The atmospheric concentration of methane \((CH_4)\) - the most significant non-\(CO_2\) anthropogenic long-lived greenhouse gas - stabilized between 1999 and 2006 and then began to rise again. Explanations for this behavior differ but studies agree that more measurements and better modeling are needed to reliably explain the model-data discrepancies and predict future change. This dissertation focuses on measurements of \(CH_4\) and inverse modeling of atmospheric \(CH_4\) fluxes using field measurements at a variety of spatial scales. We first present a new fast-response instrument to measure the isotopic composition of \(CH_4\) in ambient air. The instrument was used to characterize mass fluxes and isofluxes (a isotopically-weighted mass flux) from a well-studied research fen in New Hampshire. Eddy-covariance and automatic chamber techniques produced consistent estimates of both the \(CH_4\) fluxes and their isotopic composition at sub-hourly resolution. We then characterize fluxes of \(CH_4\) from aircraft engines using measurements made with the same instrument during the Alternative Aviation Fuel Experiment (AAFEX), a study that aimed to determine the atmospheric impacts of alternative fuel use in the growing aviation industry. Emissions of \(CO_2\), \(CH_4\), and \(N_2O\) from different synthetic fuels were statistically indistinguishable from those of the widely used JP-8 jet fuel. We then present airborne observations of the long-lived greenhouse gas suite – \(CO_2\), \(CH_4\), \(N_2O\), and CO – during two aircraft campaigns, HIPPO and CalNex, made using a similar instrument built specifically for the NCAR HIAPER GV aircraft. These measurements are compared to data from other onboard sensors and show excellent agreement. We discuss the details of the end-to-end calibration procedures and the data quality-assurance and quality-control (QA/QC). Lastly, we quantify a top-down estimate of California’s \(CH_4\) emission inventory using the CalNex \(CH_4\) observations. Observed \(CH_4\) enhancements above background concentrations are simulated using a lagrangian transport model driven by validated meteorology. A priori source-specific emission inventories are optimized in a Bayesian inversion framework to show that California’s \(CH_4\) budget is 1.6 ± 0.34 times larger than the current estimate of California’s Air Resources Board (CARB), the body charged with enforcing the California Global Solutions Act and tracking emission changes over time. Findings highlight large underestimates of emissions from cattle and natural gas infrastructure. / Earth and Planetary Sciences

Methane is the second most influential anthropogenic greenhouse gas. There are large uncertainties in the magnitudes and trends of methane emissions from different source types and source regions. Satellite observations of methane offer dense spatial coverage unachievable by suborbital observations. This thesis evaluates the capabilities of using satellite observations of atmospheric methane to provide high-resolution constraints on continental scale methane emissions. In doing so, I seek to evaluate the supporting role of suborbital observations, to inform the emission inventories on which policy decisions are based, and to enable inverse modeling of the next generation of satellite observations. / Earth and Planetary Sciences

Three related electromagnetic scattering problems, namely, high frequency electromagnetic (EM) ray tracing, scattering feature extraction, and inverse scattering are studied in this dissertation. New approaches are presented to advance the state of the art in each of the areas. The presented study in electromagnetic ray tracing leads to an alternative ray tracing algorithm which can outperform the traditional algorithms for complex targets. The performance of the proposed techniques demonstrates their potential application to the study of high-frequency EM scattering prediction. Second, a genetic algorithm (GA)-based algorithm with an adaptive-feeding technique is developed to simultaneously extract both scattering centers and resonances. Scattering feature extraction algorithms are then developed with the consideration of the visibility of scattering centers. Inverse scattering problems with strong multiple scattering effects are also studied. A GA-based method is presented to invert the shapes with multiple scattering effects. An approach combining hybrid GA with the tabu list idea are then developed to further improve the performance of the GA-based inversion algorithms. / text

I present results from quantitative evaluation of the capability of hosting and trapping CO₂ of a carbonate brine reservoir from Dickman Field, Kansas. The analysis includes estimation of some reservoir parameters such as porosity and permeability of this formation using pre-stack seismic inversion followed by simulating flow of injected CO₂ using a simple injection technique. Liner et at (2009) carried out a feasibility study to seismically monitor CO₂ sequestration at Dickman Field. Their approach is based on examining changes of seismic amplitudes at different production time intervals to show the effects of injected gas within the host formation. They employ Gassmann's fluid substitution model to calculate the required parameters for the seismic amplitude estimation. In contrast, I employ pre-stack seismic inversion to successfully estimate some important reservoir parameters (P- impedance, S- impedance and density), which can be related to the changes in subsurface rocks due to injected gas. These are then used to estimate reservoir porosity using multi-attribute analysis. The estimated porosity falls within a reported range of 8-25%, with an average of 19%. The permeability is obtained from porosity assuming a simple mathematical relationship between porosity and permeability and classifying the rocks into different classes by using Winland R35 rock classification method. I finally perform flow simulation for a simple injection technique that involves direct injection of CO₂ gas into the target formation within a small region of Dickman Field. The simulator takes into account three trapping mechanisms: residual trapping, solubility trapping and mineral trapping. The flow simulation predicts unnoticeable changes in porosity and permeability values of the target formation. The injected gas is predicted to migrate upward quickly, while it migrates slowly in lateral directions. A large amount of gas is concentrated around the injection well bore. Thus my flow simulation results suggest low trapping capability of the original target formation unless a more advanced injection technique is employed. My results suggest further that a formation below our original target reservoir, with high and continuously distributed porosity, is perhaps a better candidate for CO₂ storage. / text

The marine boundary layer (MBL) is the region where energy, momentum and masses are exchanged between the ocean surface and the free troposphere. The lack of observations with high vertical resolution over the ocean significantly restricts the understanding of the complex physical processes that occur inside the MBL. The relatively short vertical extent of the MBL (average about 1~2 km) and the frequent cloudiness at its top make probing the MBL extremely difficult from the space. Several features of the Global Positioning System (GPS) radio occultation (RO) technique suggest that it has a great potential for sensing the MBL. These features include global coverage, high vertical resolution, and the ability of GPS signals to penetrate clouds.Over moist marine areas, a large negative moisture gradient often exists across the thermal inversion capping the MBL, which can cause super-refraction (SR) or ducting. A large number of high-resolution soundings have shown that SR occurs about 90% of the time in a year over the subtropical and tropical oceans and even 50% at high-latitudes during the summer. In the presence of SR, the reconstruction of refractivity from RO data becomes an ill-posed inverse problem, i.e., a given RO bending angle profile is consistent with a continuum (an infinite number) of refractivity profiles. The standard Abel retrieval gives the minimum refractivity solution of the continuum and thus produces the largest negative bias, consistent with a negative bias that is often present in the retrieved refractivity profiles in the moist lower troposphere. Simulation studies indicate a large variation of the negative refractivity biases (could be over -15%). The impact of diffraction effects and the open-loop receiver tracking on the bending angle and refractivity retrievals are assessed. A novel approach is developed and tested to reconstruct the vertical refractivity structure within and below the SR layer, which yields a much-improved retrieval, especially below the SR layer (less than 0.5% error). Such a reconstruction method should greatly enhance our ability to measure the MBL globally using the GPS RO technique as well as to improve the MBL parameterizations used in weather and climate models.

The use of geophysical techniques to image the interiors of active volcanoes can provide a better understanding of their structure and plumbing. The need for such information is especially critical for undersea volcanoes, whose environment makes them difficult to investigate. Because undersea volcanoes are made up of highly magnetic basaltic rock, it is possible to use variations in the magnetic field to explore the internal structure of such edifices. This study combines magnetic survey data from 12 research cruises to make a magnetic anomaly map of volcanically active Loihi, located in the Hawaiian Island chain. NRM intensities and susceptibility measurements were measured from recovered rock samples and suggest that magnetic properties of Loihi are widely varied (NRM intensities range from 1-157 A/m and susceptibilities from 1.26 x 10-3 to 3.62 x 10-2 S.I.). The average NRM intensity is 26 A/m. The size and strength of magnetic source bodies were determined by using various modeling techniques. A strongly magnetized shield can explain most of the anomaly with a large nonmagnetic zone inside, beneath the summit. Prominent magnetic highs are located along Loihi's north and south rift zone dikes and modeling solutions suggest strongly magnetized source bodies in these areas as well as a thin, magnetic layer atop the nonmagnetic zone. The strong magnetic anomalies found along the volcano's rift zones cannot be readily attributed to recent lava flows at the surface. Instead, the source bodies must continue several kilometers in depth to give reasonable magnetization values and are interpreted as dike intrusions. Nonmagnetic anomalies at the summit and south of the summit suggest the presence of a magma system. The model solution suggests Loihi is an inhomogeneously magnetized seamount with highly magnetic dike intrusions along the rift zones with a nonmagnetic body at its center overlain with a magnetic layer.

The first part of the dissertation concerns the Ising problem proposed to Ernst Ising by his supervisor Wilhelm Lenz in the early 20s. The Ising model, or perhaps more correctly the Lenz-Ising model, tries to capture the behaviour of phase transitions, i.e. how local rules of engagement can produce large scale behaviour. Two decades later Lars Onsager solved the Ising problem for the quadratic lattice without an outer field. Using his ideas solutions for other lattices in two dimensions have been constructed. We describe a method for calculating the Ising partition function for immense square grids, up to linear order 320 (i.e. 102400 vertices). In three dimensions however only a few results are known. One of the most important unanswered questions is at which temperature the Ising model has its phase transition. In this dissertation it is shown that an upper bound for the critical coupling Kc, the inverse absolute temperature, is 0.29 for the tree dimensional cubic lattice. To be able to get more information one has to use different statistical methods. We describe one sampling method that can use simple state generation like the Metropolis algorithm for large lattices. We also discuss how to reconstruct the entropy from the model, in order to obtain parameters as the free energy. The Ising model gives a partition function associated with all finite graphs. In this dissertation we show that a number of interesting graph invariants can be calculated from the coefficients of the Ising partition function. We also give some interesting observations about the partition function in general and show that there are, for any N, N non-isomorphic graphs with the same Ising partition function. The second part of the dissertation is about matrix operations. We consider the problem of multiplying them when the entries are elements in a finite semiring or in an additively finitely generated semiring. We describe a method that uses O(n3 / log n) arithmetic operations. We also consider the problem of reducing n x n matrices over a finite field of size q using O(n2 / logq n) row operations in the worst case.

Seismic data is often irregularly and/or sparsely sampled along spatial coordinates. We show that these acquisition geometries are not necessarily a source of adversity in order to accurately reconstruct adequately-sampled data. We use two examples to illustrate that it may actually be better than equivalent regularly subsampled data. This comment was already made in earlier works by other authors. We explain this behavior by two key observations. Firstly, a noise-free underdetermined problem can be seen as a noisy well-determined problem. Secondly, regularly subsampling creates strong coherent acquisition noise (aliasing) difficult to remove unlike the noise created by irregularly subsampling that is typically weaker and Gaussian-like

In this overview of the recent Curvelet Reconstruction with Sparsity-promoting Inversion (CRSI) method, we present our latest 2-D and 3-D interpolation results on both synthetic and real datasets. We compare these results to interpolated data using other existing methods. Finally, we discuss the challenges related to sparsity-promoting solvers for the large-scale problems the industry faces.

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