Advancements in seismic tomography with application to tunnel detection and volcano imaging

Thesis (Ph.D.) University of Alaska Fairbanks, 1998Practical geotomography is an inverse problem with no unique solution. A priori information must be imposed for a stable solution to exist. Commonly used types of a priori information smooth and attenuate anomalies, resulting in 'blurred' tomographic images. Small or discrete anomalies, such as tunnels, magma conduits, or buried channels are extremely difficult imaging objectives. Composite distribution inversion (CDI) is introduced as a theory seeking physically simple, rather than distributionally simple, solutions of non-unique problems. Parameters are assumed to be members of a composite population, including both well-known and anomalous components. Discrete and large amplitude anomalies are allowed, while a well-conditioned inverse is maintained. Tunnel detection is demonstrated using CDI tomography and data collected near the northern border of South Korea. Accurate source and receiver location information is necessary. Borehole deviation corrections are estimated by minimizing the difference between empirical distributions of apparent parameter values as a function of location correction. Improved images result. Traveltime computation and raytracing are the most computationally intensive components of seismic tomography when imaging structurally complex media. Efficient, accurate, and robust raytracing is possible by first recovering approximate raypaths from traveltime fields, and then refining the raypaths to a desired accuracy level. Dynamically binned queuing is introduced. The approach optimizes graph-theoretic traveltime computation costs. Pseudo-bending is modified to efficiently refine raypaths in general media. Hypocentral location density functions and relative phase arrival population analysis are used to investigate the Spring, 1996, earthquake swarm at Akutan Volcano, Alaska. The main swarm is postulated to have been associated with a 0.2 km\sp3 intrusion at a depth of less than four kilometers. Decay sequence seismicity is postulated to be a passive response to the stress transient caused by the intrusion. Tomograms are computed for Mt. Spurr, Augustine, and Redoubt Volcanoes, Alaska. Relatively large amplitude, shallow anomalies explain most of the traveltime residual. No large amplitude anomalies are found at depth, and no magma storage areas are imaged. A large amplitude low-velocity anomaly is coincident with a previously proposed geothermal region on the southeast flank of Mt. Spurr. Mt. St. Augustine is found to have a high velocity core

Velocity estimation using seismic ray tomography

RESUMEN: En esta trabajo se presenta un trazador de rayos el cual es bastante versátil y que posee características de la teoría de rayos importantes a la hora de hacer tomografía, ya que permite calcular trayectorias de rayos reflejados y refractados simultáneamente, generar rayos con varias fuentes y varios receptores, escoger puntos en interfaces de interés para generar reflexiones en dichos puntos, entre otras. El trazador está basado en el método del camino más corto y fundamentado en el principio de Fermat, en donde el camino del rayo a lo largo del espacio posee un tiempo de propagación que es estacionario [Moser 1991]. A partir de este modelado, se implementó una tomografía de tiempos de propagación usando las técnicas de reconstrucción algebraica (ART y SIRT), para estimar velocidades de propagaci on de ondas en el subsuelo. Se realizaron experimentos para resolver sistemas de ecuaciones lineales Gm = d, donde G es mal condicionada y sparse. También se realizaron experimentos donde se aplicaron el modelado y las técnicas de reconstrucción algebraica en Inversión Basada en Modelos sintéticos.ABSTRACT: In this work we present a ray tracer which is quite versatile and has characteristics of the ray theory important when doing tomography, since it allows to calculate trajectories of reflected and refracted rays simultaneously, generate rays with several sources and several receivers, choose points in interest interfaces to generate re ections in said points, among others. The tracer is based on the shortest path method and based on the Fermat principle, where the ray path along the space has a taveltime that is stationary [Moser 1991]. From this modeling, a traveltime tomography was implemented using the algebraic reconstruction techniques (ART and SIRT), to estimate waves velocities in the subsurface. Experiments were performed to solve systems of linear equations Gm = d, where G is ill conditioned matrix and sparse. Also, experiments were also performed where modeling and algebraic reconstruction techniques were applied in Inversion Based on synthetic models

Traveltime computation and migration in anisotropic media

For seismic imaging of complex 3-D structures by e.g. prestack Kirchhoff depth migration large amounts of traveltime tables are required. This work provides a wavefront-oriented ray tracing technique for multi-valued traveltimes in smooth 3-D heterogeneous anisotropic media. In this method, wavefronts are propagated stepwise through the model and output quantities are interpolate (e.g., traveltimes, slowness) from rays to gridpoints. In contrast to isotropic media, where the input is a velocity model, the model for an anisotropic medium is defined by 21 elastic parameters at each gridpoint. To provide an efficient, accurate and fast algorithm for the interpolation of the elastic parameters to arbitrary points, the Cardinal Spline interpolation has been used, which produces an interpolated function that is continuous through the second derivative. The insertion of a new ray is performed by tracing it directly from the source. To calculate traveltimes at gridpoints a distance-weighted averaging method is used. To demonstrate the accuracy of the method the traveltimes computed for a homogeneous anisotropic model with elliptical symmetry are compared to exact traveltimes available for this medium. Since it exists no analytical solution for an inhomogeneous anisotropic model, I compare the results with an alternative method for traveltime computation, the FD perturbation method...thesi

Seismic characterization of naturally fractured reservoirs

Many hydrocarbon reservoirs have sufficient porosity but low permeability (for example, tight gas sands and coal beds). However, such reservoirs are often naturally fractured. The fracture patterns in these reservoirs can control flow and transport properties, and therefore, play an important role in drilling production wells. On the scale of seismic wavelengths, closely spaced parallel fractures behave like an anisotropic media, which precludes the response of individual fractures in the seismic data. There are a number of fracture parameters which are needed to fully characterize a fractured reservoir. However, seismic data may reveal only certain fracture parameters and those are fracture orientation, crack density and fracture infill. Most of the widely used fracture characterization methods such as Swave splitting analysis or amplitude vs. offset and azimuth (AVOA) analysis fail to render desired results in laterally varying media. I have conducted a systematic study of the response of fractured reservoirs with laterally varying elastic and fracture properties, and I have developed a scheme to invert for the fracture parameters. I have implemented a 3D finite-difference method to generate multicomponent synthetic seismic data in general anisotropic media. I applied the finite-difference algorithm in both Standard and Rotated Staggered grids. Standard Staggered grid is used for media having symmetry up to orthorhombic (isotropic, transversely isotropic, and orthorhombic), whereas Rotated Staggered grid is implemented for monoclinic and triclinic media. I have also developed an efficient and accurate ray-bending algorithm to compute seismic traveltimes in 3D anisotropic media. AVOA analysis is equivalent to the first-order Born approximation. However, AVOA analysis can be applied only in a laterally uniform medium, whereas the Born-approximation does not pose any restriction on the subsurface structure. I have developed an inversion scheme based on a ray-Born approximation to invert for the fracture parameters. Best results are achieved when both vertical and horizontal components of the seismic data are inverted simultaneously. I have also developed an efficient positivity constraint which forbids the inverted fracture parameters to be negative in value. I have implemented the inversion scheme in the frequency domain and I show, using various numerical examples, that all frequency samples up to the Nyquist are not required to achieve desired inversion results.Geological Science

Quantitative imaging of water, ice and air in permafrost systems through petrophysical joint inversion of seismic refraction and electrical resistivity data

Quantitative estimation of pore fractions filled with liquid water, ice and air is crucial for a process-based understanding of permafrost and its hazard potential upon climate- induced degradation. Geophysical methods offer opportunities to image distributions of permafrost constituents in a non-invasive manner. We present a method to jointly estimate the volumetric fractions of liquid water, ice, air and the rock matrix from seismic refraction and electrical resistivity data. Existing approaches rely on conventional inversions of both data sets and a suitable a priori estimate of the porosity distribution to transform velocity and resistivity models into estimates for the four-phase system, often leading to non-physical results. Based on two synthetic experiments and a field data set from an Alpine permafrost site (Schilthorn, Bernese Alps and Switzerland), it is demonstrated that the developed petrophysical joint inversion provides physically plausible solutions, even in the absence of prior porosity estimates. An assessment of the model covariance matrix for the coupled inverse problem reveals remaining petrophysical ambiguities, in particular between ice and rock matrix. Incorporation of petrophysical a priori information is demonstrated by penalizing ice occurrence within the first two meters of the subsurface where the measured borehole temperatures are positive. Joint inversion of the field data set reveals a shallow air-rich layer with high porosity on top of a lower-porosity subsurface with laterally varying ice and liquid water contents. Non-physical values (e.g. negative saturations) do not occur and estimated ice saturations of 0–50 per cent as well as liquid water saturations of 15–75 per cent are in agreement with the relatively warm borehole temperatures between −0.5  and 3 ° C. The presented method helps to improve quantification of water, ice and air from geophysical observations

Numerical Geometric Acoustics

Sound propagation in air is accurately described by a small perturbation of the ambient pressure away from a quiescent state. This is the realm of linear acoustics, where the propagation of a time-harmonic wave can be modeled using the Helmholtz equation. When the wavelength is small relative to the size of a scattering obstacle, techniques from geometric optics are applicable. Geometric methods such as raytracing are often used for computational room acoustics simulations in situations where the geometry of the built environment is sufficiently complicated. At the same time, the high-frequency approximation of the Helmholtz equation is described by two partial differential equations: the eikonal equation, whose solution gives the first arrival time of a geometric acoustics/optics wavefront as a field; and a transport equation, the solution of which describes the amplitude of that wavefield. Phenomena related to high-frequency acoustic diffraction are frequently omitted from these models because of their complexity. These phenomena can be modeled using a high-frequency diffraction theory, such as the uniform theory of diffraction. Despite their shortcomings, geometric methods for room acoustics provide a useful trade-off between realism and computational efficiency. Motivated by the limitations of geometric methods, we approach the problem of geometric acoustics using numerical methods for solving partial differential equations. Our focus is offline sound propagation in a high-frequency regime where directly solving the wave or Helmholtz equations is infeasible. To this end, we conduct a broad-based survey of semi-Lagrangian solvers for the eikonal equation, which make the local ray information of the solution explicit. We develop efficient, first-order solvers for the eikonal equation in 3D, called ordered line integral methods (OLIMs). The OLIMs provide intuition about how to design work-efficient semi-Lagrangian eikonal solvers, but their first order accuracy is not sufficient to compute the amplitude consistently. Motivated by the requirements of sound propagation simulations, we develop higher-order semi-Lagrangian eikonal solvers which we term jet marching methods (JMMs). JMMs augment the efficiency of OLIMs by additionally transporting higher-order derivative information of the eikonal in a causal fashion, which allows for high-order solution of the eikonal equation using compact stencils. We use the information made available locally by our JMMs to use paraxial raytracing to simultaneously solve the transport equation yielding the amplitude. We initially develop a JMM which handles a smoothly varying speed of sound on a regular grid in 2D. Motivated by the requirements of room acoustics applications, we develop a second-order JMM for solving the eikonal equation on a tetrahedron mesh for a constant speed of sound as a special case. As before, we use paraxial raytracing to compute the amplitude. Additionally, we compute multiple arrivals by reinitializing the eikonal equation on reflecting walls and diffracting edges. To compute these scattered fields, we devise algorithms which allow us to apply reflection and diffraction boundary conditions for the eikonal and amplitude. For the amplitude, we construct algorithms that allow us to apply the uniform theory of diffraction in a semi-Lagrangian setting efficiently

Image resolution analysis: a new, robust approach to seismic survey design

Seismic survey design methods often rely on qualitative measures to provide an optimal image of their objective target. Fold, ray tracing techniques counting ray hits on binned interfaces, and even advanced 3-D survey design methods that try to optimize o?set and azimuth coverage are prone to fail (especially in complex geological or structural settings) in their imaging predictions. The reason for the potential failure of these commonly used approaches derives from the fact that they do not take into account the ray geometry at the target points. Inverse theory results can provide quantitative and objective constraints on acquisition design. Beylkin??s contribution to this ?eld is an elegant and simple equation describing a reconstructed point scatterer given the source/receiver distribution used in the imaging experiment. Quantitative measures of spatial image resolution were developed to assess the e?cacy of competing acquisition geometries. Apart from the source/receiver con?guration, parameters such as the structure and seismic velocity also in?uence image resolution. Understanding their e?ect on image quality, allows us to better interpret the resolution results for the surveys under examination. A salt model was used to simulate imaging of target points located underneath and near the ?anks of the diapir. Three di?erent survey designs were examined. Results from these simulations show that contrary to simple models, near-o?sets do not always produce better resolved images than far-o?sets. However, consideration of decreasing signal-to-noise ratio revealed that images obtained from the far-o?set experiment are degrading faster than the near-o?set ones. The image analysis was performed on VSP ?eld data as well as synthetics generated by ?nite di?erence forward modeling. The predicted image resolution results were compared to measured resolution from the migrated sections of both the ?eld data and the synthetics. This comparison con?rms that image resolution analysis provides as good a resolution prediction as the prestack Kirchho? depth migrated section of the synthetic gathers. Even in the case of the migrated ?eld data, despite the presence of error introducing factors (di?erent signal-to-noise ratios, shape and frequency content of source wavelets, etc.), image resolution performed well exhibiting the same trends of resolution changes at di?erent test points

The Perception of Sonic Environments: Representing Soundscapes in Semi-Open Spaces

What we hear plays a crucial role in our experience of the outdoors; however, cities have long been polluted with unwanted sound levels. Semi-open spaces are most critically affected yet also provide spatial capabilities to lessen the perceived impact of noise. In response, soundscape studies view sound as a resource to be explored rather than inhibited, placing the listener's perception and awareness at the forefront of evaluating sonic environments. The research presented in this dissertation aims to understand the relationships between soundscape evaluations and design preferences for the outdoor environment, particularly in semi-open spaces. A user-interactive approach exposes the participant to visual representation methods from a reflection of the literature on the perceptual process of sound stimuli and historical modes of analysing sound. The sonic and spatial characteristics studied will be drawn from a series of soundwalks that evaluate semi-open spaces. The research is thus interested in discrepancies found in soundscape appraisals due to visual differences in the representations, including visual renders, raytracing diagrams, and heatmap animations. The results confirm the influence of visual preferences on soundscape judgments and further reveal the impact of listener sensitivities to sounds. The findings respond to suggestions that affective responses to the outdoor environment can be described dimensionally, which strongly correlate with participant design responses perceived to improve the sonic environment. Promoting user engagement and soundscapes analysis may provide new data on personal expectations and preferences in the design workflow. For this reason, perhaps designers can develop ways towards a holistic approach that can communicate the qualities of the environment to the participant and, in turn, place the end user at the centre of the workflow, delicately balancing the built environment with the overlap of daily activities

Proceedings of the Sixth General Meeting of the International VLBI Service for Geodesy and Astrometry

This volume is the proceedings of the sixth General Meeting of the International VLBI Service for Geodesy and Astrometry (IVS), held in Hobart, Tasmania, Australia, February 7-13, 2010. The contents of this volume also appear on the IVS Web site at http://ivscc.gsfc.nasa.gov/publications/gm2010. The keynote of the sixth GM was the new perspectives of the next generation VLBI system under the theme "VLBI2010: From Vision to Reality". The goal of the meeting was to provide an interesting and informative program for a wide cross-section of IVS members, including station operators, program managers, and analysts. This volume contains 88 papers. All papers were edited by the editors for usage of the English language, form, and minor content-related issues