<p> CO₂ sequestration involves storing CO₂ in a deep geological formation and may help to mitigate the increasing emission of carbon. To monitor the migration of injected fluid in the reservoir, seismic observations may be used to observe changes in reflection character. Conventional methods to image the subsurface, using active seismic measurements, with man-made sources, have been applied at a few test sites, and the use of passive measurements, with natural sources, has been considered as a probable cost-efficient method to monitor CO₂ migration and leakage. This numerical modeling study examines the use of seismic interferometry to retrieve weak seismic reflections from background noise, a form of passive monitoring.</p><p> The factors that influence the quality of the retrieved reflections from interferometry include geophone interval, geophone depth, and effect of shallow noise sources, assuming we seek reflections from deep noise sources, representing either teleseismic events or local events as expected in a field of active injection. Using model data, geophone interval had no significant effect on the reflection quality, but buried geophones produce ghost reflections, suggesting that shallow geophones might be optimal. Shallow noise sources produce a destructive effect on the reflections from deeper noise sources and damage the resulting image.</p>

<p> The Green's function is the impulse response of a system and is used to infer the properties of the system from surface measurements. In exploration seismology, imaging algorithms use estimates of the Green's functions along with surface measurements to image the subsurface, i.e. locate the Earth's interfaces and its properties, so as to identify valuable energy resources. These conventional imaging algorithms only account for singly reflected waves (primaries) in the subsurface and hence, in the subsurface image, produce false interfaces in the presence of multiply reflected waves (internal and free-surface multiples). </p><p> Recent work has shown that we can retrieve the Green's function that accounts for primaries and internal multiples. Imaging with these Green's functions reduces the artifacts caused by internal multiples compared to conventional imaging algorithms. These Green's functions require the free-surface multiples to be removed from the surface measurements before retrieval and imaging. </p><p> I modify the retrieval of the Green's function to account for free-surface reflections and therefore no longer require the free-surface multiples to be removed from the surface measurements. Thus the Green's function, in the method I propose, includes not only primaries and internal multiples but also free-surface multiples. These Green's functions are constructed from an arbitrary point <i>in the subsurface</i> (no physical receiver is required at this location) to <i>the surface.</i> </p><p> The method I use to retrieve the Green's function does not specify the approach to image the subsurface. In this thesis I also analyze different imaging strategies using the retrieved Green's functions. Imaging with these Green's functions reduces the artifacts caused by multiply reflected waves compared to standard imaging algorithms. Significantly, the Green's function that I retrieve and use for imaging require the same inputs as conventional imaging algorithms: the surface measurements and a smooth version of the subsurface velocity. </p><p> I also extend the construction of the Green's function from the subsurface to the surface to any two arbitrary points in the <i>subsurface</i> (no physical source or physical receiver is required at either of these locations). This Green's function is called the virtual Green's function and includes all the primaries, internal and free-surface multiples. The virtual Green's function retrieval requires the same inputs as the previously mentioned Green's functions.</p>

<p> Extracting fault, unconformity, and horizon surfaces from a seismic image is useful for interpretation of geologic structures and stratigraphic features. Although interpretation of these surfaces has been automated to some extent by others, significant manual effort is still required for extracting each type of these geologic surfaces. I propose methods to automatically extract all the fault, unconformity, and horizon surfaces from a 3D seismic image. To a large degree, these methods just involve image processing or array processing which is achieved by efficiently solving partial differential equations. </p><p> For fault interpretation, I propose a linked data structure, which is simpler than triangle or quad meshes, to represent a fault surface. In this simple data structure, each sample of a fault corresponds to exactly one image sample. Using this linked data structure, I extract complete and intersecting fault surfaces without holes from 3D seismic images. I use the same structure in subsequent processing to estimate fault slip vectors. I further propose two methods, using precomputed fault surfaces and slips, to undo faulting in seismic images by simultaneously moving fault blocks and faults themselves. </p><p> For unconformity interpretation, I first propose a new method to compute a unconformity likelihood image that highlights both the termination areas and the corresponding parallel unconformities and correlative conformities. I then extract unconformity surfaces from the likelihood image and use these surfaces as constraints to more accurately estimate seismic normal vectors that are discontinuous near the unconformities. Finally, I use the estimated normal vectors and use the unconformities as constraints to compute a flattened image, in which seismic reflectors are all flat and vertical gaps correspond to the unconformities. Horizon extraction is straightforward after computing a map of image flattening; we can first extract horizontal slices in the flattened space and then map these slices back to the original space to obtain the curved seismic horizon surfaces. </p><p> The fault and unconformity processing methods above facilitate automatic flattening and horizon extraction by providing an unfaulted image with continuous reflectors across faults and unconformities as constraints for an automatic flattening method. However, human interaction is still desirable for flattening and horizon extraction because of limitations in seismic imaging and computing systems, but the interaction can be enhanced. Instead of picking or tracking horizons one at a time, I propose a method to compute a volume of horizons that honor interpreted constraints, specified as sets of control points in a seismic image. I incorporate the control points with simple constraint preconditioners in the conjugate gradient method used to compute horizons.</p>

<p> Full-waveform inversion (FWI) is a technique designed to produce a high-resolution model of the subsurface by using information contained in entire seismic waveforms. This thesis presents a methodology for FWI in elastic VTI (transversely isotropic with a vertical axis of symmetry) media and discusses synthetic results for heterogeneous VTI models. </p><p> First, I develop FWI for multicomponent data from a horizontally layered VTI model. The reflectivity method, which permits computation of only PP reflections or a combination of PP and PSV events, is employed to model the data. The Gauss-Newton technique is used to invert for the interval Thomsen parameters, while keeping the densities fixed at the correct values. Eigenvalue/eigenvector decompostion of the Hessian matrix helps analyze the sensitivity of the objective function to the model parameters. Whereas PP data alone are generally sufficient to constrain all four Thomsen parameters even for conventional spreads, including PS reflections provides better constraints, especially for the deeper part of the model. </p><p> Next, I derive the gradients of the FWI objective function with respect to the stiffness coefficients of arbitrarily anisotropic media by employing the adjoint-state method. From these expressions, it is straightforward to compute the gradients for parameters of 2D heterogeneous VTI media. FWI is implemented in the time domain with the steepest-descent method used to iteratively update the model. The algorithm is tested on transmitted multicomponent data generated for Gaussian anomalies in Thomsen parameters embedded in homogeneous VTI media. </p><p> To test the sensitivity of the objective function to different model parameters, I derive an an- alytic expression for the Fr&eacute;chet kernel of FWI for arbitrary anisotropic symmetry by using the Born approximation and asymptotic Green&rsquo;s functions. The amplitude of the kernel, which represents the radiation pattern of a secondary source (that source describes a perturbation in a model parameter), yields the angle-dependent energy scattered by the perturbation. Then the radiation patterns are obtained for anomalies in VTI parameters embedded in isotropic homogeneous media and employed to analyze the inversion results for the transmission FWI experiments. </p><p> To understand some of the challenges posed by data recorded in surface surveys, I generate the multicomponent wavefield for a model based on a geologic section of the Valhall Field in the North Sea. A multiscale approach is adopted to perform FWI in the time domain. For the available offset range, diving-wave energy illuminates the top 1.5 km of the section, with the updates in the deeper regions due primarily to the reflections. FWI is tested for three model parameterizations and the results are explained in terms of the P- and SV-radiation patterns described above. These parameterizations lead to different trade-offs, and the choice of parameterization for a given data set depends on the recorded offset range, the quality of the initial model, and the parameter that needs to be recovered most accurately.</p>

Solar and geomagnetic fields modulate the flux of galactic cosmic rays (GCR) by electromagnetic and turbulent forcing. GCR flux into the Earth's atmosphere produces cosmogenic isotopes such as ¹⁴C. Cosmogenic isotopes then mix into their respective geochemical systems. Cosmogenic isotope archives reflect environmental levels during deposition and provide records of production, GCR flux and solar-geomagnetic modulation. Solar activity indices verify that ¹⁴C activities in tree rings record century-scale solar activity variations including profound solar activity minima, such as the Maunder Minimum, during the past millennium. The radiocarbon calibration tree-ring ¹⁴C data set spans nearly the length of the Holocene providing a well-dated solar-geomagnetic modulation record. Spectral analyses of earlier ¹⁴C data sets have suggested a complex pattern of fundamental, harmonic and combination tones. Many of these features result from a non-stationary higher ¹⁴C variability persisting about 600 years between 1500-year hiati with lower ¹⁴C variability. We have termed this variation the Hallstattzeit cycle (Damon and Jirikowic, 1992a) after a profound episode during the first millennium BC. Two better-known ¹⁴C variations, the ≈210-year Suess cycle, and ≈88-year Gleissberg, respond quite differently to the Hallstattzeit variation. The Suess is strongly amplitude modulated, the Gleissberg is not. Both show evidence of continuous phase change during the high-variability intervals. The Gleissberg and the Suess show amplitude modulation with the inverse of the geomagnetic field intensity. These modulations produce associated side-band spectral peaks confirming the influence of the ≈2100-year Hallstattzeit variance on the Suess and the influence of the Suess cycle upon the phase of the Gleissberg cycle. All periods between ≈2000 and ≈250 years reported by spectral analysis reflect the non-stationary Hallstattzeit variation, most likely through Gibbs phenomena. The Holocene history of solar-wind and geomagnetic modulation of GCR can be reconstructed from the tree-ring ¹⁴C data set. Quasi-periodicity limits extrapolating these variations into the future.

The objectives of this research were to provide accurate geotomography data and to subsequently use these data to investigate the ability of a two dimensional (2-D), rigorous wave equation model to describe the data. This was approached by constructing a physical, scale model EM tomography system to make measurements over a known, controllable medium. These data were used in the evaluation of a 2-D, exact, integral wave equation model as part of a reconstruction algorithm to image the conductivity and permittivity distribution of the planar region under investigation. Measured data exhibited precision, symmetry and repeatability, and also accuracy in determining the conductivity and permittivity of an aqueous solution. Analysis of the data indicates that the tomography system can detect and accurately locate a target. Adjustments in the 2-D mathematical model were needed in order to accurately fit the radiation pattern of the electric dipole antenna used in the physical scale model. Subsequently, the 2-D model was able to successfully describe tomography data over a 2-D target.

<p> The spatial distribution of deep earthquakes remains elusive, as the earthquakes below 30 km depth cannot be explained using the brittle frictional processes due to the fluid behavior of rocks under high pressure and temperature conditions. Several models that have been developed to identify the source distribution fall largely into categories like negative buoyancy and viscous friction to the flow, anti-crack faulting due to metastable olivine, volume reductions from phase transformations etc. Still none of them were able to satisfactorily explain the spatial distribution of deep earthquakes. We propose a new method using the visco-elastic nature of the earth material to model the deformation, stress, and elastic energy of the subducting lithosphere using &ldquo;Marker in cell method&rdquo; in combination with a conservative finite difference scheme. The software is written in Python and NumPy. We have tested this code for the known results of a Rayleigh&ndash;Taylor instability of solid-fluid interaction, and for a general subduction benchmark (Schmeling et al., 2008). We show a large set of numerical models in which we investigate the role of volatiles in the transition zone by varying the viscosity of the lithosphere and the presence of a high viscosity zone below the upper-lower mantle transition zone. Finally, we compare the rate of inner energy dissipation and the stored elastic energy in the subducting lithosphere with deep earthquake spatial distribution and discuss which constrains geodynamic models offer to deep earthquake location.</p>

In April 1991, tropical cyclone 02B (TC02B) devastated the coastal city of Chittagong, Bangladesh and caused 138,000 deaths. This cyclone was one of the most severe storms in the Bay of Bengal. Although this region can be considered the most dangerous tropical cyclone basin in the world, there have been very few studies performed on cyclones in this area. The purpose of this study is to examine the effects of surface parameters on TC02B. The parameters that were investigated include: sea-surface temperature (SST), evaporation in the area of low wind speed, ground wetness, surface layer height, ocean surface wind speed from the Special Sensor Microwave/Imager (SSM/I), and the mountain along the east coast of the Bay of Bengal. / In order to study the effects of these parameters, a series of sensitivity experiments were performed using the Florida State University (FSU) limited-area model with 15 layers. The domain of study is between latitude 6$\sp\circ$S to 41$\sp\circ$N and longitude 62$\sp\circ$E to 117$\sp\circ$E. The period of study is from 0000UTC 28 April to 1200UTC 30 April 1991. Since the ECMWF analyses underestimated the strength of the cyclone, an idealized vortex was inserted into the initial wind field to enhance the circulation. / Sea-surface temperature had significant effects on the development and movement of TC02B. Latent heat flux was the main source of energy from the surface, especially over the ocean. Changes in surface parameters that affected latent heat flux caused significant changes in the storm intensity. However, increased surface evaporation could have resulted in a weakening of the storm if the moisture fluxes were not effectively transported into the atmosphere. In general, rainfall amounts were directly related to latent heat fluxes, but the mountain also enhanced rainfall. For SSM/I wind speed, even though the data were not available in the area of heavy rainfall, utilization of this information showed positive impacts on the forecast of the cyclone. / Source: Dissertation Abstracts International, Volume: 53-11, Section: B, page: 5614. / Major Professor: T. N. Krishnamurti. / Thesis (Ph.D.)--The Florida State University, 1992.

Source: Dissertation Abstracts International, Volume: 41-07, Section: B, page: 2531. / Thesis (Ph.D.)--The Florida State University, 1980.

Source: Dissertation Abstracts International, Volume: 40-06, Section: B, page: 2579. / Thesis (Ph.D.)--The Florida State University, 1979.