Seismic waves are used to study the Earth, exploit its hydrocarbon resources, and understand its hazards. Extracting information from seismic waves about the Earth’s subsurface, however, is becoming more challenging as our questions become more complex and our demands for higher resolution increase. This dissertation introduces two new methods that use scattered waves for improving the resolution of subsurface images: natural migration of passive seismic data and convergent full-waveform inversion. In the first part of this dissertation, I describe a method where the recorded seismic data are used to image subsurface heterogeneities like fault planes. This method, denoted as natural migration of backscattered surface waves, provides higher resolution images for near-surface faults that is complementary to surface-wave tomography images. Our proposed method differ from contemporary methods in that it does not (1) require a velocity model of the earth, (2) assumes weak scattering, or (3) have a high computational cost. This method is applied to ambient noise recorded by the US-Array to map regional faults across the American continent. Natural migration can be formulated as a least-squares inversion to furtherer enhance the resolution and the quality of the fault images. This inversion is applied to ambient noise recorded in Long Beach, California to reveal a matrix of shallow subsurface faults. The second part of this dissertation describes a convergent full waveform inversion method for controlled source data. A controlled source excites waves that scatter from subsurface reflectors. The scattered waves are recorded by a large array of geophones. These recorded waves can be inverted for a high-resolution image of the subsurface by FWI, which is typically convergent for transmitted arrivals but often does not converge for deep reflected events. I propose a preconditioning approach that extends the ability of FWI to image deep parts of the velocity model, which significantly improves the chances for finding hydrocarbon deposits.

Full waveform inversion (FWI) for reflection events is limited by its linearized update requirements given by a process equivalent to migration. Unless the background velocity model is reasonably accurate the resulting gradient can have an inaccurate update direction leading the inversion to converge into what we refer to as local minima of the objective function. In this thesis, I first look into the subject of full model wavenumber to analysis the root of local minima and suggest the possible ways to avoid this problem. And then I analysis the possibility of recovering the corresponding wavenumber components through the existing inversion and migration algorithms. Migration can be taken as a generalized inversion method which mainly retrieves the high wavenumber part of the model. Conventional impedance inversion method gives a mapping relationship between the migration image (high wavenumber) and model parameters (full wavenumber) and thus provides a possible cascade inversion strategy to retrieve the full wavenumber components from seismic data. In the proposed approach, consider a mild lateral variation in the model, I find an analytical Frechet derivation corresponding to the new objective function. In the proposed approach, the gradient is given by the oriented time-domain imaging method. This is independent of the background velocity. Specifically, I apply the oriented time-domain imaging (which depends on the reflection slope instead of a background velocity) on the data residual to obtain the geometrical features of the velocity perturbation. Assuming that density is constant, the conventional 1D impedance inversion method is also applicable for 2D or 3D velocity inversion within the process of FWI. This method is not only capable of inverting for velocity, but it is also capable of retrieving anisotropic parameters relying on linearized representations of the reflection response. To eliminate the cross-talk artifacts between different parameters, I utilize what I consider being an optimal parameterization. To do so, I extend the prestack time-domain migration image in incident angle dimension to incorporate angular dependence needed by the multiparameter inversion. For simple models, this approach provides an efficient and stable way to do full waveform inversion or modified seismic inversion and makes the anisotropic inversion more practical. Results based on synthetic data of isotropic and anisotropic case examples illustrate the benefits and limitations of this method.

Airborne Laserbathymetrie stellt eine effiziente und flächenhafte Messmethode für die Erfassung der sich ständig im Wandel befindlichen Gewässersohlen von Inlandgewässern und küstennahen Flachwasserbereichen dar. Bei diesem Verfahren wird ein kurzer grüner Laserpuls ausgesandt, welcher mit allen Objekten entlang des Laserpulspfades interagiert (z.B. Wasseroberfläche und Gewässerboden). Die zum Sensor zurückgestreuten Laserpulsanteile (Echos) werden in einem zeitlich hochaufgelösten Messsignal (Full-Waveform) digitalisiert und gespeichert. Allerdings ist das Messverfahren aufgrund von Gewässertrübung in seiner Eindringtiefe in den Wasserkörper limitiert. Die Gewässerbodenechos werden bei zunehmender Gewässertiefe schwächer, bis sie nicht mehr zuverlässig detektierbar sind. Diese Arbeit zeigt, wie mit neuartigen Methoden schwache Gewässerbodenechos in Full-Waveforms detektiert werden können, welche durch die Standardauswerteverfahren nicht mehr berücksichtigt werden. Im Kernstück der Arbeit werden zwei Verfahren vorgestellt, die auf einer gemeinsamen Auswertung dicht benachbarter Messdaten basieren. Unter der Annahme eines stetigen Gewässerbodens mit geringer bis moderater Geländeneigung führt die Zusammenfassung mehrerer Full-Waveforms zu einer Verbesserung des Signal/Rausch-Verhältnisses und einer Verstärkung von schwachen Gewässerbodenechos, welche folglich zuverlässiger detektiert werden können. Die Ergebnisse zeigen eine erhebliche Erhöhung der auswertbaren Gewässertiefe (bis zu +30 %), wodurch eine deutlich größere Fläche des Gewässerbodens abgedeckt werden konnte (Flächenzuwachs von bis zu +113 %). In umfassenden Analysen der Ergebnisse konnte nachgewiesen werden, dass die hinzugewonnenen Gewässerbodenpunkte eine gute Repräsentation des Gewässerbodens darstellen. Somit leisten die in dieser Arbeit entwickelten Verfahren einen wertvollen Beitrag zur Steigerung der eingangs beschriebenen Effizienz der Airborne Laserbathymetrie.:Kurzfassung Abstract 1 Einleitung 1.1 Motivation 1.2 Ziele der Dissertation 1.3 Aufbau der Arbeit 2 Einführung in bathymetrische Messverfahren 2.1 Hydrographie und Bathymetrie 2.2 Airborne LiDAR Bathymetrie 2.2.1 Grundlagen Airborne Laserscanning 2.2.2 Der Pfad des Laserpulses 2.2.3 Fehlereinflüsse 2.3 Die Full-Waveform 2.3.1 Aufbau und Merkmale einer Full-Waveform 2.3.2 Systemwaveform 2.3.3 Full-Waveform Auswerteverfahren 2.4 Hydroakustische Messverfahren 2.4.1 Messprinzip 2.4.2 Echolot Varianten 2.4.3 Fehlereinflüsse 3 Nichtlineare Full-Waveform Stacking-Verfahren zur Detektion und Extraktion von Gewässerbodenpunkten – Beitrag 1, Beitrag 2, Beitrag 3 3.1 Signalbasiertes nichtlineares Full-Waveform Stacking 3.2 Volumetrisches nichtlineares Ortho-Full-Waveform Stacking 4 Anwendung von nichtlinearen Full-Waveform Stacking-Methoden auf maritime Gewässer – Beitrag 4 4.1 Studiengebiet in der Nordsee 4.2 Datengrundlage 4.3 Erste Ergebnisse einer Pilotstudie in küstennahen Bereichen der Nordsee 4.4 Untersuchungsgebiet 4.5 Klassifikation der Wasseroberflächenpunkte 4.6 Visualisierung der Ergebnisse 4.7 Genauigkeit und Zuverlässigkeit 4.8 Mehrwert der Verfahren 5 Potential der Full-Waveform Stacking-Methoden zur Ableitung der Gewässertrübung – Beitrag 5 6 Diskussion und weiterführende Arbeiten 6.1 Geometrische Modellierung der Laserpulsausbreitung 6.2 Einfluss der Gewässereigenschaften auf die Gewässerbodenbestimmung 6.3 Unterschätzung der Wasseroberfläche 6.4 Nutzung von Gewässertrübungsinformation für die Beurteilung der Zuverlässigkeit der Gewässertiefenbestimmung 6.5 Auswirkung der Nachbarschaftsdefinition beim signalbasiertem Full-Waveform Stacking 6.6 Gegenüberstellung signalbasiertes und volumetrisches Full-Waveform Stacking 6.7 Erweiterung des Full-Waveform Stackings mit dem Multi-Layer-Ansatz 7 Fazit der Dissertation 7.1 Zusammenfassung 7.2 Einordnung der Dissertation 7.3 Mehrwert der Dissertation Literaturverzeichnis Abbildungsverzeichnis Tabellenverzeichnis Symbolverzeichnis Abkürzungsverzeichnis / Airborne laser bathymetry is an efficient and area-wide measurement method for the detection of the permanently changing water bottoms of inland waters and shallow water areas close to the coast. In this method, a short green laser pulse is emitted, which interacts with all objects along the laser pulse path (e.g. water surface and bottom). The backscattered laser pulse components (echoes) are digitized and stored in a high temporal resolution measurement signal (full-waveform). However, the measurement method is limited in its penetration depth into the water body due to water turbidity. The water bottom echoes become weaker as the water depth increases until they are no longer reliably detectable. This work shows how novel methods can be used to detect weak water bottom echoes in full-waveforms that are no longer accounted for by standard processing methods. In the core of the work, two methods are presented which are based on a joint evaluation of closely adjacent measurement data. Under the assumption of a steady water bottom with low to moderate slope, the combination of several full-waveforms leads to an improvement of the signal-to-noise ratio and an enhancement of weak water bottom echoes, which consequently can be detected more reliably. The results show a significant increase in the analyzable water depth (up to +30 %), allowing a much larger area of the water bottom to be covered (increase up to +113 %). Comprehensive analyses of the results proved that the added water bottom points are a good representation of the water bottom. Thus, the methods developed in this work constitute a valuable contribution to increase the efficiency of airborne laser bathymetry described at the beginning.:Kurzfassung Abstract 1 Einleitung 1.1 Motivation 1.2 Ziele der Dissertation 1.3 Aufbau der Arbeit 2 Einführung in bathymetrische Messverfahren 2.1 Hydrographie und Bathymetrie 2.2 Airborne LiDAR Bathymetrie 2.2.1 Grundlagen Airborne Laserscanning 2.2.2 Der Pfad des Laserpulses 2.2.3 Fehlereinflüsse 2.3 Die Full-Waveform 2.3.1 Aufbau und Merkmale einer Full-Waveform 2.3.2 Systemwaveform 2.3.3 Full-Waveform Auswerteverfahren 2.4 Hydroakustische Messverfahren 2.4.1 Messprinzip 2.4.2 Echolot Varianten 2.4.3 Fehlereinflüsse 3 Nichtlineare Full-Waveform Stacking-Verfahren zur Detektion und Extraktion von Gewässerbodenpunkten – Beitrag 1, Beitrag 2, Beitrag 3 3.1 Signalbasiertes nichtlineares Full-Waveform Stacking 3.2 Volumetrisches nichtlineares Ortho-Full-Waveform Stacking 4 Anwendung von nichtlinearen Full-Waveform Stacking-Methoden auf maritime Gewässer – Beitrag 4 4.1 Studiengebiet in der Nordsee 4.2 Datengrundlage 4.3 Erste Ergebnisse einer Pilotstudie in küstennahen Bereichen der Nordsee 4.4 Untersuchungsgebiet 4.5 Klassifikation der Wasseroberflächenpunkte 4.6 Visualisierung der Ergebnisse 4.7 Genauigkeit und Zuverlässigkeit 4.8 Mehrwert der Verfahren 5 Potential der Full-Waveform Stacking-Methoden zur Ableitung der Gewässertrübung – Beitrag 5 6 Diskussion und weiterführende Arbeiten 6.1 Geometrische Modellierung der Laserpulsausbreitung 6.2 Einfluss der Gewässereigenschaften auf die Gewässerbodenbestimmung 6.3 Unterschätzung der Wasseroberfläche 6.4 Nutzung von Gewässertrübungsinformation für die Beurteilung der Zuverlässigkeit der Gewässertiefenbestimmung 6.5 Auswirkung der Nachbarschaftsdefinition beim signalbasiertem Full-Waveform Stacking 6.6 Gegenüberstellung signalbasiertes und volumetrisches Full-Waveform Stacking 6.7 Erweiterung des Full-Waveform Stackings mit dem Multi-Layer-Ansatz 7 Fazit der Dissertation 7.1 Zusammenfassung 7.2 Einordnung der Dissertation 7.3 Mehrwert der Dissertation Literaturverzeichnis Abbildungsverzeichnis Tabellenverzeichnis Symbolverzeichnis Abkürzungsverzeichnis

Accounting for azimuthal anisotropy is necessary for the processing and inversion of wide-azimuth and wide-aperture seismic data because wave speeds naturally depend on the wave propagation direction. Orthorhombic anisotropy is considered the most effective anisotropic model that approximates the azimuthal anisotropy we observe in seismic data. In the framework of full wave form inversion (FWI), the large number of parameters describing orthorhombic media exerts a considerable trade-off and increases the non-linearity of the inversion problem. Choosing a suitable parameterization for the model, and identifying which parameters in that parameterization could be well resolved, are essential to a successful inversion. In this thesis, I derive the radiation patterns for different acoustic orthorhombic parameterization. Analyzing the angular dependence of the scattering of the parameters of different parameterizations starting with the conventionally used notation, I assess the potential trade-off between the parameters and the resolution in describing the data and inverting for the parameters. In order to build practical inversion strategies, I suggest new parameters (called deviation parameters) for a new parameterization style in orthorhombic media. The novel parameters denoted ∈d, ƞd and δd are dimensionless and represent a measure of deviation between the vertical planes in orthorhombic anisotropy. The main feature of the deviation parameters consists of keeping the scattering of the vertical transversely isotropic (VTI) parameters stationary with azimuth. Using these scattering features, we can condition FWI to invert for the parameters which the data are sensitive to, at different stages, scales, and locations in the model. With this parameterization, the data are mainly sensitive to the scattering of 3 parameters (out of six that describe an acoustic orthorhombic medium): the horizontal velocity in the x1 direction, ∈1 which provides scattering mainly near the zero offset in the x1-x3 vertical plane, and ∈d, which is the ratio of the horizontal velocity squared in the x1 and x2 direction. Since, with this parameterization, the radiation pattern for the horizontal velocity is azimuth independent, we can perform an initial VTI inversion for two parameters (velocity and ∈1), then use ∈d to fit the azimuth variation in the data. This can be done at the reservoir level or any region of the model.

ITC/USA 2014 Conference Proceedings / The Fiftieth Annual International Telemetering Conference and Technical Exhibition / October 20-23, 2014 / Town and Country Resort & Convention Center, San Diego, CA / Massive amounts of data are typically acquired in third generation full-waveform (FW) LIDAR systems to generate image-like depthmaps of a scene of acceptable quality. The sampling systems acquiring this data, however, seldom take into account the low information rate generally present in the FW signals and, consequently, they sample very inefficiently. Our main goal here is to compare two efficient sampling models and processes for the individual time-resolved FW signals collected by a LIDAR system. Specifically, we compare two approaches of sub-Nyquist sampling of the continuous-time LIDAR FW return pulses: (i) modeling FW signals as short-duration pulses with multiple bandlimited echoes, and (ii) modeling them as signals with finite rates of innovation (FRI).

ITC/USA 2013 Conference Proceedings / The Forty-Ninth Annual International Telemetering Conference and Technical Exhibition / October 21-24, 2013 / Bally's Hotel & Convention Center, Las Vegas, NV / Third generation LIDAR full-waveform (FW) based systems collect 1D FW signals of the echoes generated by laser pulses of wide bandwidth reflected at the intercepted objects to construct depth profiles along each pulse path. By emitting a series of pulses towards a scene using a predefined scanning patter, a 3D image containing spatial-depth information can be constructed. Unfortunately, acquisition of a high number of wide bandwidth pulses is necessary to achieve high depth and spatial resolutions of the scene. This implies the collection of massive amounts of data which generate problems for the storage, processing and transmission of the FW signal set. In this research, we explore the recovery of individual continuous-time FW signals at sub-Nyquist rates. The key step to achieve this is to exploit the sparsity in FW signals. Doing this allows one to sub-sample and recover FW signals at rates much lower than that implied by Shannon's theorem. Here, we describe the theoretical framework supporting recovery and present the reader with examples using real LIDAR data.

Third generation full-waveform (FW) LIDAR systems image an entire scene by emitting laser pulses in particular directions and measuring the echoes. Each of these echoes provides range measurements about the objects intercepted by the laser pulse along a specified direction. By scanning through a specified region using a series of emitted pulses and observing their echoes, connected 1D profiles of 3D scenes can be readily obtained. This extra information has proven helpful in providing additional insight into the scene structure which can be used to construct effective characterizations and classifications. Unfortunately, massive amounts of data are typically collected which impose storage, processing and transmission limitations. To address these problems, a number of compression approaches have been developed in the literature. These, however, generally require the initial acquisition of large amounts of data only to later discard most of it by exploiting redundancies, thus sampling inefficiently. Based on this, our main goal is to apply efficient and effective LIDAR sampling schemes that achieve acceptable reconstruction quality of the 3D scenes. To achieve this goal, we propose on using compressive sampling by emitting pulses only into random locations within the scene and collecting only the corresponding returned FW signals. Under this framework, the number of emissions would typically be much smaller than what traditional LIDAR systems require. Application of this requires, however, that scenes contain many degrees of freedom. Fortunately, such a requirement is satisfied in most natural and man-made scenes. Here, we propose to use a measure of rank as the measure of degrees of freedom. To recover the connected 1D profiles of the 3D scene, matrix completion is applied to the tensor slices. In this paper, we test our approach by showing that recovery of compressively sampled 1D profiles of actual 3D scenes is possible using only a subset of measurements.

Micro-seismology is attracting more and more attention in the exploration seismology community. The main goal in micro-seismic imaging is to find the source location and the ignition time in order to track the fracture expansion, which will help engineers monitor the reservoirs. Conventional imaging methods work fine in this field but there are many limitations such as manual picking, incorrect migration velocity and low signal to noise ratio (S/N). In traditional surface survey imaging, full waveform inversion (FWI) is widely used. The FWI method updates the velocity model by minimizing the misfit between the observed data and the predicted data. Using FWI to locate and image microseismic events allows for an automatic process (free of picking) that utilizes the full wavefield. Use the FWI technique, and overcomes the difficulties of manual pickings and incorrect velocity model for migration. However, the technique of waveform inversion of micro-seismic events faces its own problems. There is significant nonlinearity due to the unknown source location (space) and function (time). We have developed a source independent FWI of micro-seismic events to simultaneously invert for the source image, source function and velocity model. It is based on convolving reference traces with the observed and modeled data to mitigate the effect of an unknown source ignition time. The adjoint-state method is used to derive the gradient for the source image, source function and velocity updates. To examine the accuracy of the inverted source image and velocity model the extended image for source wavelet in z-axis is extracted. Also the angle gather is calculated to check the applicability of the migration velocity. By inverting for the source image, source wavelet and the velocity model simultaneously, the proposed method produces good estimates of the source location, ignition time and the background velocity in the synthetic experiments with both parts of the Marmousi and the SEG Overthrust model. On the other hand, a new imaging condition of natural Green’s function has been implemented to mitigate the effect of the unknown velocity model. It is based on putting receivers in a horizontal well close to the micro-seismic events so that only a small part of the velocity model is required for the imaging. In order to focus the multi scattering energy to the source location, as well as to suppress the influence of the noise in the data, we introduced a new method to compensate the energy in the receiver wavefield. It is based on reflection waveform inversion (RWI) theory. We simply migrate for the scatters (reflectors) in the medium, and set the image as a secondary source to compensate for the multi scattering energy in the receiver wavefield. By applying the same imaging condition, the energy of those scattering events can be traced to the source location. Thus the source point has higher energy in the source image. A simple two-layer medium test demonstrates the features.

The main goal in seismic exploration is to identify locations of hydrocarbons reservoirs and give insights on where to drill new wells. Therefore, estimating an Earth model that represents the right physics of the Earth's subsurface is crucial in identifying these targets. Recent seismic data, with long offsets and wide azimuth features, are more sensitive to anisotropy. Accordingly, multiple anisotropic parameters need to be extracted from the recorded data on the surface to properly describe the model. I study the prospect of applying a scattering integral approach for multi-parameter inversion for a transversely isotropic model with a vertical axis of symmetry. I mainly analyze the sensitivity kernels to understand the sensitivity of seismic data to anisotropy parameters. Then, I use a frequency domain scattering integral approach to invert for the optimal parameterization. The scattering integral approach is based on the explicit computation of the sensitivity kernels. I present a new method to compute the traveltime sensitivity kernels for wave equation tomography using the unwrapped phase. I show that the new kernels are a better alternative to conventional cross-correlation/Rytov kernels. I also derive and analyze the sensitivity kernels for a transversely isotropic model with a vertical axis of symmetry. The kernels structure, for various opening/scattering angles, highlights the trade-off regions between the parameters. For a surface recorded data, I show that the normal move-out velocity vn, ƞ and δ parameterization is suitable for a simultaneous inversion of diving waves and reflections. Moreover, when seismic data is inverted hierarchically, the horizontal velocity vh, ƞ and ϵ is the parameterization with the least trade-off. In the frequency domain, the hierarchical inversion approach is naturally implemented using frequency continuation, which makes vh, ƞ and ϵ parameterization attractive. I formulate the multi-parameter inversion using the scattering integral method. Application to various synthetic and real data examples show accurate inversion results. I show that a good background ƞ model is required to accurately recover vh. For 3-D problems, I promote a hybrid approach, where efficient ray tracing is used to compute the sensitivity kernels. The proposed method highly reduces the computational cost.

L’atténuation sismique est un paramètre physique très utile pour décrire et imager les propriétés du sous-sol, et tout particulièrement les roches saturées et les nuages de gaz. Les approches classiques analysent l’amplitude du spectre des données ou bien la distorsion de ce spectre, avec des méthodes asymptotiques. L’inversion des formes d’onde (Full Waveform Inversion en anglais, FWI) est une approche alternative qui prend en compte les aspects de fréquences finies. En pratique, à la fois les vitesses et l’atténuation doivent être déterminées. Il est connu que l’inversion multi-paramètre ne conduit pas à un résultat unique.Ce travail se focalise sur la détermination des vitesses et de l’atténuation. La dispersion liée à l’atténuation produit des modèles de vitesse équivalents en termes de cinématique. Je propose une inversion hybride : la « relation cinématique » est un moyen de guider l’inversion des formes d’onde non-linéaire. Elle se décompose en deux étapes. Dans un premier temps, l’information cinématique est remise à jour, et ensuite les vitesses et l’atténuation sont modifiées, pour une cinématique donnée. Différentes approches sont proposées et discutées au travers d’applications sur des données synthétiques 2D, en particulier sur les modèles Midlle-East et Marmousi. / Seismic attenuation is a useful physical parameter to describe and to image the properties of specific geological bodies, e.g., saturated rocks and gas clouds. Classical approaches consist of analyzing seismic spectrum amplitudes or spectrum distortions based on ray methods. Full waveform inversion is an alternative approach that takes into account the finite frequency aspect of seismic waves. In practice, both seismic velocities and attenuation have to be determined. It is known that the multi-parameter inversion suffers from cross-talks.This thesis focuses on retrieving velocity and attenuation. Attenuation dispersion leads to equivalent kinematic velocity models, as different combinations of velocity and attenuation have the same kinematic effects. I propose a hybrid inversion strategy: the kinematic relationship is a way to guide the non-linear full waveform inversion. The hybrid inversion strategy includes two steps. It first updates the kinematic velocity, and then retrieves the velocity and attenuation models for a fixed kinematic velocity. The different approaches are discussed through applications on 2D synthetic data sets, including the Midlle-East and Marmousi models.