We have developed a new tomographic inversion method that is able to determine the properties of complex surface waves, which are multimodal and heterogeneous. These properties can be used to generate a detailed near-surface earth model or to predict and remove the surface waves, while protecting reflection signals even with aliased data. The inversion assumes plane-wave physics and generates surface-consistent model parameters as a function of frequency. In this paper, we validate our method with 2D models and data. In a companion paper, we demonstrate its application to 3D data. Inversion for a single mode is linear, but the linearity does not hold at higher frequencies, where multiple modes interfere. However, single-mode inversion results can be used to create a starting model for the subsequent nonlinear multimode tomography. The resulting velocity-frequency grid has greater resolution compared with a beam-forming method. The dispersion curves can be used as input to a subsequent standard 1D surface-wave inversion to generate a velocity-depth model. The tomographic method also determines a grid of attenuation quality factors and variations in the source amplitude and bandwidth, which correlate with the near-surface elevation changes. The amplitude and phase properties can be used together to predict the surface-wave waveforms, which can then be adaptively subtracted from the data on a trace-to-trace basis.