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In this study, I investigate the crustal and upper mantle velocity structure beneath the Rwenzori Mountains in western Uganda. This mountain range is situated within the western branch of the East African Rift and reaches altitudes of more than 5000 m. I use four different approaches that belong to the travel-time tomography method. The first approach is based on the isotropic tomographic inversion of local data, which contain information about 2053 earthquakes recorded by a network of up to 35 stations covering an area of 140×90 km2. The LOTOS-09 algorithm described here is used to realize this approach. The second approach is based on the anisotropic tomographic inversion of the same local dataset. This method employs the tomographic code ANITA, developed with my participation, which provides 3D anisotropic P and isotropic S velocity distributions based on P and S travel-times from local seismicity. For the P anisotropic model, four parameters for each parameterization cell are determined. This represents an orthorhombic anisotropy with one vertically-oriented predefined direction. Three of the parameters describe slowness variations along three horizontal orientations with azimuths of 0°, 60° and 120°, and one is a perturbation along the vertical axis. The third approach is based on tomographic inversion of the teleseismic data, which contain information about the traveltimes of P-waves coming from 284 teleseismic events recorded by the seismic network stations. The TELELOTOS code, which is my own modification of the LOTOS-09 algorithm, is used in this approach. The TELELOTOS code is designed to iteratively invert the local and/or teleseismic datasets. Finally, I present the results of the new tomographic approach, which is based on the simultaneous inversion of the joint local and teleseismic data. The simultaneous use of these datasets for the tomographic inversion has several advantages. In this case, the velocity structure in the study area can be resolved as deep as in the teleseismic approach. At the same time, in the upper part of the study volume, the resolution of the obtained models is as good as in the local tomography. The TELELOTOS algorithm is used to perform the joint tomographic inversion. Special attention is paid in this work to synthetic testing. A number of different synthetic and real data tests are performed to estimate the resolution ability and robustness of the obtained models. In particular, synthetic tests have shown that the results of the anisotropic tomographic inversion of the local data have to be considered as unsatisfactory. For all approaches used in this study, I present synthetic models that reproduce the same pattern of anomalies as that obtained by inverting the real data. These models are used to interpret the results and estimate the real amplitudes of the obtained anomalies. The obtained models exhibit a relatively strong negative P anomaly (up to -10%) beneath the Rwenzori Mountains. Low velocities are found in the northeastern part of the array at shallower depths and are most likely related to sedimentary deposits, while higher velocities are found beneath the eastern rift shoulder and are thought to be related to old cratonic crust. The presence of low velocities in the northwestern part of the array may be caused by a magmatic intrusion beneath the Buranga hot springs. Relatively low velocities were observed within the lower crust and upper mantle in the western and southern parts of the study area (beneath the rift valley and the entire length of the Rwenzori range). The higher amplitude of the low-velocity anomaly in the south can be related to the thinner lithosphere in the southern part of the Albertine rift. In the center of the study area, a small negative anomaly is observed, with the intensity increasing with depth. This anomaly is presumably related to a fluids rising up from a plume branch in the deeper part of the mantle. According to the interpretation of the local earthquake distribution, the Rwenzori Mountains are located between two rift valleys with flanks marked by normal faults. The Rwenzori block is bounded by thrust faults that are probably due to compression.