Efficient Computation of Electromagnetic Waves in Hydrocarbon Exploration Using the Improved Numerical Mode Matching (NMM) Method

In this study, we developed and improved the numerical mode matching (NMM) method which has previously been shown to be a fast and robust semi-analytical solver to investigate the propagation of electromagnetic (EM) waves in an isotropic layered medium. The applicable models, such as cylindrical waveguide, optical fiber, and borehole with earth geological formation, are generally modeled as an axisymmetric structure which is an orthogonal-plano-cylindrically layered (OPCL) medium consisting of materials stratified planarly and layered concentrically in the orthogonal directions.

In this report, several important improvements have been made to extend applications of this efficient solver to the anisotropic OCPL medium. The formulas for anisotropic media with three different diagonal elements in the cylindrical coordinate system are deduced to expand its application to more general materials. The perfectly matched layer (PML) is incorporated along the radial direction as an absorbing boundary condition (ABC) to make the NMM method more accurate and efficient for wave diffusion problems in unbounded media and applicable to scattering problems with lossless media. We manipulate the weak form of Maxwell's equations and impose the correct boundary conditions at the cylindrical axis to solve the singularity problem which is ignored by all previous researchers. The spectral element method (SEM) is introduced to more efficiently compute the eigenmodes of higher accuracy with less unknowns, achieving a faster mode matching procedure between different horizontal layers. We also prove the relationship of the field between opposite mode indices for different types of excitations, which can reduce the computational time by half. The formulas for computing EM fields excited by an electric or magnetic dipole located at any position with an arbitrary orientation are deduced. And the excitation are generalized to line and surface current sources which can extend the application of NMM to the simulations of controlled source electromagnetic techniques. Numerical simulations have demonstrated the efficiency and accuracy of this method.

Finally, the improved numerical mode matching (NMM) method is introduced to efficiently compute the electromagnetic response of the induction tool from orthogonal transverse hydraulic fractures in open or cased boreholes in hydrocarbon exploration. The hydraulic fracture is modeled as a slim circular disk which is symmetric with respect to the borehole axis and filled with electrically conductive or magnetic proppant. The NMM solver is first validated by comparing the normalized secondary field with experimental measurements and a commercial software. Then we analyze quantitatively the induction response sensitivity of the fracture with different parameters, such as length, conductivity and permeability of the filled proppant, to evaluate the effectiveness of the induction logging tool for fracture detection and mapping. Casings with different thicknesses, conductivities and permeabilities are modeled together with the fractures in boreholes to investigate their effects for fracture detection. It reveals that the normalized secondary field will not be weakened at low frequencies, ensuring the induction tool is still applicable for fracture detection, though the attenuation of electromagnetic field through the casing is significant. A hybrid approach combining the NMM method and BCGS-FFT solver based integral equation has been proposed to efficiently simulate the open or cased borehole with tilted fractures which is a non-axisymmetric model.

Cervical cancer precursors and hormonal contraceptive use in HIV-positive women: application of a causal model and semi-parametric estimation methods.

OBJECTIVE: To demonstrate the application of causal inference methods to observational data in the obstetrics and gynecology field, particularly causal modeling and semi-parametric estimation. BACKGROUND: Human immunodeficiency virus (HIV)-positive women are at increased risk for cervical cancer and its treatable precursors. Determining whether potential risk factors such as hormonal contraception are true causes is critical for informing public health strategies as longevity increases among HIV-positive women in developing countries. METHODS: We developed a causal model of the factors related to combined oral contraceptive (COC) use and cervical intraepithelial neoplasia 2 or greater (CIN2+) and modified the model to fit the observed data, drawn from women in a cervical cancer screening program at HIV clinics in Kenya. Assumptions required for substantiation of a causal relationship were assessed. We estimated the population-level association using semi-parametric methods: g-computation, inverse probability of treatment weighting, and targeted maximum likelihood estimation. RESULTS: We identified 2 plausible causal paths from COC use to CIN2+: via HPV infection and via increased disease progression. Study data enabled estimation of the latter only with strong assumptions of no unmeasured confounding. Of 2,519 women under 50 screened per protocol, 219 (8.7%) were diagnosed with CIN2+. Marginal modeling suggested a 2.9% (95% confidence interval 0.1%, 6.9%) increase in prevalence of CIN2+ if all women under 50 were exposed to COC; the significance of this association was sensitive to method of estimation and exposure misclassification. CONCLUSION: Use of causal modeling enabled clear representation of the causal relationship of interest and the assumptions required to estimate that relationship from the observed data. Semi-parametric estimation methods provided flexibility and reduced reliance on correct model form. Although selected results suggest an increased prevalence of CIN2+ associated with COC, evidence is insufficient to conclude causality. Priority areas for future studies to better satisfy causal criteria are identified.

They’re There, Now What?: The Identities, Behaviors, and Perceptions of Black Judges

Prior to the Civil Rights Movement, fewer than 50 Black judges had been elected or appointed to the judiciary. As of August 2015, there are over 1,000 Black state and federal judges. As the number of black judges has increased, one question arises: have American courts been altered purely by this substantial increase? One expectation—and, at times, a prediction—behind the increased descriptive representation of Black judges is that their mere presence would alter the judiciary. It was supposed that these judges would substantively represent Black interests in the decisions they made. In other words, it was suspected, and predicted, that Blacks in the judiciary would enhance equality and justice by being aware of, responsive to, and advocating for African Americans. This theory about the likely role of Black judges derives from theoretical work on political representation and racial group consciousness, and empirical studies of Black elite behavior in other political institutions.

Despite such predictions, there is no corresponding scholarly consensus regarding whether Black judges possess a racial group consciousness and have racially distinctive judicial behavior. Therefore, the theory undergirding the demand for increased diversification, as a means to transform the judiciary, remains unsubstantiated. This is precisely where this project, “They’re There, Now What?: The Identities, Behavior, and Perceptions of Black Judges,” seeks to intervene in and explore, if not settle, the matter of whether black judges possess a racial group consciousness and exhibit racially-distinctive judicial behavior. It addresses a set of interrelated questions relevant to understanding whether we can view Black judges as representatives in ways that are similar to how we view other Black political officials. I examine these questions using a multi-method approach. For my analyses, I draw on diverse materials: the published biographies of every Black judge appointed to the federal bench, a survey experiment with a nationally-representative adult sample, and semi-structured interviews with 30 Black judges.

This research, which engages with scholarship on representation, group consciousness, judicial behavior, and candidate perceptions, offers new insights into the lives, perceptions, and behavior of Black judges, as well as the manifestations of Black substantive representation in the judiciary. My dissertation argues that, despite the general reluctance to use the term “representation” when referring to judges, we can consider Black judges as representatives. Black judges behave as substantive representatives by (1) sharing and understanding the experience, history, and perspectives of Black Americans, (2) challenging language, persons, policies, and laws they feel negatively affect, or violate the rights and liberties of, African Americans, (3) respecting African American litigants, and (4) ensuring the rights of African Americans are protected and the needs of black Americans are being met.

Only through research that considers the perspectives, identities, perceptions, and behavior of Black judges will we arrive at a more comprehensive understanding of the importance of racial diversity in the courts. As this project finds, a link between descriptive representation and substantive representation can, and frequently does exist within the judicial context. Such a link is significant given that Blacks’ liberty and justice through the American legal system continues to be subject to those who exercise judicial power. This dissertation has implications for the discourse surrounding the need for increased descriptive and substantive representation of Blacks in the judiciary, and the factors that affect representation in the justice system.