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One of the most important topics in seismology is to construct detailed tomographic images beneath the surface, which can be interpreted geologically and geochemically to understand geodynamic processes happening in the interior of the Earth. Classically, these images are usually produced based upon linearized traveltime anomalies involving several particular seismic phases, whereas nonlinear inversion fitting synthetic seismograms and recorded signals based upon the adjoint method becomes more and more favorable. The adjoint tomography, also referred to as waveform inversion, is advantageous over classical techniques in several aspects, such as better resolution, while it also has several drawbacks, eg, slow convergence and lack of quantitative resolution analysis. In this dissertation, we focus on solving these remaining issues in adjoint tomography, from a theoretical perspective and based upon …