We conducted a tomographic inversion of 20-s Rayleigh wave spectral amplitudes to obtain a two-dimensional (2-D) attenuation model for central and southeastern Asia. We designed an amplitude-measuring procedure, making use of the phase match filtering technique and available source and path information, to minimize the measurement error. The resulting amplitude measurements showed much reduced scatter with consistent average attenuation estimates. The average quality factor Q from the measurements is about 220, lower than most global estimates. We took a two-step approach in our tomographic inversion. We first inverted the two-station amplitude ratios for a coarse-grid attenuation model. We then used this model as the a priori model and inverted the single-station spectral amplitudes to obtain the final attenuation model along with source and site response terms. The attenuation model from the inversion has a broad correlation with the geology and tectonics of the region. Low attenuation is seen in stable cratonic regions. High attenuation correlates with tectonically active regions. Compared with 1-D distance corrections, the use of 2-D attenuation model for path correction in Ms calculations reduced the station magnitude scatter by 16--18% on the average.