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Array Processing for Seismic Surface Waves Diss. ETH No. 21291 Array Processing for Seismic Surface Waves A dissertation submitted to ETH Zurich for the degree of Doctor of Sciences presented by Stefano Maranò Laurea Specialistica in Ingegneria delle Telecomunicazioni, Università degli Studi di Trento born on December 23, 1983 citizen of Italy accepted on the recommendation of Prof. Dr. Donat Fäh, examiner Prof. Dr. Hans-Andrea Loeliger, co-examiner Prof. Dr. Domenico Giardini, co-examiner Prof. Dr. Heiner Igel, co-examiner 2013 ii Abstract The analysis of seismic surface waves plays a major role in the under- standing of geological and geophysical features of the subsoil. Indeed seis- mic wave attributes such as velocity of propagation or wave polarization reflect the properties of the materials in which the wave is propagating. The analysis of properties of surface waves allows geophysicists to gain insight into the structure of the subsoil avoiding more expensive invasive techniques (e.g., borehole techniques). A myriad of applications benefit from the knowledge about the subsoil gained through seismic sur- veys. Microzonation studies are an important application of the analysis of surface waves with direct impact on damage mitigation and earthquake preparedness. This thesis aims at improving signal processing techniques for the analysis of surface waves in different directions. In particular, the main goal is to deliver accurate estimates of the geophysical parameters of interest. The availability of improved estimates of the quantities of in- terest will provide better constraints for the geophysical inversion and thus enabling us to obtain an improved structural earth model. For a rigorous treatment of the estimation of wavefield parameters we rely on tools from statistical signal processing. Wavefield parameters are estimated using the maximum likelihood (ML) method. A compu- tationally efficient implementation of such an estimator is obtained by modelling seismic surface waves with a factor graph, a particular type of probabilistic graphical model. A theoretical bound on estimation accu- racy, the Cramér-Rao bound (CRB), enables us to quantify the sources of uncertainty and provides a benchmark for evaluating estimation algo- rithms. One main contribution of this work is the development of a method for the analysis of seismic surface waves. The method is versatile enough to model different types of waves and to handle measurements of dif- ferent type. All the wavefield parameters of Love waves and Rayleigh waves, together with all the measurements, are jointly modelled within the proposed framework. The method ensures an optimal usage of the available measurements according to the ML criterion. The method also deals with the simultaneous presence of multiple waves, possibly of different type. The proposed algorithm decomposes the wavefield by gradually increasing the number of waves modelled and iteratively refining estimates of the parameters of each wave. Sensors with different noise level are also accounted for and the estimation ac- counts for the possible different quality of the measurements. Performance is assessed on field measurements of ambient vibrations from sensor arrays. It is shown how the proposed method outperforms methods in the literature in different ways, namely: Rayleigh wave el- lipticity is retrieved with increased accuracy, the retrograde/prograde particle motion of the Rayleigh wave is retrieved for the first time, and the simultaneous presence of multiple waves is considered. It is also shown that the implementation of the proposed method exhibits, for a sufficiently large signal-to-noise ratio (SNR), the smallest achievable mean-squared estimation error (MSEE) indicated by the CRB. The joint processing of translational and rotational motions is tested on recordings from controlled explosions. We show the retrieval of Love and Rayleigh wave parameters in several settings not considered in the literature, both in the case of a single six-component sensor and the case iii of an array of three and six-component sensors. Analytic expressions of the CRB of each parameter of geophysical interest are derived. These expressions allow us to quantify and understand the sources of uncer- tainty limiting the estimation accuracy of the wavefield parameters. The statistical models for Love and Rayleigh waves relying on translational measurements, rotational measurements, and both translational and ro- tational measurements are considered. The impact of array geometry on the estimation of parameters of Love and Rayleigh waves is also investigated. It is explained in detail how the array geometry affects the MSEE of parameters of interest, such as the velocity and direction of propagation, both at low and high SNRs. A cost function suitable for the design of the array geometry is proposed, with particular focus on the estimation of the wavenumber of both Love and Rayleigh waves. Several computational approaches to minimize the proposed cost function are presented and compared. Finally, numerical experiments verify the effectiveness of the proposed cost function and resulting array geometry designs, leading to greatly improved estimation performance in comparison to arbitrary array geometries, both at low and high SNR levels. iv Kurzfassung Die Analyse von seismischen Oberflächenwellen spielt für das Ver- ständnis der geologischen und geophysikalischen Eigenschaften des Un- tergrundes eine wichtige Rolle. Tatsächlich spiegeln Attribute der seismi- schen Welle, wie die Ausbreitungsgeschwindigkeit oder die Polarisierung, die Eigenschaften des Materials wieder, in dem sich die Welle ausbreitet. Die Analyse der Eigenschaften von Oberflächenwellen erlauben Geo- physikern, einen Einblick in die Struktur des Untergrundes zu gewinnen, und dadurch teurere invasive Techniken (wie z. B. Bohrungen) zu ver- meiden. Die Kenntnisse über den Untergrund, welche durch seismische Messungen gewonnen werden, kommen einer Vielzahl von Anwendungen zugute. Mikrozonierungen stellen eine wichtige Anwendung in der Ana- lyse von Oberflächenwellen dar, und haben einen direkten Einfluss auf die Vorbereitung auf Erdbeben und die Begrenzung von Schäden. Diese Dissertation zielt darauf ab, Signalverarbeitungstechniken zur Analyse von Oberflächenwellen bezüglich mehrere Aspekte zu verbessern. Insbesondere besteht das Hauptziel darin, möglichst genaue Schätzun- gen der relevanten geophysikalischen Parameter zu bestimmen. Die Ver- fügbarkeit von verbesserten Schätzungen wird bessere Randbedingungen für die geophysikalische Inversion bereitstellen und erlauben, verbesserte strukturelle Modelle der Erde zu erhalten. Für eine rigorose Behandlung der Schätzung der Wellenfeldparameter setzen wir auf Werkzeuge aus der statistischen Signalverarbeitung. Wel- lenfeldparameter werden mit Hilfe der Maximum-Likelihood-Methode geschätzt. Eine rechnerisch effiziente Umsetzung solcher Schätzer wird durch Modellierung seismischer Oberflächenwellen mit einem Faktorgra- fen, einer bestimmten Art eines probabilistischen graphischen Modells, erhalten. Eine theoretische Grenze der Schätzgenauigkeit, die Cramér- Rao Ungleichung (CRU), ermöglicht es uns, die Quellen der Unsicher- heit zu quantifizieren und stellt einen Vergleichspunkt zur Bewertung der Schätzalgorithmen dar. Ein Hauptbeitrag dieser Arbeit ist die Entwicklung eines Verfahrens zur Analyse von seismischen Oberflächenwellen. Das Verfahren ist flexi- bel genug, um verschiedene Arten von Wellen zu modellieren und unter- schiedliche Messmethoden zu handhaben. Alle Wellenfeldparameter der Love- und Rayleighwellen zusammen mit all den Messungen werden ge- meinsam modelliert. Das Verfahren gewährleistet eine optimale Nutzung der verfügbaren Messungen nach dem Maximum-Likelihood Kriterium. Das Verfahren behandelt auch die gleichzeitige Anwesenheit von meh- reren Wellen, möglicherweise von unterschiedlichen Wellentypen. Der vorgestellte Algorithmus zerlegt das Wellenfeld durch allmähliches Er- höhen der Anzahl modellierter Wellen und verfeinert die Schätzung der Parameter der einzelnen Wellen iterativ. Sensoren mit unterschiedlichem Geräuschpegel werden auch berücksichtigt und die Schätzung berück- sichtigt die mögliche unterschiedliche Qualität der Messungen. Die Effizienz der Methode wird aufgrund von Feldmessungen der na- türlichen Bodenunruhe mit einem Array von Sensoren beurteilt. Es wird gezeigt, dass das vorgeschlagene Verfahren den Methoden aus der Li- teratur in unterschiedlichen Aspekten überlegen ist. Insbesondere wird die Elliptizität der Rayleighwelle mit verbesserter Auflösung wiederge- geben, die retrograde/prograde Partikelbewegung wird zum ersten Mal hergeleitet, und die gleichzeitige Anwesenheit von mehreren Wellen wird betrachtet. v Es wird auch gezeigt, dass die Umsetzung der vorgestellten Methode für ein ausreichend grosses Signal-Rausch-Verhältnis (SRV) den kleinsten erreichbaren mittleren quadratischen Schätzungsfehler (MSEE) aufweist, welcher von der CRU vorgegeben wird. Die gemeinsame Bearbeitung von Translations- und Rotationsbewe- gungen wird mit Aufzeichnungen von kontrollierten Explosionen gete- stet. Wir demonstrieren die Herleitung der Paramter der Love- und Ray- leighwellen in mehreren Konfigurationen, welche in der Literatur bis- her nicht berücksichtigt wurden, sowohl im Fall eines einzelnen sechs- Komponenten-Sensors und bei einer Anordnung von Sensoren mit drei und sechs Komponenten. Es werden analytische Ausdrücke der CRU für jeden geophysikalisch relevanten Parameter hergeleitet. Diese Ausdrücke ermöglichen es uns, die Quellen der Unsicherheit
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