Undulating well trajectories are often drilled to improve length exposure to rock formations, target desirable hydrocarbon-saturated zones, and enhance resolution of borehole measurements. Despite these merits, undulating wells can introduce adverse conditions to the interpretation of borehole measurements which are seldom observed in vertical wells penetrating horizontal layers. Common examples are polarization horns observed across formation bed boundaries in borehole resistivity measurements acquired in highly-deviated wells. Consequently, conventional interpretation practices developed for vertical wells can yield inaccurate results in HA/HZ wells. A reliable approach to account for well trajectory and bed-boundary effects in the petrophysical interpretation of well logs is the application of forward and inverse modeling techniques because of their explicit use of measurement response functions. The main objective of this dissertation is to develop inversion-based petrophysical interpretation methods that quantitatively integrate logging-while-drilling (LWD) multi-sector nuclear (i.e., density, neutron porosity, photoelectric factor, natural gamma ray) and multi-array propagation resistivity measurements. Under the assumption of a multi-layer formation model, the inversion approach estimates formation properties specific to a given measurement domain by numerically reproducing the available measurements. Subsequently, compositional multi-mineral analysis of inverted layer-by-layer properties is implemented for volumetric estimation of rock and fluid constituents. The most important prerequisite for efficient petrophysical inversion is fast and accurate forward models that incorporate specific measurement response functions for numerical simulation of LWD measurements. In the nuclear measurement domain, first-order perturbation theory and flux sensitivity functions (FSFs) are reliable and accurate for rapid numerical simulation. Albeit efficient, these first-order approximations can be inaccurate when modeling neutron porosity logs, especially in the presence of borehole environmental effects (tool standoff or/and invasion) and across highly contrasting beds and complex formation geometries. Accordingly, a secondary thrust of this dissertation is the introduction of two new methods for improving the accuracy of rapid numerical simulation of LWD neutron porosity measurements. The two methods include: (1) a neutron-density petrophysical parameterization approach for describing formation macroscopic cross section, and (2) a one-group neutron diffusion flux-difference method for estimating perturbed spatial neutron porosity fluxes. Both methods are validated with full Monte Carlo (MC) calculations of spatial neutron detector FSFs and subsequent simulations of neutron porosity logs in the presence of LWD azimuthal standoff, invasion, and highly dipping beds. Analysis of field and synthetic verification examples with the combined resistivity-nuclear inversion method confirms that inversion-based estimation of hydrocarbon pore volume in HA/HZ wells is more accurate than conventional well-log analysis. Estimated hydrocarbon pore volume from conventional analysis can give rise to errors as high as 15% in undulating HA/HZ intervals. / text