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.

Single-Cell Transcriptome Analysis of Olfactory Sensory Neurons

Olfactory sensory neurons (OSNs), which detect a myriad of odorants, are known to express one allele of one olfactory receptor (OR) gene (Olfr) from the largest gene family in the mammalian genome. The OSNs expressing the same OR project their axons to the main olfactory bulb where they converge to form glomeruli. This “One neuron-one receptor rule” makes the olfactory epithelium (OE), which consists of a vast number of OSNs expressing unique ORs, one of the most heterogeneous cell populations. However, the mechanism of how the single OR allele is chosen remains unclear along with the question of whether one OSN only expresses a single OR gene, a hypothesis that has not been rigorously verified while we performed the experiments. Moreover, failure of axonal targeting to single glomerulus was observed in MeCP2 deficient OSNs where delayed development was proposed as an explanation for the phenotype. How Mecp2 mutation caused this aberrant targeting is not entirely understood.

In this dissertation, we explored the transcriptomes of single and mature OSNs by single-cell RNA-Seq to reveal their heterogeneity and further studied the OR gene expression from these isolated OSNs. The singularity of sequenced OSNs was ensured by the observation of monoallelic expression of X-linked genes from the hybrid samples from crosses between mice of different strains where strain-specific polymorphisms could be used to track the allelic origins of SNP-containing reads. The clustering of expression profiles from triplicates that originated from the same cell assured that the transcriptomic identities of OSNs were maintained through the experimental process. The average gene expression profiles of sequenced OSNs correlated well to the conventional transcriptome data of FACS-sorted Omp-positive cells, and the top-ranked expression of OR was conceded in the single-OSN transcriptomes. While exploring cellular diversity, in addition to OR genes, we revealed nearly 200 differentially expressed genes among the sequenced OSNs in this study. Among the 36 sequenced OSNs, eight cells (22.2%) showed multiple OR gene expression and the presences of additional ORs were not restricted to the neighbor loci that shared the transcriptional effect of the primary OR expression, suggesting that the “One neuron-one receptor rule” might not be strictly true at the transcription level. All of the inferable ORs, including additional co-expressed ORs, were shown to be monoallelic. Our sequencing of 21 Mecp2308 mutant OSNs, of which 62% expressed more than one OR genes, and the expression levels of the additional ORs were significantly higher than those in the wild-type, suggested that MeCP2 plays a role in the regulation of singular OR gene expression. Dual label in situ hybridization along with the sequence data revealed that dorsal and ventral ORs were co-expressed in the same Mecp2 mutant OSN, further implying that MeCP2 might be involved in regulation of OR territories in the OE. Our results suggested a new role of MeCP2 in OR gene choice and ratified that this multiple-OR expression caused by Mecp2 mutation did not accompany delayed OSN development that has been observed in the previous studies on the Mecp2 mutants.