um die Forschungsfelder der theoretischen, numerischen und beobachtenden Seismologie voranzutreiben.. iii.

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(11) Contents. Abstract. i. Zusammenfassung. iii. List of Figures. xiii. 1 Introduction 1.1 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Properties of DAS measurements 2.1 Chapter summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Introduction to DAS and instrument responses . . . . . . . . . . . . . . . 2.3 Instrument response estimation . . . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Comparison with co-located reference measurements . . . . . . . . 2.3.2 Conversion of observed quantities . . . . . . . . . . . . . . . . . . . 2.4 Empirical instrument study . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.1 Experiment location and instrumentations . . . . . . . . . . . . . . 2.4.2 Workflow and data processing . . . . . . . . . . . . . . . . . . . . . 2.4.2.1 Preprocessing, apparent phase-velocity estimation and conversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.2.2 Instrument response estimation . . . . . . . . . . . . . . . 2.5 Results of the instrument response study . . . . . . . . . . . . . . . . . . . 2.5.1 Time-domain waveforms . . . . . . . . . . . . . . . . . . . . . . . . 2.5.2 Instrument response curves . . . . . . . . . . . . . . . . . . . . . . 2.6 Discussion of instrument response results . . . . . . . . . . . . . . . . . . 2.6.1 Possible causes of instrument response variations . . . . . . . . . . 2.6.2 Implications for current and future DAS applications . . . . . . . . 2.7 Conclusions and outlook on instrument responses . . . . . . . . . . . . . . 2.8 Data and resources for the instrument response study . . . . . . . . . . .. 1 4. . . . . . . . .. 7 7 8 9 10 10 12 12 13. . . . . . . . . . .. 13 14 15 15 15 17 18 19 20 21. 3 Connecting gradient observations 29 3.1 Chapter summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.2 Introduction to waveform gradients . . . . . . . . . . . . . . . . . . . . . . . 30. v.

(12) 3.3. Wave equation and gradients . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.3.1. Strain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.3.1.1. 3.3.2. 3.3.3 3.4. 3.3.2.1. Time domain rescaling . . . . . . . . . . . . . . . . . . . . 32. 3.3.2.2. Frequency-wavenumber rescaling . . . . . . . . . . . . . . . 33. Rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33. 3.4.1. Strain and gauge length . . . . . . . . . . . . . . . . . . . . . . . . . 36. 3.4.2. Scaling from strain to velocity. . . . . . . . . . . . . . . . . . . . . . 37. 3.4.2.1. Time domain rescaling . . . . . . . . . . . . . . . . . . . . 37. 3.4.2.2. Frequency-wavenumber domain rescaling . . . . . . . . . . 38. 3.4.2.3. Discussion of rescaling algorithms . . . . . . . . . . . . . . 39. Rotations from DAS . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 3.4.3.1. Synthetic rotation data . . . . . . . . . . . . . . . . . . . . 42. 3.4.3.2. Effect of finite-difference stencil size on rotation derived from strain . . . . . . . . . . . . . . . . . . . . . . . . . . . 42. 3.4.3.3. Effect of gauge length on rotation derived from strain . . . 42. 3.4.3.4. Combining the effects of gauge length and finite-difference stencil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43. Real-data example: Rotations from strain . . . . . . . . . . . . . . . . . . . 46 3.5.1. Experiment overview . . . . . . . . . . . . . . . . . . . . . . . . . . . 46. 3.5.2. Results for strain-derived rotations . . . . . . . . . . . . . . . . . . . 48. 3.5.3. Discussion of real rotation data and strain-derived approximations . 49. 3.6. Conclusions and outlook on strain-derived rotations . . . . . . . . . . . . . 51. 3.7. Supplementary information on strain-derived rotations . . . . . . . . . . . . 52 3.7.1. vi. From strain to particle velocity . . . . . . . . . . . . . . . . . . . . . 32. Numerical examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35. 3.4.3. 3.5. Gauge length . . . . . . . . . . . . . . . . . . . . . . . . . . 31. Finite-difference accuracies as a function of offset and gauge length for random noise wavefields . . . . . . . . . . . . . . . . . . . . . . . 52 3.7.1.1. Effect of finite-difference stencil size on rotations from strain 52. 3.7.1.2. Effect of gauge length on rotations from strain . . . . . . . 53. 3.7.1.3. Effect of gauge length and finite-difference stencil size on rotations from strain . . . . . . . . . . . . . . . . . . . . . . 54. 3.7.2. Rotation waveforms for source location SRC2 . . . . . . . . . . . . . 55. 3.7.3. Instrument comparison between ROMY and blueSeis-3A . . . . . . . 55 3.7.3.1. Source location SRC1 . . . . . . . . . . . . . . . . . . . . . 57. 3.7.3.2. Source location SRC2 . . . . . . . . . . . . . . . . . . . . . 59. 3.7.3.3. Signal-to-Noise ratios . . . . . . . . . . . . . . . . . . . . . 61.

(13) 4 Seismic interferometry with spatial gradients 4.1 Chapter summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Introduction to DAS and seismic interferometry . . . . . . . . . . . . . . . 4.2.1 Rotational and strain seismology . . . . . . . . . . . . . . . . . . . 4.2.2 Ambient noise interferometry . . . . . . . . . . . . . . . . . . . . . 4.2.3 Motivation and outline . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Ambient noise interferometry of strain and rotation data . . . . . . . . . . 4.3.1 Displacement interferometry . . . . . . . . . . . . . . . . . . . . . 4.3.2 Strain interferometry . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.2.1 Derivation of the interferometric strain representation theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.2.2 Representation theorem modification to include DAS gauge length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.3 Rotational interferometry . . . . . . . . . . . . . . . . . . . . . . . 4.3.3.1 Derivation of the interferometric rotation representation theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Generalized forward equations for interferometric wavefields . . . . . . . . 4.4.1 Mixing observations . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Numerical examples of interferometric wavefields . . . . . . . . . . . . . . 4.5.1 Numerical setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.2 Computational recipe . . . . . . . . . . . . . . . . . . . . . . . . . 4.5.3 Modelling correlation wavefields . . . . . . . . . . . . . . . . . . . 4.5.3.1 Displacement interferograms . . . . . . . . . . . . . . . . 4.5.3.2 Strain interferograms . . . . . . . . . . . . . . . . . . . . 4.5.4 Homogeneous medium and homogeneous sources . . . . . . . . . . 4.5.5 Heterogeneous medium and homogeneous sources . . . . . . . . . . 4.5.6 Homogeneous medium and heterogeneous sources . . . . . . . . . . 4.6 Discussion of seismic interferometry with spatial gradients . . . . . . . . . 4.6.1 Computational implementation and requirements . . . . . . . . . . 4.6.2 Interferometry without Green’s function retrieval . . . . . . . . . . 4.6.3 Effects of processing . . . . . . . . . . . . . . . . . . . . . . . . . . 4.7 Conclusions on interferometry utilizing spatial gradients . . . . . . . . . . 5 Towards ambient noise inversion with spatial gradients 5.1 Chapter summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Introduction to seismic interferometry . . . . . . . . . . . . . . . . . . . . 5.2.1 Motivation and outline for noise tomography with spatial gradients 5.3 Generalized interferometry . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.1 Displacement interferometry . . . . . . . . . . . . . . . . . . . . .. . . . . . . . .. 63 63 64 64 64 65 65 66 67. . 68 . 71 . 71 . . . . . . . . . . . . . . . . .. 72 73 74 74 74 74 75 75 77 78 79 79 81 81 83 83 84. . . . . .. 85 85 86 87 87 88. vii.

(14) 5.3.2 5.3.3 5.3.4 5.3.5. 5.4. 5.5 5.6. Strain interferometry . . . . . . . . . . . . . . . . . . . . . . . . . Rotation interferometry . . . . . . . . . . . . . . . . . . . . . . . Mixing observational quantities . . . . . . . . . . . . . . . . . . . Forward modelling of interferometric wavefields . . . . . . . . . . 5.3.5.1 Forward modelling recipe . . . . . . . . . . . . . . . . . Generalized adjoint methods . . . . . . . . . . . . . . . . . . . . . . . . 5.4.1 Conceptual introduction to full waveform ambient noise inversion 5.4.1.1 Synthetic and observed data . . . . . . . . . . . . . . . 5.4.1.2 Misfit . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.1.3 From misfit to model update . . . . . . . . . . . . . . . 5.4.1.4 Sensitivity kernel . . . . . . . . . . . . . . . . . . . . . . 5.4.2 Misfit functional . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.3 Source kernels . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.4 Structure kernels . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.4.1 Computation of structure kernels . . . . . . . . . . . . . Numerical examples for sensitivity kernels . . . . . . . . . . . . . . . . . 5.5.1 Source kernels for displacement and strain . . . . . . . . . . . . . Conclusions and outlook on noise inversion utilizing spatial gradients . .. 6 Fieldwork and data catalogue 6.1 Overview of experiments . . . . . . . . . . 6.1.1 Grimsel experiments . . . . . . . . 6.1.2 Rhonegletscher experiment part 1 6.1.3 Valais experiment . . . . . . . . . 6.1.4 Yverdon experiment . . . . . . . . 6.1.5 Fürstenfeldbruck experiment . . . 6.1.6 Mt. Meager experiment . . . . . . 6.1.7 Bern experiment . . . . . . . . . . 6.1.8 Rhonegletscher experiment part 2 6.2 Data management plan . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . .. 7 Future research opportunities 7.1 Continuous monitoring of source and structure 7.2 Theoretical considerations for gradient sensing 7.3 Leveraging statistical learning methods . . . . . 7.4 DAS in the context of smart cities . . . . . . . 7.5 Instrument and data standards . . . . . . . . . 8 Conclusions. viii. . . . . . . . . . .. . . . . .. . . . . . . . . . .. . . . . .. . . . . . . . . . .. . . . . .. . . . . . . . . . .. . . . . .. . . . . . . . . . .. . . . . .. . . . . . . . . . .. . . . . .. . . . . . . . . . .. . . . . .. . . . . . . . . . .. . . . . .. . . . . . . . . . .. . . . . .. . . . . . . . . . .. . . . . .. . . . . . . . . . .. . . . . .. . . . . . . . . . .. . . . . .. . . . . . . . . . .. . . . . .. . . . . . . . . . .. . . . . .. . . . . . . . . . . . . . . . . . .. . . . . . . . . . .. . . . . .. . . . . . . . . . . . . . . . . . .. 90 91 92 92 94 94 94 94 95 95 95 95 97 99 101 101 102 102. . . . . . . . . . .. 105 105 108 109 109 110 112 112 114 114 115. . . . . .. 117 117 118 118 119 120 123.

(15) References. 125. Acknowledgments. 143. ix.

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(17) List of Figures. Figure 2.1 Frequencies covered by previous instrument studies compared to the frequencies covered by the presented instrument response study . . . . . . .. 9. Figure 2.2 Overview of the different experiments utilized within the presented instrument response study . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Figure 2.3 Example waveforms from the instruments utilized in the presented instrument response study . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 Figure 2.4 Instrument response results for all experiments discussed in the instrument response study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Figure 2.5 Example waveforms from the hydraulic injection used in the instrument response study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 Figure 2.6 Example waveforms from the teleseismic Fiji earthquake used in the instrument response study . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 Figure 2.7 Example waveforms from the teleseismic Ionian Sea earthquake used in the instrument response study . . . . . . . . . . . . . . . . . . . . . . . . 25 Figure 2.8 Example waveforms from the regional Linthal earthquake used in the instrument response study . . . . . . . . . . . . . . . . . . . . . . . . . . 26 Figure 2.9 Example waveforms from the active source sweeps in Yverdon-lesBains used in the instrument response study . . . . . . . . . . . . . . . . . . 27 Figure 2.10 Example waveforms from the icequake recordings used in the instrument response study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 Figure 3.1. Schematic visualization of discretized strain . . . . . . . . . . . . . . 32. Figure 3.2. Schematic visualization of discretized finite-difference rotation . . . . 34. Figure 3.3. Numerical setup used to compute synthetic strain data . . . . . . . . 36. Figure 3.4 Synthetic examples for the effect of the gauge length on strain measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 Figure 3.5 Synthetic examples for the time domain conversion from strain to particle velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 Figure 3.6 Synthetic examples for the frequency-wavenumber conversion from strain to particle velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 Figure 3.7. Numerical setup used to compute synthetic strain and rotation data. 41. xi.

(18) Figure 3.8 Synthetic examples of the effect of finite-difference stencil size on strain-derived rotations for a Ricker wavelet source . . . . . . . . . . . . . . 43 Figure 3.9 Synthetic examples of the effect of the gauge length on strain-derived rotations for a Ricker wavelet source . . . . . . . . . . . . . . . . . . . . . . 44 Figure 3.10 Synthetic examples of the gauge length and offset dependent waveform fit between reference rotation and strain-derived rotation . . . . . . . 45 Figure 3.11 Real-data experiment setup for DAS-derived rotations . . . . . . . . 47 Figure 3.12 DAS-derived rotation rate (time domain) compared to ROMY rotation rate for source SRC1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 Figure 3.13 DAS-derived rotation rate (ω-k domain) compared to ROMY rotation rate for source SRC1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 Figure 3.14 Synthetic examples of the effect of finite-difference stencil on strainderived rotations for random noise field . . . . . . . . . . . . . . . . . . . . 52 Figure 3.15 Synthetic examples of the effect of gauge length on strain-derived rotations for a random noise field . . . . . . . . . . . . . . . . . . . . . . . . 53 Figure 3.16 Synthetic examples of the effect of gauge length and offset on the waveform fit between reference rotation and strain-derived rotations for a random wavefield . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 Figure 3.17 DAS-derived rotation rate (time domain) compared to ROMY rotation rate for source SRC2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 Figure 3.18 DAS-derived rotation rate (ω-k domain) compared to ROMY rotation rate for source SRC2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 Figure 3.19 Rotation rate from blueSeis-3A BGR compared to ROMY and DASderived rotation rate for SRC1 . . . . . . . . . . . . . . . . . . . . . . . . . 57 Figure 3.20 Rotation rate from blueSeis-3A BS1 sensor compared to ROMY and DAS-derived rotation rate for SRC1 . . . . . . . . . . . . . . . . . . . . . . 58 Figure 3.21 Rotation rate from blueSeis-3A BS2 sensor compared to ROMY and DAS-derived rotation rate for SRC1 . . . . . . . . . . . . . . . . . . . . . . 58 Figure 3.22 Rotation rate from blueSeis-3A BGR compared to ROMY and DASderived rotation rate for SRC2 . . . . . . . . . . . . . . . . . . . . . . . . . 59 Figure 3.23 Rotation rate from blueSeis-3A BS1 sensor compared to ROMY and DAS-derived rotation rate for SRC2 . . . . . . . . . . . . . . . . . . . . . . 59 Figure 3.24 Rotation rate from blueSeis-3A BS2 sensor compared to ROMY and DAS-derived rotation rate for SRC2 . . . . . . . . . . . . . . . . . . . . . . 60 Figure 3.25 Signal-to-Noise ratio of different rotation waveforms in three different windows and correlation between different rotation waveforms for SRC1 . . 61 Figure 3.26 Signal-to-Noise ratio of different rotation waveforms in three different windows and correlation between different rotation waveforms for SRC2 . . 62. xii.

(19) Figure 4.1 Numerical domain used to calculate synthetic interferometric wavefields 75 Figure 4.2 Schematic overview on the computational recipe for the simulation of interferometric strain wavefields . . . . . . . . . . . . . . . . . . . . . . . 76 Figure 4.3 Interferometric wavefields for displacements, strain and mixed-observations 78 Figure 4.4 Schematic particle motions for inline, horizontal and vertical motions 79 Figure 4.5 Interferometric wavefields for displacements, strain and mixed-observations for two different media. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 Figure 4.6 Interferometric wavefields for displacements, strain and mixed-observations for three different noise source distributions . . . . . . . . . . . . . . . . . . 82 Figure 5.1 Synthetic examples for noise source sensitivity kernels for displacement and strain measurements . . . . . . . . . . . . . . . . . . . . . . . . . 103 Figure 6.1 Cumulative acquired DAS data for the experiments conducted as part of this thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Figure 6.2 Fiber layout for the Grimsel Test Site DAS experiment . . . . . . . . Figure 6.3 Fiber layout for the Rhonegletscher DAS experiment (part 1) . . . . Figure 6.4 Fiber layout for the Valais DAS experiment . . . . . . . . . . . . . . Figure 6.5 Fiber layout for the Yverdon-les-Bains DAS experiment . . . . . . . Figure 6.6 Fiber layout for the Fürstenfeldbruck rotation and DAS experiment Figure 6.7 Fiber layout for the Mt. Meager DAS experiment . . . . . . . . . . . Figure 6.8 Fiber layout for the Bern urban fiber DAS experiment . . . . . . . . Figure 7.1. 105 108 110 111 112 113 114 115. IRIS Data Management Center (DMC) archive size . . . . . . . . . . 121. xiii.

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(21) List of Tables. 2.1. Instrument response study experiment overview . . . . . . . . . . . . . . . . 22. 4.1. Overview on interferometric wavefields, observational effects and virtual source terms for displacement, strain and rotation . . . . . . . . . . . . . . 74. 5.1. Overview of the operator-based observational effects on the interferometric wavefield for displacement, strain and rotation . . . . . . . . . . . . . . . . 93. 6.1 6.2. Overview of all DAS experiments conducted as part of this thesis . . . . . . 106 Overview of the fiber types and installations for all DAS experiments . . . . 107. xv.

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(23) Introduction. 1. This chapter provides a general introduction to the content of this thesis and introduces each chapter. All chapters are structured such that they can be read individually. Each chapter therefore has its individual introduction if it has been published or submitted already, or if a publication is in preparation. Since the invention of the first seismoscope around 130 A.D., a wide range of technologies have been developed to sense the ground motions of the Earth. This very first seismic instrument consisted of a cylinder of six feet diameter with eight dragon heads with bronze balls in their mouths on the outside, resembling 8 principal compass directions. When an earthquake occurred, a bronze ball fell out of the mouth of a dragon into the mouth of a toad standing next to the cylinder, making a loud noise and alarming people nearby. The azimuth of the earthquake could be identified by checking which dragon lost its bronze ball. This instrument is told to have measured an earthquake that occurred around 650 km away and was not felt at the location of the instrument. Most sources assume that the interior of the cylinder was some sort of pendulum contraption (Needham, 1959; Dewey and Byerly, 1969). Later iterations of seismographs included systems based on pendulums and inverted pendulums (both vertical and horizontal) and electromagnetic seismographs (Dewey and Byerly, 1969). A breakthrough in seismology was the development of forcebalance ’Leaf-Spring’ systems, as well as the first commercial STS-1 seismometers (Wielandt and Streckeisen, 1982), which are still in use today. Most conventional modern geophones and seismometers are based on damped inertial pendulum systems (Lay and Wallace, 1995) that either record ground velocity or acceleration in one or multiple directions. These inertial sensors provide measurements at a specific point in space. Recordings of earthquakes or active seismic sources with arrays or networks of such receivers can be utilized to localize these sources (Dziewonski et al., 1981; Aki and Richards, 2002), to obtain tomographic images of the Earth’s interior (Dziewonski and Anderson, 1981; Lay and Wallace, 1995; Aki and Richards, 2002; Fichtner et al., 2008), and to monitor shallow subsurface changes over time (Poupinet et al., 1984; Landrø et al., 2003). Besides these active measurements, passive recordings allow us to investigate the Earth’s ambient seismic noise field (Ermert et al., 2016, 2017; Sager et al., 2018a,b). In addition to the developments in the field of inertial sensors for seismology, new types of. 1.

(24) 1. Introduction sensors emerged in the last decades: rotational sensors and distributed fiber-optic strain sensors. The technological foundation for distributed fiber-optic sensors was developed by Barnoski and Jensen (1976) and Personick (1977). Since then, backscattered light caused by the interaction of laser pulses with small imperfections along the fiber has been proposed for distributed sensing applications (Rogers, 1981), and then been tested for a wide range of applications such as bending detection of fiber (Asawa et al., 1984), structural monitoring (Griffiths, 1987), distributed temperature sensing (Hartog, 1983) and distributed strain sensing (Horiguchi et al., 1990; Tateda et al., 1990). A breakthrough in distributed fiber-optic sensing was the discovery that the coherent Rayleigh backscatter can be used for distributed strain sensing, as discussed e.g. by Posey et al. (2000), which lead to the development of distributed strain and strain rate sensors such as the Silixa iDAST M (Parker et al., 2014a,b). For a detailed historic review on distributed fiber-optic sensing, the reader is referred to Hartog (2017). At the same time the inertial and distributed fiber-optic sensors have been developed further, ringlaser (Rodloff , 1987) recordings showed the potential to also measure seismic waves (McLeod et al., 1998; Pancha et al., 2000). Since then, efforts have been made to build rotational sensors for seismology (Schreiber et al., 2006), both as large high-resolution stationary sensors (Schreiber et al., 2009; Hurst et al., 2017) such as the ROMY ringlaser (Gebauer et al., 2020) and as portable sensors such as the blueSeis-3A (Wassermann et al., 2016, 2020). Whereas measurements of rotational sensors are related to the asymmetric part of the spatial displacement gradient tensor, distributed fiber-optic sensor measurements are related to the symmetric part of the spatial gradient tensor. While observations of rotational ground motions have a wide range of potential applications, including elastic wavefield separation (Aki and Richards, 2002; Curtis and Robertsson, 2002; Edme et al., 2013; Sollberger et al., 2016a; Van Renterghem et al., 2016; Sollberger et al., 2016b), apparent phase velocity estimation (Langston, 2007a,b; De Ridder and Biondi, 2015; Sollberger et al., 2016b), and earthquake source inversion (Schmelzbach et al., 2018), rotational seismology remains a niche field, mainly due to the small number of reliable sensors that are currently available. This is in contrast to the unprecedented spatial resolution provided by Distributed Acoustic Sensing1 systems that can measure strain or strain rate along fiber-optic cables over 10s of kilometers - even in remote or urban areas (Mateeva et al., 2012; Parker et al., 2014a; Zhan, 2020; Walter et al., 2020).. 1. 2. The term Distributed Acoustic Sensing is somewhat misleading. Whereas these systems are true distributed systems, the phrase ’acoustic’ seems to be misplaced, because of two reasons: (1) The fiber that is utilized for the measurement is an elastic medium as opposed to an acoustic medium and (2) the measured waves are therefore elastic waves and not acoustic waves. Other terms like ’Distributed Vibration Sensing’ or ’Fiber-Optic Sensing’ exist, but the term DAS is the most popular, why I adapted this term in this thesis..

(25) The quality of DAS measurements, as compared to more traditional instrumentation, has been the focus of numerous recent works ranging from very long periods of several hours in laboratory environments (Becker and Coleman, 2019), to ambient noise studies (Dou et al., 2017; Martin et al., 2018a, 2016) and earthquake detection (Lindsey et al., 2017; Wang et al., 2018; Ajo-Franklin et al., 2018), to active-source seismic experiments (Daley et al., 2013). Most studies have not gone through the rigorous step of quantifying an instrument response function, though initial responses were presented in Jousset et al. (2018) (0.1 to 100 s period) and Lindsey et al. (2020) (1 to 120 s period). These existing analyses of the DAS response function are typically in a limited part of the frequency band from 0.01 to 10 Hz and are based on comparisons with well-coupled conventional seismometers for which the instrument response is sufficiently well known to be removed from the signal (Lindsey et al., 2020). While Jousset et al. (2018) investigate the strain instrument response theoretically and compare displacement spectra of (corrected) DAS recordings with displacement recordings of a broadband seismometer and a geophone, Lindsey et al. (2020) show the first extensive empirical instrument response study in which DAS data are converted to velocity in the frequency-wavenumber domain and then compared to recordings of a broadband seismometer. One potential of DAS, however, is to cover a much broader range of frequencies than any other instrument previously, and most of these existing studies were restricted to a given application and frequency range.2 Recent studies also showed that fiber-optic cables can be deployed over large distances efficiently, especially in difficult terrain (Jousset et al., 2018; Walter et al., 2020). Furthermore, strain measurements have been adopted recently for seismological methods such as ambient noise interferometry (Martin et al., 2016; Dou et al., 2017; Martin et al., 2018a; Paitz et al., 2018a). Ambient noise interferometry transforms recordings of quasi-random wavefields into deterministic signals that may be used, for instance, to constrain Earth structure (e.g. Shapiro et al., 2005; Sabra et al., 2005; Stehly et al., 2009; Saygin and Kennett, 2012; Nakata et al., 2015) or noise sources (Yang and Ritzwoller, 2008; Tian and Ritzwoller, 2015; Ermert et al., 2017). Most commonly, ambient noise interferometry is based on Green’s function retrieval. Under the assumption of a homogeneous noise source distribution or equipartitioned wavefields, the correlation of two displacement recordings is equal to a scaled version of the Green’s function (e.g. Lobkis and Weaver, 2001; Wapenaar, 2004; Tsai, 2009; Wapenaar et al., 2010; Tsai, 2011; Fichtner and Tsai, 2018). Since noise sources are, however, heterogeneous and transient (Ardhuin et al., 2011; Stutzmann et al., 2012; Ermert et al., 2016), traveltimes and amplitudes in the correlation may deviate from those in the Green’s function, and additional spurious phases may appear (Halliday and Curtis, 2. This paragraph is taken from Paitz et al. (2020a).. 3.

(26) 1. Introduction 2008; Tsai, 2009, 2011; Zhan et al., 2013; Fichtner, 2014). To eliminate the effect of noise sources and earthquakes, ambient noise correlations require preprocessing (e.g. Bensen et al., 2007; Stehly et al., 2011; Hanasoge and Branicki, 2013; Ritzwoller and Feng, 2018) and careful data selection, using, for instance, machine learning approaches (e.g. Paitz et al., 2018b; Martin et al., 2018b). Despite the known difficulties of Green’s function retrieval, the method has been adapted to DAS measurements, e.g. by Dou et al. (2017), Martin et al. (2017a), Martin and Biondi (2017), Martin et al. (2018b) and by Martin et al. (2018a) using plane-wave theory.3 By dropping the assumption of homogeneous noise source distributions, it becomes possible to extract information on the structure and noise source distributions from the interferometric wavefields individually, utilizing full-waveform based ambient noise tomography (Sager et al., 2018a). This thesis explores the potentials of Distributed Acoustic Sensing in seismic imaging, by investigating a variety of important aspects: (1) Empirical assessment of DAS recordings in different environments to estimate the instrument responses. (2) A connection between strain and rotation measurements to potentially derive rotations from DAS recordings. (3) The extension of ambient noise interferometry to gradient measurements, including strain and rotation measurements. (4) The adaptation of full-waveform based ambient noise tomography to the interferometric gradient wavefields incorporating strain and rotation.. 1.1 Outline In Chapter 2 we4 introduce the necessary theory for gradient wavefield observations and instrument responses in the context of DAS recordings. In addition to the theoretical foundation, we show the result of empirical instrument response investigations for the Silixa iDAS(T M ) DAS interrogator, for a series of experiments including low-frequency strain due to hydraulic injection in a borehole, local to teleseismic earthquake recordings, active controlled-source vibroseis experiments and stick slip icequake recordings. That chapter was written in collaboration with Pascal Edme, Dominik Gräff, Fabian Walter, Joseph Doetsch, Athena Chalari, Cédric Schmelzbach and Andreas Fichtner and is published in (see next page):. 3 4. 4. This paragraph is taken from Paitz et al. (2018a). The choice of the the first person plural in this thesis was made on purpose, because this thesis is based on publications that would not have been possible without a wide range of collaborations. In the scientific field of Distributed Acoustic Sensing, fieldwork and collaborations with other scientists is inevitable, and hence I prefer the first person plural for most of the thesis..

(27) 1.1. Outline Paitz, P., P. Edme, D. Gräff, F. Walter, J. Doetsch, A. Chalari, C. Schmelzbach, and A. Fichtner (2020), Empirical Investigations of the Instrument Response for Distributed Acoustic Sensing (DAS) across 17 Octaves, Bulletin of the Seismological Society of America. Issn 0037-1106. In Chapter 3, we emphasize the similarities and differences between measurements of strain and rotations. The measurements of rotations, related to the the anti-symmetric part of the gradient tensor, are usually used in single station deployments, whereas measurements of strain, related to the symmetric part of the gradient tensor, are often used in high spatial resolution arrays. Due to the availability of new instruments such as portable instruments to measure rotational motion and distributed strain measurements such as from Distributed Acoustic Sensing (DAS) systems, the data acquired with such systems is continuously increasing. Measuring these spatial gradients enables a wide range of applications, such as elastic wavefield separation and improved earthquake source inversion. We introduce a way to obtain rotational ground motion from arrays of strain recordings, potentially increasing the insights retrieved from DAS measurements. Chapter 3 was written in collaboration with Pascal Edme, Cédric Schmelzbach, David Sollberger, Felix Bernauer, Krystyna Smolinski, Jonas Igel, Joachim Wassermann, Heiner Igel and Andreas Fichtner. A publication with the following preliminary title is currently in preparation: Paitz, P., P. Edme, C. Schmelzbach, D. Sollberger, F. Bernauer, K. Smolinski, J. Igel, J. Wassermann, K. H. Igel and A. Fichtner, From strain to rotation: On the use of Distributed Acoustic Sensing systems for ground rotation measurements, in preparation Based on the developments discussed in the previous chapters, we propose a theory for ambient noise interferometry utilizing strain and rotation measurements in Chapter 4. In this context, we demonstrate that displacement, strain and rotation interferograms can be generically written in the form of a representation theorem, that is, as a solution to the seismic wave equation that we refer to as the interferometric wavefield. The physical quantity (displacement, strain or rotation) determines the distributed source of the interferometric wavefield, as well as an observational operator that extracts the correct type of noise correlation function. The proposed interferometric equations are free of assumptions on the distribution of noise sources or the equipartitioning of the ambient field, typically required for Green’s function retrieval. In addition to being valid for any kind of heterogeneous source and visco-elastic medium, they allow us to account for measurement details, such as the gauge length in DAS. We illustrate the practical feasibility of our approach with a series of numerical examples, based on regional-scale, spectral-element simulations of the. 5.

(28) 1. Introduction interferometric wavefield. Specifically, we compare displacement and strain interferograms for homogeneous and heterogeneous Earth models, and for homogeneous and heterogeneous noise sources.5 This chapter was written in collaboration with Korbinian Sager and Andreas Fichtner and is published in: Paitz, P., K. Sager and A. Fichtner (2018), Rotation and strain ambient noise interferometry, Geophysical Journal International, 216(3),1983-1952 Building on the results from Chapter 4, we extend the theory of full-waveform ambient noise inversion in Chapter 5, to enable adjoint-based waveform inversion with new emerging measurement technologies utilizing spatial gradient information in addition to observations of displacement. This chapter was written in collaboration with Korbinian Sager, Christian Böhm and Andreas Fichtner. A corresponding publication under the following preliminary title is currently in preparation: Paitz, P., K. Sager, C. Böhm and A. Fichtner, Combining seismological observables in full waveform ambient noise inversion: Cross-observational sensitivity kernels, in preparation In addition to the presented studies, a wide range of DAS experiments and field campaigns have been performed as part of this thesis. An overview of these experiments, the acquired data and ongoing collaborations is given in Chapter 6. Based on the gained insights and performed experiments, future research possibilities and ideas are summarized in Chapter 7. The topics discussed in this thesis are then summarized in Chapter 8, concluding the key points of this work.. 5. 6. This paragraph is adapted after Paitz et al. (2018a)..

(29) Properties of DAS measurements. 2. This chapter is adapted after Paitz et al. (2020a), in collaboration with Pascal Edme, Dominik Gräff, Fabian Walter, Joesph Doetsch, Athena Chalari, Cédric Schmelzbach and Andreas Fichtner. It extends existing DAS instrument response analyses in the frequency band from 1/120 Hz to 10 Hz to an instrument-specific DAS response of the Silixa iDASTM , covering a frequency range of more than 17 octaves, from around 0.3 mHz to 60 Hz. Some sections have been renamed from the original publication.. 2.1 Chapter summary With the potential of high temporal and spatial sampling and the capability of utilizing existing fiber optic infrastructure, Distributed Acoustic Sensing (DAS) is in the process of revolutionizing geophysical ground motion measurements, especially in remote and urban areas, where conventional seismic networks may be difficult to deploy. Yet, for DAS to become an established method, we must ensure that accurate amplitude and phase information can be obtained. Furthermore, as DAS is spreading into many different application domains, we need to understand the extent to which the instrument response depends on the local environmental properties. Based on recent DAS response research, we present a general workflow to empirically quantify the quality of DAS measurements based on the transfer function between true ground motion and observed DAS waveforms. With a variety of DAS data and reference measurements, we adapt existing instrument response workflows typically in the frequency band from 0.01 to 10 Hz to different experiments, with signal frequencies ranging from 1/3000 Hz to 60 Hz. These experiments include earthquake recordings in an underground rock laboratory, hydraulic injection experiments in granite, active seismics in agricultural soil, and icequake recordings in snow on a glacier. The results show that the average standard deviations of both amplitude and phase responses within the analysed frequency ranges are on the order of 4 dB and 0.167π radians, respectively among all experiments. Possible explanations for variations in the instrument responses include the violation of the assumption of constant phase velocities within the workflow due to dispersion and incorrect ground-motion observations from reference measurements. The results encourage further integration of DAS-based strain measurements into methods. 7.

(30) 2. Properties of DAS measurements that exploit complete waveforms and not merely traveltimes, such as full-waveform inversion. Ultimately, our developments are intended to provide a quantitative assessment of siteand frequency-dependent DAS data that may help to establish best practices for upcoming DAS surveys.. 2.2 Introduction to DAS and instrument responses Distributed Acoustic Sensing (DAS) is a method to utilize an optical fiber as an instrument to measure strain or strain rate along the fiber. Following successful early DAS applications in border and pipeline monitoring and as downhole seismic instruments in the seismic exploration industry, the method was recently adopted in longer-period seismology (Daley et al., 2013; Li et al., 2015; Hartog, 2017; Martin et al., 2017b). With the benefit of high temporal and dense spatial sampling even in remote areas, and the potential to use existing fiber-optic infrastructure e.g. in urban areas, Distributed Acoustic Sensing (DAS) is in the process of revolutionizing seismic and seismological data acquisition on multiple scales across the Earth. However, the quality of DAS measurements for seismological applications needs further quantitative assessments. In addition to site and orientation effects due to limited broadside sensitivity of DAS along straight fibers (Kuvshinov, 2016), data quality is affected by the transfer function between the deforming medium (i.e., the Earth) and the fiber, which in turn depends on fiber coupling and cable properties. Optical noise also influences the quality of the DAS measurement and is further discussed in Lindsey et al. (2020). The quality of DAS measurements, as compared to more traditional instrumentation, has been the focus of numerous recent works ranging from very long periods of several hours in laboratory environments (Becker and Coleman, 2019), to ambient noise studies (Dou et al., 2017; Martin et al., 2018a, 2016) and earthquake detection (Lindsey et al., 2017; Wang et al., 2018; Ajo-Franklin et al., 2018), to active-source seismic experiments (Daley et al., 2013). Most studies have not gone through the rigorous step of quantifying an instrument response function, though initial responses were presented in Jousset et al. (2018) (0.1 to 100 s period) and Lindsey et al. (2020) (1 to 120 s period). These existing analyses of the DAS response function are typically in a limited part of the frequency band from 0.01 to 10 Hz and are based on comparisons with well-coupled conventional seismometers for which the instrument response is sufficiently well known to be removed from the signal (Lindsey et al., 2020). Whereas Jousset et al. (2018) investigate the strain instrument response theoretically and compare displacement spectra of (corrected) DAS recordings with displacement recordings of a broadband seismometer and a geophone, Lindsey et al. (2020) shows the first comprehensive empirical instrument response study in which DAS data is converted to velocity in the f -k domain and then compared to recordings of a broadband seismometer.. 8.

(31) 2.3. Instrument response estimation One potential of DAS, however, is to cover a much broader range of frequencies than any other instrument previously, and most of these existing studies were restricted to a given application and frequency range. In this study, we extend the existing analyses in the frequency band from 1/120 Hz to 10 Hz to an instrument-specific DAS response of the Silixa iDASTM , covering a frequency range of more than 17 octaves, from around 0.3 mHz to 60 Hz. This is based on a series of experiments, including (1) low-frequency strain induced by hydraulic injection in a borehole with co-located fiber-Bragg-Grating (FBG) strainmeters, (2) local to teleseismic earthquake recordings with a co-located broadband seismometer station, (3) active controlled-source experiments with co-located geophones and (4) stick-slip icequake recordings with colocated seismometers on a glacier. The frequencies covered in this chapter, as well as the frequencies covered in the work by Jousset et al. (2018) and Lindsey et al. (2020), are visualised in Fig. 2.1. For all experiments, co-located instruments with known response functions were installed to obtain estimates of ground motion for comparison and quantification of the DAS response. 1000.0. Period [s] 10.0. 100.0. 1.0. 0.1. 100. 101. 0.01. Lindsey et al., (2020) Jousset et al., (2018) HI. HI 10. 3. EQ 10. 2. EQ 10 1 Frequency [Hz]. VIB. IQ 102. Figure 2.1: Overview of the frequencies covered by the experiments in this chapter, in context to existing instrument response studies of DAS (black). The instrument response study covers hydraulic injection experiments (denoted HI), earthquake recordings (denoted EQ), active vibroseis shots (denoted VIB) and icequake recordings (denoted IQ).. This chapter is organized as follows: In the Section 2.3, we introduce the necessary theory for instrument response and gradient wavefield observations in the context of DAS seismology. Section 2.4 contains an overview of the DAS experiments discussed in this study, and a summary of the data processing workflow. The resulting instrument response curves and example waveforms are then shown in Section 2.5 and further discussed in Section 2.6, with an emphasis on current and future applications of DAS for subsurface monitoring.. 2.3 Instrument response estimation Estimates of the effective DAS instrument response require two main ingredients: (1) A co-located instrument with known response, and (2) a conversion of the measurements into the same physical quantity, which is most commonly displacement in the direction of the fiber. In the following sections, we elaborate on these two ingredients. We follow the derivations of Daley et al. (2016); Wang et al. (2018) and Lindsey et al. (2020). 9.

(32) 2. Properties of DAS measurements. 2.3.1 Comparison with co-located reference measurements Assuming sufficiently small displacements, the ith -component of an observed displacement waveform u(x, ω) at the point location x and circular frequency ω can be expressed in terms of true ground deformation g(x, ω) and a linear transfer operator or instrument response T(ω), ui (x, ω) =. 3 X. Tij (ω)gj (x, ω) ,. (2.1). j=1. where j is the component of ground deformation is some suitable 3-D coordinate system. The off-diagonal elements of T describe the mostly undesirable mapping of components into each other, and they may be non-zero, for instance, when an instrument is mis-oriented or the Poisson effect of a fiber-optic cable in the case of a DAS acquisition system is significant. While being of general interest, the complete set of transfer tensor elements is not accessible with DAS measurements along a straight cable, because the measurements are confined to the cable direction, described by the unit vector e(x). Hence, we are forced to base our analysis on an approximate scalar version of Eq. (2.1), ue (x, ω) = Te (ω)ge (x, ω) ,. (2.2). with the projections ue = uT e and ge = gT e. The estimation of the scalar instrument response is possible when co-located measurements u0e with known instrument response Te0 are available. For example, we might use u’ and T’ to refer to the observations and response of a known broadband instrument that we use for comparison. Solving u0e (x, ω) = Te0 (ω)ge (x, ω). (2.3). for ge and inserting into Eq. (2.2), yields Te (ω) = Te0 (ω). ue (x, ω) ue (x, ω)u0∗ e (x, ω) 0 = T (ω) , e 0 0 ue (x, ω) |ue (x, ω)|2. (2.4). where ∗ denotes complex conjugation. To prevent division by small numbers, it is important to limit the instrument response estimation to frequencies for which the power spectra of both observations are significantly non-zero or to add a waterlevel to the denominator in Eq. 2.4.. 2.3.2 Conversion of observed quantities Eq. (2.4) rests on the assumption that ue and u0e are identical physical quantities. Since most of our co-located reference measurements are velocity recordings, the DAS measurements of strain or strain rate therefore need to be converted.. 10.

(33) 2.3. Instrument response estimation The output quantity of DAS measurements depends on the interrogator. For this study, we use the Silixa iDASTM that measures strain rate. Within a few meters of the DAS interrogator, and depending on the specific experiment (see Section 2.4, we performed reference measurements using either a fiber-bragg-grating (FBG) strain sensor, geophones or seismometers measuring ground velocity. Strain εe in the direction e(x) of the fiber, can be expressed in terms of the displacement field u(x, ω) as 3 X. 1 εe (x, ω) = ei (x) 2 i,j=1. !. ∂ui (x, ω) ∂uj (x, ω) + ej (x) . ∂xj ∂xi. (2.5). Generally, DAS measurements are averages over an interval along the fiber called the gauge length γ (Daley et al., 2016). This largely controls spatial resolution and the signal-to-noise ratio. As the apparent wavelength λ of the incident wave approaches γ, the measurement of averaged strain is significantly different from the actual strain. In our experiments, the minimum apparent wavelength is on the order of 50 − 100 m. Since this is large compared to the 10 m gauge length of the iDASTM , the averaging effect can safely be ignored. Invoking plane-wave decomposition, the relationship between strain εe and particle velocity ve = due /dt can be expressed as (Daley et al., 2016; Wang et al., 2018) εe (x, ω) =. 1 ve (x, ω) , c(x, ω). (2.6). where c is the apparent phase velocity along the cable direction, defined in terms of wavenumber k and frequency ω, as c = ω/k. The apparent phase velocity depends on frequency, incidence angle, and subsurface properties in the vicinity of the measurement location x. Under the assumption of a single plane wave, the conversion of strain to particle velocity, or vice versa, can either be performed in the time domain for any known c, or by rescaling in the frequency-wavenumber domain (Wang et al., 2018). For the comparison between DAS and geophone or seismometer data, we integrate DAS data from strainrate to strain and then convert to velocity in the time domain using apparent phase velocity estimates. The FBG-sensors used in our experiments measure strain directly, and hence integrated DAS data from strain-rate to strain can be compared directly to these measurements. Recent experiments have shown that conversion in the f -k domain may be more accurate (Wang et al., 2018). However, this was not possible in our case due to the narrow wavenumber content in our individual experiments. Additionally, when analyzing data with narrow wavenumber content, the introduction of a waterlevel is required in f -k domain conversion (Lindsey et al., 2020). This waterlevel may have a strong effect on the phase velocity and may therefore yield an unphysical modification. Finally, because the exact physical co-location of two instruments is not possible, site effects together with imperfect. 11.

(34) 2. Properties of DAS measurements fiber to ground coupling can influence the measurement as well.. 2.4 Empirical instrument study In the following, we describe the individual narrowband experiments that contribute to the final broadband instrument response . This includes information on the experimental setup, the data processing, and the instrument response estimation. A more detailed and technical description of the cable installations and the investigated signals is summarized in Table 2.1.. 2.4.1 Experiment location and instrumentations To analyze instrument responses of DAS in a wide frequency range and under different conditions, we conducted a series of active and passive experiments in different settings: (1) active hydraulic stimulation experiments between 1/3600 Hz and 1/200 Hz at the Grimsel Test Site (GTS) rock laboratory in the Swiss Alps (Doetsch et al., 2018; Krietsch et al., 2018) with co-located Micron Optics Inc. os3600 FBG sensors, (2) passive earthquake recordings between 1/26 Hz and 13 Hz in a tunnel within the Grimsel Test Site rock laboratory with a co-located Streckeisen STS2 seismometer (Quanterra Q330HRS digitizer), (3) active-source seismics with signals between 20 Hz and 40 Hz on an agricultural field near the city of Yverdon-les-Bains in western Switzerland and co-located INPUT/OUTPUT INC. SM6 (14 Hz) geophones (Geometrics ES-3000 digitizer), and (4) passive icequake recordings between 40 Hz and 60 Hz on Rhonegletscher, a temperate glacier in the Swiss Alps, with a co-located three-component Lennartz 3D/BHs sensor (Nanometrics Centaur digitizer). A detailed description of the experiment on Rhonegletscher can be found in Walter et al. (2020). An overview on the locations of the experiments is shown in Fig. 2.2. The fiber installation and environmental conditions strongly varied between the various experiments. Whereas the cable was cemented in a 40 m deep borehole for the hydraulic stimulation experiment (1), it was just loosely lying on the ground for the Grimsel Test Site passive earthquake recordings (3) in a 60 m long tunnel, looping back and forth with some parts of the cable covered by gravel bags (over a 10 m section), some parts taped to the ground (over a 10 m section) and some parts of the cable covered with wooden blocks (over a 10 m section). For the active seismics (2), the cable was trenched in soil at a depth of approximately 10 cm over a length of 100 m and for the icequake recordings (4), the fiber-optic cable was trenched in snow at a depth of between 2 and 10 cm.. 12.

(35) 2.4. Empirical instrument study (a). (b). (c) Germany. France Switzerland. Zurich. Austria (d). 47°N (d). (e). (c) (e). 46°N 7°E. Italy 9°E. Figure 2.2: The geographic location of the individual experiments is shown in panels (a) and (b), indicated by the triangles. Experimental conditions are shown in (c) for the Rhonegletscher icequake recording, in (d) for the active seismics field test in western Switzerland close to Yverdonles-Bains, and in (e) for the Grimsel Test Site earthquake recordings. The lines in (a) and (b) show the backazimuths of the surface waves for the earthquake recordings at the GTS (black and white, respectively). The arrows point to the installed cable (c and e) and to the trench in which the cable was installed (d). The arrows in (c) to (e) are approximately 1 meter apart. In addition to the cable visible for the Grimsel Test Site in (e), a borehole installation at the same test site was used for the hydraulic stimulation experiment. (c) is adapted after Walter et al. (2020).. 2.4.2 Workflow and data processing 2.4.2.1 Preprocessing, apparent phase-velocity estimation and conversion We pre-processed the data recorded in the various experiments before estimating the instrument response. This included de-trending and tapering, the integration of iDASTM data from strain rate to strain, and finally the application of a Butterworth bandpass filter. The filter frequencies are specified in Table 2.1. With the exception of the long-period experiment at the Grimsel Test Site, with co-located FBG strain sensors, strain from DAS measurements had to be converted to velocity, in order to ensure comparability of DAS and co-located velocity data. As explained in Section 2.3.2, the most suitable conversion approach for our experiments is re-scaling with an estimated apparent phase velocity. In addition to avoiding potential numerical instabilities of f -kdomain re-scaling, the approach is numerically robust, and it enables a channel-by-channel instrument response analysis. For the Grimsel Test Site experiments, we look at a range of earthquakes from various distances and frequencies. For the teleseismic and regional earthquake recordings (distances of 16000 km and 1300 km and denoted EQ Fiji and EQ Ionian, respectively) at the Grimsel. 13.

(36) 2. Properties of DAS measurements Test Site, with frequencies around 0.05 Hz, we use a Rayleigh-wave phase velocity of 3.6 km/s, typical for the Alpine region (Fry et al., 2010), and around 10 % lower than the global continental average (Dziewoński et al., 1975). The local event (distance of 60 km, denoted EQ Linthal) has a dominant frequency of around 10 Hz, corresponding to wavelengths of a few hundred meters. We therefore work with a Rayleigh wave phase velocity calculated for a homogeneous half space with S velocity of 3000 m/s, typical for granite at the Grimsel Test Site. After calculating the backazimuth of the surface wave, we used the Rayleigh wave window to calculate the apparent phase velocity. For the Yverdon-les-Bains active source experiment, the phase velocity was estimated from a seismic section by comparing the arrival times of the high amplitude surface wave for the first and last DAS cable channel. This gave a phase velocity along the cable of 1200 m/s for the surface wave arrival with the largest amplitude. It was difficult to obtain a phase velocity estimate for the icequake recording of the Rhonegletscher experiment. We picked an apparent phase velocity of a seismic section of only 10 DAS channels and obtained an estimated apparent phase velocity of 5500 m/s for the direct S-wave arrival. The phase velocity estimates required for the conversion from strain to velocity are apparent phase velocities along the fiber for specific seismic phases. The windows indicated in Fig. 2.3, for which we estimated DAS instrument responses, are chosen for their high signal-to-noise ratio, with the additional constraint to minimize overlap with other arrivals with potentially different apparent phase velocities. An incorrect estimate of apparent phase velocity affects the estimated amplitude response, but not the phase response of the DAS. This is further discussed in the Section 2.6.1.. 2.4.2.2 Instrument response estimation After pre-processing, we estimate a site-specific instrument response of the DAS system using Eq. 2.4 within an appropriate frequency range where recorded power spectra are significantly non-zero. To analyze the instrument response, we consider its amplitude and phase independently. To avoid complications with phase unwrapping, we note that the phase of Te (ω) is typically the small phase difference between the converted DAS recording ue (ω) and the ground motion ge (ω), estimated from Eq. (2.2). This phase difference can be conveniently computed from the correlation of ue (ω) and ge (ω). Since DAS measurements record ground motion on numerous closely spaced channels, we compute a DAS response for every channel individually. Ideally, there would be a co-located measurement of ground motion available for every DAS channel, but in reality this is not feasible. Instead, we often have to rely on a single reference measurement in the vicinity of a DAS array. This is legitimate when the distance between each DAS channel and the reference measurement is only a fraction of the wavelength and the medium in which the. 14.

(37) 2.5. Results of the instrument response study instruments are installed have the same properties. In our experiments, this was generally the case. If the interrogated fiber had homogeneous backscattering properties and identical coupling with exact physical co-location, all investigated DAS channels had an identical response function. Because this is not met in reality, we will compare all available DAS channels.. 2.5 Results of the instrument response study 2.5.1 Time-domain waveforms To illustrate the effect of the pre-processing and conversion, Fig. 2.3 shows a selection of time-domain DAS and reference waveforms from each of the experiments described in the Section 2.4. The examples are representative of the more general observation that the main features of reference and pre-processed DAS measurements are visibly similar, while the corresponding raw recordings may have little in common. This is more quantitatively reflected in the unnormalized cross-correlation coefficients between raw reference and DAS data, which range between 0.01 and 0.08 (absolute correlation coefficient). In contrast, the correlation coefficient for the processed data ranges between 0.78 and 0.95 for the examples shown in Fig. 2.3. Despite the similarities of processed reference and DAS waveforms, there are obvious small differences between them. To investigate them in more detail, we analyze frequencydependent instrument responses for the events from Fig. 2.3 in the following section.. 2.5.2 Instrument response curves The estimated instrument responses for all available DAS channels, including the few examples from Fig. 2.3, are visualized in Fig. 2.4. For readability, the range of the instrument response functions within the standard deviations and the mean values of amplitude and phase response are plotted in each subfigure. In addition, the minimum and maximum values of the response curves are plotted as well. If the DAS data were exactly ground motion measurements, the instrument response curves in Fig. 2.4 would show flat horizontal lines at 0 dB and 0 rad, respectively. Each of the subplots in Fig. 2.4 visualizes a collection of effective instrument response curves for each DAS experiment in a certain frequency band and at a specific site. The number of available DAS and reference measurements depends on the site and the experimental setup. For the hydraulic injection experiment, for instance, we could compare only two DAS channels to two separate co-located FBG measurements. For the Grimsel Test Site tunnel recordings, we compared 206 and 250 DAS channels respectively, to one nearly co-located seismometer. The maximum distance between seismometer and DAS channels at the Grimsel Test Site is 50 m. With 15 DAS channels and almost exactly. 15.

(38) 2. Properties of DAS measurements. DAS Proc.. REF Proc.. DAS Raw. REF Raw. (a) GTS hydraulic. (b) GTS EQ Fiji. (c) GTS EQ Ionian. (d) GTS EQ Linthal. (e) YVD active. (f) RHN icequake. 0.5 0.5. 0.5 0.5. 0.5 0.5. 0.5 0.5 0. 2000. 4000. Time [s]. 0. 200. Time [s]. 400 0. 200. 400. Time [s]. 0. 1. 2. Time [s]. 3 0.0. 0.5. 1.0. Time [s]. 1.5 0.0. 0.1. 0.2. Time [s]. 0.3. Figure 2.3: Normalized waveforms (w.r.t. maximum amplitude) of raw reference data (top row, denoted REF Raw), raw DAS data (second row, denoted DAS Raw), processed reference data (third row, denoted REF Proc.) and processed and converted DAS data (4th row, denoted DAS Proc.). The first column shows the waveforms for the hydraulic stimulation experiment (a) in the boreholes at the Grimsel Test Site (GTS, FBG and DAS data). The second to fourth columns (b to d) show earthquake recordings from the tunnel installation at GTS (seismometer and DAS data). The fifth column (e) shows waveforms from the active seismic experiment in Yverdon-les-Bains (YVD, geophone and DAS data), and the last column (f) visualizes icequake recordings from the Rhonegletscher (RHN, seismometer and DAS data). The raw reference data (REF Raw) is always raw velocity data, except for the hydraulic injection experiment, where it is strain. The raw DAS data (DAS raw) is the recorded raw strain-rate signal. The processed waveforms are in the unit of velocity [m/s] except for the hydraulic injection experiment, where the processed waveforms are strain waveforms. The grey boxes indicate the signal window for which we estimated the instrument response. The two different grey boxes in (a) indicate two different signal windows used for different frequency bands of the instrument response. Since this summary plot is primarily intended to show overall similarities and differences, we present enlarged versions of each subplot in Figures 2.5 to 2.10. The detailed instrument descriptions for the reference data are available in Table 2.1.. co-located geophones, we compared the data from Yverdon-les-Bains channel-by-channel. In the response analysis from Rhonegletscher, we used 2 DAS channels in the vicinity of a single seismometer, with a maximum distance of 10 m. The number of available sufficiently co-located channels is limited by the receiver layout and the wavelength. From Fig. 2.4 we observe that instrument responses vary in both amplitude and phase. Across frequency bands, the mean amplitude response varies between −12.45 dB (Grimsel Test Site Fiji earthquake recording) and 10.42 dB (Rhonegletscher icequake recording). Mean phase responses range from −0.06π rad (Grimsel Test Site hydraulic stimulation experiment) to 0.04π rad (Grimsel Test Site Linthal earthquake recording). Excluding experiments with only 2 DAS measurements, the standard deviation of the amplitude. 16.

(39) 2.6. Discussion of instrument response results (a). (b). 0. 65. Phase [rad]. Amplitude [dB]. 1/ GTS hydraulic. 20. (c). 1/. (d). 5. 37. GTS hydraulic. 22. 1/. GTS EQ Fiji. (e). 19. 1/. (f). 16. 1/. GTS EQ Ionian. 20 GTS EQ Linthal. (g). 30. 40. YVD active. RHN icequake. 10 0 -10 -20. /2 0. /2 1/. 29. 00. 1/. 12. 00. 1/. 26. 1/. 22. 1/. 18. 9. 11. 13. 40. 50. 60. Frequency [Hz]. Figure 2.4: Summary of estimated instrument responses for all experiments. The top row shows the amplitude responses in dB as DAS ground motion with respect to ground motion from reference measurements (20 log10 of the ratio between DAS spectrum and the spectrum of the ground motion), and the bottom row shows the phase responses as phase difference between DAS ground motion and ground motion from reference measurements in radians. Columns correspond to different frequency ranges covered by the hydraulic stimulation experiment ((a) and (b)), earthquake recordings at the Grimsel Test Site (GTS, panels (c) to (e)), the active experiment near Yverdon-les-Bains (YVD, panel (f)), and the icequake on Rhonegletscher (RHN, panel (g)). The black lines in the center indicate the mean amplitude and phase responses from all available DAS channels, and the greyshaded area around the mean represents the corresponding standard deviation. Black dashed lines indicate the minimum and maximum instrument response values. The shaded area between (c) and (d) indicates an overlap in frequencies between the two columns. The number of DAS channels is n=2 for (a) and (b), n=250 for (c) and (e), n=206 for (d), n=15 for (f) and n=2 for (g). (Clearly, the standard deviation for n=2 has limited meaning.) For the investigated signals, if the DAS data were recordings of true ground motion, both amplitude and phase response should be horizontal lines at 0 dB and 0 rad respectively. For details on the instrumentation, see Table 2.1 and for a larger image of each subfigure with more details, see Figures 2.5 to 2.10. response is on the order of 4 dB. For the effective phase responses, the standard deviations range from 0.035π rad for the Grimsel Test Site earthquake recording in (d) to 0.36π rad for the Grimsel Test Site earthquake recording in (e). The average standard deviations of amplitude and phase response among all experiments are 4.0 dB and 0.17π rad, respectively.. 2.6 Discussion of instrument response results The most important result of this work is the observation that, despite all sources of errors and differences in experimental setups, the DAS amplitude response only varies by around ±10 dB over a frequency range from 1/2900 Hz to 60 Hz, that is, over more than 17 octaves. The phase response is typically on the order of 0.1π. In the following sections,. 17.

(40) 2. Properties of DAS measurements we discuss possible reasons for the instrument response variations, as well as implications for current and future applications. Comparing the results to the instrument response curves in Lindsey et al. (2020) for the frequency range from 1/120 Hz to 1 Hz, we find a instrument response that is up to 10 dB lower. The authors in Lindsey et al. (2020) stack data over five gauge lengths (10 m), whereas our results are channel-by-channel.. 2.6.1 Possible causes of instrument response variations While deviations of the instrument response from a flat response might be a property of the DAS interrogator itself, they are more likely to result from assumptions and approximations used during the approximation procedure. The variations of the amplitude response within and across experiments may be related to incorrect phase velocity estimates. Largely owing to the small size of the DAS arrays used in this study, the DAS data conversion via Eq. (2.6) is based on a frequency-independent phase velocity for each frequency band. Within the relatively narrow frequency bands of the individual experiments, one may expect phase velocity variations on the order of 10 %, which translates to amplitude response errors of around 1 dB. This is sufficient to explain amplitude response variations at the Grimsel Test Site. The small standard deviation of the amplitude response within the individual experiments indicates that the details of cable-to-ground coupling play a relatively minor role, as long as the cable is shielded from wind. This is particularly evident for the surface-cable experiment in the Grimsel Test Site tunnel. Though different cable segments were coupled very differently (i.e., not at all, glued to the surface with tape, weighted with wooden blocks or sand bags), the standard deviation of the amplitude response is typically around 1 dB, i.e., around 10 %. An additional source of error are inaccuracies of the instrument responses in the reference measurements. This seems to be the most plausible explanation of the strong response variations at the Yverdon-les-Bains test site, where each DAS channel is compared to a separate geophone and is the subject of further ongoing research. An outlier in the response analysis is the Rhonegletscher experiment. A possible explanation of the strong overestimation of the amplitude response is a local site-effect, or imperfect co-location. In fact, we performed the reference measurement on ice below a snow cover of about 2 m, while the DAS cable was located on the snow surface, which has different elastic properties that could potentially result in amplitude amplifications similar to amplifications in sedimentary basins. We also calculated the signal to noise ratio (SNR), defined as the ratio of root-meansquare amplitudes of the indicated signal windows and the root-mean-square amplitude of a manually picked noise window of the same length for every DAS channel individually. We did this for all experiments, except for the hydraulic injection experiment where picking a. 18.

(41) 2.6. Discussion of instrument response results noise window was not possible, and for the Fiji earthquake recording where the trimmed data was too short to pick a large enough noise window. The mean SNR of the DAS data ranges from 6.3 for the active seismic experiment to 15.1 for the Linthal earthquake recordings, whereas the mean SNR of the reference instruments ranges from 6.1 for the Ionian Sea earthquake recordings to 19.6 for the Linthal earthquake recordings. There seems to be no obvious connection between the SNR and the instrument response values for the investigated signals. Finally, and in addition to the previously mentioned factors, sub-wavelength heterogeneities may contribute to an effective instrument response for strain measurements that is not perfectly flat (Singh et al., 2019). Given that (1) phase velocity errors only account for around 1 dB in amplitude response, (2) the amplitude response variations vary smoothly with frequency, and (3) cable-to-ground coupling seems to play a minor role, one may hypothesize that sub-wavelength heterogeneities play a significant role.. 2.6.2 Implications for current and future DAS applications The frequency bandwidth of the DAS instrument response enables applications ranging from mHz in normal-mode seismology to several tens of Hz in seismic exploration and seismic hazard analysis. This would be particularly attractive for environmental seismology, as a broad spectrum of phenomena may be captured with a single instrument. These phenomena include longperiod temperature variations, precipitation, induced seismicity, mass movement and subsurface velocity changes due to natural or anthropogenic activity. In fact, the potential of DAS in seismic hazard analysis largely derives from the co-use of existing telecommunication cables. The comparatively small effect of cable-to-ground coupling makes applications that leverage existing fiber infrastructure more viable. The most likely, and closely related, bottlenecks are unknown sub-wavelength structure and reliable phase velocity estimates. These may hinder accurate conversions from strain to displacement or velocity amplitudes, and later to ground-motion proxies such as spectral acceleration or peak-ground acceleration. This may be overcome by incorporating strain observations into seismic hazard frameworks. The small phase response of the DAS system enables traveltime measurements with an error typically below 5 % of the dominant period. To put this in perspective: In the case of the local Linthal event (Fig. 2.4a), the traveltime error would result in an error of 0.025 % of the estimated Rayleigh wave velocity along the path from source to receiver. Since corresponding numbers are similar for other examples, this suggests that seismic tomography based on DAS traveltime measurements is entirely feasible, even without instrument response removal. This is also shown theoretically for apparent wavelengths exceeding the gauge length, e.g., in the supplementary material of Walter et al. (2020).. 19.