Multi-component induction resistivity and sonic measurements acquired in high-angle wells can be strongly influenced by shoulder-bed effects, anisotropy resulting from sand-shale laminations, and presence of mud-filtrate invasion. Understanding the corresponding biasing effects aids in the interpretation of resistivity and sonic measurements and subsequently leads to more accurate and reliable formation evaluation. This dissertation describes numerical simulation studies examining the effects on multi-component induction and sonic measurements in a variety of complex formation models. Subsequently, a joint inversion scheme is presented that combines resistivity and sonic measurements to estimate in situ petrophysical and elastic properties in the presence of mud-filtrate invasion. To facilitate the simulation study of multi-component induction logs, I develop a new finite-difference algorithm for the numerical simulation of frequency-domain electromagnetic borehole measurements. The algorithm~uses a coupled scalar-vector potential formulation for arbitrary three-dimensional inhomogeneous and electrically anisotropic media. Simulations show that shoulder-bed anisotropy: enhances shoulder-bed effects across sand layers; and impacts invasion sensitivities to significantly alter the assessment of invasion in terms of invaded- and virgin-zone resistivities, radial length, and front shape. For the simulation study of sonic logs, I develop a three-dimensional, finite-difference time-domain algorithm that models elastic wave propagation in a fluid-filled borehole. Simulations show that presence of anisotropy not only alters the degree of dispersion observed in flexural and Stoneley waves, but also alters their responses to invasion. In addition, presence of a dipping shoulder bed can significantly distort flexural dispersion, making it difficult to identify the low frequency asymptote corresponding to formation shear wave velocity. Lastly, I consider a radial one-dimensional model in the development of a joint resistivity and sonic inversion algorithm. This scheme simultaneously inverts array-induction apparent conductivities and sonic flexural and Stoneley dispersions for the rock's elastic moduli and water saturation in the presence of mud-filtrate invasion. Inversions are performed on numerically simulated data for a variety of models reflecting soft and hard rock formations with presence of water- and oil-based mud-filtrate invasion. Results show the estimated invasion profiles display excellent agreement with the true models, and the elastic moduli are estimated to within a few percent of the true values. / text